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  <title>Trivial Relocatability For C++26</title>
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l.CharacterMap("AMSsymbols-mathchar0mi",u.default.mathchar0mi,{digamma:"\u03dd",varkappa:"\u03f0",varGamma:["\u0393",{mathvariant:c.TexConstant.Variant.ITALIC}],varDelta:["\u0394",{mathvariant:c.TexConstant.Variant.ITALIC}],varTheta:["\u0398",{mathvariant:c.TexConstant.Variant.ITALIC}],varLambda:["\u039b",{mathvariant:c.TexConstant.Variant.ITALIC}],varXi:["\u039e",{mathvariant:c.TexConstant.Variant.ITALIC}],varPi:["\u03a0",{mathvariant:c.TexConstant.Variant.ITALIC}],varSigma:["\u03a3",{mathvariant:c.TexConstant.Variant.ITALIC}],varUpsilon:["\u03a5",{mathvariant:c.TexConstant.Variant.ITALIC}],varPhi:["\u03a6",{mathvariant:c.TexConstant.Variant.ITALIC}],varPsi:["\u03a8",{mathvariant:c.TexConstant.Variant.ITALIC}],varOmega:["\u03a9",{mathvariant:c.TexConstant.Variant.ITALIC}],beth:"\u2136",gimel:"\u2137",daleth:"\u2138",backprime:["\u2035",{variantForm:!0}],hslash:"\u210f",varnothing:["\u2205",{variantForm:!0}],blacktriangle:"\u25b4",triangledown:["\u25bd",{variantForm:!0}],blacktriangledown:"\u25be",square:"\u25fb",Box:"\u25fb",blacksquare:"\u25fc",lozenge:"\u25ca",Diamond:"\u25ca",blacklozenge:"\u29eb",circledS:["\u24c8",{mathvariant:c.TexConstant.Variant.NORMAL}],bigstar:"\u2605",sphericalangle:"\u2222",measuredangle:"\u2221",nexists:"\u2204",complement:"\u2201",mho:"\u2127",eth:["\xf0",{mathvariant:c.TexConstant.Variant.NORMAL}],Finv:"\u2132",diagup:"\u2571",Game:"\u2141",diagdown:"\u2572",Bbbk:["k",{mathvariant:c.TexConstant.Variant.DOUBLESTRUCK}],yen:"\xa5",circledR:"\xae",checkmark:"\u2713",maltese:"\u2720"}),new l.CharacterMap("AMSsymbols-mathchar0mo",u.default.mathchar0mo,{dotplus:"\u2214",ltimes:"\u22c9",smallsetminus:["\u2216",{variantForm:!0}],rtimes:"\u22ca",Cap:"\u22d2",doublecap:"\u22d2",leftthreetimes:"\u22cb",Cup:"\u22d3",doublecup:"\u22d3",rightthreetimes:"\u22cc",barwedge:"\u22bc",curlywedge:"\u22cf",veebar:"\u22bb",curlyvee:"\u22ce",doublebarwedge:"\u2a5e",boxminus:"\u229f",circleddash:"\u229d",boxtimes:"\u22a0",circledast:"\u229b",boxdot:"\u22a1",circledcirc:"\u229a",boxplus:"\u229e",centerdot:["\u22c5",{variantForm:!0}],divideontimes:"\u22c7",intercal:"\u22ba",leqq:"\u2266",geqq:"\u2267",leqslant:"\u2a7d",geqslant:"\u2a7e",eqslantless:"\u2a95",eqslantgtr:"\u2a96",lesssim:"\u2272",gtrsim:"\u2273",lessapprox:"\u2a85",gtrapprox:"\u2a86",approxeq:"\u224a",lessdot:"\u22d6",gtrdot:"\u22d7",lll:"\u22d8",llless:"\u22d8",ggg:"\u22d9",gggtr:"\u22d9",lessgtr:"\u2276",gtrless:"\u2277",lesseqgtr:"\u22da",gtreqless:"\u22db",lesseqqgtr:"\u2a8b",gtreqqless:"\u2a8c",doteqdot:"\u2251",Doteq:"\u2251",eqcirc:"\u2256",risingdotseq:"\u2253",circeq:"\u2257",fallingdotseq:"\u2252",triangleq:"\u225c",backsim:"\u223d",thicksim:["\u223c",{variantForm:!0}],backsimeq:"\u22cd",thickapprox:["\u2248",{variantForm:!0}],subseteqq:"\u2ac5",supseteqq:"\u2ac6",Subset:"\u22d0",Supset:"\u22d1",sqsubset:"\u228f",sqsupset:"\u2290",preccurlyeq:"\u227c",succcurlyeq:"\u227d",curlyeqprec:"\u22de",curlyeqsucc:"\u22df",precsim:"\u227e",succsim:"\u227f",precapprox:"\u2ab7",succapprox:"\u2ab8",vartriangleleft:"\u22b2",lhd:"\u22b2",vartriangleright:"\u22b3",rhd:"\u22b3",trianglelefteq:"\u22b4",unlhd:"\u22b4",trianglerighteq:"\u22b5",unrhd:"\u22b5",vDash:["\u22a8",{variantForm:!0}],Vdash:"\u22a9",Vvdash:"\u22aa",smallsmile:["\u2323",{variantForm:!0}],shortmid:["\u2223",{variantForm:!0}],smallfrown:["\u2322",{variantForm:!0}],shortparallel:["\u2225",{variantForm:!0}],bumpeq:"\u224f",between:"\u226c",Bumpeq:"\u224e",pitchfork:"\u22d4",varpropto:["\u221d",{variantForm:!0}],backepsilon:"\u220d",blacktriangleleft:"\u25c2",blacktriangleright:"\u25b8",therefore:"\u2234",because:"\u2235",eqsim:"\u2242",vartriangle:["\u25b3",{variantForm:!0}],Join:"\u22c8",nless:"\u226e",ngtr:"\u226f",nleq:"\u2270",ngeq:"\u2271",nleqslant:["\u2a87",{variantForm:!0}],ngeqslant:["\u2a88",{variantForm:!0}],nleqq:["\u2270",{variantForm:!0}],ngeqq:["\u2271",{variantForm:!0}],lneq:"\u2a87",gneq:"\u2a88",lneqq:"\u2268",gneqq:"\u2269",lvertneqq:["\u2268",{variantForm:!0}],gvertneqq:["\u2269",{variantForm:!0}],lnsim:"\u22e6",gnsim:"\u22e7",lnapprox:"\u2a89",gnapprox:"\u2a8a",nprec:"\u2280",nsucc:"\u2281",npreceq:["\u22e0",{variantForm:!0}],nsucceq:["\u22e1",{variantForm:!0}],precneqq:"\u2ab5",succneqq:"\u2ab6",precnsim:"\u22e8",succnsim:"\u22e9",precnapprox:"\u2ab9",succnapprox:"\u2aba",nsim:"\u2241",ncong:"\u2247",nshortmid:["\u2224",{variantForm:!0}],nshortparallel:["\u2226",{variantForm:!0}],nmid:"\u2224",nparallel:"\u2226",nvdash:"\u22ac",nvDash:"\u22ad",nVdash:"\u22ae",nVDash:"\u22af",ntriangleleft:"\u22ea",ntriangleright:"\u22eb",ntrianglelefteq:"\u22ec",ntrianglerighteq:"\u22ed",nsubseteq:"\u2288",nsupseteq:"\u2289",nsubseteqq:["\u2288",{variantForm:!0}],nsupseteqq:["\u2289",{variantForm:!0}],subsetneq:"\u228a",supsetneq:"\u228b",varsubsetneq:["\u228a",{variantForm:!0}],varsupsetneq:["\u228b",{variantForm:!0}],subsetneqq:"\u2acb",supsetneqq:"\u2acc",varsubsetneqq:["\u2acb",{variantForm:!0}],varsupsetneqq:["\u2acc",{variantForm:!0}],leftleftarrows:"\u21c7",rightrightarrows:"\u21c9",leftrightarrows:"\u21c6",rightleftarrows:"\u21c4",Lleftarrow:"\u21da",Rrightarrow:"\u21db",twoheadleftarrow:"\u219e",twoheadrightarrow:"\u21a0",leftarrowtail:"\u21a2",rightarrowtail:"\u21a3",looparrowleft:"\u21ab",looparrowright:"\u21ac",leftrightharpoons:"\u21cb",rightleftharpoons:["\u21cc",{variantForm:!0}],curvearrowleft:"\u21b6",curvearrowright:"\u21b7",circlearrowleft:"\u21ba",circlearrowright:"\u21bb",Lsh:"\u21b0",Rsh:"\u21b1",upuparrows:"\u21c8",downdownarrows:"\u21ca",upharpoonleft:"\u21bf",upharpoonright:"\u21be",downharpoonleft:"\u21c3",restriction:"\u21be",multimap:"\u22b8",downharpoonright:"\u21c2",leftrightsquigarrow:"\u21ad",rightsquigarrow:"\u21dd",leadsto:"\u21dd",dashrightarrow:"\u21e2",dashleftarrow:"\u21e0",nleftarrow:"\u219a",nrightarrow:"\u219b",nLeftarrow:"\u21cd",nRightarrow:"\u21cf",nleftrightarrow:"\u21ae",nLeftrightarrow:"\u21ce"}),new l.DelimiterMap("AMSsymbols-delimiter",u.default.delimiter,{"\\ulcorner":"\u231c","\\urcorner":"\u231d","\\llcorner":"\u231e","\\lrcorner":"\u231f"}),new l.CommandMap("AMSsymbols-macros",{implies:["Macro","\\;\\Longrightarrow\\;"],impliedby:["Macro","\\;\\Longleftarrow\\;"]},s.AmsMethods)},4387:function(t,e,r){var n=this&&this.__assign||function(){return n=Object.assign||function(t){for(var e,r=1,n=arguments.length;r<n;r++)for(var o in e=arguments[r])Object.prototype.hasOwnProperty.call(e,o)&&(t[o]=e[o]);return t},n.apply(this,arguments)},o=this&&this.__read||function(t,e){var r="function"==typeof Symbol&&t[Symbol.iterator];if(!r)return t;var n,o,i=r.call(t),a=[];try{for(;(void 0===e||e-- >0)&&!(n=i.next()).done;)a.push(n.value)}catch(t){o={error:t}}finally{try{n&&!n.done&&(r=i.return)&&r.call(i)}finally{if(o)throw o.error}}return a},i=this&&this.__importDefault||function(t){return t&&t.__esModule?t:{default:t}};Object.defineProperty(e,"__esModule",{value:!0}),e.NEW_OPS=e.AmsMethods=void 0;var a=i(r(1130)),s=i(r(5450)),l=i(r(1256)),c=r(8317),u=i(r(8417)),p=i(r(3971)),h=r(8803),d=i(r(7693)),f=r(9007);function m(t){if(!t||t.isInferred&&0===t.childNodes.length)return[null,null];if(t.isKind("msubsup")&&y(t))return[t,null];var e=l.default.getChildAt(t,0);return t.isInferred&&e&&y(e)?(t.childNodes.splice(0,1),[e,t]):[null,t]}function y(t){var e=t.childNodes[0];return e&&e.isKind("mi")&&""===e.getText()}e.AmsMethods={},e.AmsMethods.AmsEqnArray=function(t,e,r,n,o,i,s){var l=t.GetBrackets("\\begin{"+e.getName()+"}"),c=d.default.EqnArray(t,e,r,n,o,i,s);return a.default.setArrayAlign(c,l)},e.AmsMethods.AlignAt=function(t,r,n,o){var i,s,l=r.getName(),c="",u=[];if(o||(s=t.GetBrackets("\\begin{"+l+"}")),(i=t.GetArgument("\\begin{"+l+"}")).match(/[^0-9]/))throw new p.default("PositiveIntegerArg","Argument to %1 must me a positive integer","\\begin{"+l+"}");for(var h=parseInt(i,10);h>0;)c+="rl",u.push("0em 0em"),h--;var d=u.join(" ");if(o)return e.AmsMethods.EqnArray(t,r,n,o,c,d);var f=e.AmsMethods.EqnArray(t,r,n,o,c,d);return a.default.setArrayAlign(f,s)},e.AmsMethods.Multline=function(t,e,r){t.Push(e),a.default.checkEqnEnv(t);var n=t.itemFactory.create("multline",r,t.stack);return n.arraydef={displaystyle:!0,rowspacing:".5em",columnspacing:"100%",width:t.options.ams.multlineWidth,side:t.options.tagSide,minlabelspacing:t.options.tagIndent,framespacing:t.options.ams.multlineIndent+" 0",frame:"","data-width-includes-label":!0},n},e.AmsMethods.XalignAt=function(t,r,n,o){var i=t.GetArgument("\\begin{"+r.getName()+"}");if(i.match(/[^0-9]/))throw new p.default("PositiveIntegerArg","Argument to %1 must me a positive integer","\\begin{"+r.getName()+"}");var a=o?"crl":"rlc",s=o?"fit auto auto":"auto auto fit",l=e.AmsMethods.FlalignArray(t,r,n,o,!1,a,s,!0);return l.setProperty("xalignat",2*parseInt(i)),l},e.AmsMethods.FlalignArray=function(t,e,r,n,o,i,s,l){void 0===l&&(l=!1),t.Push(e),a.default.checkEqnEnv(t),i=i.split("").join(" ").replace(/r/g,"right").replace(/l/g,"left").replace(/c/g,"center");var c=t.itemFactory.create("flalign",e.getName(),r,n,o,t.stack);return c.arraydef={width:"100%",displaystyle:!0,columnalign:i,columnspacing:"0em",columnwidth:s,rowspacing:"3pt",side:t.options.tagSide,minlabelspacing:l?"0":t.options.tagIndent,"data-width-includes-label":!0},c.setProperty("zeroWidthLabel",l),c},e.NEW_OPS="ams-declare-ops",e.AmsMethods.HandleDeclareOp=function(t,r){var n=t.GetStar()?"*":"",o=a.default.trimSpaces(t.GetArgument(r));"\\"===o.charAt(0)&&(o=o.substr(1));var i=t.GetArgument(r);t.configuration.handlers.retrieve(e.NEW_OPS).add(o,new h.Macro(o,e.AmsMethods.Macro,["\\operatorname".concat(n,"{").concat(i,"}")]))},e.AmsMethods.HandleOperatorName=function(t,e){var r=t.GetStar(),o=a.default.trimSpaces(t.GetArgument(e)),i=new u.default(o,n(n({},t.stack.env),{font:c.TexConstant.Variant.NORMAL,multiLetterIdentifiers:/^[-*a-z]+/i,operatorLetters:!0}),t.configuration).mml();if(i.isKind("mi")||(i=t.create("node","TeXAtom",[i])),l.default.setProperties(i,{movesupsub:r,movablelimits:!0,texClass:f.TEXCLASS.OP}),!r){var s=t.GetNext(),p=t.i;"\\"===s&&++t.i&&"limits"!==t.GetCS()&&(t.i=p)}t.Push(i)},e.AmsMethods.SideSet=function(t,e){var r=o(m(t.ParseArg(e)),2),n=r[0],i=r[1],s=o(m(t.ParseArg(e)),2),c=s[0],u=s[1],p=t.ParseArg(e),h=p;n&&(i?n.replaceChild(t.create("node","mphantom",[t.create("node","mpadded",[a.default.copyNode(p,t)],{width:0})]),l.default.getChildAt(n,0)):(h=t.create("node","mmultiscripts",[p]),c&&l.default.appendChildren(h,[l.default.getChildAt(c,1)||t.create("node","none"),l.default.getChildAt(c,2)||t.create("node","none")]),l.default.setProperty(h,"scriptalign","left"),l.default.appendChildren(h,[t.create("node","mprescripts"),l.default.getChildAt(n,1)||t.create("node","none"),l.default.getChildAt(n,2)||t.create("node","none")]))),c&&h===p&&(c.replaceChild(p,l.default.getChildAt(c,0)),h=c);var d=t.create("node","TeXAtom",[],{texClass:f.TEXCLASS.OP,movesupsub:!0,movablelimits:!0});i&&(n&&d.appendChild(n),d.appendChild(i)),d.appendChild(h),u&&d.appendChild(u),t.Push(d)},e.AmsMethods.operatorLetter=function(t,e){return!!t.stack.env.operatorLetters&&s.default.variable(t,e)},e.AmsMethods.MultiIntegral=function(t,e,r){var n=t.GetNext();if("\\"===n){var o=t.i;n=t.GetArgument(e),t.i=o,"\\limits"===n&&(r="\\idotsint"===e?"\\!\\!\\mathop{\\,\\,"+r+"}":"\\!\\!\\!\\mathop{\\,\\,\\,"+r+"}")}t.string=r+" "+t.string.slice(t.i),t.i=0},e.AmsMethods.xArrow=function(t,e,r,n,o){var i={width:"+"+a.default.Em((n+o)/18),lspace:a.default.Em(n/18)},s=t.GetBrackets(e),c=t.ParseArg(e),p=t.create("node","mspace",[],{depth:".25em"}),h=t.create("token","mo",{stretchy:!0,texClass:f.TEXCLASS.REL},String.fromCodePoint(r));h=t.create("node","mstyle",[h],{scriptlevel:0});var d=t.create("node","munderover",[h]),m=t.create("node","mpadded",[c,p],i);if(l.default.setAttribute(m,"voffset","-.2em"),l.default.setAttribute(m,"height","-.2em"),l.default.setChild(d,d.over,m),s){var y=new u.default(s,t.stack.env,t.configuration).mml(),g=t.create("node","mspace",[],{height:".75em"});m=t.create("node","mpadded",[y,g],i),l.default.setAttribute(m,"voffset",".15em"),l.default.setAttribute(m,"depth","-.15em"),l.default.setChild(d,d.under,m)}l.default.setProperty(d,"subsupOK",!0),t.Push(d)},e.AmsMethods.HandleShove=function(t,e,r){var n=t.stack.Top();if("multline"!==n.kind)throw new p.default("CommandOnlyAllowedInEnv","%1 only allowed in %2 environment",t.currentCS,"multline");if(n.Size())throw new p.default("CommandAtTheBeginingOfLine","%1 must come at the beginning of the line",t.currentCS);n.setProperty("shove",r)},e.AmsMethods.CFrac=function(t,e){var r=a.default.trimSpaces(t.GetBrackets(e,"")),n=t.GetArgument(e),o=t.GetArgument(e),i={l:c.TexConstant.Align.LEFT,r:c.TexConstant.Align.RIGHT,"":""},s=new u.default("\\strut\\textstyle{"+n+"}",t.stack.env,t.configuration).mml(),h=new u.default("\\strut\\textstyle{"+o+"}",t.stack.env,t.configuration).mml(),d=t.create("node","mfrac",[s,h]);if(null==(r=i[r]))throw new p.default("IllegalAlign","Illegal alignment specified in %1",t.currentCS);r&&l.default.setProperties(d,{numalign:r,denomalign:r}),t.Push(d)},e.AmsMethods.Genfrac=function(t,e,r,n,o,i){null==r&&(r=t.GetDelimiterArg(e)),null==n&&(n=t.GetDelimiterArg(e)),null==o&&(o=t.GetArgument(e)),null==i&&(i=a.default.trimSpaces(t.GetArgument(e)));var s=t.ParseArg(e),c=t.ParseArg(e),u=t.create("node","mfrac",[s,c]);if(""!==o&&l.default.setAttribute(u,"linethickness",o),(r||n)&&(l.default.setProperty(u,"withDelims",!0),u=a.default.fixedFence(t.configuration,r,u,n)),""!==i){var h=parseInt(i,10),d=["D","T","S","SS"][h];if(null==d)throw new p.default("BadMathStyleFor","Bad math style for %1",t.currentCS);u=t.create("node","mstyle",[u]),"D"===d?l.default.setProperties(u,{displaystyle:!0,scriptlevel:0}):l.default.setProperties(u,{displaystyle:!1,scriptlevel:h-1})}t.Push(u)},e.AmsMethods.HandleTag=function(t,e){if(!t.tags.currentTag.taggable&&t.tags.env)throw new p.default("CommandNotAllowedInEnv","%1 not allowed in %2 environment",t.currentCS,t.tags.env);if(t.tags.currentTag.tag)throw new p.default("MultipleCommand","Multiple %1",t.currentCS);var r=t.GetStar(),n=a.default.trimSpaces(t.GetArgument(e));t.tags.tag(n,r)},e.AmsMethods.HandleNoTag=d.default.HandleNoTag,e.AmsMethods.HandleRef=d.default.HandleRef,e.AmsMethods.Macro=d.default.Macro,e.AmsMethods.Accent=d.default.Accent,e.AmsMethods.Tilde=d.default.Tilde,e.AmsMethods.Array=d.default.Array,e.AmsMethods.Spacer=d.default.Spacer,e.AmsMethods.NamedOp=d.default.NamedOp,e.AmsMethods.EqnArray=d.default.EqnArray,e.AmsMethods.Equation=d.default.Equation},583:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.AmsCdConfiguration=void 0;var n=r(9899);r(8289),e.AmsCdConfiguration=n.Configuration.create("amscd",{handler:{character:["amscd_special"],macro:["amscd_macros"],environment:["amscd_environment"]},options:{amscd:{colspace:"5pt",rowspace:"5pt",harrowsize:"2.75em",varrowsize:"1.75em",hideHorizontalLabels:!1}}})},8289:function(t,e,r){var n=this&&this.__createBinding||(Object.create?function(t,e,r,n){void 0===n&&(n=r);var 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e(){return null!==t&&t.apply(this,arguments)||this}return o(e,t),Object.defineProperty(e.prototype,"kind",{get:function(){return"style"},enumerable:!1,configurable:!0}),e.prototype.checkItem=function(e){if(!e.isClose)return t.prototype.checkItem.call(this,e);var r=this.create("node","mstyle",this.nodes,this.getProperty("styles"));return[[this.factory.create("mml",r),e],!0]},e}(f.BaseItem);e.StyleItem=C;var w=function(t){function e(){return null!==t&&t.apply(this,arguments)||this}return o(e,t),Object.defineProperty(e.prototype,"kind",{get:function(){return"position"},enumerable:!1,configurable:!0}),e.prototype.checkItem=function(e){if(e.isClose)throw new p.default("MissingBoxFor","Missing box for %1",this.getName());if(e.isFinal){var r=e.toMml();switch(this.getProperty("move")){case"vertical":return r=this.create("node","mpadded",[r],{height:this.getProperty("dh"),depth:this.getProperty("dd"),voffset:this.getProperty("dh")}),[[this.factory.create("mml",r)],!0];case"horizontal":return[[this.factory.create("mml",this.getProperty("left")),e,this.factory.create("mml",this.getProperty("right"))],!0]}}return t.prototype.checkItem.call(this,e)},e}(f.BaseItem);e.PositionItem=w;var T=function(t){function e(){return null!==t&&t.apply(this,arguments)||this}return o(e,t),Object.defineProperty(e.prototype,"kind",{get:function(){return"cell"},enumerable:!1,configurable:!0}),Object.defineProperty(e.prototype,"isClose",{get:function(){return!0},enumerable:!1,configurable:!0}),e}(f.BaseItem);e.CellItem=T;var N=function(t){function e(){return null!==t&&t.apply(this,arguments)||this}return o(e,t),Object.defineProperty(e.prototype,"isFinal",{get:function(){return!0},enumerable:!1,configurable:!0}),Object.defineProperty(e.prototype,"kind",{get:function(){return"mml"},enumerable:!1,configurable:!0}),e}(f.BaseItem);e.MmlItem=N;var L=function(t){function e(){return null!==t&&t.apply(this,arguments)||this}return o(e,t),Object.defineProperty(e.prototype,"kind",{get:function(){return"fn"},enumerable:!1,configurable:!0}),e.prototype.checkItem=function(e){var r=this.First;if(r){if(e.isOpen)return f.BaseItem.success;if(!e.isKind("fn")){var n=e.First;if(!e.isKind("mml")||!n)return[[r,e],!0];if(d.default.isType(n,"mstyle")&&n.childNodes.length&&d.default.isType(n.childNodes[0].childNodes[0],"mspace")||d.default.isType(n,"mspace"))return[[r,e],!0];d.default.isEmbellished(n)&&(n=d.default.getCoreMO(n));var o=d.default.getForm(n);if(null!=o&&[0,0,1,1,0,1,1,0,0,0][o[2]])return[[r,e],!0]}var i=this.create("token","mo",{texClass:u.TEXCLASS.NONE},c.entities.ApplyFunction);return[[r,i,e],!0]}return t.prototype.checkItem.apply(this,arguments)},e}(f.BaseItem);e.FnItem=L;var P=function(t){function e(){var e=null!==t&&t.apply(this,arguments)||this;return e.remap=l.MapHandler.getMap("not_remap"),e}return o(e,t),Object.defineProperty(e.prototype,"kind",{get:function(){return"not"},enumerable:!1,configurable:!0}),e.prototype.checkItem=function(t){var e,r,n;if(t.isKind("open")||t.isKind("left"))return f.BaseItem.success;if(t.isKind("mml")&&(d.default.isType(t.First,"mo")||d.default.isType(t.First,"mi")||d.default.isType(t.First,"mtext"))&&(e=t.First,1===(r=d.default.getText(e)).length&&!d.default.getProperty(e,"movesupsub")&&1===d.default.getChildren(e).length))return this.remap.contains(r)?(n=this.create("text",this.remap.lookup(r).char),d.default.setChild(e,0,n)):(n=this.create("text","\u0338"),d.default.appendChildren(e,[n])),[[t],!0];n=this.create("text","\u29f8");var o=this.create("node","mtext",[],{},n),i=this.create("node","mpadded",[o],{width:0});return[[e=this.create("node","TeXAtom",[i],{texClass:u.TEXCLASS.REL}),t],!0]},e}(f.BaseItem);e.NotItem=P;var I=function(t){function e(){return null!==t&&t.apply(this,arguments)||this}return o(e,t),Object.defineProperty(e.prototype,"kind",{get:function(){return"nonscript"},enumerable:!1,configurable:!0}),e.prototype.checkItem=function(t){if(t.isKind("mml")&&1===t.Size()){var e=t.First;if(e.isKind("mstyle")&&e.notParent&&(e=d.default.getChildren(d.default.getChildren(e)[0])[0]),e.isKind("mspace")){if(e!==t.First){var r=this.create("node","mrow",[t.Pop()]);t.Push(r)}this.factory.configuration.addNode("nonscript",t.First)}}return[[t],!0]},e}(f.BaseItem);e.NonscriptItem=I;var k=function(t){function e(){return null!==t&&t.apply(this,arguments)||this}return o(e,t),Object.defineProperty(e.prototype,"kind",{get:function(){return"dots"},enumerable:!1,configurable:!0}),e.prototype.checkItem=function(t){if(t.isKind("open")||t.isKind("left"))return f.BaseItem.success;var e=this.getProperty("ldots"),r=t.First;if(t.isKind("mml")&&d.default.isEmbellished(r)){var n=d.default.getTexClass(d.default.getCoreMO(r));n!==u.TEXCLASS.BIN&&n!==u.TEXCLASS.REL||(e=this.getProperty("cdots"))}return[[e,t],!0]},e}(f.BaseItem);e.DotsItem=k;var R=function(t){function e(){var e=null!==t&&t.apply(this,arguments)||this;return e.table=[],e.row=[],e.frame=[],e.hfill=[],e.arraydef={},e.dashed=!1,e}return o(e,t),Object.defineProperty(e.prototype,"kind",{get:function(){return"array"},enumerable:!1,configurable:!0}),Object.defineProperty(e.prototype,"isOpen",{get:function(){return!0},enumerable:!1,configurable:!0}),Object.defineProperty(e.prototype,"copyEnv",{get:function(){return!1},enumerable:!1,configurable:!0}),e.prototype.checkItem=function(e){if(e.isClose&&!e.isKind("over")){if(e.getProperty("isEntry"))return this.EndEntry(),this.clearEnv(),f.BaseItem.fail;if(e.getProperty("isCR"))return this.EndEntry(),this.EndRow(),this.clearEnv(),f.BaseItem.fail;this.EndTable(),this.clearEnv();var r=this.factory.create("mml",this.createMml());if(this.getProperty("requireClose")){if(e.isKind("close"))return[[r],!0];throw new p.default("MissingCloseBrace","Missing close brace")}return[[r,e],!0]}return t.prototype.checkItem.call(this,e)},e.prototype.createMml=function(){var t=this.arraydef.scriptlevel;delete this.arraydef.scriptlevel;var e=this.create("node","mtable",this.table,this.arraydef);return t&&e.setProperty("scriptlevel",t),4===this.frame.length?d.default.setAttribute(e,"frame",this.dashed?"dashed":"solid"):this.frame.length&&(this.arraydef.rowlines&&(this.arraydef.rowlines=this.arraydef.rowlines.replace(/none( none)+$/,"none")),d.default.setAttribute(e,"frame",""),e=this.create("node","menclose",[e],{notation:this.frame.join(" ")}),"none"===(this.arraydef.columnlines||"none")&&"none"===(this.arraydef.rowlines||"none")||d.default.setAttribute(e,"data-padding",0)),(this.getProperty("open")||this.getProperty("close"))&&(e=h.default.fenced(this.factory.configuration,this.getProperty("open"),e,this.getProperty("close"))),e},e.prototype.EndEntry=function(){var t=this.create("node","mtd",this.nodes);this.hfill.length&&(0===this.hfill[0]&&d.default.setAttribute(t,"columnalign","right"),this.hfill[this.hfill.length-1]===this.Size()&&d.default.setAttribute(t,"columnalign",d.default.getAttribute(t,"columnalign")?"center":"left")),this.row.push(t),this.Clear(),this.hfill=[]},e.prototype.EndRow=function(){var t;this.getProperty("isNumbered")&&3===this.row.length?(this.row.unshift(this.row.pop()),t=this.create("node","mlabeledtr",this.row)):t=this.create("node","mtr",this.row),this.table.push(t),this.row=[]},e.prototype.EndTable=function(){(this.Size()||this.row.length)&&(this.EndEntry(),this.EndRow()),this.checkLines()},e.prototype.checkLines=function(){if(this.arraydef.rowlines){var t=this.arraydef.rowlines.split(/ /);t.length===this.table.length?(this.frame.push("bottom"),t.pop(),this.arraydef.rowlines=t.join(" ")):t.length<this.table.length-1&&(this.arraydef.rowlines+=" none")}if(this.getProperty("rowspacing")){for(var e=this.arraydef.rowspacing.split(/ /);e.length<this.table.length;)e.push(this.getProperty("rowspacing")+"em");this.arraydef.rowspacing=e.join(" ")}},e.prototype.addRowSpacing=function(t){if(this.arraydef.rowspacing){var e=this.arraydef.rowspacing.split(/ /);if(!this.getProperty("rowspacing")){var r=h.default.dimen2em(e[0]);this.setProperty("rowspacing",r)}for(var n=this.getProperty("rowspacing");e.length<this.table.length;)e.push(h.default.Em(n));e[this.table.length-1]=h.default.Em(Math.max(0,n+h.default.dimen2em(t))),this.arraydef.rowspacing=e.join(" ")}},e}(f.BaseItem);e.ArrayItem=R;var j=function(t){function e(e){for(var r=[],n=1;n<arguments.length;n++)r[n-1]=arguments[n];var o=t.call(this,e)||this;return o.maxrow=0,o.factory.configuration.tags.start(r[0],r[2],r[1]),o}return o(e,t),Object.defineProperty(e.prototype,"kind",{get:function(){return"eqnarray"},enumerable:!1,configurable:!0}),e.prototype.EndEntry=function(){this.row.length&&h.default.fixInitialMO(this.factory.configuration,this.nodes);var t=this.create("node","mtd",this.nodes);this.row.push(t),this.Clear()},e.prototype.EndRow=function(){this.row.length>this.maxrow&&(this.maxrow=this.row.length);var t="mtr",e=this.factory.configuration.tags.getTag();e&&(this.row=[e].concat(this.row),t="mlabeledtr"),this.factory.configuration.tags.clearTag();var r=this.create("node",t,this.row);this.table.push(r),this.row=[]},e.prototype.EndTable=function(){t.prototype.EndTable.call(this),this.factory.configuration.tags.end(),this.extendArray("columnalign",this.maxrow),this.extendArray("columnwidth",this.maxrow),this.extendArray("columnspacing",this.maxrow-1)},e.prototype.extendArray=function(t,e){if(this.arraydef[t]){var r=this.arraydef[t].split(/ /),n=a([],i(r),!1);if(n.length>1){for(;n.length<e;)n.push.apply(n,a([],i(r),!1));this.arraydef[t]=n.slice(0,e).join(" ")}}},e}(R);e.EqnArrayItem=j;var B=function(t){function e(e){for(var r=[],n=1;n<arguments.length;n++)r[n-1]=arguments[n];var o=t.call(this,e)||this;return o.factory.configuration.tags.start("equation",!0,r[0]),o}return o(e,t),Object.defineProperty(e.prototype,"kind",{get:function(){return"equation"},enumerable:!1,configurable:!0}),Object.defineProperty(e.prototype,"isOpen",{get:function(){return!0},enumerable:!1,configurable:!0}),e.prototype.checkItem=function(e){if(e.isKind("end")){var r=this.toMml(),n=this.factory.configuration.tags.getTag();return this.factory.configuration.tags.end(),[[n?this.factory.configuration.tags.enTag(r,n):r,e],!0]}if(e.isKind("stop"))throw new p.default("EnvMissingEnd","Missing \\end{%1}",this.getName());return t.prototype.checkItem.call(this,e)},e}(f.BaseItem);e.EquationItem=B},1267:function(t,e,r){var n=this&&this.__createBinding||(Object.create?function(t,e,r,n){void 0===n&&(n=r);var o=Object.getOwnPropertyDescriptor(e,r);o&&!("get"in o?!e.__esModule:o.writable||o.configurable)||(o={enumerable:!0,get:function(){return e[r]}}),Object.defineProperty(t,n,o)}:function(t,e,r,n){void 0===n&&(n=r),t[n]=e[r]}),o=this&&this.__setModuleDefault||(Object.create?function(t,e){Object.defineProperty(t,"default",{enumerable:!0,value:e})}:function(t,e){t.default=e}),i=this&&this.__importStar||function(t){if(t&&t.__esModule)return t;var e={};if(null!=t)for(var r in t)"default"!==r&&Object.prototype.hasOwnProperty.call(t,r)&&n(e,t,r);return o(e,t),e},a=this&&this.__importDefault||function(t){return t&&t.__esModule?t:{default:t}};Object.defineProperty(e,"__esModule",{value:!0});var s=i(r(9140)),l=r(8317),c=a(r(7693)),u=a(r(5450)),p=a(r(1130)),h=r(9007),d=r(6010);new s.RegExpMap("letter",u.default.variable,/[a-z]/i),new s.RegExpMap("digit",u.default.digit,/[0-9.,]/),new s.RegExpMap("command",u.default.controlSequence,/^\\/),new s.MacroMap("special",{"{":"Open","}":"Close","~":"Tilde","^":"Superscript",_:"Subscript"," ":"Space","\t":"Space","\r":"Space","\n":"Space","'":"Prime","%":"Comment","&":"Entry","#":"Hash","\xa0":"Space","\u2019":"Prime"},c.default),new s.CharacterMap("mathchar0mi",u.default.mathchar0mi,{alpha:"\u03b1",beta:"\u03b2",gamma:"\u03b3",delta:"\u03b4",epsilon:"\u03f5",zeta:"\u03b6",eta:"\u03b7",theta:"\u03b8",iota:"\u03b9",kappa:"\u03ba",lambda:"\u03bb",mu:"\u03bc",nu:"\u03bd",xi:"\u03be",omicron:"\u03bf",pi:"\u03c0",rho:"\u03c1",sigma:"\u03c3",tau:"\u03c4",upsilon:"\u03c5",phi:"\u03d5",chi:"\u03c7",psi:"\u03c8",omega:"\u03c9",varepsilon:"\u03b5",vartheta:"\u03d1",varpi:"\u03d6",varrho:"\u03f1",varsigma:"\u03c2",varphi:"\u03c6",S:["\xa7",{mathvariant:l.TexConstant.Variant.NORMAL}],aleph:["\u2135",{mathvariant:l.TexConstant.Variant.NORMAL}],hbar:["\u210f",{variantForm:!0}],imath:"\u0131",jmath:"\u0237",ell:"\u2113",wp:["\u2118",{mathvariant:l.TexConstant.Variant.NORMAL}],Re:["\u211c",{mathvariant:l.TexConstant.Variant.NORMAL}],Im:["\u2111",{mathvariant:l.TexConstant.Variant.NORMAL}],partial:["\u2202",{mathvariant:l.TexConstant.Variant.ITALIC}],infty:["\u221e",{mathvariant:l.TexConstant.Variant.NORMAL}],prime:["\u2032",{variantForm:!0}],emptyset:["\u2205",{mathvariant:l.TexConstant.Variant.NORMAL}],nabla:["\u2207",{mathvariant:l.TexConstant.Variant.NORMAL}],top:["\u22a4",{mathvariant:l.TexConstant.Variant.NORMAL}],bot:["\u22a5",{mathvariant:l.TexConstant.Variant.NORMAL}],angle:["\u2220",{mathvariant:l.TexConstant.Variant.NORMAL}],triangle:["\u25b3",{mathvariant:l.TexConstant.Variant.NORMAL}],backslash:["\u2216",{mathvariant:l.TexConstant.Variant.NORMAL}],forall:["\u2200",{mathvariant:l.TexConstant.Variant.NORMAL}],exists:["\u2203",{mathvariant:l.TexConstant.Variant.NORMAL}],neg:["\xac",{mathvariant:l.TexConstant.Variant.NORMAL}],lnot:["\xac",{mathvariant:l.TexConstant.Variant.NORMAL}],flat:["\u266d",{mathvariant:l.TexConstant.Variant.NORMAL}],natural:["\u266e",{mathvariant:l.TexConstant.Variant.NORMAL}],sharp:["\u266f",{mathvariant:l.TexConstant.Variant.NORMAL}],clubsuit:["\u2663",{mathvariant:l.TexConstant.Variant.NORMAL}],diamondsuit:["\u2662",{mathvariant:l.TexConstant.Variant.NORMAL}],heartsuit:["\u2661",{mathvariant:l.TexConstant.Variant.NORMAL}],spadesuit:["\u2660",{mathvariant:l.TexConstant.Variant.NORMAL}]}),new s.CharacterMap("mathchar0mo",u.default.mathchar0mo,{surd:"\u221a",coprod:["\u2210",{texClass:h.TEXCLASS.OP,movesupsub:!0}],bigvee:["\u22c1",{texClass:h.TEXCLASS.OP,movesupsub:!0}],bigwedge:["\u22c0",{texClass:h.TEXCLASS.OP,movesupsub:!0}],biguplus:["\u2a04",{texClass:h.TEXCLASS.OP,movesupsub:!0}],bigcap:["\u22c2",{texClass:h.TEXCLASS.OP,movesupsub:!0}],bigcup:["\u22c3",{texClass:h.TEXCLASS.OP,movesupsub:!0}],int:["\u222b",{texClass:h.TEXCLASS.OP}],intop:["\u222b",{texClass:h.TEXCLASS.OP,movesupsub:!0,movablelimits:!0}],iint:["\u222c",{texClass:h.TEXCLASS.OP}],iiint:["\u222d",{texClass:h.TEXCLASS.OP}],prod:["\u220f",{texClass:h.TEXCLASS.OP,movesupsub:!0}],sum:["\u2211",{texClass:h.TEXCLASS.OP,movesupsub:!0}],bigotimes:["\u2a02",{texClass:h.TEXCLASS.OP,movesupsub:!0}],bigoplus:["\u2a01",{texClass:h.TEXCLASS.OP,movesupsub:!0}],bigodot:["\u2a00",{texClass:h.TEXCLASS.OP,movesupsub:!0}],oint:["\u222e",{texClass:h.TEXCLASS.OP}],bigsqcup:["\u2a06",{texClass:h.TEXCLASS.OP,movesupsub:!0}],smallint:["\u222b",{largeop:!1}],triangleleft:"\u25c3",triangleright:"\u25b9",bigtriangleup:"\u25b3",bigtriangledown:"\u25bd",wedge:"\u2227",land:"\u2227",vee:"\u2228",lor:"\u2228",cap:"\u2229",cup:"\u222a",ddagger:"\u2021",dagger:"\u2020",sqcap:"\u2293",sqcup:"\u2294",uplus:"\u228e",amalg:"\u2a3f",diamond:"\u22c4",bullet:"\u2219",wr:"\u2240",div:"\xf7",divsymbol:"\xf7",odot:["\u2299",{largeop:!1}],oslash:["\u2298",{largeop:!1}],otimes:["\u2297",{largeop:!1}],ominus:["\u2296",{largeop:!1}],oplus:["\u2295",{largeop:!1}],mp:"\u2213",pm:"\xb1",circ:"\u2218",bigcirc:"\u25ef",setminus:"\u2216",cdot:"\u22c5",ast:"\u2217",times:"\xd7",star:"\u22c6",propto:"\u221d",sqsubseteq:"\u2291",sqsupseteq:"\u2292",parallel:"\u2225",mid:"\u2223",dashv:"\u22a3",vdash:"\u22a2",leq:"\u2264",le:"\u2264",geq:"\u2265",ge:"\u2265",lt:"<",gt:">",succ:"\u227b",prec:"\u227a",approx:"\u2248",succeq:"\u2ab0",preceq:"\u2aaf",supset:"\u2283",subset:"\u2282",supseteq:"\u2287",subseteq:"\u2286",in:"\u2208",ni:"\u220b",notin:"\u2209",owns:"\u220b",gg:"\u226b",ll:"\u226a",sim:"\u223c",simeq:"\u2243",perp:"\u22a5",equiv:"\u2261",asymp:"\u224d",smile:"\u2323",frown:"\u2322",ne:"\u2260",neq:"\u2260",cong:"\u2245",doteq:"\u2250",bowtie:"\u22c8",models:"\u22a8",notChar:"\u29f8",Leftrightarrow:"\u21d4",Leftarrow:"\u21d0",Rightarrow:"\u21d2",leftrightarrow:"\u2194",leftarrow:"\u2190",gets:"\u2190",rightarrow:"\u2192",to:["\u2192",{accent:!1}],mapsto:"\u21a6",leftharpoonup:"\u21bc",leftharpoondown:"\u21bd",rightharpoonup:"\u21c0",rightharpoondown:"\u21c1",nearrow:"\u2197",searrow:"\u2198",nwarrow:"\u2196",swarrow:"\u2199",rightleftharpoons:"\u21cc",hookrightarrow:"\u21aa",hookleftarrow:"\u21a9",longleftarrow:"\u27f5",Longleftarrow:"\u27f8",longrightarrow:"\u27f6",Longrightarrow:"\u27f9",Longleftrightarrow:"\u27fa",longleftrightarrow:"\u27f7",longmapsto:"\u27fc",ldots:"\u2026",cdots:"\u22ef",vdots:"\u22ee",ddots:"\u22f1",dotsc:"\u2026",dotsb:"\u22ef",dotsm:"\u22ef",dotsi:"\u22ef",dotso:"\u2026",ldotp:[".",{texClass:h.TEXCLASS.PUNCT}],cdotp:["\u22c5",{texClass:h.TEXCLASS.PUNCT}],colon:[":",{texClass:h.TEXCLASS.PUNCT}]}),new 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e=t.padding/2,r=t.thickness;return[2*e,e,e+r,3*e+r]},border:function(t){return[0,0,t.thickness,0]},remove:"bottom"}],h.Arrow("up"),h.Arrow("down"),h.Arrow("left"),h.Arrow("right"),h.Arrow("updown"),h.Arrow("leftright"),h.DiagonalArrow("updiagonal"),h.DiagonalArrow("northeast"),h.DiagonalArrow("southeast"),h.DiagonalArrow("northwest"),h.DiagonalArrow("southwest"),h.DiagonalArrow("northeastsouthwest"),h.DiagonalArrow("northwestsoutheast"),["longdiv",{renderer:function(t,e){var r=t.adaptor;r.setStyle(e,"border-top",t.em(t.thickness)+" solid");var n=r.append(t.chtml,t.html("dbox")),o=t.thickness,i=t.padding;o!==h.THICKNESS&&r.setStyle(n,"border-width",t.em(o)),i!==h.PADDING&&(r.setStyle(n,"left",t.em(-1.5*i)),r.setStyle(n,"width",t.em(3*i)),r.setStyle(n,"clip-path","inset(0 0 0 "+t.em(1.5*i)+")"))},bbox:function(t){var e=t.padding,r=t.thickness;return[e+r,e,e,2*e+r/2]}}],["radical",{renderer:function(t,e){t.msqrt.toCHTML(e);var 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mjx-cell":{"text-align":"right"},'[script-align="left"] > mjx-row > mjx-cell':{"text-align":"left"},'[script-align="center"] > mjx-row > mjx-cell':{"text-align":"center"},'[script-align="right"] > mjx-row > mjx-cell':{"text-align":"right"}},e}((0,s.CommonMmultiscriptsMixin)(a.CHTMLmsubsup));e.CHTMLmmultiscripts=u},6460:function(t,e,r){var n,o=this&&this.__extends||(n=function(t,e){return n=Object.setPrototypeOf||{__proto__:[]}instanceof Array&&function(t,e){t.__proto__=e}||function(t,e){for(var r in e)Object.prototype.hasOwnProperty.call(e,r)&&(t[r]=e[r])},n(t,e)},function(t,e){if("function"!=typeof e&&null!==e)throw new TypeError("Class extends value "+String(e)+" is not a constructor or null");function r(){this.constructor=t}n(t,e),t.prototype=null===e?Object.create(e):(r.prototype=e.prototype,new r)});Object.defineProperty(e,"__esModule",{value:!0}),e.CHTMLmn=void 0;var i=r(5355),a=r(5023),s=r(3050),l=function(t){function e(){return null!==t&&t.apply(this,arguments)||this}return 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l=i(this.tableRows),c=l.next();!c.done;c=l.next()){var u=c.value,p=0;try{for(var h=(r=void 0,i(u.tableCells)),d=h.next();!d.done;d=h.next()){var f=d.value,m=a[p++],y=a[p],g=f?f.chtml:this.adaptor.childNodes(u.chtml)[p];(p>1&&"0.4em"!==m||s&&1===p)&&this.adaptor.setStyle(g,"paddingLeft",m),(p<this.numCols&&"0.4em"!==y||s&&p===this.numCols)&&this.adaptor.setStyle(g,"paddingRight",y)}}catch(t){r={error:t}}finally{try{d&&!d.done&&(n=h.return)&&n.call(h)}finally{if(r)throw r.error}}}}catch(e){t={error:e}}finally{try{c&&!c.done&&(e=l.return)&&e.call(l)}finally{if(t)throw t.error}}},e.prototype.handleColumnLines=function(){var t,e,r,n;if("none"!==this.node.attributes.get("columnlines")){var o=this.getColumnAttributes("columnlines");try{for(var a=i(this.childNodes),s=a.next();!s.done;s=a.next()){var l=s.value,c=0;try{for(var u=(r=void 0,i(this.adaptor.childNodes(l.chtml).slice(1))),p=u.next();!p.done;p=u.next()){var h=p.value,d=o[c++];"none"!==d&&this.adaptor.setStyle(h,"borderLeft",".07em "+d)}}catch(t){r={error:t}}finally{try{p&&!p.done&&(n=u.return)&&n.call(u)}finally{if(r)throw r.error}}}}catch(e){t={error:e}}finally{try{s&&!s.done&&(e=a.return)&&e.call(a)}finally{if(t)throw t.error}}}},e.prototype.handleColumnWidths=function(){var t,e,r,n;try{for(var o=i(this.childNodes),a=o.next();!a.done;a=o.next()){var s=a.value,l=0;try{for(var c=(r=void 0,i(this.adaptor.childNodes(s.chtml))),u=c.next();!u.done;u=c.next()){var p=u.value,h=this.cWidths[l++];if(null!==h){var d="number"==typeof h?this.em(h):h;this.adaptor.setStyle(p,"width",d),this.adaptor.setStyle(p,"maxWidth",d),this.adaptor.setStyle(p,"minWidth",d)}}}catch(t){r={error:t}}finally{try{u&&!u.done&&(n=c.return)&&n.call(c)}finally{if(r)throw r.error}}}}catch(e){t={error:e}}finally{try{a&&!a.done&&(e=o.return)&&e.call(o)}finally{if(t)throw t.error}}},e.prototype.handleRowSpacing=function(){var t,e,r,n,o=this.childNodes[0]?1/this.childNodes[0].getBBox().rscale:1,a=this.getEmHalfSpacing(this.fSpace[1],this.rSpace,o),s=this.frame,l=0;try{for(var c=i(this.childNodes),u=c.next();!u.done;u=c.next()){var p=u.value,h=a[l++],d=a[l];try{for(var f=(r=void 0,i(p.childNodes)),m=f.next();!m.done;m=f.next()){var y=m.value;(l>1&&"0.215em"!==h||s&&1===l)&&this.adaptor.setStyle(y.chtml,"paddingTop",h),(l<this.numRows&&"0.215em"!==d||s&&l===this.numRows)&&this.adaptor.setStyle(y.chtml,"paddingBottom",d)}}catch(t){r={error:t}}finally{try{m&&!m.done&&(n=f.return)&&n.call(f)}finally{if(r)throw r.error}}}}catch(e){t={error:e}}finally{try{u&&!u.done&&(e=c.return)&&e.call(c)}finally{if(t)throw t.error}}},e.prototype.handleRowLines=function(){var t,e,r,n;if("none"!==this.node.attributes.get("rowlines")){var o=this.getRowAttributes("rowlines"),a=0;try{for(var s=i(this.childNodes.slice(1)),l=s.next();!l.done;l=s.next()){var c=l.value,u=o[a++];if("none"!==u)try{for(var p=(r=void 0,i(this.adaptor.childNodes(c.chtml))),h=p.next();!h.done;h=p.next()){var d=h.value;this.adaptor.setStyle(d,"borderTop",".07em "+u)}}catch(t){r={error:t}}finally{try{h&&!h.done&&(n=p.return)&&n.call(p)}finally{if(r)throw r.error}}}}catch(e){t={error:e}}finally{try{l&&!l.done&&(e=s.return)&&e.call(s)}finally{if(t)throw t.error}}}},e.prototype.handleRowHeights=function(){this.node.attributes.get("equalrows")&&this.handleEqualRows()},e.prototype.handleEqualRows=function(){for(var t=this.getRowHalfSpacing(),e=this.getTableData(),r=e.H,n=e.D,o=e.NH,i=e.ND,a=this.getEqualRowHeight(),s=0;s<this.numRows;s++){var l=this.childNodes[s];this.setRowHeight(l,a+t[s]+t[s+1]+this.rLines[s]),a!==o[s]+i[s]&&this.setRowBaseline(l,a,(a-r[s]+n[s])/2)}},e.prototype.setRowHeight=function(t,e){this.adaptor.setStyle(t.chtml,"height",this.em(e))},e.prototype.setRowBaseline=function(t,e,r){var n,o,a=t.node.attributes.get("rowalign");try{for(var s=i(t.childNodes),l=s.next();!l.done;l=s.next()){var c=l.value;if(this.setCellBaseline(c,a,e,r))break}}catch(t){n={error:t}}finally{try{l&&!l.done&&(o=s.return)&&o.call(s)}finally{if(n)throw n.error}}},e.prototype.setCellBaseline=function(t,e,r,n){var o=t.node.attributes.get("rowalign");if("baseline"===o||"axis"===o){var i=this.adaptor,a=i.lastChild(t.chtml);i.setStyle(a,"height",this.em(r)),i.setStyle(a,"verticalAlign",this.em(-n));var s=t.parent;if(!(s.node.isKind("mlabeledtr")&&t===s.childNodes[0]||"baseline"!==e&&"axis"!==e))return!0}return!1},e.prototype.handleFrame=function(){this.frame&&this.fLine&&this.adaptor.setStyle(this.itable,"border",".07em "+this.node.attributes.get("frame"))},e.prototype.handleWidth=function(){var t=this.adaptor,e=this.getBBox(),r=e.w,n=e.L,o=e.R;t.setStyle(this.chtml,"minWidth",this.em(n+r+o));var i=this.node.attributes.get("width");if((0,u.isPercent)(i))t.setStyle(this.chtml,"width",""),t.setAttribute(this.chtml,"width","full");else if(!this.hasLabels){if("auto"===i)return;i=this.em(this.length2em(i)+2*this.fLine)}var a=t.firstChild(this.chtml);if(t.setStyle(a,"width",i),t.setStyle(a,"minWidth",this.em(r)),n||o){t.setStyle(this.chtml,"margin","");var s=this.node.attributes.get("data-width-includes-label")?"padding":"margin";n===o?t.setStyle(a,s,"0 "+this.em(o)):t.setStyle(a,s,"0 "+this.em(o)+" 0 "+this.em(n))}t.setAttribute(this.itable,"width","full")},e.prototype.handleAlign=function(){var t=a(this.getAlignmentRow(),2),e=t[0],r=t[1];if(null===r)"axis"!==e&&this.adaptor.setAttribute(this.chtml,"align",e);else{var n=this.getVerticalPosition(r,e);this.adaptor.setAttribute(this.chtml,"align","top"),this.adaptor.setStyle(this.chtml,"verticalAlign",this.em(n))}},e.prototype.handleJustify=function(){var t=this.getAlignShift()[0];"center"!==t&&this.adaptor.setAttribute(this.chtml,"justify",t)},e.prototype.handleLabels=function(){if(this.hasLabels){var t=this.labels,e=this.node.attributes,r=this.adaptor,n=e.get("side");r.setAttribute(this.chtml,"side",n),r.setAttribute(t,"align",n),r.setStyle(t,n,"0");var o=a(this.addLabelPadding(n),2),i=o[0],s=o[1];if(s){var l=r.firstChild(this.chtml);this.setIndent(l,i,s)}this.updateRowHeights(),this.addLabelSpacing()}},e.prototype.addLabelPadding=function(t){var e=a(this.getPadAlignShift(t),3),r=e[1],n=e[2],o={};if("right"===t&&!this.node.attributes.get("data-width-includes-label")){var i=this.node.attributes.get("width"),s=this.getBBox(),l=s.w,c=s.L,p=s.R;o.style={width:(0,u.isPercent)(i)?"calc("+i+" + "+this.em(c+p)+")":this.em(c+l+p)}}return this.adaptor.append(this.chtml,this.html("mjx-labels",o,[this.labels])),[r,n]},e.prototype.updateRowHeights=function(){for(var t=this.getTableData(),e=t.H,r=t.D,n=t.NH,o=t.ND,i=this.getRowHalfSpacing(),a=0;a<this.numRows;a++){var s=this.childNodes[a];this.setRowHeight(s,e[a]+r[a]+i[a]+i[a+1]+this.rLines[a]),e[a]!==n[a]||r[a]!==o[a]?this.setRowBaseline(s,e[a]+r[a],r[a]):s.node.isKind("mlabeledtr")&&this.setCellBaseline(s.childNodes[0],"",e[a]+r[a],r[a])}},e.prototype.addLabelSpacing=function(){for(var t=this.adaptor,e=this.node.attributes.get("equalrows"),r=this.getTableData(),n=r.H,o=r.D,i=e?this.getEqualRowHeight():0,a=this.getRowHalfSpacing(),s=this.fLine,l=t.firstChild(this.labels),c=0;c<this.numRows;c++){this.childNodes[c].node.isKind("mlabeledtr")?(s&&t.insert(this.html("mjx-mtr",{style:{height:this.em(s)}}),l),t.setStyle(l,"height",this.em((e?i:n[c]+o[c])+a[c]+a[c+1])),l=t.next(l),s=this.rLines[c]):s+=a[c]+(e?i:n[c]+o[c])+a[c+1]+this.rLines[c]}},e.kind=c.MmlMtable.prototype.kind,e.styles={"mjx-mtable":{"vertical-align":".25em","text-align":"center",position:"relative","box-sizing":"border-box","border-spacing":0,"border-collapse":"collapse"},'mjx-mstyle[size="s"] mjx-mtable':{"vertical-align":".354em"},"mjx-labels":{position:"absolute",left:0,top:0},"mjx-table":{display:"inline-block","vertical-align":"-.5ex","box-sizing":"border-box"},"mjx-table > mjx-itable":{"vertical-align":"middle","text-align":"left","box-sizing":"border-box"},"mjx-labels > mjx-itable":{position:"absolute",top:0},'mjx-mtable[justify="left"]':{"text-align":"left"},'mjx-mtable[justify="right"]':{"text-align":"right"},'mjx-mtable[justify="left"][side="left"]':{"padding-right":"0 ! important"},'mjx-mtable[justify="left"][side="right"]':{"padding-left":"0 ! important"},'mjx-mtable[justify="right"][side="left"]':{"padding-right":"0 ! important"},'mjx-mtable[justify="right"][side="right"]':{"padding-left":"0 ! important"},"mjx-mtable[align]":{"vertical-align":"baseline"},'mjx-mtable[align="top"] > mjx-table':{"vertical-align":"top"},'mjx-mtable[align="bottom"] > mjx-table':{"vertical-align":"bottom"},'mjx-mtable[side="right"] mjx-labels':{"min-width":"100%"}},e}((0,l.CommonMtableMixin)(s.CHTMLWrapper));e.CHTMLmtable=p},7056:function(t,e,r){var n,o=this&&this.__extends||(n=function(t,e){return n=Object.setPrototypeOf||{__proto__:[]}instanceof Array&&function(t,e){t.__proto__=e}||function(t,e){for(var r in e)Object.prototype.hasOwnProperty.call(e,r)&&(t[r]=e[r])},n(t,e)},function(t,e){if("function"!=typeof e&&null!==e)throw new TypeError("Class extends value "+String(e)+" is not a constructor or null");function r(){this.constructor=t}n(t,e),t.prototype=null===e?Object.create(e):(r.prototype=e.prototype,new r)});Object.defineProperty(e,"__esModule",{value:!0}),e.CHTMLmtd=void 0;var i=r(5355),a=r(5164),s=r(4359),l=function(t){function e(){return null!==t&&t.apply(this,arguments)||this}return o(e,t),e.prototype.toCHTML=function(e){t.prototype.toCHTML.call(this,e);var r=this.node.attributes.get("rowalign"),n=this.node.attributes.get("columnalign");r!==this.parent.node.attributes.get("rowalign")&&this.adaptor.setAttribute(this.chtml,"rowalign",r),"center"===n||"mlabeledtr"===this.parent.kind&&this===this.parent.childNodes[0]&&n===this.parent.parent.node.attributes.get("side")||this.adaptor.setStyle(this.chtml,"textAlign",n),this.parent.parent.node.getProperty("useHeight")&&this.adaptor.append(this.chtml,this.html("mjx-tstrut"))},e.kind=s.MmlMtd.prototype.kind,e.styles={"mjx-mtd":{display:"table-cell","text-align":"center",padding:".215em .4em"},"mjx-mtd:first-child":{"padding-left":0},"mjx-mtd:last-child":{"padding-right":0},"mjx-mtable > * > mjx-itable > *:first-child > mjx-mtd":{"padding-top":0},"mjx-mtable > * > mjx-itable > *:last-child > mjx-mtd":{"padding-bottom":0},"mjx-tstrut":{display:"inline-block",height:"1em","vertical-align":"-.25em"},'mjx-labels[align="left"] > mjx-mtr > mjx-mtd':{"text-align":"left"},'mjx-labels[align="right"] > mjx-mtr > mjx-mtd':{"text-align":"right"},"mjx-mtd[extra]":{padding:0},'mjx-mtd[rowalign="top"]':{"vertical-align":"top"},'mjx-mtd[rowalign="center"]':{"vertical-align":"middle"},'mjx-mtd[rowalign="bottom"]':{"vertical-align":"bottom"},'mjx-mtd[rowalign="baseline"]':{"vertical-align":"baseline"},'mjx-mtd[rowalign="axis"]':{"vertical-align":".25em"}},e}((0,a.CommonMtdMixin)(i.CHTMLWrapper));e.CHTMLmtd=l},1259:function(t,e,r){var n,o=this&&this.__extends||(n=function(t,e){return n=Object.setPrototypeOf||{__proto__:[]}instanceof Array&&function(t,e){t.__proto__=e}||function(t,e){for(var r in e)Object.prototype.hasOwnProperty.call(e,r)&&(t[r]=e[r])},n(t,e)},function(t,e){if("function"!=typeof e&&null!==e)throw new TypeError("Class extends value "+String(e)+" is not a constructor or null");function r(){this.constructor=t}n(t,e),t.prototype=null===e?Object.create(e):(r.prototype=e.prototype,new r)});Object.defineProperty(e,"__esModule",{value:!0}),e.CHTMLmtext=void 0;var i=r(5355),a=r(6319),s=r(4770),l=function(t){function e(){return null!==t&&t.apply(this,arguments)||this}return o(e,t),e.kind=s.MmlMtext.prototype.kind,e}((0,a.CommonMtextMixin)(i.CHTMLWrapper));e.CHTMLmtext=l},3571:function(t,e,r){var n,o=this&&this.__extends||(n=function(t,e){return n=Object.setPrototypeOf||{__proto__:[]}instanceof Array&&function(t,e){t.__proto__=e}||function(t,e){for(var r in e)Object.prototype.hasOwnProperty.call(e,r)&&(t[r]=e[r])},n(t,e)},function(t,e){if("function"!=typeof e&&null!==e)throw new TypeError("Class extends value "+String(e)+" is not a constructor or null");function r(){this.constructor=t}n(t,e),t.prototype=null===e?Object.create(e):(r.prototype=e.prototype,new r)});Object.defineProperty(e,"__esModule",{value:!0}),e.CHTMLmlabeledtr=e.CHTMLmtr=void 0;var i=r(5355),a=r(5766),s=r(5766),l=r(5022),c=function(t){function e(){return null!==t&&t.apply(this,arguments)||this}return o(e,t),e.prototype.toCHTML=function(e){t.prototype.toCHTML.call(this,e);var r=this.node.attributes.get("rowalign");"baseline"!==r&&this.adaptor.setAttribute(this.chtml,"rowalign",r)},e.kind=l.MmlMtr.prototype.kind,e.styles={"mjx-mtr":{display:"table-row"},'mjx-mtr[rowalign="top"] > mjx-mtd':{"vertical-align":"top"},'mjx-mtr[rowalign="center"] > mjx-mtd':{"vertical-align":"middle"},'mjx-mtr[rowalign="bottom"] > mjx-mtd':{"vertical-align":"bottom"},'mjx-mtr[rowalign="baseline"] > mjx-mtd':{"vertical-align":"baseline"},'mjx-mtr[rowalign="axis"] > mjx-mtd':{"vertical-align":".25em"}},e}((0,a.CommonMtrMixin)(i.CHTMLWrapper));e.CHTMLmtr=c;var u=function(t){function e(){return null!==t&&t.apply(this,arguments)||this}return o(e,t),e.prototype.toCHTML=function(e){t.prototype.toCHTML.call(this,e);var r=this.adaptor.firstChild(this.chtml);if(r){this.adaptor.remove(r);var n=this.node.attributes.get("rowalign"),o="baseline"!==n&&"axis"!==n?{rowalign:n}:{},i=this.html("mjx-mtr",o,[r]);this.adaptor.append(this.parent.labels,i)}},e.prototype.markUsed=function(){t.prototype.markUsed.call(this),this.jax.wrapperUsage.add(c.kind)},e.kind=l.MmlMlabeledtr.prototype.kind,e.styles={"mjx-mlabeledtr":{display:"table-row"},'mjx-mlabeledtr[rowalign="top"] > mjx-mtd':{"vertical-align":"top"},'mjx-mlabeledtr[rowalign="center"] > mjx-mtd':{"vertical-align":"middle"},'mjx-mlabeledtr[rowalign="bottom"] > mjx-mtd':{"vertical-align":"bottom"},'mjx-mlabeledtr[rowalign="baseline"] > mjx-mtd':{"vertical-align":"baseline"},'mjx-mlabeledtr[rowalign="axis"] > mjx-mtd':{"vertical-align":".25em"}},e}((0,s.CommonMlabeledtrMixin)(c));e.CHTMLmlabeledtr=u},6590:function(t,e,r){var n,o=this&&this.__extends||(n=function(t,e){return n=Object.setPrototypeOf||{__proto__:[]}instanceof Array&&function(t,e){t.__proto__=e}||function(t,e){for(var r in e)Object.prototype.hasOwnProperty.call(e,r)&&(t[r]=e[r])},n(t,e)},function(t,e){if("function"!=typeof e&&null!==e)throw new TypeError("Class extends value "+String(e)+" is not a constructor or null");function r(){this.constructor=t}n(t,e),t.prototype=null===e?Object.create(e):(r.prototype=e.prototype,new r)});Object.defineProperty(e,"__esModule",{value:!0}),e.CHTMLmunderover=e.CHTMLmover=e.CHTMLmunder=void 0;var i=r(4300),a=r(1971),s=r(1971),l=r(1971),c=r(5184),u=function(t){function e(){return null!==t&&t.apply(this,arguments)||this}return o(e,t),e.prototype.toCHTML=function(e){if(this.hasMovableLimits())return t.prototype.toCHTML.call(this,e),void this.adaptor.setAttribute(this.chtml,"limits","false");this.chtml=this.standardCHTMLnode(e);var r=this.adaptor.append(this.adaptor.append(this.chtml,this.html("mjx-row")),this.html("mjx-base")),n=this.adaptor.append(this.adaptor.append(this.chtml,this.html("mjx-row")),this.html("mjx-under"));this.baseChild.toCHTML(r),this.scriptChild.toCHTML(n);var o=this.baseChild.getOuterBBox(),i=this.scriptChild.getOuterBBox(),a=this.getUnderKV(o,i)[0],s=this.isLineBelow?0:this.getDelta(!0);this.adaptor.setStyle(n,"paddingTop",this.em(a)),this.setDeltaW([r,n],this.getDeltaW([o,i],[0,-s])),this.adjustUnderDepth(n,i)},e.kind=c.MmlMunder.prototype.kind,e.styles={"mjx-over":{"text-align":"left"},'mjx-munder:not([limits="false"])':{display:"inline-table"},"mjx-munder > mjx-row":{"text-align":"left"},"mjx-under":{"padding-bottom":".1em"}},e}((0,a.CommonMunderMixin)(i.CHTMLmsub));e.CHTMLmunder=u;var p=function(t){function e(){return null!==t&&t.apply(this,arguments)||this}return o(e,t),e.prototype.toCHTML=function(e){if(this.hasMovableLimits())return t.prototype.toCHTML.call(this,e),void 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e=[],r=0;r<arguments.length;r++)e[r]=arguments[r];var n=t.apply(this,i([],o(e),!1))||this;if(n.bevel=null,n.pad=n.node.getProperty("withDelims")?0:n.font.params.nulldelimiterspace,n.node.attributes.get("bevelled")){var a=n.getBevelData(n.isDisplay()).H,s=n.bevel=n.createMo("/");s.node.attributes.set("symmetric",!0),s.canStretch(1),s.getStretchedVariant([a],!0)}return n}return n(e,t),e.prototype.computeBBox=function(t,e){void 0===e&&(e=!1),t.empty();var r=this.node.attributes.getList("linethickness","bevelled"),n=r.linethickness,o=r.bevelled,i=this.isDisplay(),a=null;if(o)this.getBevelledBBox(t,i);else{var s=this.length2em(String(n),.06);a=-2*this.pad,0===s?this.getAtopBBox(t,i):(this.getFractionBBox(t,i,s),a-=.2),a+=t.w}t.clean(),this.setChildPWidths(e,a)},e.prototype.getFractionBBox=function(t,e,r){var n=this.childNodes[0].getOuterBBox(),o=this.childNodes[1].getOuterBBox(),i=this.font.params.axis_height,a=this.getTUV(e,r),s=a.T,l=a.u,c=a.v;t.combine(n,0,i+s+Math.max(n.d*n.rscale,l)),t.combine(o,0,i-s-Math.max(o.h*o.rscale,c)),t.w+=2*this.pad+.2},e.prototype.getTUV=function(t,e){var r=this.font.params,n=r.axis_height,o=(t?3.5:1.5)*e;return{T:(t?3.5:1.5)*e,u:(t?r.num1:r.num2)-n-o,v:(t?r.denom1:r.denom2)+n-o}},e.prototype.getAtopBBox=function(t,e){var r=this.getUVQ(e),n=r.u,o=r.v,i=r.nbox,a=r.dbox;t.combine(i,0,n),t.combine(a,0,-o),t.w+=2*this.pad},e.prototype.getUVQ=function(t){var e=this.childNodes[0].getOuterBBox(),r=this.childNodes[1].getOuterBBox(),n=this.font.params,i=o(t?[n.num1,n.denom1]:[n.num3,n.denom2],2),a=i[0],s=i[1],l=(t?7:3)*n.rule_thickness,c=a-e.d*e.scale-(r.h*r.scale-s);return c<l&&(a+=(l-c)/2,s+=(l-c)/2,c=l),{u:a,v:s,q:c,nbox:e,dbox:r}},e.prototype.getBevelledBBox=function(t,e){var r=this.getBevelData(e),n=r.u,o=r.v,i=r.delta,a=r.nbox,s=r.dbox,l=this.bevel.getOuterBBox();t.combine(a,0,n),t.combine(l,t.w-i/2,0),t.combine(s,t.w-i/2,o)},e.prototype.getBevelData=function(t){var e=this.childNodes[0].getOuterBBox(),r=this.childNodes[1].getOuterBBox(),n=t?.4:.15,o=Math.max(e.scale*(e.h+e.d),r.scale*(r.h+r.d))+2*n,i=this.font.params.axis_height;return{H:o,delta:n,u:e.scale*(e.d-e.h)/2+i+n,v:r.scale*(r.d-r.h)/2+i-n,nbox:e,dbox:r}},e.prototype.canStretch=function(t){return!1},e.prototype.isDisplay=function(){var t=this.node.attributes.getList("displaystyle","scriptlevel"),e=t.displaystyle,r=t.scriptlevel;return e&&0===r},e.prototype.getWrapWidth=function(t){var e=this.node.attributes;return e.get("bevelled")?this.childNodes[t].getOuterBBox().w:this.getBBox().w-(this.length2em(e.get("linethickness"))?.2:0)-2*this.pad},e.prototype.getChildAlign=function(t){var e=this.node.attributes;return e.get("bevelled")?"left":e.get(["numalign","denomalign"][t])},e}(t)}},5636:function(t,e){var r,n=this&&this.__extends||(r=function(t,e){return r=Object.setPrototypeOf||{__proto__:[]}instanceof Array&&function(t,e){t.__proto__=e}||function(t,e){for(var r in e)Object.prototype.hasOwnProperty.call(e,r)&&(t[r]=e[r])},r(t,e)},function(t,e){if("function"!=typeof e&&null!==e)throw new TypeError("Class extends value "+String(e)+" is not a constructor or null");function n(){this.constructor=t}r(t,e),t.prototype=null===e?Object.create(e):(n.prototype=e.prototype,new n)}),o=this&&this.__read||function(t,e){var r="function"==typeof Symbol&&t[Symbol.iterator];if(!r)return t;var n,o,i=r.call(t),a=[];try{for(;(void 0===e||e-- >0)&&!(n=i.next()).done;)a.push(n.value)}catch(t){o={error:t}}finally{try{n&&!n.done&&(r=i.return)&&r.call(i)}finally{if(o)throw o.error}}return a},i=this&&this.__spreadArray||function(t,e,r){if(r||2===arguments.length)for(var n,o=0,i=e.length;o<i;o++)!n&&o in e||(n||(n=Array.prototype.slice.call(e,0,o)),n[o]=e[o]);return t.concat(n||Array.prototype.slice.call(e))};Object.defineProperty(e,"__esModule",{value:!0}),e.CommonMglyphMixin=void 0,e.CommonMglyphMixin=function(t){return function(t){function e(){for(var e=[],r=0;r<arguments.length;r++)e[r]=arguments[r];var n=t.apply(this,i([],o(e),!1))||this;return n.getParameters(),n}return n(e,t),e.prototype.getParameters=function(){var t=this.node.attributes.getList("width","height","valign","src","index"),e=t.width,r=t.height,n=t.valign,o=t.src,i=t.index;if(o)this.width="auto"===e?1:this.length2em(e),this.height="auto"===r?1:this.length2em(r),this.valign=this.length2em(n||"0");else{var a=String.fromCodePoint(parseInt(i)),s=this.node.factory;this.charWrapper=this.wrap(s.create("text").setText(a)),this.charWrapper.parent=this}},e.prototype.computeBBox=function(t,e){void 0===e&&(e=!1),this.charWrapper?t.updateFrom(this.charWrapper.getBBox()):(t.w=this.width,t.h=this.height+this.valign,t.d=-this.valign)},e}(t)}},5723:function(t,e){var r,n=this&&this.__extends||(r=function(t,e){return r=Object.setPrototypeOf||{__proto__:[]}instanceof Array&&function(t,e){t.__proto__=e}||function(t,e){for(var r in e)Object.prototype.hasOwnProperty.call(e,r)&&(t[r]=e[r])},r(t,e)},function(t,e){if("function"!=typeof e&&null!==e)throw new TypeError("Class extends value "+String(e)+" is not a constructor or null");function n(){this.constructor=t}r(t,e),t.prototype=null===e?Object.create(e):(n.prototype=e.prototype,new n)});Object.defineProperty(e,"__esModule",{value:!0}),e.CommonMiMixin=void 0,e.CommonMiMixin=function(t){return function(t){function e(){return null!==t&&t.apply(this,arguments)||this}return n(e,t),e.prototype.computeBBox=function(e,r){void 0===r&&(r=!1),t.prototype.computeBBox.call(this,e),this.copySkewIC(e)},e}(t)}},8009:function(t,e,r){var n,o=this&&this.__extends||(n=function(t,e){return n=Object.setPrototypeOf||{__proto__:[]}instanceof Array&&function(t,e){t.__proto__=e}||function(t,e){for(var r in e)Object.prototype.hasOwnProperty.call(e,r)&&(t[r]=e[r])},n(t,e)},function(t,e){if("function"!=typeof e&&null!==e)throw new TypeError("Class extends value "+String(e)+" is not a constructor or null");function r(){this.constructor=t}n(t,e),t.prototype=null===e?Object.create(e):(r.prototype=e.prototype,new r)}),i=this&&this.__read||function(t,e){var r="function"==typeof Symbol&&t[Symbol.iterator];if(!r)return t;var n,o,i=r.call(t),a=[];try{for(;(void 0===e||e-- >0)&&!(n=i.next()).done;)a.push(n.value)}catch(t){o={error:t}}finally{try{n&&!n.done&&(r=i.return)&&r.call(i)}finally{if(o)throw o.error}}return a},a=this&&this.__spreadArray||function(t,e,r){if(r||2===arguments.length)for(var n,o=0,i=e.length;o<i;o++)!n&&o in e||(n||(n=Array.prototype.slice.call(e,0,o)),n[o]=e[o]);return t.concat(n||Array.prototype.slice.call(e))},s=this&&this.__values||function(t){var e="function"==typeof Symbol&&Symbol.iterator,r=e&&t[e],n=0;if(r)return r.call(t);if(t&&"number"==typeof t.length)return{next:function(){return t&&n>=t.length&&(t=void 0),{value:t&&t[n++],done:!t}}};throw new TypeError(e?"Object is not iterable.":"Symbol.iterator is not defined.")};Object.defineProperty(e,"__esModule",{value:!0}),e.CommonMmultiscriptsMixin=e.ScriptNames=e.NextScript=void 0;var l=r(6469);e.NextScript={base:"subList",subList:"supList",supList:"subList",psubList:"psupList",psupList:"psubList"},e.ScriptNames=["sup","sup","psup","psub"],e.CommonMmultiscriptsMixin=function(t){return function(t){function r(){for(var e=[],r=0;r<arguments.length;r++)e[r]=arguments[r];var n=t.apply(this,a([],i(e),!1))||this;return n.scriptData=null,n.firstPrescript=0,n.getScriptData(),n}return o(r,t),r.prototype.combinePrePost=function(t,e){var r=new l.BBox(t);return r.combine(e,0,0),r},r.prototype.computeBBox=function(t,e){void 0===e&&(e=!1);var r=this.font.params.scriptspace,n=this.scriptData,o=this.combinePrePost(n.sub,n.psub),a=this.combinePrePost(n.sup,n.psup),s=i(this.getUVQ(o,a),2),l=s[0],c=s[1];if(t.empty(),n.numPrescripts&&(t.combine(n.psup,r,l),t.combine(n.psub,r,c)),t.append(n.base),n.numScripts){var u=t.w;t.combine(n.sup,u,l),t.combine(n.sub,u,c),t.w+=r}t.clean(),this.setChildPWidths(e)},r.prototype.getScriptData=function(){var t=this.scriptData={base:null,sub:l.BBox.empty(),sup:l.BBox.empty(),psub:l.BBox.empty(),psup:l.BBox.empty(),numPrescripts:0,numScripts:0},e=this.getScriptBBoxLists();this.combineBBoxLists(t.sub,t.sup,e.subList,e.supList),this.combineBBoxLists(t.psub,t.psup,e.psubList,e.psupList),t.base=e.base[0],t.numPrescripts=e.psubList.length,t.numScripts=e.subList.length},r.prototype.getScriptBBoxLists=function(){var t,r,n={base:[],subList:[],supList:[],psubList:[],psupList:[]},o="base";try{for(var i=s(this.childNodes),a=i.next();!a.done;a=i.next()){var l=a.value;l.node.isKind("mprescripts")?o="psubList":(n[o].push(l.getOuterBBox()),o=e.NextScript[o])}}catch(e){t={error:e}}finally{try{a&&!a.done&&(r=i.return)&&r.call(i)}finally{if(t)throw t.error}}return this.firstPrescript=n.subList.length+n.supList.length+2,this.padLists(n.subList,n.supList),this.padLists(n.psubList,n.psupList),n},r.prototype.padLists=function(t,e){t.length>e.length&&e.push(l.BBox.empty())},r.prototype.combineBBoxLists=function(t,e,r,n){for(var o=0;o<r.length;o++){var a=i(this.getScaledWHD(r[o]),3),s=a[0],l=a[1],c=a[2],u=i(this.getScaledWHD(n[o]),3),p=u[0],h=u[1],d=u[2],f=Math.max(s,p);t.w+=f,e.w+=f,l>t.h&&(t.h=l),c>t.d&&(t.d=c),h>e.h&&(e.h=h),d>e.d&&(e.d=d)}},r.prototype.getScaledWHD=function(t){var e=t.w,r=t.h,n=t.d,o=t.rscale;return[e*o,r*o,n*o]},r.prototype.getUVQ=function(e,r){var n;if(!this.UVQ){var o=i([0,0,0],3),a=o[0],s=o[1],l=o[2];0===e.h&&0===e.d?a=this.getU():0===r.h&&0===r.d?a=-this.getV():(a=(n=i(t.prototype.getUVQ.call(this,e,r),3))[0],s=n[1],l=n[2]),this.UVQ=[a,s,l]}return this.UVQ},r}(t)}},5023:function(t,e){var r,n=this&&this.__extends||(r=function(t,e){return r=Object.setPrototypeOf||{__proto__:[]}instanceof Array&&function(t,e){t.__proto__=e}||function(t,e){for(var r in e)Object.prototype.hasOwnProperty.call(e,r)&&(t[r]=e[r])},r(t,e)},function(t,e){if("function"!=typeof e&&null!==e)throw new TypeError("Class extends value "+String(e)+" is not a constructor or null");function n(){this.constructor=t}r(t,e),t.prototype=null===e?Object.create(e):(n.prototype=e.prototype,new n)});Object.defineProperty(e,"__esModule",{value:!0}),e.CommonMnMixin=void 0,e.CommonMnMixin=function(t){return function(t){function e(){return null!==t&&t.apply(this,arguments)||this}return n(e,t),e.prototype.remapChars=function(t){if(t.length){var e=this.font.getRemappedChar("mn",t[0]);if(e){var 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n=t.apply(this,l([],s(e),!1))||this;return n.size=null,n.isAccent=n.node.isAccent,n}return i(e,t),e.prototype.computeBBox=function(t,e){if(void 0===e&&(e=!1),this.protoBBox(t),this.node.attributes.get("symmetric")&&2!==this.stretch.dir){var r=this.getCenterOffset(t);t.h+=r,t.d-=r}this.node.getProperty("mathaccent")&&(0===this.stretch.dir||this.size>=0)&&(t.w=0)},e.prototype.protoBBox=function(e){var r=0!==this.stretch.dir;r&&null===this.size&&this.getStretchedVariant([0]),r&&this.size<0||(t.prototype.computeBBox.call(this,e),this.copySkewIC(e))},e.prototype.getAccentOffset=function(){var t=u.BBox.empty();return this.protoBBox(t),-t.w/2},e.prototype.getCenterOffset=function(e){return void 0===e&&(e=null),e||(e=u.BBox.empty(),t.prototype.computeBBox.call(this,e)),(e.h+e.d)/2+this.font.params.axis_height-e.h},e.prototype.getVariant=function(){this.node.attributes.get("largeop")?this.variant=this.node.attributes.get("displaystyle")?"-largeop":"-smallop":this.node.attributes.getExplicit("mathvariant")||!1!==this.node.getProperty("pseudoscript")?t.prototype.getVariant.call(this):this.variant="-tex-variant"},e.prototype.canStretch=function(t){if(0!==this.stretch.dir)return this.stretch.dir===t;if(!this.node.attributes.get("stretchy"))return!1;var e=this.getText();if(1!==Array.from(e).length)return!1;var r=this.font.getDelimiter(e.codePointAt(0));return this.stretch=r&&r.dir===t?r:h.NOSTRETCH,0!==this.stretch.dir},e.prototype.getStretchedVariant=function(t,e){var r,n;if(void 0===e&&(e=!1),0!==this.stretch.dir){var o=this.getWH(t),i=this.getSize("minsize",0),s=this.getSize("maxsize",1/0),l=this.node.getProperty("mathaccent");o=Math.max(i,Math.min(s,o));var 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t.concat(n||Array.prototype.slice.call(e))},s=this&&this.__values||function(t){var e="function"==typeof Symbol&&Symbol.iterator,r=e&&t[e],n=0;if(r)return r.call(t);if(t&&"number"==typeof t.length)return{next:function(){return t&&n>=t.length&&(t=void 0),{value:t&&t[n++],done:!t}}};throw new TypeError(e?"Object is not iterable.":"Symbol.iterator is not defined.")};Object.defineProperty(e,"__esModule",{value:!0}),e.CommonMtableMixin=void 0;var l=r(6469),c=r(505),u=r(7875);e.CommonMtableMixin=function(t){return function(t){function e(){for(var e=[],r=0;r<arguments.length;r++)e[r]=arguments[r];var n=t.apply(this,a([],i(e),!1))||this;n.numCols=0,n.numRows=0,n.data=null,n.pwidthCells=[],n.pWidth=0,n.numCols=(0,u.max)(n.tableRows.map((function(t){return t.numCells}))),n.numRows=n.childNodes.length,n.hasLabels=n.childNodes.reduce((function(t,e){return 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o=(n-(e[t]+r[t]))/2;o<1e-5||(e[t]+=o,r[t]+=o)},e.prototype.recordPWidthCell=function(t,e){t.childNodes[0]&&t.childNodes[0].getBBox().pwidth&&this.pwidthCells.push([t,e])},e.prototype.computeBBox=function(t,e){void 0===e&&(e=!1);var r,n,o=this.getTableData(),a=o.H,s=o.D;if(this.node.attributes.get("equalrows")){var l=this.getEqualRowHeight();r=(0,u.sum)([].concat(this.rLines,this.rSpace))+l*this.numRows}else r=(0,u.sum)(a.concat(s,this.rLines,this.rSpace));r+=2*(this.fLine+this.fSpace[1]);var p=this.getComputedWidths();n=(0,u.sum)(p.concat(this.cLines,this.cSpace))+2*(this.fLine+this.fSpace[0]);var h=this.node.attributes.get("width");"auto"!==h&&(n=Math.max(this.length2em(h,0)+2*this.fLine,n));var d=i(this.getBBoxHD(r),2),f=d[0],m=d[1];t.h=f,t.d=m,t.w=n;var y=i(this.getBBoxLR(),2),g=y[0],b=y[1];t.L=g,t.R=b,(0,c.isPercent)(h)||this.setColumnPWidths()},e.prototype.setChildPWidths=function(t,e,r){var n=this.node.attributes.get("width");if(!(0,c.isPercent)(n))return!1;this.hasLabels||(this.bbox.pwidth="",this.container.bbox.pwidth="");var o=this.bbox,i=o.w,a=o.L,s=o.R,l=this.node.attributes.get("data-width-includes-label"),p=Math.max(i,this.length2em(n,Math.max(e,a+i+s)))-(l?a+s:0),h=this.node.attributes.get("equalcolumns")?Array(this.numCols).fill(this.percent(1/Math.max(1,this.numCols))):this.getColumnAttributes("columnwidth",0);this.cWidths=this.getColumnWidthsFixed(h,p);var d=this.getComputedWidths();return this.pWidth=(0,u.sum)(d.concat(this.cLines,this.cSpace))+2*(this.fLine+this.fSpace[0]),this.isTop&&(this.bbox.w=this.pWidth),this.setColumnPWidths(),this.pWidth!==i&&this.parent.invalidateBBox(),this.pWidth!==i},e.prototype.setColumnPWidths=function(){var t,e,r=this.cWidths;try{for(var n=s(this.pwidthCells),o=n.next();!o.done;o=n.next()){var a=i(o.value,2),l=a[0],c=a[1];l.setChildPWidths(!1,r[c])&&(l.invalidateBBox(),l.getBBox())}}catch(e){t={error:e}}finally{try{o&&!o.done&&(e=n.return)&&e.call(n)}finally{if(t)throw t.error}}},e.prototype.getBBoxHD=function(t){var e=i(this.getAlignmentRow(),2),r=e[0],n=e[1];if(null===n){var o=this.font.params.axis_height,a=t/2;return{top:[0,t],center:[a,a],bottom:[t,0],baseline:[a,a],axis:[a+o,a-o]}[r]||[a,a]}var s=this.getVerticalPosition(n,r);return[s,t-s]},e.prototype.getBBoxLR=function(){if(this.hasLabels){var t=this.node.attributes,e=t.get("side"),r=i(this.getPadAlignShift(e),2),n=r[0],o=r[1],a=this.hasLabels&&!!t.get("data-width-includes-label");return a&&this.frame&&this.fSpace[0]&&(n-=this.fSpace[0]),"center"!==o||a?"left"===e?[n,0]:[0,n]:[n,n]}return[0,0]},e.prototype.getPadAlignShift=function(t){var 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this.node.attributes.get("equalcolumns")&&(r=Array(r.length).fill((0,u.max)(r))),r},e.prototype.getColumnWidths=function(){var t=this.node.attributes.get("width");if(this.node.attributes.get("equalcolumns"))return this.getEqualColumns(t);var e=this.getColumnAttributes("columnwidth",0);return"auto"===t?this.getColumnWidthsAuto(e):(0,c.isPercent)(t)?this.getColumnWidthsPercent(e):this.getColumnWidthsFixed(e,this.length2em(t))},e.prototype.getEqualColumns=function(t){var e,r=Math.max(1,this.numCols);if("auto"===t){var n=this.getTableData().W;e=(0,u.max)(n)}else if((0,c.isPercent)(t))e=this.percent(1/r);else{var o=(0,u.sum)([].concat(this.cLines,this.cSpace))+2*this.fSpace[0];e=Math.max(0,this.length2em(t)-o)/r}return Array(this.numCols).fill(e)},e.prototype.getColumnWidthsAuto=function(t){var e=this;return t.map((function(t){return"auto"===t||"fit"===t?null:(0,c.isPercent)(t)?t:e.length2em(t)}))},e.prototype.getColumnWidthsPercent=function(t){var 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/*!
 *************************************************************************
 *
 *  mhchemParser.ts
 *  4.1.1
 *
 *  Parser for the \ce command and \pu command for MathJax and Co.
 *
 *  mhchem's \ce is a tool for writing beautiful chemical equations easily.
 *  mhchem's \pu is a tool for writing physical units easily.
 *
 *  ----------------------------------------------------------------------
 *
 *  Copyright (c) 2015-2021 Martin Hensel
 *
 *  Licensed under the Apache License, Version 2.0 (the "License");
 *  you may not use this file except in compliance with the License.
 *  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 *  Unless required by applicable law or agreed to in writing, software
 *  distributed under the License is distributed on an "AS IS" BASIS,
 *  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  See the License for the specific language governing permissions and
 *  limitations under the License.
 *
 *  ----------------------------------------------------------------------
 *
 *  https://github.com/mhchem/mhchemParser
 *
 */
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e=this.html;e.appendChild(this.generateTitle()),e.appendChild(this.contentDiv),e.appendChild(this.generateSignature()),e.appendChild(this.close.html),e.setAttribute("tabindex","0")},e.prototype.post=function(){t.prototype.post.call(this);var e=document.documentElement,r=this.html,n=window.innerHeight||e.clientHeight||e.scrollHeight||0,o=Math.floor(-r.offsetWidth/2),i=Math.floor((n-r.offsetHeight)/3);r.setAttribute("style","margin-left: "+o+"px; top: "+i+"px;"),window.event instanceof MouseEvent&&r.classList.add(a.HtmlClasses.MOUSEPOST),r.focus()},e.prototype.display=function(){this.menu.registerWidget(this),this.contentDiv.innerHTML=this.content();var t=this.menu.html;t.parentNode&&t.parentNode.removeChild(t),this.menu.frame.appendChild(this.html)},e.prototype.click=function(t){},e.prototype.keydown=function(e){this.bubbleKey(),t.prototype.keydown.call(this,e)},e.prototype.escape=function(t){this.unpost()},e.prototype.unpost=function(){t.prototype.unpost.call(this),this.html.classList.remove(a.HtmlClasses.MOUSEPOST),this.menu.unregisterWidget(this)},e.prototype.generateClose=function(){var t=new i.CloseButton(this),e=t.html;return e.classList.add(a.HtmlClasses.INFOCLOSE),e.setAttribute("aria-label","Close Dialog Box"),t},e.prototype.generateTitle=function(){var t=document.createElement("span");return t.innerHTML=this.title,t.classList.add(a.HtmlClasses.INFOTITLE),t},e.prototype.generateContent=function(){var t=document.createElement("div");return t.classList.add(a.HtmlClasses.INFOCONTENT),t.setAttribute("tabindex","0"),t},e.prototype.generateSignature=function(){var t=document.createElement("span");return t.innerHTML=this.signature,t.classList.add(a.HtmlClasses.INFOSIGNATURE),t},e.prototype.toJson=function(){return{type:""}},e}(r(8372).AbstractPostable);e.Info=s},1409:function(t,e,r){var n,o=this&&this.__extends||(n=function(t,e){return n=Object.setPrototypeOf||{__proto__:[]}instanceof Array&&function(t,e){t.__proto__=e}||function(t,e){for(var r in e)e.hasOwnProperty(r)&&(t[r]=e[r])},n(t,e)},function(t,e){function r(){this.constructor=t}n(t,e),t.prototype=null===e?Object.create(e):(r.prototype=e.prototype,new r)});Object.defineProperty(e,"__esModule",{value:!0}),e.Checkbox=void 0;var i=r(6765),a=r(2556),s=r(2165),l=function(t){function e(e,r,n,o){var i=t.call(this,e,"checkbox",r,o)||this;return i.role="menuitemcheckbox",i.variable=e.pool.lookup(n),i.register(),i}return o(e,t),e.fromJson=function(t,e,r){return new 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this(r,e.content,e.variable,e.id)},e.prototype.executeAction=function(){this.variable.setValue(this.input.value,a.MenuUtil.getActiveElement(this))},e.prototype.space=function(e){t.prototype.space.call(this,e),a.MenuUtil.close(this)},e.prototype.focus=function(){t.prototype.focus.call(this),this.input.focus()},e.prototype.unfocus=function(){t.prototype.unfocus.call(this),this.updateSpan()},e.prototype.generateHtml=function(){t.prototype.generateHtml.call(this),this.html.classList.add(s.HtmlClasses.MENUCOMBOBOX)},e.prototype.generateSpan=function(){this.span=document.createElement("span"),this.span.classList.add(s.HtmlClasses.MENUINPUTBOX),this.input=document.createElement("input"),this.input.addEventListener("keydown",this.inputKey.bind(this)),this.input.setAttribute("size","10em"),this.input.setAttribute("type","text"),this.input.setAttribute("tabindex","-1"),this.span.appendChild(this.input)},e.prototype.inputKey=function(t){this.bubbleKey(),this.inputEvent=!0},e.prototype.keydown=function(e){if(this.inputEvent&&e.keyCode!==l.KEY.ESCAPE&&e.keyCode!==l.KEY.RETURN)return this.inputEvent=!1,void e.stopPropagation();t.prototype.keydown.call(this,e),e.stopPropagation()},e.prototype.updateAria=function(){},e.prototype.updateSpan=function(){var t;try{t=this.variable.getValue(a.MenuUtil.getActiveElement(this))}catch(e){t=""}this.input.value=t},e.prototype.toJson=function(){return{type:""}},e}(i.AbstractVariableItem);e.Combo=c},3467:function(t,e,r){var n,o=this&&this.__extends||(n=function(t,e){return n=Object.setPrototypeOf||{__proto__:[]}instanceof Array&&function(t,e){t.__proto__=e}||function(t,e){for(var r in e)e.hasOwnProperty(r)&&(t[r]=e[r])},n(t,e)},function(t,e){function r(){this.constructor=t}n(t,e),t.prototype=null===e?Object.create(e):(r.prototype=e.prototype,new r)});Object.defineProperty(e,"__esModule",{value:!0}),e.Command=void 0;var i=r(1340),a=r(2556),s=function(t){function e(e,r,n,o){var i=t.call(this,e,"command",r,o)||this;return i.command=n,i}return o(e,t),e.fromJson=function(t,e,r){return new 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r,n=1;r=t.childNodes[n];n++)e.push(c.walkTree(r));t=t.childNodes[0]}const a=n.createElement("dummy"),s=o.childNodes[0];n.replaceNode(o,a),n.replaceNode(r,o),n.replaceNode(o.childNodes[0],r),n.replaceNode(a,s),e||(e=o)}return c.walkTree(this.ofence),c.walkTree(this.cfence),this.cleanupParents_(),e||r}specialCase_(t,e){const r=n.tagName(e);let o,i=null;if("MSUBSUP"===r?(i=t.childNodes[0],o=a.CaseDoubleScript):"MMULTISCRIPTS"===r&&("superscript"===t.type||"subscript"===t.type?o=s.CaseMultiscripts:"tensor"===t.type&&(o=l.CaseTensor),i=o&&t.childNodes[0]&&"subsup"===t.childNodes[0].role?t.childNodes[0]:t),!i)return null;const c=i.childNodes[0],u=p.makeEmptyNode_(c.id);return i.childNodes[0]=u,e=new o(t).getMathml(),i.childNodes[0]=c,this.parentCleanup.push(e),i.childNodes[0]}introduceNewLayer_(){const t=this.fullFence(this.ofenceMml),e=this.fullFence(this.cfenceMml);let r=n.createElement("mrow");if(n.replaceNode(this.fencedMml,r),this.fencedMmlNodes.forEach((t=>r.appendChild(t))),r.insertBefore(t,this.fencedMml),r.appendChild(e),!r.parentNode){const t=n.createElement("mrow");for(;r.childNodes.length>0;)t.appendChild(r.childNodes[0]);r.appendChild(t),r=t}return r}fullFence(t){const e=this.fencedMml.parentNode;let r=t;for(;r.parentNode&&r.parentNode!==e;)r=r.parentNode;return r}cleanupParents_(){this.parentCleanup.forEach((function(t){const e=t.childNodes[1].getAttribute(u.Attribute.PARENT);t.childNodes[0].setAttribute(u.Attribute.PARENT,e)}))}}e.CaseEmbellished=p},6265:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.CaseLimit=void 0;const n=r(5740),o=r(9268),i=r(5452),a=r(2298);class s extends o.AbstractEnrichCase{constructor(t){super(t),this.mml=t.mathmlTree}static test(t){if(!t.mathmlTree||!t.childNodes.length)return!1;const e=n.tagName(t.mathmlTree),r=t.type;return("limupper"===r||"limlower"===r)&&("MSUBSUP"===e||"MUNDEROVER"===e)||"limboth"===r&&("MSUB"===e||"MUNDER"===e||"MSUP"===e||"MOVER"===e)}static walkTree_(t){t&&i.walkTree(t)}getMathml(){const t=this.semantic.childNodes;return"limboth"!==this.semantic.type&&this.mml.childNodes.length>=3&&(this.mml=i.introduceNewLayer([this.mml],this.semantic)),(0,a.setAttributes)(this.mml,this.semantic),t[0].mathmlTree||(t[0].mathmlTree=this.semantic.mathmlTree),t.forEach(s.walkTree_),this.mml}}e.CaseLimit=s},6514:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.CaseLine=void 0;const n=r(9268),o=r(5452),i=r(2298);class a extends n.AbstractEnrichCase{constructor(t){super(t),this.mml=t.mathmlTree}static test(t){return!!t.mathmlTree&&"line"===t.type}getMathml(){return this.semantic.contentNodes.length&&o.walkTree(this.semantic.contentNodes[0]),this.semantic.childNodes.length&&o.walkTree(this.semantic.childNodes[0]),(0,i.setAttributes)(this.mml,this.semantic),this.mml}}e.CaseLine=a},6839:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.CaseMultiindex=void 0;const n=r(5740),o=r(9268),i=r(5452),a=r(2298);class s extends o.AbstractEnrichCase{constructor(t){super(t),this.mml=t.mathmlTree}static multiscriptIndex(t){return"punctuated"===t.type&&"dummy"===t.contentNodes[0].role?i.collapsePunctuated(t):(i.walkTree(t),t.id)}static createNone_(t){const e=n.createElement("none");return t&&(0,a.setAttributes)(e,t),e.setAttribute(a.Attribute.ADDED,"true"),e}completeMultiscript(t,e){const r=n.toArray(this.mml.childNodes).slice(1);let o=0;const l=t=>{for(let e,n=0;e=t[n];n++){const t=r[o];if(t&&e===parseInt(i.getInnerNode(t).getAttribute(a.Attribute.ID)))i.getInnerNode(t).setAttribute(a.Attribute.PARENT,this.semantic.id.toString()),o++;else{const r=this.semantic.querySelectorAll((t=>t.id===e));this.mml.insertBefore(s.createNone_(r[0]),t||null)}}};l(t),r[o]&&"MPRESCRIPTS"!==n.tagName(r[o])?this.mml.insertBefore(r[o],n.createElement("mprescripts")):o++,l(e)}}e.CaseMultiindex=s},7014:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.CaseMultiscripts=void 0;const n=r(5740),o=r(5656),i=r(6839),a=r(5452),s=r(2298);class l extends i.CaseMultiindex{static test(t){if(!t.mathmlTree)return!1;return"MMULTISCRIPTS"===n.tagName(t.mathmlTree)&&("superscript"===t.type||"subscript"===t.type)}constructor(t){super(t)}getMathml(){let t,e,r;if((0,s.setAttributes)(this.mml,this.semantic),this.semantic.childNodes[0]&&"subsup"===this.semantic.childNodes[0].role){const n=this.semantic.childNodes[0];t=n.childNodes[0],e=i.CaseMultiindex.multiscriptIndex(this.semantic.childNodes[1]),r=i.CaseMultiindex.multiscriptIndex(n.childNodes[1]);const l=[this.semantic.id,[n.id,t.id,r],e];a.addCollapsedAttribute(this.mml,l),this.mml.setAttribute(s.Attribute.TYPE,n.role),this.completeMultiscript(o.SemanticSkeleton.interleaveIds(r,e),[])}else{t=this.semantic.childNodes[0],e=i.CaseMultiindex.multiscriptIndex(this.semantic.childNodes[1]);const r=[this.semantic.id,t.id,e];a.addCollapsedAttribute(this.mml,r)}const n=o.SemanticSkeleton.collapsedLeafs(r||[],e),l=a.walkTree(t);return a.getInnerNode(l).setAttribute(s.Attribute.PARENT,this.semantic.id.toString()),n.unshift(t.id),this.mml.setAttribute(s.Attribute.CHILDREN,n.join(",")),this.mml}}e.CaseMultiscripts=l},3416:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.CaseProof=void 0;const n=r(9268),o=r(5452),i=r(2298);class a extends n.AbstractEnrichCase{constructor(t){super(t),this.mml=t.mathmlTree}static test(t){return!!t.mathmlTree&&("inference"===t.type||"premises"===t.type)}getMathml(){return this.semantic.childNodes.length?(this.semantic.contentNodes.forEach((function(t){o.walkTree(t),(0,i.setAttributes)(t.mathmlTree,t)})),this.semantic.childNodes.forEach((function(t){o.walkTree(t)})),(0,i.setAttributes)(this.mml,this.semantic),this.mml.getAttribute("data-semantic-id")===this.mml.getAttribute("data-semantic-parent")&&this.mml.removeAttribute("data-semantic-parent"),this.mml):this.mml}}e.CaseProof=a},5699:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.CaseTable=void 0;const n=r(5740),o=r(9268),i=r(5452),a=r(2298);class s extends o.AbstractEnrichCase{constructor(t){super(t),this.inner=[],this.mml=t.mathmlTree}static test(t){return"matrix"===t.type||"vector"===t.type||"cases"===t.type}getMathml(){const t=i.cloneContentNode(this.semantic.contentNodes[0]),e=this.semantic.contentNodes[1]?i.cloneContentNode(this.semantic.contentNodes[1]):null;if(this.inner=this.semantic.childNodes.map(i.walkTree),this.mml)if("MFENCED"===n.tagName(this.mml)){const r=this.mml.childNodes;this.mml.insertBefore(t,r[0]||null),e&&this.mml.appendChild(e),this.mml=i.rewriteMfenced(this.mml)}else{const r=[t,this.mml];e&&r.push(e),this.mml=i.introduceNewLayer(r,this.semantic)}else this.mml=i.introduceNewLayer([t].concat(this.inner,[e]),this.semantic);return(0,a.setAttributes)(this.mml,this.semantic),this.mml}}e.CaseTable=s},6887:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.CaseTensor=void 0;const n=r(5656),o=r(6839),i=r(5452),a=r(2298);class s extends o.CaseMultiindex{static test(t){return!!t.mathmlTree&&"tensor"===t.type}constructor(t){super(t)}getMathml(){i.walkTree(this.semantic.childNodes[0]);const t=o.CaseMultiindex.multiscriptIndex(this.semantic.childNodes[1]),e=o.CaseMultiindex.multiscriptIndex(this.semantic.childNodes[2]),r=o.CaseMultiindex.multiscriptIndex(this.semantic.childNodes[3]),s=o.CaseMultiindex.multiscriptIndex(this.semantic.childNodes[4]);(0,a.setAttributes)(this.mml,this.semantic);const l=[this.semantic.id,this.semantic.childNodes[0].id,t,e,r,s];i.addCollapsedAttribute(this.mml,l);const c=n.SemanticSkeleton.collapsedLeafs(t,e,r,s);return c.unshift(this.semantic.childNodes[0].id),this.mml.setAttribute(a.Attribute.CHILDREN,c.join(",")),this.completeMultiscript(n.SemanticSkeleton.interleaveIds(r,s),n.SemanticSkeleton.interleaveIds(t,e)),this.mml}}e.CaseTensor=s},9236:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.CaseText=void 0;const n=r(9268),o=r(5452),i=r(2298);class a extends n.AbstractEnrichCase{constructor(t){super(t),this.mml=t.mathmlTree}static test(t){return"punctuated"===t.type&&("text"===t.role||t.contentNodes.every((t=>"dummy"===t.role)))}getMathml(){const t=[],e=o.collapsePunctuated(this.semantic,t);return this.mml=o.introduceNewLayer(t,this.semantic),(0,i.setAttributes)(this.mml,this.semantic),this.mml.removeAttribute(i.Attribute.CONTENT),o.addCollapsedAttribute(this.mml,e),this.mml}}e.CaseText=a},5714:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.prepareMmlString=e.testTranslation__=e.semanticMathml=e.semanticMathmlSync=e.semanticMathmlNode=void 0;const n=r(2057),o=r(5740),i=r(5897),a=r(1414),s=r(5452),l=r(2298);function c(t){const e=o.cloneNode(t),r=a.getTree(e);return s.enrich(e,r)}function u(t){return c(o.parseInput(t))}function p(t){return t.match(/^<math/)||(t="<math>"+t),t.match(/\/math>$/)||(t+="</math>"),t}r(1513),e.semanticMathmlNode=c,e.semanticMathmlSync=u,e.semanticMathml=function(t,e){i.EnginePromise.getall().then((()=>{const r=o.parseInput(t);e(c(r))}))},e.testTranslation__=function(t){n.Debugger.getInstance().init();const e=u(p(t)).toString();return(0,l.removeAttributePrefix)(e),n.Debugger.getInstance().exit(),e},e.prepareMmlString=p},2298:function(t,e){var r;function n(t){return t.map((function(t){return t.id})).join(",")}function o(t,e){const n=[];"mglyph"===e.role&&n.push("image"),e.attributes.href&&n.push("link"),n.length&&t.setAttribute(r.POSTFIX,n.join(" "))}Object.defineProperty(e,"__esModule",{value:!0}),e.addPrefix=e.removeAttributePrefix=e.setPostfix=e.setAttributes=e.makeIdList=e.EnrichAttributes=e.Attribute=e.Prefix=void 0,e.Prefix="data-semantic-",function(t){t.ADDED="data-semantic-added",t.ALTERNATIVE="data-semantic-alternative",t.CHILDREN="data-semantic-children",t.COLLAPSED="data-semantic-collapsed",t.CONTENT="data-semantic-content",t.EMBELLISHED="data-semantic-embellished",t.FENCEPOINTER="data-semantic-fencepointer",t.FONT="data-semantic-font",t.ID="data-semantic-id",t.ANNOTATION="data-semantic-annotation",t.OPERATOR="data-semantic-operator",t.OWNS="data-semantic-owns",t.PARENT="data-semantic-parent",t.POSTFIX="data-semantic-postfix",t.PREFIX="data-semantic-prefix",t.ROLE="data-semantic-role",t.SPEECH="data-semantic-speech",t.STRUCTURE="data-semantic-structure",t.TYPE="data-semantic-type"}(r=e.Attribute||(e.Attribute={})),e.EnrichAttributes=[r.ADDED,r.ALTERNATIVE,r.CHILDREN,r.COLLAPSED,r.CONTENT,r.EMBELLISHED,r.FENCEPOINTER,r.FONT,r.ID,r.ANNOTATION,r.OPERATOR,r.OWNS,r.PARENT,r.POSTFIX,r.PREFIX,r.ROLE,r.SPEECH,r.STRUCTURE,r.TYPE],e.makeIdList=n,e.setAttributes=function(t,i){t.setAttribute(r.TYPE,i.type);const a=i.allAttributes();for(let r,n=0;r=a[n];n++)t.setAttribute(e.Prefix+r[0].toLowerCase(),r[1]);i.childNodes.length&&t.setAttribute(r.CHILDREN,n(i.childNodes)),i.contentNodes.length&&t.setAttribute(r.CONTENT,n(i.contentNodes)),i.parent&&t.setAttribute(r.PARENT,i.parent.id.toString()),o(t,i)},e.setPostfix=o,e.removeAttributePrefix=function(t){return t.toString().replace(new RegExp(e.Prefix,"g"),"")},e.addPrefix=function(t){return e.Prefix+t}},3532:function(t,e){Object.defineProperty(e,"__esModule",{value:!0}),e.factory=e.getCase=void 0,e.getCase=function(t){for(let r,n=0;r=e.factory[n];n++)if(r.test(t))return r.constr(t);return null},e.factory=[]},1513:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0});const n=r(6061),o=r(5765),i=r(7251),a=r(6265),s=r(6514),l=r(7014),c=r(3416),u=r(5699),p=r(6887),h=r(9236);r(3532).factory.push({test:a.CaseLimit.test,constr:t=>new a.CaseLimit(t)},{test:i.CaseEmbellished.test,constr:t=>new i.CaseEmbellished(t)},{test:o.CaseDoubleScript.test,constr:t=>new o.CaseDoubleScript(t)},{test:p.CaseTensor.test,constr:t=>new p.CaseTensor(t)},{test:l.CaseMultiscripts.test,constr:t=>new l.CaseMultiscripts(t)},{test:s.CaseLine.test,constr:t=>new s.CaseLine(t)},{test:n.CaseBinomial.test,constr:t=>new n.CaseBinomial(t)},{test:c.CaseProof.test,constr:t=>new c.CaseProof(t)},{test:u.CaseTable.test,constr:t=>new u.CaseTable(t)},{test:h.CaseText.test,constr:t=>new h.CaseText(t)})},5452:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.printNodeList__=e.collapsePunctuated=e.formattedOutput_=e.formattedOutput=e.getInnerNode=e.setOperatorAttribute_=e.createInvisibleOperator_=e.rewriteMfenced=e.cloneContentNode=e.addCollapsedAttribute=e.parentNode_=e.isIgnorable_=e.unitChild_=e.descendNode_=e.ascendNewNode=e.validLca_=e.pathToRoot_=e.attachedElement_=e.prunePath_=e.mathmlLca_=e.lcaType=e.functionApplication_=e.isDescendant_=e.insertNewChild_=e.mergeChildren_=e.collectChildNodes_=e.collateChildNodes_=e.childrenSubset_=e.moveSemanticAttributes_=e.introduceLayerAboveLca=e.introduceNewLayer=e.walkTree=e.enrich=e.SETTINGS=void 0;const n=r(2057),o=r(5740),i=r(5897),a=r(3588),s=r(7516),l=r(5656),c=r(4795),u=r(2298),p=r(3532);function h(t){const e=(0,p.getCase)(t);let r;if(e)return r=e.getMathml(),T(r);if(1===t.mathml.length)return n.Debugger.getInstance().output("Walktree Case 0"),r=t.mathml[0],u.setAttributes(r,t),t.childNodes.length&&(n.Debugger.getInstance().output("Walktree Case 0.1"),t.childNodes.forEach((function(t){"empty"===t.type&&r.appendChild(h(t))}))),T(r);const o=t.contentNodes.map(k);B(t,o);const i=t.childNodes.map(h),a=l.SemanticSkeleton.combineContentChildren(t,o,i);if(r=t.mathmlTree,null===r)n.Debugger.getInstance().output("Walktree Case 1"),r=d(a,t);else{const t=A(a);n.Debugger.getInstance().output("Walktree Case 2"),t?(n.Debugger.getInstance().output("Walktree Case 2.1"),r=t.parentNode):(n.Debugger.getInstance().output("Walktree Case 2.2"),r=D(r))}return r=R(r),v(r,a,t),u.setAttributes(r,t),T(r)}function d(t,e){const r=O(t);let i=r.node;const a=r.type;if(a!==M.VALID||!c.hasEmptyTag(i))if(n.Debugger.getInstance().output("Walktree Case 1.1"),i=o.createElement("mrow"),a===M.PRUNED)n.Debugger.getInstance().output("Walktree Case 1.1.0"),i=f(i,r.node,t);else if(t[0]){n.Debugger.getInstance().output("Walktree Case 1.1.1");const e=A(t),r=y(e.parentNode,t);o.replaceNode(e,i),r.forEach((function(t){i.appendChild(t)}))}return e.mathmlTree||(e.mathmlTree=i),i}function f(t,e,r){let i=N(e);if(c.hasMathTag(i)){n.Debugger.getInstance().output("Walktree Case 1.1.0.0"),m(i,t),o.toArray(i.childNodes).forEach((function(e){t.appendChild(e)}));const e=t;t=i,i=e}const a=r.indexOf(e);return r[a]=i,o.replaceNode(i,t),t.appendChild(i),r.forEach((function(e){t.appendChild(e)})),t}function m(t,e){for(const r of u.EnrichAttributes)t.hasAttribute(r)&&(e.setAttribute(r,t.getAttribute(r)),t.removeAttribute(r))}function y(t,e){const r=o.toArray(t.childNodes);let n=1/0,i=-1/0;return e.forEach((function(t){const e=r.indexOf(t);-1!==e&&(n=Math.min(n,e),i=Math.max(i,e))})),r.slice(n,i+1)}function g(t,e,r){const n=[];let i=o.toArray(t.childNodes),a=!1;for(;i.length;){const t=i.shift();if(t.hasAttribute(u.Attribute.TYPE)){n.push(t);continue}const 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${r}`}:{convertible:!0,enumerator:i,denominator:o}}Object.defineProperty(e,"__esModule",{value:!0}),e.vulgarFractionSmall=e.convertVulgarFraction=e.Combiners=e.siCombiner=e.identityTransformer=e.pluralCase=void 0,e.pluralCase=function(t,e){return t.toString()},e.identityTransformer=function(t){return t.toString()},e.siCombiner=function(t,e){return t+e.toLowerCase()},e.Combiners={},e.Combiners.identityCombiner=function(t,e,r){return t+e+r},e.Combiners.prefixCombiner=function(t,e,r){return t=r?r+" "+t:t,e?e+" "+t:t},e.Combiners.postfixCombiner=function(t,e,r){return t=r?r+" "+t:t,e?t+" "+e:t},e.Combiners.romanceCombiner=function(t,e,r){return t=r?t+" "+r:t,e?t+" "+e:t},e.convertVulgarFraction=r,e.vulgarFractionSmall=function(t,e,n){const o=r(t);if(o.convertible){const t=o.enumerator,r=o.denominator;return t>0&&t<e&&r>0&&r<n}return!1}},4504:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.Condition=e.BaseRuleStore=void 0;const n=r(7052),o=r(1676),i=r(4650),a=r(4106);class s{constructor(){this.context=new a.SpeechRuleContext,this.parseOrder=o.DynamicCstr.DEFAULT_ORDER,this.parser=new o.DynamicCstrParser(this.parseOrder),this.locale=o.DynamicCstr.DEFAULT_VALUES[o.Axis.LOCALE],this.modality=o.DynamicCstr.DEFAULT_VALUES[o.Axis.MODALITY],this.domain="",this.initialized=!1,this.inherits=null,this.kind="standard",this.customTranscriptions={},this.preconditions=new Map,this.speechRules_=[],this.rank=0,this.parseMethods={Rule:this.defineRule,Generator:this.generateRules,Action:this.defineAction,Precondition:this.definePrecondition,Ignore:this.ignoreRules}}static compareStaticConstraints_(t,e){if(t.length!==e.length)return!1;for(let r,n=0;r=t[n];n++)if(-1===e.indexOf(r))return!1;return!0}static comparePreconditions_(t,e){const r=t.precondition,n=e.precondition;return r.query===n.query&&s.compareStaticConstraints_(r.constraints,n.constraints)}defineRule(t,e,r,n,...o){const a=this.parseAction(r),s=this.parsePrecondition(n,o),l=this.parseCstr(e);if(!(a&&s&&l))return console.error(`Rule Error: ${n}, (${e}): ${r}`),null;const c=new i.SpeechRule(t,l,s,a);return c.precondition.rank=this.rank++,this.addRule(c),c}addRule(t){t.context=this.context,this.speechRules_.unshift(t)}deleteRule(t){const e=this.speechRules_.indexOf(t);-1!==e&&this.speechRules_.splice(e,1)}findRule(t){for(let e,r=0;e=this.speechRules_[r];r++)if(t(e))return e;return null}findAllRules(t){return this.speechRules_.filter(t)}evaluateDefault(t){const e=t.textContent.slice(0);return e.match(/^\s+$/)?this.evaluateWhitespace(e):this.evaluateString(e)}evaluateWhitespace(t){return[]}evaluateCustom(t){const e=this.customTranscriptions[t];return void 0!==e?n.AuditoryDescription.create({text:e},{adjust:!0,translate:!1}):null}evaluateCharacter(t){return this.evaluateCustom(t)||n.AuditoryDescription.create({text:t},{adjust:!0,translate:!0})}removeDuplicates(t){for(let e,r=this.speechRules_.length-1;e=this.speechRules_[r];r--)e!==t&&t.dynamicCstr.equal(e.dynamicCstr)&&s.comparePreconditions_(e,t)&&this.speechRules_.splice(r,1)}getSpeechRules(){return this.speechRules_}setSpeechRules(t){this.speechRules_=t}getPreconditions(){return this.preconditions}parseCstr(t){try{return this.parser.parse(this.locale+"."+this.modality+(this.domain?"."+this.domain:"")+"."+t)}catch(e){if("RuleError"===e.name)return console.error("Rule Error ",`Illegal Dynamic Constraint: ${t}.`,e.message),null;throw e}}parsePrecondition(t,e){try{const r=this.parsePrecondition_(t);t=r[0];let n=r.slice(1);for(const t of e)n=n.concat(this.parsePrecondition_(t));return new i.Precondition(t,...n)}catch(r){if("RuleError"===r.name)return console.error("Rule Error ",`Illegal preconditions: ${t}, ${e}.`,r.message),null;throw r}}parseAction(t){try{return i.Action.fromString(t)}catch(e){if("RuleError"===e.name)return console.error("Rule Error ",`Illegal action: ${t}.`,e.message),null;throw e}}parse(t){this.modality=t.modality||this.modality,this.locale=t.locale||this.locale,this.domain=t.domain||this.domain,this.context.parse(t.functions||[]),"actions"!==t.kind&&(this.kind=t.kind||this.kind,this.inheritRules()),this.parseRules(t.rules||[])}parseRules(t){for(let e,r=0;e=t[r];r++){const t=e[0],r=this.parseMethods[t];t&&r&&r.apply(this,e.slice(1))}}generateRules(t){const e=this.context.customGenerators.lookup(t);e&&e(this)}defineAction(t,e){let r;try{r=i.Action.fromString(e)}catch(t){if("RuleError"===t.name)return void console.error("Action Error ",e,t.message);throw t}const n=this.getFullPreconditions(t);if(!n)return void console.error(`Action Error: No precondition for action ${t}`);this.ignoreRules(t);const o=new RegExp("^\\w+\\.\\w+\\."+(this.domain?"\\w+\\.":""));n.conditions.forEach((([e,n])=>{const a=this.parseCstr(e.toString().replace(o,""));this.addRule(new i.SpeechRule(t,a,n,r))}))}getFullPreconditions(t){const e=this.preconditions.get(t);return e||!this.inherits?e:this.inherits.getFullPreconditions(t)}definePrecondition(t,e,r,...n){const o=this.parsePrecondition(r,n),i=this.parseCstr(e);o&&i?(o.rank=this.rank++,this.preconditions.set(t,new l(i,o))):console.error(`Precondition Error: ${r}, (${e})`)}inheritRules(){if(!this.inherits||!this.inherits.getSpeechRules().length)return;const t=new RegExp("^\\w+\\.\\w+\\."+(this.domain?"\\w+\\.":""));this.inherits.getSpeechRules().forEach((e=>{const r=this.parseCstr(e.dynamicCstr.toString().replace(t,""));this.addRule(new i.SpeechRule(e.name,r,e.precondition,e.action))}))}ignoreRules(t,...e){let r=this.findAllRules((e=>e.name===t));if(!e.length)return void r.forEach(this.deleteRule.bind(this));let n=[];for(const t of e){const e=this.parseCstr(t);for(const t of r)e.equal(t.dynamicCstr)?this.deleteRule(t):n.push(t);r=n,n=[]}}parsePrecondition_(t){const e=this.context.customGenerators.lookup(t);return e?e():[t]}}e.BaseRuleStore=s;class l{constructor(t,e){this.base=t,this._conditions=[],this.constraints=[],this.allCstr={},this.constraints.push(t),this.addCondition(t,e)}get conditions(){return this._conditions}addConstraint(t){if(this.constraints.filter((e=>e.equal(t))).length)return;this.constraints.push(t);const e=[];for(const[r,n]of this.conditions)this.base.equal(r)&&e.push([t,n]);this._conditions=this._conditions.concat(e)}addBaseCondition(t){this.addCondition(this.base,t)}addFullCondition(t){this.constraints.forEach((e=>this.addCondition(e,t)))}addCondition(t,e){const r=t.toString()+" "+e.toString();this.allCstr.condStr||(this.allCstr[r]=!0,this._conditions.push([t,e]))}}e.Condition=l},2469:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.BrailleStore=void 0;const n=r(7630),o=r(9935);class i extends o.MathStore{constructor(){super(...arguments),this.modality="braille",this.customTranscriptions={"\u22ca":"\u2808\u2821\u2833"}}evaluateString(t){const e=[],r=Array.from(t);for(let t=0;t<r.length;t++)e.push(this.evaluateCharacter(r[t]));return e}annotations(){for(let t,e=0;t=this.annotators[e];e++)(0,n.activate)(this.locale,t)}}e.BrailleStore=i},1676:function(t,e){var r;Object.defineProperty(e,"__esModule",{value:!0}),e.DefaultComparator=e.DynamicCstrParser=e.DynamicCstr=e.DynamicProperties=e.Axis=void 0,function(t){t.DOMAIN="domain",t.STYLE="style",t.LOCALE="locale",t.TOPIC="topic",t.MODALITY="modality"}(r=e.Axis||(e.Axis={}));class n{constructor(t,e=Object.keys(t)){this.properties=t,this.order=e}static createProp(...t){const e=o.DEFAULT_ORDER,r={};for(let n=0,o=t.length,i=e.length;n<o&&n<i;n++)r[e[n]]=t[n];return new n(r)}getProperties(){return this.properties}getOrder(){return this.order}getAxes(){return this.order}getProperty(t){return this.properties[t]}updateProperties(t){this.properties=t}allProperties(){const t=[];return this.order.forEach((e=>t.push(this.getProperty(e).slice()))),t}toString(){const t=[];return this.order.forEach((e=>t.push(e+": "+this.getProperty(e).toString()))),t.join("\n")}}e.DynamicProperties=n;class o extends n{constructor(t,e){const r={};for(const[e,n]of Object.entries(t))r[e]=[n];super(r,e),this.components=t}static createCstr(...t){const e=o.DEFAULT_ORDER,r={};for(let n=0,o=t.length,i=e.length;n<o&&n<i;n++)r[e[n]]=t[n];return new o(r)}static defaultCstr(){return o.createCstr.apply(null,o.DEFAULT_ORDER.map((function(t){return o.DEFAULT_VALUES[t]})))}static validOrder(t){const e=o.DEFAULT_ORDER.slice();return t.every((t=>{const r=e.indexOf(t);return-1!==r&&e.splice(r,1)}))}getComponents(){return this.components}getValue(t){return this.components[t]}getValues(){return this.order.map((t=>this.getValue(t)))}allProperties(){const t=super.allProperties();for(let e,r,n=0;e=t[n],r=this.order[n];n++){const t=this.getValue(r);-1===e.indexOf(t)&&e.unshift(t)}return t}toString(){return this.getValues().join(".")}equal(t){const e=t.getAxes();if(this.order.length!==e.length)return!1;for(let r,n=0;r=e[n];n++){const e=this.getValue(r);if(!e||t.getValue(r)!==e)return!1}return!0}}e.DynamicCstr=o,o.DEFAULT_ORDER=[r.LOCALE,r.MODALITY,r.DOMAIN,r.STYLE,r.TOPIC],o.BASE_LOCALE="base",o.DEFAULT_VALUE="default",o.DEFAULT_VALUES={[r.LOCALE]:"en",[r.DOMAIN]:o.DEFAULT_VALUE,[r.STYLE]:o.DEFAULT_VALUE,[r.TOPIC]:o.DEFAULT_VALUE,[r.MODALITY]:"speech"};e.DynamicCstrParser=class{constructor(t){this.order=t}parse(t){const e=t.split("."),r={};if(e.length>this.order.length)throw new Error("Invalid dynamic constraint: "+r);let n=0;for(let t,o=0;t=this.order[o],e.length;o++,n++){const n=e.shift();r[t]=n}return new o(r,this.order.slice(0,n))}};e.DefaultComparator=class{constructor(t,e=new n(t.getProperties(),t.getOrder())){this.reference=t,this.fallback=e,this.order=this.reference.getOrder()}getReference(){return this.reference}setReference(t,e){this.reference=t,this.fallback=e||new n(t.getProperties(),t.getOrder()),this.order=this.reference.getOrder()}match(t){const e=t.getAxes();return e.length===this.reference.getAxes().length&&e.every((e=>{const r=t.getValue(e);return r===this.reference.getValue(e)||-1!==this.fallback.getProperty(e).indexOf(r)}))}compare(t,e){let r=!1;for(let n,o=0;n=this.order[o];o++){const o=t.getValue(n),i=e.getValue(n);if(!r){const t=this.reference.getValue(n);if(t===o&&t!==i)return-1;if(t===i&&t!==o)return 1;if(t===o&&t===i)continue;t!==o&&t!==i&&(r=!0)}const a=this.fallback.getProperty(n),s=a.indexOf(o),l=a.indexOf(i);if(s<l)return-1;if(l<s)return 1}return 0}toString(){return this.reference.toString()+"\n"+this.fallback.toString()}}},2105:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.numbersToAlpha=e.Grammar=e.ATTRIBUTE=void 0;const n=r(5740),o=r(5897),i=r(2536),a=r(4356);e.ATTRIBUTE="grammar";class s{constructor(){this.currentFlags={},this.parameters_={},this.corrections_={},this.preprocessors_={},this.stateStack_=[]}static getInstance(){return s.instance=s.instance||new s,s.instance}static parseInput(t){const e={},r=t.split(":");for(let t=0,n=r.length;t<n;t++){const n=r[t].split("="),o=n[0].trim();n[1]?e[o]=n[1].trim():o.match(/^!/)?e[o.slice(1)]=!1:e[o]=!0}return e}static parseState(t){const e={},r=t.split(" ");for(let t=0,n=r.length;t<n;t++){const n=r[t].split(":"),o=n[0],i=n[1];e[o]=i||!0}return e}static translateString_(t){if(t.match(/:unit$/))return s.translateUnit_(t);const e=o.default.getInstance();let r=e.evaluator(t,e.dynamicCstr);return r=null===r?t:r,s.getInstance().getParameter("plural")&&(r=a.LOCALE.FUNCTIONS.plural(r)),r}static translateUnit_(t){t=s.prepareUnit_(t);const e=o.default.getInstance(),r=s.getInstance().getParameter("plural"),n=e.strict,i=`${e.locale}.${e.modality}.default`;let l,c;return e.strict=!0,r&&(l=e.defaultParser.parse(i+".plural"),c=e.evaluator(t,l)),c?(e.strict=n,c):(l=e.defaultParser.parse(i+".default"),c=e.evaluator(t,l),e.strict=n,c?(r&&(c=a.LOCALE.FUNCTIONS.plural(c)),c):s.cleanUnit_(t))}static prepareUnit_(t){const e=t.match(/:unit$/);return e?t.slice(0,e.index).replace(/\s+/g," ")+t.slice(e.index):t}static cleanUnit_(t){return t.match(/:unit$/)?t.replace(/:unit$/,""):t}clear(){this.parameters_={},this.stateStack_=[]}setParameter(t,e){const r=this.parameters_[t];return e?this.parameters_[t]=e:delete this.parameters_[t],r}getParameter(t){return this.parameters_[t]}setCorrection(t,e){this.corrections_[t]=e}setPreprocessor(t,e){this.preprocessors_[t]=e}getCorrection(t){return this.corrections_[t]}getState(){const t=[];for(const e in this.parameters_){const r=this.parameters_[e];t.push("string"==typeof r?e+":"+r:e)}return t.join(" ")}pushState(t){for(const e in t)t[e]=this.setParameter(e,t[e]);this.stateStack_.push(t)}popState(){const t=this.stateStack_.pop();for(const e in t)this.setParameter(e,t[e])}setAttribute(t){if(t&&t.nodeType===n.NodeType.ELEMENT_NODE){const r=this.getState();r&&t.setAttribute(e.ATTRIBUTE,r)}}preprocess(t){return this.runProcessors_(t,this.preprocessors_)}correct(t){return this.runProcessors_(t,this.corrections_)}apply(t,e){return this.currentFlags=e||{},t=this.currentFlags.adjust||this.currentFlags.preprocess?s.getInstance().preprocess(t):t,(this.parameters_.translate||this.currentFlags.translate)&&(t=s.translateString_(t)),t=this.currentFlags.adjust||this.currentFlags.correct?s.getInstance().correct(t):t,this.currentFlags={},t}runProcessors_(t,e){for(const r in this.parameters_){const n=e[r];if(!n)continue;const o=this.parameters_[r];t=!0===o?n(t):n(t,o)}return t}}function l(t,e){if(!e||!t)return t;const r=a.LOCALE.FUNCTIONS.fontRegexp(i.localFont(e));return t.replace(r,"")}function c(t){return t.match(/\d+/)?a.LOCALE.NUMBERS.numberToWords(parseInt(t,10)):t}e.Grammar=s,e.numbersToAlpha=c,s.getInstance().setCorrection("localFont",i.localFont),s.getInstance().setCorrection("localRole",i.localRole),s.getInstance().setCorrection("localEnclose",i.localEnclose),s.getInstance().setCorrection("ignoreFont",l),s.getInstance().setPreprocessor("annotation",(function(t,e){return t+":"+e})),s.getInstance().setPreprocessor("noTranslateText",(function(t){return t.match(new RegExp("^["+a.LOCALE.MESSAGES.regexp.TEXT+"]+$"))&&(s.getInstance().currentFlags.translate=!1),t})),s.getInstance().setCorrection("ignoreCaps",(function(t){let e=a.LOCALE.ALPHABETS.capPrefix[o.default.getInstance().domain];return void 0===e&&(e=a.LOCALE.ALPHABETS.capPrefix.default),l(t,e)})),s.getInstance().setPreprocessor("numbers2alpha",c)},2780:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.enumerate=e.lookupString=e.lookupCategory=e.lookupRule=e.addSiUnitRules=e.addUnitRules=e.addFunctionRules=e.addSymbolRules=e.defineRule=e.defineRules=e.setSiPrefixes=void 0;const n=r(2057),o=r(5897),i=r(7491),a=r(4658),s=r(1676);let l=s.DynamicCstr.DEFAULT_VALUES[s.Axis.LOCALE],c=s.DynamicCstr.DEFAULT_VALUES[s.Axis.MODALITY],u={};e.setSiPrefixes=function(t){u=t};const p={};function h(t,e,r,n){const o=_(e);S(o,r),o.defineRulesFromMappings(t,l,c,e,n)}function d(t){if(v(t))return;const e=t.names,r=t.mappings,n=t.category;for(let t,o=0;t=e[o];o++)h(t,t,n,r)}function f(t){for(const e of Object.keys(u)){const r=Object.assign({},t);r.mappings={};const n=u[e];r.key=e+r.key,r.names=r.names.map((function(t){return e+t}));for(const e of Object.keys(t.mappings)){r.mappings[e]={};for(const o of Object.keys(t.mappings[e]))r.mappings[e][o]=i.locales[l]().FUNCTIONS.si(n,t.mappings[e][o])}b(r)}b(t)}function m(t,e){const r=p[t];return r?r.lookupRule(null,e):null}function y(t,e){const r=m(t,e);return r?r.action:null}function g(t,e){return e=e||{},t.length?(e[t[0]]=g(t.slice(1),e[t[0]]),e):e}function b(t){const e=t.names;e&&(t.names=e.map((function(t){return t+":unit"}))),d(t)}function v(t){return!(!t.locale&&!t.modality)&&(l=t.locale||l,c=t.modality||c,!0)}function _(t){let e=p[t];return e?(n.Debugger.getInstance().output("Store exists! "+t),e):(e=new a.MathSimpleStore,p[t]=e,e)}function S(t,e){e&&(t.category=e)}e.defineRules=h,e.defineRule=function(t,e,r,n,o,i){const a=_(o);S(a,n),a.defineRuleFromStrings(t,l,c,e,r,o,i)},e.addSymbolRules=function(t){if(v(t))return;const e=a.MathSimpleStore.parseUnicode(t.key);h(t.key,e,t.category,t.mappings)},e.addFunctionRules=d,e.addUnitRules=function(t){v(t)||(t.si?f(t):b(t))},e.addSiUnitRules=f,e.lookupRule=m,e.lookupCategory=function(t){const e=p[t];return e?e.category:""},e.lookupString=y,o.default.getInstance().evaluator=y,e.enumerate=function(t={}){for(const e of Object.values(p))for(const[,r]of e.rules.entries())for(const{cstr:e}of r)t=g(e.getValues(),t);return t}},4658:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.MathSimpleStore=void 0;const n=r(5897),o=r(1676);class i{constructor(){this.category="",this.rules=new Map}static parseUnicode(t){const e=parseInt(t,16);return String.fromCodePoint(e)}static testDynamicConstraints_(t,e){return n.default.getInstance().strict?e.cstr.equal(t):n.default.getInstance().comparator.match(e.cstr)}defineRulesFromMappings(t,e,r,n,o){for(const i in o)for(const a in o[i]){const s=o[i][a];this.defineRuleFromStrings(t,e,r,i,a,n,s)}}getRules(t){let e=this.rules.get(t);return e||(e=[],this.rules.set(t,e)),e}defineRuleFromStrings(t,e,r,o,i,a,s){let l=this.getRules(e);const c=n.default.getInstance().parsers[o]||n.default.getInstance().defaultParser,u=n.default.getInstance().comparators[o],p=`${e}.${r}.${o}.${i}`,h=c.parse(p),d=u?u():n.default.getInstance().comparator,f=d.getReference();d.setReference(h);const m={cstr:h,action:s};l=l.filter((t=>!h.equal(t.cstr))),l.push(m),this.rules.set(e,l),d.setReference(f)}lookupRule(t,e){let r=this.getRules(e.getValue(o.Axis.LOCALE));return r=r.filter((function(t){return i.testDynamicConstraints_(e,t)})),1===r.length?r[0]:r.length?r.sort(((t,e)=>n.default.getInstance().comparator.compare(t.cstr,e.cstr)))[0]:null}}e.MathSimpleStore=i},9935:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.MathStore=void 0;const n=r(707),o=r(4356),i=r(7630),a=r(4504),s=r(4650);class l extends a.BaseRuleStore{constructor(){super(),this.annotators=[],this.parseMethods.Alias=this.defineAlias,this.parseMethods.SpecializedRule=this.defineSpecializedRule,this.parseMethods.Specialized=this.defineSpecialized}initialize(){this.initialized||(this.annotations(),this.initialized=!0)}annotations(){for(let t,e=0;t=this.annotators[e];e++)(0,i.activate)(this.domain,t)}defineAlias(t,e,...r){const n=this.parsePrecondition(e,r);if(!n)return void console.error(`Precondition Error: ${e} ${r}`);const o=this.preconditions.get(t);o?o.addFullCondition(n):console.error(`Alias Error: No precondition by the name of ${t}`)}defineRulesAlias(t,e,...r){const n=this.findAllRules((function(e){return e.name===t}));if(0===n.length)throw new s.OutputError("Rule with name "+t+" does not exist.");const o=[];n.forEach((t=>{(t=>{const e=t.dynamicCstr.toString(),r=t.action.toString();for(let t,n=0;t=o[n];n++)if(t.action===r&&t.cstr===e)return!1;return o.push({cstr:e,action:r}),!0})(t)&&this.addAlias_(t,e,r)}))}defineSpecializedRule(t,e,r,n){const o=this.parseCstr(e),i=this.findRule((e=>e.name===t&&o.equal(e.dynamicCstr))),a=this.parseCstr(r);if(!i&&n)throw new s.OutputError("Rule named "+t+" with style "+e+" does not exist.");const l=n?s.Action.fromString(n):i.action,c=new s.SpeechRule(i.name,a,i.precondition,l);this.addRule(c)}defineSpecialized(t,e,r){const n=this.parseCstr(r);if(!n)return void console.error(`Dynamic Constraint Error: ${r}`);const o=this.preconditions.get(t);o?o.addConstraint(n):console.error(`Alias Error: No precondition by the name of ${t}`)}evaluateString(t){const e=[];if(t.match(/^\s+$/))return e;let r=this.matchNumber_(t);if(r&&r.length===t.length)return e.push(this.evaluateCharacter(r.number)),e;const i=n.removeEmpty(t.replace(/\s/g," ").split(" "));for(let t,n=0;t=i[n];n++)if(1===t.length)e.push(this.evaluateCharacter(t));else if(t.match(new RegExp("^["+o.LOCALE.MESSAGES.regexp.TEXT+"]+$")))e.push(this.evaluateCharacter(t));else{let n=t;for(;n;){r=this.matchNumber_(n);const t=n.match(new RegExp("^["+o.LOCALE.MESSAGES.regexp.TEXT+"]+"));if(r)e.push(this.evaluateCharacter(r.number)),n=n.substring(r.length);else if(t)e.push(this.evaluateCharacter(t[0])),n=n.substring(t[0].length);else{const t=Array.from(n),r=t[0];e.push(this.evaluateCharacter(r)),n=t.slice(1).join("")}}}return e}parse(t){super.parse(t),this.annotators=t.annotators||[]}addAlias_(t,e,r){const n=this.parsePrecondition(e,r),o=new s.SpeechRule(t.name,t.dynamicCstr,n,t.action);o.name=t.name,this.addRule(o)}matchNumber_(t){const e=t.match(new RegExp("^"+o.LOCALE.MESSAGES.regexp.NUMBER)),r=t.match(new RegExp("^"+l.regexp.NUMBER));if(!e&&!r)return null;const n=r&&r[0]===t;if(e&&e[0]===t||!n)return e?{number:e[0],length:e[0].length}:null;return{number:r[0].replace(new RegExp(l.regexp.DIGIT_GROUP,"g"),"X").replace(new RegExp(l.regexp.DECIMAL_MARK,"g"),o.LOCALE.MESSAGES.regexp.DECIMAL_MARK).replace(/X/g,o.LOCALE.MESSAGES.regexp.DIGIT_GROUP.replace(/\\/g,"")),length:r[0].length}}}e.MathStore=l,l.regexp={NUMBER:"((\\d{1,3})(?=(,| ))((,| )\\d{3})*(\\.\\d+)?)|^\\d*\\.\\d+|^\\d+",DECIMAL_MARK:"\\.",DIGIT_GROUP:","}},4650:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.OutputError=e.Precondition=e.Action=e.Component=e.ActionType=e.SpeechRule=void 0;const n=r(5897),o=r(2105);var i;function a(t){switch(t){case"[n]":return i.NODE;case"[m]":return i.MULTI;case"[t]":return i.TEXT;case"[p]":return i.PERSONALITY;default:throw"Parse error: "+t}}e.SpeechRule=class{constructor(t,e,r,n){this.name=t,this.dynamicCstr=e,this.precondition=r,this.action=n,this.context=null}toString(){return this.name+" | "+this.dynamicCstr.toString()+" | "+this.precondition.toString()+" ==> "+this.action.toString()}},function(t){t.NODE="NODE",t.MULTI="MULTI",t.TEXT="TEXT",t.PERSONALITY="PERSONALITY"}(i=e.ActionType||(e.ActionType={}));class s{constructor({type:t,content:e,attributes:r,grammar:n}){this.type=t,this.content=e,this.attributes=r,this.grammar=n}static grammarFromString(t){return o.Grammar.parseInput(t)}static fromString(t){const e={type:a(t.substring(0,3))};let r=t.slice(3).trim();if(!r)throw new u("Missing content.");switch(e.type){case i.TEXT:if('"'===r[0]){const t=p(r,"\\(")[0].trim();if('"'!==t.slice(-1))throw new u("Invalid string syntax.");e.content=t,r=r.slice(t.length).trim(),-1===r.indexOf("(")&&(r="");break}case i.NODE:case i.MULTI:{const t=r.indexOf(" (");if(-1===t){e.content=r.trim(),r="";break}e.content=r.substring(0,t).trim(),r=r.slice(t).trim()}}if(r){const t=s.attributesFromString(r);t.grammar&&(e.grammar=t.grammar,delete t.grammar),Object.keys(t).length&&(e.attributes=t)}return new s(e)}static attributesFromString(t){if("("!==t[0]||")"!==t.slice(-1))throw new u("Invalid attribute expression: "+t);const e={},r=p(t.slice(1,-1),",");for(let t=0,n=r.length;t<n;t++){const n=r[t],i=n.indexOf(":");if(-1===i)e[n.trim()]="true";else{const t=n.substring(0,i).trim(),r=n.slice(i+1).trim();e[t]=t===o.ATTRIBUTE?s.grammarFromString(r):r}}return e}toString(){let t="";t+=function(t){switch(t){case i.NODE:return"[n]";case i.MULTI:return"[m]";case i.TEXT:return"[t]";case i.PERSONALITY:return"[p]";default:throw"Unknown type error: "+t}}(this.type),t+=this.content?" "+this.content:"";const e=this.attributesToString();return t+=e?" "+e:"",t}grammarToString(){return this.getGrammar().join(":")}getGrammar(){const t=[];for(const e in this.grammar)!0===this.grammar[e]?t.push(e):!1===this.grammar[e]?t.push("!"+e):t.push(e+"="+this.grammar[e]);return t}attributesToString(){const t=this.getAttributes(),e=this.grammarToString();return e&&t.push("grammar:"+e),t.length>0?"("+t.join(", ")+")":""}getAttributes(){const t=[];for(const e in this.attributes){const r=this.attributes[e];"true"===r?t.push(e):t.push(e+":"+r)}return t}}e.Component=s;class l{constructor(t){this.components=t}static fromString(t){const e=p(t,";").filter((function(t){return t.match(/\S/)})).map((function(t){return t.trim()})),r=[];for(let t=0,n=e.length;t<n;t++){const n=s.fromString(e[t]);n&&r.push(n)}return new l(r)}toString(){return this.components.map((function(t){return t.toString()})).join("; ")}}e.Action=l;class c{constructor(t,...e){this.query=t,this.constraints=e;const[r,n]=this.presetPriority();this.priority=r?n:this.calculatePriority()}static constraintValue(t,e){for(let r,n=0;r=e[n];n++)if(t.match(r))return++n;return 0}toString(){const t=this.constraints.join(", ");return`${this.query}, ${t} (${this.priority}, ${this.rank})`}calculatePriority(){const t=c.constraintValue(this.query,c.queryPriorities);if(!t)return 0;const e=this.query.match(/^self::.+\[(.+)\]/)[1];return 100*t+10*c.constraintValue(e,c.attributePriorities)}presetPriority(){if(!this.constraints.length)return[!1,0];const t=this.constraints[this.constraints.length-1].match(/^priority=(.*$)/);if(!t)return[!1,0];this.constraints.pop();const e=parseFloat(t[1]);return[!0,isNaN(e)?0:e]}}e.Precondition=c,c.queryPriorities=[/^self::\*\[.+\]$/,/^self::[\w-]+\[.+\]$/],c.attributePriorities=[/^@[\w-]+$/,/^@[\w-]+!=".+"$/,/^not\(contains\(@[\w-]+,\s*".+"\)\)$/,/^contains\(@[\w-]+,".+"\)$/,/^@[\w-]+=".+"$/];class u extends n.SREError{constructor(t){super(t),this.name="RuleError"}}function p(t,e){const r=[];let n="";for(;""!==t;){const o=t.search(e);if(-1===o){if((t.match(/"/g)||[]).length%2!=0)throw new u("Invalid string in expression: "+t);r.push(n+t),n="",t=""}else if((t.substring(0,o).match(/"/g)||[]).length%2==0)r.push(n+t.substring(0,o)),n="",t=t.substring(o+1);else{const e=t.substring(o).search('"');if(-1===e)throw new u("Invalid string in expression: "+t);n+=t.substring(0,o+e+1),t=t.substring(o+e+1)}}return n&&r.push(n),r}e.OutputError=u},4106:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.SpeechRuleContext=void 0;const n=r(5274),o=r(5662);e.SpeechRuleContext=class{constructor(){this.customQueries=new o.CustomQueries,this.customStrings=new o.CustomStrings,this.contextFunctions=new o.ContextFunctions,this.customGenerators=new o.CustomGenerators}applyCustomQuery(t,e){const r=this.customQueries.lookup(e);return r?r(t):null}applySelector(t,e){return this.applyCustomQuery(t,e)||n.evalXPath(e,t)}applyQuery(t,e){const r=this.applySelector(t,e);return r.length>0?r[0]:null}applyConstraint(t,e){return!!this.applyQuery(t,e)||n.evaluateBoolean(e,t)}constructString(t,e){if(!e)return"";if('"'===e.charAt(0))return e.slice(1,-1);const r=this.customStrings.lookup(e);return r?r(t):n.evaluateString(e,t)}parse(t){const e=Array.isArray(t)?t:Object.entries(t);for(let t,r=0;t=e[r];r++){switch(t[0].slice(0,3)){case"CQF":this.customQueries.add(t[0],t[1]);break;case"CSF":this.customStrings.add(t[0],t[1]);break;case"CTF":this.contextFunctions.add(t[0],t[1]);break;case"CGF":this.customGenerators.add(t[0],t[1]);break;default:console.error("FunctionError: Invalid function name "+t[0])}}}}},2362:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.storeFactory=e.SpeechRuleEngine=void 0;const n=r(7052),o=r(2057),i=r(5740),a=r(5897),s=r(4440),l=r(5274),c=r(7283),u=r(7599),p=r(2469),h=r(1676),d=r(2105),f=r(9935),m=r(4650),y=r(4508);class g{constructor(){this.trie=null,this.evaluators_={},this.trie=new y.Trie}static getInstance(){return g.instance=g.instance||new g,g.instance}static debugSpeechRule(t,e){const r=t.precondition,n=t.context.applyQuery(e,r.query);o.Debugger.getInstance().output(r.query,n?n.toString():n),r.constraints.forEach((r=>o.Debugger.getInstance().output(r,t.context.applyConstraint(e,r))))}static debugNamedSpeechRule(t,e){const r=g.getInstance().trie.collectRules().filter((e=>e.name==t));for(let n,i=0;n=r[i];i++)o.Debugger.getInstance().output("Rule",t,"DynamicCstr:",n.dynamicCstr.toString(),"number",i),g.debugSpeechRule(n,e)}evaluateNode(t){(0,l.updateEvaluator)(t);const e=(new Date).getTime();let r=[];try{r=this.evaluateNode_(t)}catch(t){console.error("Something went wrong computing speech."),o.Debugger.getInstance().output(t)}const n=(new Date).getTime();return o.Debugger.getInstance().output("Time:",n-e),r}toString(){return this.trie.collectRules().map((t=>t.toString())).join("\n")}runInSetting(t,e){const r=a.default.getInstance(),n={};for(const e in t)n[e]=r[e],r[e]=t[e];r.setDynamicCstr();const o=e();for(const t in n)r[t]=n[t];return r.setDynamicCstr(),o}addStore(t){const e=v(t);"abstract"!==e.kind&&e.getSpeechRules().forEach((t=>this.trie.addRule(t))),this.addEvaluator(e)}processGrammar(t,e,r){const n={};for(const o in r){const i=r[o];n[o]="string"==typeof i?t.constructString(e,i):i}d.Grammar.getInstance().pushState(n)}addEvaluator(t){const e=t.evaluateDefault.bind(t),r=this.evaluators_[t.locale];if(r)return void(r[t.modality]=e);const n={};n[t.modality]=e,this.evaluators_[t.locale]=n}getEvaluator(t,e){const r=this.evaluators_[t]||this.evaluators_[h.DynamicCstr.DEFAULT_VALUES[h.Axis.LOCALE]];return r[e]||r[h.DynamicCstr.DEFAULT_VALUES[h.Axis.MODALITY]]}enumerate(t){return this.trie.enumerate(t)}evaluateNode_(t){return t?(this.updateConstraint_(),this.evaluateTree_(t)):[]}evaluateTree_(t){const e=a.default.getInstance();let r;o.Debugger.getInstance().output(e.mode!==s.Mode.HTTP?t.toString():t),d.Grammar.getInstance().setAttribute(t);const i=this.lookupRule(t,e.dynamicCstr);if(!i)return e.strict?[]:(r=this.getEvaluator(e.locale,e.modality)(t),t.attributes&&this.addPersonality_(r,{},!1,t),r);o.Debugger.getInstance().generateOutput((()=>["Apply Rule:",i.name,i.dynamicCstr.toString(),(e.mode,s.Mode.HTTP,t).toString()]));const c=i.context,u=i.action.components;r=[];for(let e,o=0;e=u[o];o++){let o=[];const i=e.content||"",s=e.attributes||{};let u=!1;e.grammar&&this.processGrammar(c,t,e.grammar);let p=null;if(s.engine){p=a.default.getInstance().dynamicCstr.getComponents();const t=d.Grammar.parseInput(s.engine);a.default.getInstance().setDynamicCstr(t)}switch(e.type){case m.ActionType.NODE:{const e=c.applyQuery(t,i);e&&(o=this.evaluateTree_(e))}break;case m.ActionType.MULTI:{u=!0;const e=c.applySelector(t,i);e.length>0&&(o=this.evaluateNodeList_(c,e,s.sepFunc,c.constructString(t,s.separator),s.ctxtFunc,c.constructString(t,s.context)))}break;case m.ActionType.TEXT:{const e=s.span,r={};if(e){const n=(0,l.evalXPath)(e,t);n.length&&(r.extid=n[0].getAttribute("extid"))}const a=c.constructString(t,i);(a||""===a)&&(o=Array.isArray(a)?a.map((function(t){return n.AuditoryDescription.create({text:t.speech,attributes:t.attributes},{adjust:!0})})):[n.AuditoryDescription.create({text:a,attributes:r},{adjust:!0})])}break;case m.ActionType.PERSONALITY:default:o=[n.AuditoryDescription.create({text:i})]}o[0]&&!u&&(s.context&&(o[0].context=c.constructString(t,s.context)+(o[0].context||"")),s.annotation&&(o[0].annotation=s.annotation)),this.addLayout(o,s,u),e.grammar&&d.Grammar.getInstance().popState(),r=r.concat(this.addPersonality_(o,s,u,t)),p&&a.default.getInstance().setDynamicCstr(p)}return r}evaluateNodeList_(t,e,r,o,i,a){if(!e.length)return[];const s=o||"",l=a||"",c=t.contextFunctions.lookup(i),u=c?c(e,l):function(){return l},p=t.contextFunctions.lookup(r),h=p?p(e,s):function(){return[n.AuditoryDescription.create({text:s},{translate:!0})]};let d=[];for(let t,r=0;t=e[r];r++){const n=this.evaluateTree_(t);if(n.length>0&&(n[0].context=u()+(n[0].context||""),d=d.concat(n),r<e.length-1)){const t=h();d=d.concat(t)}}return d}addLayout(t,e,r){const o=e.layout;o&&(o.match(/^begin/)?t.unshift(new n.AuditoryDescription({text:"",layout:o})):o.match(/^end/)?t.push(new n.AuditoryDescription({text:"",layout:o})):(t.unshift(new n.AuditoryDescription({text:"",layout:`begin${o}`})),t.push(new n.AuditoryDescription({text:"",layout:`end${o}`}))))}addPersonality_(t,e,r,o){const i={};let a=null;for(const t of s.personalityPropList){const r=e[t];if(void 0===r)continue;const n=parseFloat(r),o=isNaN(n)?'"'===r.charAt(0)?r.slice(1,-1):r:n;t===s.personalityProps.PAUSE?a=o:i[t]=o}for(let e,r=0;e=t[r];r++)this.addRelativePersonality_(e,i),this.addExternalAttributes_(e,o);if(r&&t.length&&delete t[t.length-1].personality[s.personalityProps.JOIN],a&&t.length){const e=t[t.length-1];e.text||Object.keys(e.personality).length?t.push(n.AuditoryDescription.create({text:"",personality:{pause:a}})):e.personality[s.personalityProps.PAUSE]=a}return t}addExternalAttributes_(t,e){if(e.hasAttributes()){const r=e.attributes;for(let e=r.length-1;e>=0;e--){const n=r[e].name;!t.attributes[n]&&n.match(/^ext/)&&(t.attributes[n]=r[e].value)}}}addRelativePersonality_(t,e){if(!t.personality)return t.personality=e,t;const r=t.personality;for(const t in e)r[t]&&"number"==typeof r[t]&&"number"==typeof e[t]?r[t]=r[t]+e[t]:r[t]||(r[t]=e[t]);return t}updateConstraint_(){const t=a.default.getInstance().dynamicCstr,e=a.default.getInstance().strict,r=this.trie,n={};let o=t.getValue(h.Axis.LOCALE),i=t.getValue(h.Axis.MODALITY),s=t.getValue(h.Axis.DOMAIN);r.hasSubtrie([o,i,s])||(s=h.DynamicCstr.DEFAULT_VALUES[h.Axis.DOMAIN],r.hasSubtrie([o,i,s])||(i=h.DynamicCstr.DEFAULT_VALUES[h.Axis.MODALITY],r.hasSubtrie([o,i,s])||(o=h.DynamicCstr.DEFAULT_VALUES[h.Axis.LOCALE]))),n[h.Axis.LOCALE]=[o],n[h.Axis.MODALITY]=["summary"!==i?i:h.DynamicCstr.DEFAULT_VALUES[h.Axis.MODALITY]],n[h.Axis.DOMAIN]=["speech"!==i?h.DynamicCstr.DEFAULT_VALUES[h.Axis.DOMAIN]:s];const l=t.getOrder();for(let r,o=0;r=l[o];o++)if(!n[r]){const o=t.getValue(r),i=this.makeSet_(o,t.preference),a=h.DynamicCstr.DEFAULT_VALUES[r];e||o===a||i.push(a),n[r]=i}t.updateProperties(n)}makeSet_(t,e){return e&&Object.keys(e).length?t.split(":"):[t]}lookupRule(t,e){if(!t||t.nodeType!==i.NodeType.ELEMENT_NODE&&t.nodeType!==i.NodeType.TEXT_NODE)return null;const r=this.lookupRules(t,e);return r.length>0?this.pickMostConstraint_(e,r):null}lookupRules(t,e){return this.trie.lookupRules(t,e.allProperties())}pickMostConstraint_(t,e){const r=a.default.getInstance().comparator;return e.sort((function(t,e){return r.compare(t.dynamicCstr,e.dynamicCstr)||e.precondition.priority-t.precondition.priority||e.precondition.constraints.length-t.precondition.constraints.length||e.precondition.rank-t.precondition.rank})),o.Debugger.getInstance().generateOutput((()=>e.map((t=>t.name+"("+t.dynamicCstr.toString()+")"))).bind(this)),e[0]}}e.SpeechRuleEngine=g;const b=new Map;function v(t){const e=`${t.locale}.${t.modality}.${t.domain}`;if("actions"===t.kind){const r=b.get(e);return r.parse(t),r}u.init(),t&&!t.functions&&(t.functions=c.getStore(t.locale,t.modality,t.domain));const r="braille"===t.modality?new p.BrailleStore:new f.MathStore;return b.set(e,r),t.inherits&&(r.inherits=b.get(`${t.inherits}.${t.modality}.${t.domain}`)),r.parse(t),r.initialize(),r}e.storeFactory=v,a.default.nodeEvaluator=g.getInstance().evaluateNode.bind(g.getInstance())},5662:function(t,e){Object.defineProperty(e,"__esModule",{value:!0}),e.CustomGenerators=e.ContextFunctions=e.CustomStrings=e.CustomQueries=void 0;class r{constructor(t,e){this.prefix=t,this.store=e}add(t,e){this.checkCustomFunctionSyntax_(t)&&(this.store[t]=e)}addStore(t){const e=Object.keys(t.store);for(let r,n=0;r=e[n];n++)this.add(r,t.store[r])}lookup(t){return this.store[t]}checkCustomFunctionSyntax_(t){const e=new RegExp("^"+this.prefix);return!!t.match(e)||(console.error("FunctionError: Invalid function name. 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e.type="row",e.role="cycle",e.textContent="",e.contentNodes=[],t}),(t=>"fenced"===t.type&&"infixop"===t.childNodes[0].type&&"implicit"===t.childNodes[0].role&&t.childNodes[0].childNodes.every((function(t){return"number"===t.type}))&&t.childNodes[0].contentNodes.every((function(t){return"space"===t.role})))))},7228:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.SemanticMathml=void 0;const n=r(5740),o=r(5250),i=r(5609),a=r(3308),s=r(4795);class l extends o.SemanticAbstractParser{constructor(){super("MathML"),this.parseMap_={SEMANTICS:this.semantics_.bind(this),MATH:this.rows_.bind(this),MROW:this.rows_.bind(this),MPADDED:this.rows_.bind(this),MSTYLE:this.rows_.bind(this),MFRAC:this.fraction_.bind(this),MSUB:this.limits_.bind(this),MSUP:this.limits_.bind(this),MSUBSUP:this.limits_.bind(this),MOVER:this.limits_.bind(this),MUNDER:this.limits_.bind(this),MUNDEROVER:this.limits_.bind(this),MROOT:this.root_.bind(this),MSQRT:this.sqrt_.bind(this),MTABLE:this.table_.bind(this),MLABELEDTR:this.tableLabeledRow_.bind(this),MTR:this.tableRow_.bind(this),MTD:this.tableCell_.bind(this),MS:this.text_.bind(this),MTEXT:this.text_.bind(this),MSPACE:this.space_.bind(this),"ANNOTATION-XML":this.text_.bind(this),MI:this.identifier_.bind(this),MN:this.number_.bind(this),MO:this.operator_.bind(this),MFENCED:this.fenced_.bind(this),MENCLOSE:this.enclosed_.bind(this),MMULTISCRIPTS:this.multiscripts_.bind(this),ANNOTATION:this.empty_.bind(this),NONE:this.empty_.bind(this),MACTION:this.action_.bind(this)};const t={type:"identifier",role:"numbersetletter",font:"double-struck"};["C","H","N","P","Q","R","Z","\u2102","\u210d","\u2115","\u2119","\u211a","\u211d","\u2124"].forEach((e=>this.getFactory().defaultMap.add(e,t)).bind(this))}static getAttribute_(t,e,r){if(!t.hasAttribute(e))return r;const n=t.getAttribute(e);return n.match(/^\s*$/)?null:n}parse(t){a.default.getInstance().setNodeFactory(this.getFactory());const e=n.toArray(t.childNodes),r=n.tagName(t),o=this.parseMap_[r],i=(o||this.dummy_.bind(this))(t,e);return s.addAttributes(i,t),-1!==["MATH","MROW","MPADDED","MSTYLE","SEMANTICS"].indexOf(r)||(i.mathml.unshift(t),i.mathmlTree=t),i}semantics_(t,e){return e.length?this.parse(e[0]):this.getFactory().makeEmptyNode()}rows_(t,e){const r=t.getAttribute("semantics");if(r&&r.match("bspr_"))return a.default.proof(t,r,this.parseList.bind(this));let n;return 1===(e=s.purgeNodes(e)).length?(n=this.parse(e[0]),"empty"!==n.type||n.mathmlTree||(n.mathmlTree=t)):n=a.default.getInstance().row(this.parseList(e)),n.mathml.unshift(t),n}fraction_(t,e){if(!e.length)return this.getFactory().makeEmptyNode();const r=this.parse(e[0]),n=e[1]?this.parse(e[1]):this.getFactory().makeEmptyNode();return a.default.getInstance().fractionLikeNode(r,n,t.getAttribute("linethickness"),"true"===t.getAttribute("bevelled"))}limits_(t,e){return a.default.getInstance().limitNode(n.tagName(t),this.parseList(e))}root_(t,e){return e[1]?this.getFactory().makeBranchNode("root",[this.parse(e[1]),this.parse(e[0])],[]):this.sqrt_(t,e)}sqrt_(t,e){const r=this.parseList(s.purgeNodes(e));return this.getFactory().makeBranchNode("sqrt",[a.default.getInstance().row(r)],[])}table_(t,e){const r=t.getAttribute("semantics");if(r&&r.match("bspr_"))return a.default.proof(t,r,this.parseList.bind(this));const n=this.getFactory().makeBranchNode("table",this.parseList(e),[]);return n.mathmlTree=t,a.default.tableToMultiline(n),n}tableRow_(t,e){const r=this.getFactory().makeBranchNode("row",this.parseList(e),[]);return r.role="table",r}tableLabeledRow_(t,e){if(!e.length)return this.tableRow_(t,e);const r=this.parse(e[0]);r.role="label";const n=this.getFactory().makeBranchNode("row",this.parseList(e.slice(1)),[r]);return n.role="table",n}tableCell_(t,e){const r=this.parseList(s.purgeNodes(e));let n;n=r.length?1===r.length&&i.isType(r[0],"empty")?r:[a.default.getInstance().row(r)]:[];const o=this.getFactory().makeBranchNode("cell",n,[]);return o.role="table",o}space_(t,e){const r=t.getAttribute("width"),o=r&&r.match(/[a-z]*$/);if(!o)return this.empty_(t,e);const i=o[0],s=parseFloat(r.slice(0,o.index)),l={cm:.4,pc:.5,em:.5,ex:1,in:.15,pt:5,mm:5}[i];if(!l||isNaN(s)||s<l)return this.empty_(t,e);const c=this.getFactory().makeUnprocessed(t);return a.default.getInstance().text(c,n.tagName(t))}text_(t,e){const r=this.leaf_(t,e);return t.textContent?(r.updateContent(t.textContent,!0),a.default.getInstance().text(r,n.tagName(t))):r}identifier_(t,e){const r=this.leaf_(t,e);return a.default.getInstance().identifierNode(r,a.default.getInstance().font(t.getAttribute("mathvariant")),t.getAttribute("class"))}number_(t,e){const r=this.leaf_(t,e);return a.default.number(r),r}operator_(t,e){const r=this.leaf_(t,e);return a.default.getInstance().operatorNode(r),r}fenced_(t,e){const r=this.parseList(s.purgeNodes(e)),n=l.getAttribute_(t,"separators",","),o=l.getAttribute_(t,"open","("),i=l.getAttribute_(t,"close",")"),c=a.default.getInstance().mfenced(o,i,n,r);return a.default.getInstance().tablesInRow([c])[0]}enclosed_(t,e){const r=this.parseList(s.purgeNodes(e)),n=this.getFactory().makeBranchNode("enclose",[a.default.getInstance().row(r)],[]);return n.role=t.getAttribute("notation")||"unknown",n}multiscripts_(t,e){if(!e.length)return this.getFactory().makeEmptyNode();const r=this.parse(e.shift());if(!e.length)return r;const o=[],i=[],l=[],c=[];let u=!1,p=0;for(let t,r=0;t=e[r];r++)"MPRESCRIPTS"!==n.tagName(t)?(u?1&p?o.push(t):i.push(t):1&p?l.push(t):c.push(t),p++):(u=!0,p=0);return s.purgeNodes(o).length||s.purgeNodes(i).length?a.default.getInstance().tensor(r,this.parseList(i),this.parseList(o),this.parseList(c),this.parseList(l)):a.default.getInstance().pseudoTensor(r,this.parseList(c),this.parseList(l))}empty_(t,e){return this.getFactory().makeEmptyNode()}action_(t,e){return e.length>1?this.parse(e[1]):this.getFactory().makeUnprocessed(t)}dummy_(t,e){const r=this.getFactory().makeUnprocessed(t);return r.role=t.tagName,r.textContent=t.textContent,r}leaf_(t,e){if(1===e.length&&e[0].nodeType!==n.NodeType.TEXT_NODE){const r=this.getFactory().makeUnprocessed(t);return r.role=e[0].tagName,s.addAttributes(r,e[0]),r}return this.getFactory().makeLeafNode(t.textContent,a.default.getInstance().font(t.getAttribute("mathvariant")))}}e.SemanticMathml=l},5952:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.SemanticNode=void 0;const n=r(5740),o=r(3588),i=r(4795);class a{constructor(t){this.id=t,this.mathml=[],this.parent=null,this.type="unknown",this.role="unknown",this.font="unknown",this.embellished=null,this.fencePointer="",this.childNodes=[],this.textContent="",this.mathmlTree=null,this.contentNodes=[],this.annotation={},this.attributes={},this.nobreaking=!1}static fromXml(t){const e=parseInt(t.getAttribute("id"),10),r=new a(e);return r.type=t.tagName,a.setAttribute(r,t,"role"),a.setAttribute(r,t,"font"),a.setAttribute(r,t,"embellished"),a.setAttribute(r,t,"fencepointer","fencePointer"),t.getAttribute("annotation")&&r.parseAnnotation(t.getAttribute("annotation")),i.addAttributes(r,t),a.processChildren(r,t),r}static setAttribute(t,e,r,n){n=n||r;const o=e.getAttribute(r);o&&(t[n]=o)}static processChildren(t,e){for(const r of n.toArray(e.childNodes)){if(r.nodeType===n.NodeType.TEXT_NODE){t.textContent=r.textContent;continue}const e=n.toArray(r.childNodes).map(a.fromXml);e.forEach((e=>e.parent=t)),"CONTENT"===n.tagName(r)?t.contentNodes=e:t.childNodes=e}}querySelectorAll(t){let e=[];for(let r,n=0;r=this.childNodes[n];n++)e=e.concat(r.querySelectorAll(t));for(let r,n=0;r=this.contentNodes[n];n++)e=e.concat(r.querySelectorAll(t));return t(this)&&e.unshift(this),e}xml(t,e){const r=function(r,n){const o=n.map((function(r){return r.xml(t,e)})),i=t.createElementNS("",r);for(let t,e=0;t=o[e];e++)i.appendChild(t);return i},n=t.createElementNS("",this.type);return e||this.xmlAttributes(n),n.textContent=this.textContent,this.contentNodes.length>0&&n.appendChild(r("content",this.contentNodes)),this.childNodes.length>0&&n.appendChild(r("children",this.childNodes)),n}toString(t=!1){const e=n.parseInput("<snode/>");return n.serializeXml(this.xml(e,t))}allAttributes(){const t=[];return t.push(["role",this.role]),"unknown"!==this.font&&t.push(["font",this.font]),Object.keys(this.annotation).length&&t.push(["annotation",this.xmlAnnotation()]),this.embellished&&t.push(["embellished",this.embellished]),this.fencePointer&&t.push(["fencepointer",this.fencePointer]),t.push(["id",this.id.toString()]),t}xmlAnnotation(){const t=[];for(const e in this.annotation)this.annotation[e].forEach((function(r){t.push(e+":"+r)}));return t.join(";")}toJson(){const t={};t.type=this.type;const e=this.allAttributes();for(let r,n=0;r=e[n];n++)t[r[0]]=r[1].toString();return this.textContent&&(t.$t=this.textContent),this.childNodes.length&&(t.children=this.childNodes.map((function(t){return t.toJson()}))),this.contentNodes.length&&(t.content=this.contentNodes.map((function(t){return t.toJson()}))),t}updateContent(t,e){const r=e?t.replace(/^[ \f\n\r\t\v\u200b]*/,"").replace(/[ \f\n\r\t\v\u200b]*$/,""):t.trim();if(t=t&&!r?t:r,this.textContent===t)return;const n=(0,o.lookupMeaning)(t);this.textContent=t,this.role=n.role,this.type=n.type,this.font=n.font}addMathmlNodes(t){for(let e,r=0;e=t[r];r++)-1===this.mathml.indexOf(e)&&this.mathml.push(e)}appendChild(t){this.childNodes.push(t),this.addMathmlNodes(t.mathml),t.parent=this}replaceChild(t,e){const r=this.childNodes.indexOf(t);if(-1===r)return;t.parent=null,e.parent=this,this.childNodes[r]=e;const n=t.mathml.filter((function(t){return-1===e.mathml.indexOf(t)})),o=e.mathml.filter((function(e){return-1===t.mathml.indexOf(e)}));this.removeMathmlNodes(n),this.addMathmlNodes(o)}appendContentNode(t){t&&(this.contentNodes.push(t),this.addMathmlNodes(t.mathml),t.parent=this)}removeContentNode(t){if(t){const e=this.contentNodes.indexOf(t);-1!==e&&this.contentNodes.slice(e,1)}}equals(t){if(!t)return!1;if(this.type!==t.type||this.role!==t.role||this.textContent!==t.textContent||this.childNodes.length!==t.childNodes.length||this.contentNodes.length!==t.contentNodes.length)return!1;for(let e,r,n=0;e=this.childNodes[n],r=t.childNodes[n];n++)if(!e.equals(r))return!1;for(let e,r,n=0;e=this.contentNodes[n],r=t.contentNodes[n];n++)if(!e.equals(r))return!1;return!0}displayTree(){console.info(this.displayTree_(0))}addAnnotation(t,e){e&&this.addAnnotation_(t,e)}getAnnotation(t){const e=this.annotation[t];return e||[]}hasAnnotation(t,e){const r=this.annotation[t];return!!r&&-1!==r.indexOf(e)}parseAnnotation(t){const e=t.split(";");for(let t=0,r=e.length;t<r;t++){const r=e[t].split(":");this.addAnnotation(r[0],r[1])}}meaning(){return{type:this.type,role:this.role,font:this.font}}xmlAttributes(t){const e=this.allAttributes();for(let r,n=0;r=e[n];n++)t.setAttribute(r[0],r[1]);this.addExternalAttributes(t)}addExternalAttributes(t){for(const e in this.attributes)t.setAttribute(e,this.attributes[e])}removeMathmlNodes(t){const e=this.mathml;for(let r,n=0;r=t[n];n++){const t=e.indexOf(r);-1!==t&&e.splice(t,1)}this.mathml=e}displayTree_(t){t++;const e=Array(t).join("  ");let r="";r+="\n"+e+this.toString(),r+="\n"+e+"MathmlTree:",r+="\n"+e+this.mathmlTreeString(),r+="\n"+e+"MathML:";for(let t,n=0;t=this.mathml[n];n++)r+="\n"+e+t.toString();return r+="\n"+e+"Begin Content",this.contentNodes.forEach((function(e){r+=e.displayTree_(t)})),r+="\n"+e+"End Content",r+="\n"+e+"Begin Children",this.childNodes.forEach((function(e){r+=e.displayTree_(t)})),r+="\n"+e+"End Children",r}mathmlTreeString(){return this.mathmlTree?this.mathmlTree.toString():"EMPTY"}addAnnotation_(t,e){const r=this.annotation[t];r?r.push(e):this.annotation[t]=[e]}}e.SemanticNode=a},6537:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.SemanticNodeFactory=void 0;const n=r(8158),o=r(8158),i=r(5952);e.SemanticNodeFactory=class{constructor(){this.leafMap=new o.SemanticNodeCollator,this.defaultMap=new n.SemanticDefault,this.idCounter_=-1}makeNode(t){return this.createNode_(t)}makeUnprocessed(t){const e=this.createNode_();return e.mathml=[t],e.mathmlTree=t,e}makeEmptyNode(){const t=this.createNode_();return t.type="empty",t}makeContentNode(t){const e=this.createNode_();return e.updateContent(t),e}makeMultipleContentNodes(t,e){const r=[];for(let n=0;n<t;n++)r.push(this.makeContentNode(e));return r}makeLeafNode(t,e){if(!t)return this.makeEmptyNode();const r=this.makeContentNode(t);r.font=e||r.font;const n=this.defaultMap.retrieveNode(r);return n&&(r.type=n.type,r.role=n.role,r.font=n.font),this.leafMap.addNode(r),r}makeBranchNode(t,e,r,n){const o=this.createNode_();return n&&o.updateContent(n),o.type=t,o.childNodes=e,o.contentNodes=r,e.concat(r).forEach((function(t){t.parent=o,o.addMathmlNodes(t.mathml)})),o}createNode_(t){return void 0!==t?this.idCounter_=Math.max(this.idCounter_,t):t=++this.idCounter_,new i.SemanticNode(t)}}},3882:function(t,e){Object.defineProperty(e,"__esModule",{value:!0}),e.SemanticComparator=e.reduce=e.sort=e.apply=e.add=void 0;const r=[];function n(t){r.push(t)}function o(t,e){for(let n,o=0;n=r[o];o++){const r=n.compare(t,e);if(0!==r)return r}return 0}function i(t){t.sort(o)}e.add=n,e.apply=o,e.sort=i,e.reduce=function(t){if(t.length<=1)return t;const e=t.slice();i(e);const r=[];let n;do{n=e.pop(),r.push(n)}while(n&&e.length&&0===o(e[e.length-1],n));return r};class a{constructor(t,e=null){this.comparator=t,this.type=e,n(this)}compare(t,e){return this.type&&this.type===t.type&&this.type===e.type?this.comparator(t,e):0}}e.SemanticComparator=a,new a((function(t,e){return"simple function"===t.role?1:"simple function"===e.role?-1:0}),"identifier")},5250:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.SemanticAbstractParser=void 0;const n=r(6537);e.SemanticAbstractParser=class{constructor(t){this.type=t,this.factory_=new n.SemanticNodeFactory}getFactory(){return this.factory_}setFactory(t){this.factory_=t}getType(){return this.type}parseList(t){const e=[];for(let r,n=0;r=t[n];n++)e.push(this.parse(r));return e}}},5609:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.isMembership=e.elligibleRightNeutral=e.elligibleLeftNeutral=e.compareNeutralFences=e.isNeutralFence=e.isImplicitOp=e.isImplicit=e.isPureUnit=e.isUnitCounter=e.isNumber=e.isSingletonSetContent=e.scriptedElement_=e.illegalSingleton_=e.isSetNode=e.isRightBrace=e.isLeftBrace=e.isSimpleFunction=e.singlePunctAtPosition=e.isSimpleFunctionHead=e.isLimitBase=e.isBinomial=e.lineIsLabelled=e.tableIsMultiline=e.tableIsCases=e.isFencedElement=e.tableIsMatrixOrVector=e.isTableOrMultiline=e.isElligibleEmbellishedFence=e.isFence=e.isPunctuation=e.isRelation=e.isOperator=e.isEmbellished=e.isGeneralFunctionBoundary=e.isIntegralDxBoundarySingle=e.isIntegralDxBoundary=e.isBigOpBoundary=e.isPrefixFunctionBoundary=e.isSimpleFunctionScope=e.isAccent=e.isRole=e.embellishedType=e.isType=void 0;const n=r(3588),o=r(4795);function i(t,e){return t.type===e}function a(t,e){return t.embellished===e}function s(t,e){return t.role===e}function l(t){return u(t)||p(t)}function c(t){return i(t,"operator")||a(t,"operator")}function u(t){return i(t,"relation")||a(t,"relation")}function p(t){return i(t,"punctuation")||a(t,"punctuation")}function h(t){return i(t,"fence")||a(t,"fence")}function d(t){return!t.embellished||!function(t){return i(t,"tensor")&&(!i(t.childNodes[1],"empty")||!i(t.childNodes[2],"empty"))&&(!i(t.childNodes[3],"empty")||!i(t.childNodes[4],"empty"))}(t)&&((!s(t,"close")||!i(t,"tensor"))&&((!s(t,"open")||!i(t,"subscript")&&!i(t,"superscript"))&&d(t.childNodes[0])))}function f(t){return!!t&&(i(t,"table")||i(t,"multiline"))}function m(t){return!!t&&i(t,"fenced")&&(s(t,"leftright")||v(t))&&1===t.childNodes.length}function y(t){return!!t&&-1!==["{","\ufe5b","\uff5b"].indexOf(t.textContent)}function g(t){return!!t&&-1!==["}","\ufe5c","\uff5d"].indexOf(t.textContent)}function b(t){return"number"===t.type&&("integer"===t.role||"float"===t.role)}function v(t){return"neutral"===t.role||"metric"===t.role}e.isType=i,e.embellishedType=a,e.isRole=s,e.isAccent=function(t){const e=new RegExp("\u221e|\u1ab2");return i(t,"fence")||i(t,"punctuation")||i(t,"operator")&&!t.textContent.match(e)||i(t,"relation")||i(t,"identifier")&&s(t,"unknown")&&!t.textContent.match(n.allLettersRegExp)&&!t.textContent.match(e)},e.isSimpleFunctionScope=function(t){const e=t.childNodes;if(0===e.length)return!0;if(e.length>1)return!1;const r=e[0];if("infixop"===r.type){if("implicit"!==r.role)return!1;if(r.childNodes.some((t=>i(t,"infixop"))))return!1}return!0},e.isPrefixFunctionBoundary=function(t){return c(t)&&!s(t,"division")||i(t,"appl")||l(t)},e.isBigOpBoundary=function(t){return c(t)||l(t)},e.isIntegralDxBoundary=function(t,e){return!!e&&i(e,"identifier")&&n.lookupSecondary("d",t.textContent)},e.isIntegralDxBoundarySingle=function(t){if(i(t,"identifier")){const e=t.textContent[0];return e&&t.textContent[1]&&n.lookupSecondary("d",e)}return!1},e.isGeneralFunctionBoundary=l,e.isEmbellished=function(t){return t.embellished?t.embellished:n.isEmbellishedType(t.type)?t.type:null},e.isOperator=c,e.isRelation=u,e.isPunctuation=p,e.isFence=h,e.isElligibleEmbellishedFence=function(t){return!(!t||!h(t))&&(!t.embellished||d(t))},e.isTableOrMultiline=f,e.tableIsMatrixOrVector=function(t){return!!t&&m(t)&&f(t.childNodes[0])},e.isFencedElement=m,e.tableIsCases=function(t,e){return e.length>0&&s(e[e.length-1],"openfence")},e.tableIsMultiline=function(t){return t.childNodes.every((function(t){return t.childNodes.length<=1}))},e.lineIsLabelled=function(t){return i(t,"line")&&t.contentNodes.length&&s(t.contentNodes[0],"label")},e.isBinomial=function(t){return 2===t.childNodes.length},e.isLimitBase=function t(e){return i(e,"largeop")||i(e,"limboth")||i(e,"limlower")||i(e,"limupper")||i(e,"function")&&s(e,"limit function")||(i(e,"overscore")||i(e,"underscore"))&&t(e.childNodes[0])},e.isSimpleFunctionHead=function(t){return"identifier"===t.type||"latinletter"===t.role||"greekletter"===t.role||"otherletter"===t.role},e.singlePunctAtPosition=function(t,e,r){return 1===e.length&&("punctuation"===t[r].type||"punctuation"===t[r].embellished)&&t[r]===e[0]},e.isSimpleFunction=function(t){return i(t,"identifier")&&s(t,"simple function")},e.isLeftBrace=y,e.isRightBrace=g,e.isSetNode=function(t){return y(t.contentNodes[0])&&g(t.contentNodes[1])},e.illegalSingleton_=["punctuation","punctuated","relseq","multirel","table","multiline","cases","inference"],e.scriptedElement_=["limupper","limlower","limboth","subscript","superscript","underscore","overscore","tensor"],e.isSingletonSetContent=function t(r){const n=r.type;return-1===e.illegalSingleton_.indexOf(n)&&("infixop"!==n||"implicit"===r.role)&&("fenced"===n?"leftright"!==r.role||t(r.childNodes[0]):-1===e.scriptedElement_.indexOf(n)||t(r.childNodes[0]))},e.isNumber=b,e.isUnitCounter=function(t){return b(t)||"vulgar"===t.role||"mixed"===t.role},e.isPureUnit=function(t){const e=t.childNodes;return"unit"===t.role&&(!e.length||"unit"===e[0].role)},e.isImplicit=function(t){return"implicit"===t.role||"unit"===t.role&&!!t.contentNodes.length&&t.contentNodes[0].textContent===n.invisibleTimes()},e.isImplicitOp=function(t){return"infixop"===t.type&&"implicit"===t.role},e.isNeutralFence=v,e.compareNeutralFences=function(t,e){return v(t)&&v(e)&&(0,o.getEmbellishedInner)(t).textContent===(0,o.getEmbellishedInner)(e).textContent},e.elligibleLeftNeutral=function(t){return!!v(t)&&(!t.embellished||"superscript"!==t.type&&"subscript"!==t.type&&("tensor"!==t.type||"empty"===t.childNodes[3].type&&"empty"===t.childNodes[4].type))},e.elligibleRightNeutral=function(t){return!!v(t)&&(!t.embellished||("tensor"!==t.type||"empty"===t.childNodes[1].type&&"empty"===t.childNodes[2].type))},e.isMembership=function(t){return["element","nonelement","reelement","renonelement"].includes(t.role)}},3308:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0});const n=r(5740),o=r(3588),i=r(7516),a=r(6537),s=r(5609),l=r(4795);class c{constructor(){this.funcAppls={},this.factory_=new a.SemanticNodeFactory,i.updateFactory(this.factory_)}static getInstance(){return c.instance=c.instance||new c,c.instance}static tableToMultiline(t){if(s.tableIsMultiline(t)){t.type="multiline";for(let e,r=0;e=t.childNodes[r];r++)c.rowToLine_(e,"multiline");1===t.childNodes.length&&!s.lineIsLabelled(t.childNodes[0])&&s.isFencedElement(t.childNodes[0].childNodes[0])&&c.tableToMatrixOrVector_(c.rewriteFencedLine_(t)),c.binomialForm_(t),c.classifyMultiline(t)}else c.classifyTable(t)}static number(t){"unknown"!==t.type&&"identifier"!==t.type||(t.type="number"),c.numberRole_(t),c.exprFont_(t)}static classifyMultiline(t){let e=0;const r=t.childNodes.length;let n;for(;e<r&&(!(n=t.childNodes[e])||!n.childNodes.length);)e++;if(e>=r)return;const o=n.childNodes[0].role;"unknown"!==o&&t.childNodes.every((function(t){const e=t.childNodes[0];return!e||e.role===o&&(s.isType(e,"relation")||s.isType(e,"relseq"))}))&&(t.role=o)}static classifyTable(t){const e=c.computeColumns_(t);c.classifyByColumns_(t,e,"equality")||c.classifyByColumns_(t,e,"inequality",["equality"])||c.classifyByColumns_(t,e,"arrow")||c.detectCaleyTable(t)}static detectCaleyTable(t){if(!t.mathmlTree)return!1;const e=t.mathmlTree,r=e.getAttribute("columnlines"),n=e.getAttribute("rowlines");return!(!r||!n)&&(!(!c.cayleySpacing(r)||!c.cayleySpacing(n))&&(t.role="cayley",!0))}static cayleySpacing(t){const e=t.split(" ");return("solid"===e[0]||"dashed"===e[0])&&e.slice(1).every((t=>"none"===t))}static proof(t,e,r){const n=c.separateSemantics(e);return c.getInstance().proof(t,n,r)}static findSemantics(t,e,r){const n=null==r?null:r,o=c.getSemantics(t);return!!o&&(!!o[e]&&(null==n||o[e]===n))}static getSemantics(t){const e=t.getAttribute("semantics");return e?c.separateSemantics(e):null}static removePrefix(t){const[,...e]=t.split("_");return e.join("_")}static separateSemantics(t){const e={};return t.split(";").forEach((function(t){const[r,n]=t.split(":");e[c.removePrefix(r)]=n})),e}static matchSpaces_(t,e){for(let r,n=0;r=e[n];n++){const e=t[n].mathmlTree,o=t[n+1].mathmlTree;if(!e||!o)continue;const i=e.nextSibling;if(!i||i===o)continue;const a=c.getSpacer_(i);a&&(r.mathml.push(a),r.mathmlTree=a,r.role="space")}}static getSpacer_(t){if("MSPACE"===n.tagName(t))return t;for(;l.hasEmptyTag(t)&&1===t.childNodes.length;)if(t=t.childNodes[0],"MSPACE"===n.tagName(t))return t;return null}static fenceToPunct_(t){const e=c.FENCE_TO_PUNCT_[t.role];if(e){for(;t.embellished;)t.embellished="punctuation",s.isRole(t,"subsup")||s.isRole(t,"underover")||(t.role=e),t=t.childNodes[0];t.type="punctuation",t.role=e}}static classifyFunction_(t,e){if("appl"===t.type||"bigop"===t.type||"integral"===t.type)return"";if(e[0]&&e[0].textContent===o.functionApplication()){c.getInstance().funcAppls[t.id]=e.shift();let r="simple function";return i.run("simple2prefix",t),"prefix function"!==t.role&&"limit function"!==t.role||(r=t.role),c.propagateFunctionRole_(t,r),"prefix"}const r=c.CLASSIFY_FUNCTION_[t.role];return r||(s.isSimpleFunctionHead(t)?"simple":"")}static propagateFunctionRole_(t,e){if(t){if("infixop"===t.type)return;s.isRole(t,"subsup")||s.isRole(t,"underover")||(t.role=e),c.propagateFunctionRole_(t.childNodes[0],e)}}static getFunctionOp_(t,e){if(e(t))return t;for(let r,n=0;r=t.childNodes[n];n++){const t=c.getFunctionOp_(r,e);if(t)return t}return null}static tableToMatrixOrVector_(t){const e=t.childNodes[0];s.isType(e,"multiline")?c.tableToVector_(t):c.tableToMatrix_(t),t.contentNodes.forEach(e.appendContentNode.bind(e));for(let t,r=0;t=e.childNodes[r];r++)c.assignRoleToRow_(t,c.getComponentRoles_(e));return e.parent=null,e}static tableToVector_(t){const e=t.childNodes[0];e.type="vector",1!==e.childNodes.length?c.binomialForm_(e):c.tableToSquare_(t)}static binomialForm_(t){s.isBinomial(t)&&(t.role="binomial",t.childNodes[0].role="binomial",t.childNodes[1].role="binomial")}static tableToMatrix_(t){const e=t.childNodes[0];e.type="matrix",e.childNodes&&e.childNodes.length>0&&e.childNodes[0].childNodes&&e.childNodes.length===e.childNodes[0].childNodes.length?c.tableToSquare_(t):e.childNodes&&1===e.childNodes.length&&(e.role="rowvector")}static tableToSquare_(t){const e=t.childNodes[0];s.isNeutralFence(t)?e.role="determinant":e.role="squarematrix"}static getComponentRoles_(t){const e=t.role;return e&&"unknown"!==e?e:t.type.toLowerCase()||"unknown"}static tableToCases_(t,e){for(let e,r=0;e=t.childNodes[r];r++)c.assignRoleToRow_(e,"cases");return t.type="cases",t.appendContentNode(e),s.tableIsMultiline(t)&&c.binomialForm_(t),t}static rewriteFencedLine_(t){const e=t.childNodes[0],r=t.childNodes[0].childNodes[0],n=t.childNodes[0].childNodes[0].childNodes[0];return r.parent=t.parent,t.parent=r,n.parent=e,r.childNodes=[t],e.childNodes=[n],r}static rowToLine_(t,e){const r=e||"unknown";s.isType(t,"row")&&(t.type="line",t.role=r,1===t.childNodes.length&&s.isType(t.childNodes[0],"cell")&&(t.childNodes=t.childNodes[0].childNodes,t.childNodes.forEach((function(e){e.parent=t}))))}static assignRoleToRow_(t,e){s.isType(t,"line")?t.role=e:s.isType(t,"row")&&(t.role=e,t.childNodes.forEach((function(t){s.isType(t,"cell")&&(t.role=e)})))}static nextSeparatorFunction_(t){let e;if(t){if(t.match(/^\s+$/))return null;e=t.replace(/\s/g,"").split("").filter((function(t){return t}))}else e=[","];return function(){return e.length>1?e.shift():e[0]}}static numberRole_(t){if("unknown"!==t.role)return;const e=[...t.textContent].filter((t=>t.match(/[^\s]/))),r=e.map(o.lookupMeaning);if(r.every((function(t){return"number"===t.type&&"integer"===t.role||"punctuation"===t.type&&"comma"===t.role})))return t.role="integer",void("0"===e[0]&&t.addAnnotation("general","basenumber"));r.every((function(t){return"number"===t.type&&"integer"===t.role||"punctuation"===t.type}))?t.role="float":t.role="othernumber"}static exprFont_(t){if("unknown"!==t.font)return;const e=[...t.textContent].map(o.lookupMeaning).reduce((function(t,e){return t&&e.font&&"unknown"!==e.font&&e.font!==t?"unknown"===t?e.font:null:t}),"unknown");e&&(t.font=e)}static purgeFences_(t){const e=t.rel,r=t.comp,n=[],o=[];for(;e.length>0;){const t=e.shift();let i=r.shift();s.isElligibleEmbellishedFence(t)?(n.push(t),o.push(i)):(c.fenceToPunct_(t),i.push(t),i=i.concat(r.shift()),r.unshift(i))}return o.push(r.shift()),{rel:n,comp:o}}static rewriteFencedNode_(t){const e=t.contentNodes[0],r=t.contentNodes[1];let n=c.rewriteFence_(t,e);return t.contentNodes[0]=n.fence,n=c.rewriteFence_(n.node,r),t.contentNodes[1]=n.fence,t.contentNodes[0].parent=t,t.contentNodes[1].parent=t,n.node.parent=null,n.node}static rewriteFence_(t,e){if(!e.embellished)return{node:t,fence:e};const r=e.childNodes[0],n=c.rewriteFence_(t,r);return s.isType(e,"superscript")||s.isType(e,"subscript")||s.isType(e,"tensor")?(s.isRole(e,"subsup")||(e.role=t.role),r!==n.node&&(e.replaceChild(r,n.node),r.parent=t),c.propagateFencePointer_(e,r),{node:e,fence:n.fence}):(e.replaceChild(r,n.fence),e.mathmlTree&&-1===e.mathml.indexOf(e.mathmlTree)&&e.mathml.push(e.mathmlTree),{node:n.node,fence:e})}static propagateFencePointer_(t,e){t.fencePointer=e.fencePointer||e.id.toString(),t.embellished=null}static classifyByColumns_(t,e,r,n){return!!(3===e.length&&c.testColumns_(e,1,(t=>c.isPureRelation_(t,r)))||2===e.length&&(c.testColumns_(e,1,(t=>c.isEndRelation_(t,r)||c.isPureRelation_(t,r)))||c.testColumns_(e,0,(t=>c.isEndRelation_(t,r,!0)||c.isPureRelation_(t,r)))))&&(t.role=r,!0)}static isEndRelation_(t,e,r){const n=r?t.childNodes.length-1:0;return s.isType(t,"relseq")&&s.isRole(t,e)&&s.isType(t.childNodes[n],"empty")}static isPureRelation_(t,e){return s.isType(t,"relation")&&s.isRole(t,e)}static computeColumns_(t){const e=[];for(let r,n=0;r=t.childNodes[n];n++)for(let t,n=0;t=r.childNodes[n];n++){e[n]?e[n].push(t):e[n]=[t]}return e}static testColumns_(t,e,r){const n=t[e];return!!n&&(n.some((function(t){return t.childNodes.length&&r(t.childNodes[0])}))&&n.every((function(t){return!t.childNodes.length||r(t.childNodes[0])})))}setNodeFactory(t){c.getInstance().factory_=t,i.updateFactory(c.getInstance().factory_)}getNodeFactory(){return c.getInstance().factory_}identifierNode(t,e,r){if("MathML-Unit"===r)t.type="identifier",t.role="unit";else if(!e&&1===t.textContent.length&&("integer"===t.role||"latinletter"===t.role||"greekletter"===t.role)&&"normal"===t.font)return t.font="italic",i.run("simpleNamedFunction",t);return"unknown"===t.type&&(t.type="identifier"),c.exprFont_(t),i.run("simpleNamedFunction",t)}implicitNode(t){if(t=c.getInstance().getMixedNumbers_(t),1===(t=c.getInstance().combineUnits_(t)).length)return t[0];const e=c.getInstance().implicitNode_(t);return i.run("combine_juxtaposition",e)}text(t,e){return c.exprFont_(t),t.type="text","MS"===e?(t.role="string",t):"MSPACE"===e||t.textContent.match(/^\s*$/)?(t.role="space",t):t}row(t){return 0===(t=t.filter((function(t){return!s.isType(t,"empty")}))).length?c.getInstance().factory_.makeEmptyNode():(t=c.getInstance().getFencesInRow_(t),t=c.getInstance().tablesInRow(t),t=c.getInstance().getPunctuationInRow_(t),t=c.getInstance().getTextInRow_(t),t=c.getInstance().getFunctionsInRow_(t),c.getInstance().relationsInRow_(t))}limitNode(t,e){if(!e.length)return c.getInstance().factory_.makeEmptyNode();let r,n=e[0],o="unknown";if(!e[1])return n;if(s.isLimitBase(n)){r=c.MML_TO_LIMIT_[t];const i=r.length;if(o=r.type,e=e.slice(0,r.length+1),1===i&&s.isAccent(e[1])||2===i&&s.isAccent(e[1])&&s.isAccent(e[2]))return r=c.MML_TO_BOUNDS_[t],c.getInstance().accentNode_(n,e,r.type,r.length,r.accent);if(2===i){if(s.isAccent(e[1]))return n=c.getInstance().accentNode_(n,[n,e[1]],{MSUBSUP:"subscript",MUNDEROVER:"underscore"}[t],1,!0),e[2]?c.getInstance().makeLimitNode_(n,[n,e[2]],null,"limupper"):n;if(e[2]&&s.isAccent(e[2]))return n=c.getInstance().accentNode_(n,[n,e[2]],{MSUBSUP:"superscript",MUNDEROVER:"overscore"}[t],1,!0),c.getInstance().makeLimitNode_(n,[n,e[1]],null,"limlower");e[i]||(o="limlower")}return c.getInstance().makeLimitNode_(n,e,null,o)}return r=c.MML_TO_BOUNDS_[t],c.getInstance().accentNode_(n,e,r.type,r.length,r.accent)}tablesInRow(t){let e=l.partitionNodes(t,s.tableIsMatrixOrVector),r=[];for(let t,n=0;t=e.rel[n];n++)r=r.concat(e.comp.shift()),r.push(c.tableToMatrixOrVector_(t));r=r.concat(e.comp.shift()),e=l.partitionNodes(r,s.isTableOrMultiline),r=[];for(let t,n=0;t=e.rel[n];n++){const n=e.comp.shift();s.tableIsCases(t,n)&&c.tableToCases_(t,n.pop()),r=r.concat(n),r.push(t)}return r.concat(e.comp.shift())}mfenced(t,e,r,n){if(r&&n.length>0){const t=c.nextSeparatorFunction_(r),e=[n.shift()];n.forEach((r=>{e.push(c.getInstance().factory_.makeContentNode(t())),e.push(r)})),n=e}return t&&e?c.getInstance().horizontalFencedNode_(c.getInstance().factory_.makeContentNode(t),c.getInstance().factory_.makeContentNode(e),n):(t&&n.unshift(c.getInstance().factory_.makeContentNode(t)),e&&n.push(c.getInstance().factory_.makeContentNode(e)),c.getInstance().row(n))}fractionLikeNode(t,e,r,n){let o;if(!n&&l.isZeroLength(r)){const r=c.getInstance().factory_.makeBranchNode("line",[t],[]),n=c.getInstance().factory_.makeBranchNode("line",[e],[]);return o=c.getInstance().factory_.makeBranchNode("multiline",[r,n],[]),c.binomialForm_(o),c.classifyMultiline(o),o}return o=c.getInstance().fractionNode_(t,e),n&&o.addAnnotation("general","bevelled"),o}tensor(t,e,r,n,o){const i=c.getInstance().factory_.makeBranchNode("tensor",[t,c.getInstance().scriptNode_(e,"leftsub"),c.getInstance().scriptNode_(r,"leftsuper"),c.getInstance().scriptNode_(n,"rightsub"),c.getInstance().scriptNode_(o,"rightsuper")],[]);return i.role=t.role,i.embellished=s.isEmbellished(t),i}pseudoTensor(t,e,r){const n=t=>!s.isType(t,"empty"),o=e.filter(n).length,i=r.filter(n).length;if(!o&&!i)return t;const a=o?i?"MSUBSUP":"MSUB":"MSUP",l=[t];return o&&l.push(c.getInstance().scriptNode_(e,"rightsub",!0)),i&&l.push(c.getInstance().scriptNode_(r,"rightsuper",!0)),c.getInstance().limitNode(a,l)}font(t){const e=c.MATHJAX_FONTS[t];return e||t}proof(t,e,r){if(e.inference||e.axiom||console.log("Noise"),e.axiom){const e=c.getInstance().cleanInference(t.childNodes),n=e.length?c.getInstance().factory_.makeBranchNode("inference",r(e),[]):c.getInstance().factory_.makeEmptyNode();return n.role="axiom",n.mathmlTree=t,n}const n=c.getInstance().inference(t,e,r);return e.proof&&(n.role="proof",n.childNodes[0].role="final"),n}inference(t,e,r){if(e.inferenceRule){const e=c.getInstance().getFormulas(t,[],r);return c.getInstance().factory_.makeBranchNode("inference",[e.conclusion,e.premises],[])}const o=e.labelledRule,i=n.toArray(t.childNodes),a=[];"left"!==o&&"both"!==o||a.push(c.getInstance().getLabel(t,i,r,"left")),"right"!==o&&"both"!==o||a.push(c.getInstance().getLabel(t,i,r,"right"));const s=c.getInstance().getFormulas(t,i,r),l=c.getInstance().factory_.makeBranchNode("inference",[s.conclusion,s.premises],a);return l.mathmlTree=t,l}getLabel(t,e,r,o){const i=c.getInstance().findNestedRow(e,"prooflabel",o),a=c.getInstance().factory_.makeBranchNode("rulelabel",r(n.toArray(i.childNodes)),[]);return a.role=o,a.mathmlTree=i,a}getFormulas(t,e,r){const o=e.length?c.getInstance().findNestedRow(e,"inferenceRule"):t,i="up"===c.getSemantics(o).inferenceRule,a=i?o.childNodes[1]:o.childNodes[0],s=i?o.childNodes[0]:o.childNodes[1],l=a.childNodes[0].childNodes[0],u=n.toArray(l.childNodes[0].childNodes),p=[];let h=1;for(const t of u)h%2&&p.push(t.childNodes[0]),h++;const d=r(p),f=r(n.toArray(s.childNodes[0].childNodes))[0],m=c.getInstance().factory_.makeBranchNode("premises",d,[]);m.mathmlTree=l;const y=c.getInstance().factory_.makeBranchNode("conclusion",[f],[]);return y.mathmlTree=s.childNodes[0].childNodes[0],{conclusion:y,premises:m}}findNestedRow(t,e,r){return c.getInstance().findNestedRow_(t,e,0,r)}cleanInference(t){return n.toArray(t).filter((function(t){return"MSPACE"!==n.tagName(t)}))}operatorNode(t){return"unknown"===t.type&&(t.type="operator"),i.run("multioperator",t)}implicitNode_(t){const e=c.getInstance().factory_.makeMultipleContentNodes(t.length-1,o.invisibleTimes());c.matchSpaces_(t,e);const r=c.getInstance().infixNode_(t,e[0]);return r.role="implicit",e.forEach((function(t){t.parent=r})),r.contentNodes=e,r}infixNode_(t,e){const r=c.getInstance().factory_.makeBranchNode("infixop",t,[e],l.getEmbellishedInner(e).textContent);return r.role=e.role,i.run("propagateSimpleFunction",r)}explicitMixed_(t){const e=l.partitionNodes(t,(function(t){return t.textContent===o.invisiblePlus()}));if(!e.rel.length)return t;let r=[];for(let t,n=0;t=e.rel[n];n++){const o=e.comp[n],i=e.comp[n+1],a=o.length-1;if(o[a]&&i[0]&&s.isType(o[a],"number")&&!s.isRole(o[a],"mixed")&&s.isType(i[0],"fraction")){const t=c.getInstance().factory_.makeBranchNode("number",[o[a],i[0]],[]);t.role="mixed",r=r.concat(o.slice(0,a)),r.push(t),i.shift()}else r=r.concat(o),r.push(t)}return r.concat(e.comp[e.comp.length-1])}concatNode_(t,e,r){if(0===e.length)return t;const n=e.map((function(t){return l.getEmbellishedInner(t).textContent})).join(" "),o=c.getInstance().factory_.makeBranchNode(r,[t],e,n);return e.length>1&&(o.role="multiop"),o}prefixNode_(t,e){const r=l.partitionNodes(e,(t=>s.isRole(t,"subtraction")));let n=c.getInstance().concatNode_(t,r.comp.pop(),"prefixop");for(1===n.contentNodes.length&&"addition"===n.contentNodes[0].role&&"+"===n.contentNodes[0].textContent&&(n.role="positive");r.rel.length>0;)n=c.getInstance().concatNode_(n,[r.rel.pop()],"prefixop"),n.role="negative",n=c.getInstance().concatNode_(n,r.comp.pop(),"prefixop");return n}postfixNode_(t,e){return e.length?c.getInstance().concatNode_(t,e,"postfixop"):t}combineUnits_(t){const e=l.partitionNodes(t,(function(t){return!s.isRole(t,"unit")}));if(t.length===e.rel.length)return e.rel;const r=[];let n,o;do{const t=e.comp.shift();n=e.rel.shift();let i=null;o=r.pop(),o&&(t.length&&s.isUnitCounter(o)?t.unshift(o):r.push(o)),1===t.length&&(i=t.pop()),t.length>1&&(i=c.getInstance().implicitNode_(t),i.role="unit"),i&&r.push(i),n&&r.push(n)}while(n);return r}getMixedNumbers_(t){const e=l.partitionNodes(t,(function(t){return s.isType(t,"fraction")&&s.isRole(t,"vulgar")}));if(!e.rel.length)return t;let r=[];for(let t,n=0;t=e.rel[n];n++){const o=e.comp[n],i=o.length-1;if(o[i]&&s.isType(o[i],"number")&&(s.isRole(o[i],"integer")||s.isRole(o[i],"float"))){const e=c.getInstance().factory_.makeBranchNode("number",[o[i],t],[]);e.role="mixed",r=r.concat(o.slice(0,i)),r.push(e)}else r=r.concat(o),r.push(t)}return r.concat(e.comp[e.comp.length-1])}getTextInRow_(t){if(t.length<=1)return t;const e=l.partitionNodes(t,(t=>s.isType(t,"text")));if(0===e.rel.length)return t;const r=[];let n=e.comp[0];n.length>0&&r.push(c.getInstance().row(n));for(let t,o=0;t=e.rel[o];o++)r.push(t),n=e.comp[o+1],n.length>0&&r.push(c.getInstance().row(n));return[c.getInstance().dummyNode_(r)]}relationsInRow_(t){const e=l.partitionNodes(t,s.isRelation),r=e.rel[0];if(!r)return c.getInstance().operationsInRow_(t);if(1===t.length)return t[0];const n=e.comp.map(c.getInstance().operationsInRow_);let o;return e.rel.some((function(t){return!t.equals(r)}))?(o=c.getInstance().factory_.makeBranchNode("multirel",n,e.rel),e.rel.every((function(t){return t.role===r.role}))&&(o.role=r.role),o):(o=c.getInstance().factory_.makeBranchNode("relseq",n,e.rel,l.getEmbellishedInner(r).textContent),o.role=r.role,o)}operationsInRow_(t){if(0===t.length)return c.getInstance().factory_.makeEmptyNode();if(1===(t=c.getInstance().explicitMixed_(t)).length)return t[0];const e=[];for(;t.length>0&&s.isOperator(t[0]);)e.push(t.shift());if(0===t.length)return c.getInstance().prefixNode_(e.pop(),e);if(1===t.length)return c.getInstance().prefixNode_(t[0],e);t=i.run("convert_juxtaposition",t);const r=l.sliceNodes(t,s.isOperator),n=c.getInstance().prefixNode_(c.getInstance().implicitNode(r.head),e);return r.div?c.getInstance().operationsTree_(r.tail,n,r.div):n}operationsTree_(t,e,r,n){const o=n||[];if(0===t.length){if(o.unshift(r),"infixop"===e.type){const t=c.getInstance().postfixNode_(e.childNodes.pop(),o);return e.appendChild(t),e}return c.getInstance().postfixNode_(e,o)}const i=l.sliceNodes(t,s.isOperator);if(0===i.head.length)return o.push(i.div),c.getInstance().operationsTree_(i.tail,e,r,o);const a=c.getInstance().prefixNode_(c.getInstance().implicitNode(i.head),o),u=c.getInstance().appendOperand_(e,r,a);return i.div?c.getInstance().operationsTree_(i.tail,u,i.div,[]):u}appendOperand_(t,e,r){if("infixop"!==t.type)return c.getInstance().infixNode_([t,r],e);const n=c.getInstance().appendDivisionOp_(t,e,r);return n||(c.getInstance().appendExistingOperator_(t,e,r)?t:"multiplication"===e.role?c.getInstance().appendMultiplicativeOp_(t,e,r):c.getInstance().appendAdditiveOp_(t,e,r))}appendDivisionOp_(t,e,r){return"division"===e.role?s.isImplicit(t)?c.getInstance().infixNode_([t,r],e):c.getInstance().appendLastOperand_(t,e,r):"division"===t.role?c.getInstance().infixNode_([t,r],e):null}appendLastOperand_(t,e,r){let n=t,o=t.childNodes[t.childNodes.length-1];for(;o&&"infixop"===o.type&&!s.isImplicit(o);)n=o,o=n.childNodes[t.childNodes.length-1];const i=c.getInstance().infixNode_([n.childNodes.pop(),r],e);return n.appendChild(i),t}appendMultiplicativeOp_(t,e,r){if(s.isImplicit(t))return c.getInstance().infixNode_([t,r],e);let n=t,o=t.childNodes[t.childNodes.length-1];for(;o&&"infixop"===o.type&&!s.isImplicit(o);)n=o,o=n.childNodes[t.childNodes.length-1];const i=c.getInstance().infixNode_([n.childNodes.pop(),r],e);return n.appendChild(i),t}appendAdditiveOp_(t,e,r){return c.getInstance().infixNode_([t,r],e)}appendExistingOperator_(t,e,r){return!(!t||"infixop"!==t.type||s.isImplicit(t))&&(t.contentNodes[0].equals(e)?(t.appendContentNode(e),t.appendChild(r),!0):c.getInstance().appendExistingOperator_(t.childNodes[t.childNodes.length-1],e,r))}getFencesInRow_(t){let e=l.partitionNodes(t,s.isFence);e=c.purgeFences_(e);const r=e.comp.shift();return c.getInstance().fences_(e.rel,e.comp,[],[r])}fences_(t,e,r,n){if(0===t.length&&0===r.length)return n[0];const o=t=>s.isRole(t,"open");if(0===t.length){const t=n.shift();for(;r.length>0;){if(o(r[0])){const e=r.shift();c.fenceToPunct_(e),t.push(e)}else{const e=l.sliceNodes(r,o),i=e.head.length-1,a=c.getInstance().neutralFences_(e.head,n.slice(0,i));n=n.slice(i),t.push(...a),e.div&&e.tail.unshift(e.div),r=e.tail}t.push(...n.shift())}return t}const i=r[r.length-1],a=t[0].role;if("open"===a||s.isNeutralFence(t[0])&&(!i||!s.compareNeutralFences(t[0],i))){r.push(t.shift());const o=e.shift();return o&&n.push(o),c.getInstance().fences_(t,e,r,n)}if(i&&"close"===a&&"open"===i.role){const o=c.getInstance().horizontalFencedNode_(r.pop(),t.shift(),n.pop());return n.push(n.pop().concat([o],e.shift())),c.getInstance().fences_(t,e,r,n)}if(i&&s.compareNeutralFences(t[0],i)){if(!s.elligibleLeftNeutral(i)||!s.elligibleRightNeutral(t[0])){r.push(t.shift());const o=e.shift();return o&&n.push(o),c.getInstance().fences_(t,e,r,n)}const o=c.getInstance().horizontalFencedNode_(r.pop(),t.shift(),n.pop());return n.push(n.pop().concat([o],e.shift())),c.getInstance().fences_(t,e,r,n)}if(i&&"close"===a&&s.isNeutralFence(i)&&r.some(o)){const i=l.sliceNodes(r,o,!0),a=n.pop(),s=n.length-i.tail.length+1,u=c.getInstance().neutralFences_(i.tail,n.slice(s));n=n.slice(0,s);const p=c.getInstance().horizontalFencedNode_(i.div,t.shift(),n.pop().concat(u,a));return n.push(n.pop().concat([p],e.shift())),c.getInstance().fences_(t,e,i.head,n)}const u=t.shift();return c.fenceToPunct_(u),n.push(n.pop().concat([u],e.shift())),c.getInstance().fences_(t,e,r,n)}neutralFences_(t,e){if(0===t.length)return t;if(1===t.length)return c.fenceToPunct_(t[0]),t;const r=t.shift();if(!s.elligibleLeftNeutral(r)){c.fenceToPunct_(r);const n=e.shift();return n.unshift(r),n.concat(c.getInstance().neutralFences_(t,e))}const n=l.sliceNodes(t,(function(t){return s.compareNeutralFences(t,r)}));if(!n.div){c.fenceToPunct_(r);const n=e.shift();return n.unshift(r),n.concat(c.getInstance().neutralFences_(t,e))}if(!s.elligibleRightNeutral(n.div))return c.fenceToPunct_(n.div),t.unshift(r),c.getInstance().neutralFences_(t,e);const o=c.getInstance().combineFencedContent_(r,n.div,n.head,e);if(n.tail.length>0){const t=o.shift(),e=c.getInstance().neutralFences_(n.tail,o);return t.concat(e)}return o[0]}combineFencedContent_(t,e,r,n){if(0===r.length){const r=c.getInstance().horizontalFencedNode_(t,e,n.shift());return n.length>0?n[0].unshift(r):n=[[r]],n}const o=n.shift(),i=r.length-1,a=n.slice(0,i),s=(n=n.slice(i)).shift(),l=c.getInstance().neutralFences_(r,a);o.push(...l),o.push(...s);const u=c.getInstance().horizontalFencedNode_(t,e,o);return n.length>0?n[0].unshift(u):n=[[u]],n}horizontalFencedNode_(t,e,r){const n=c.getInstance().row(r);let o=c.getInstance().factory_.makeBranchNode("fenced",[n],[t,e]);return"open"===t.role?(c.getInstance().classifyHorizontalFence_(o),o=i.run("propagateComposedFunction",o)):o.role=t.role,o=i.run("detect_cycle",o),c.rewriteFencedNode_(o)}classifyHorizontalFence_(t){t.role="leftright";const e=t.childNodes;if(!s.isSetNode(t)||e.length>1)return;if(0===e.length||"empty"===e[0].type)return void(t.role="set empty");const r=e[0].type;if(1===e.length&&s.isSingletonSetContent(e[0]))return void(t.role="set singleton");const n=e[0].role;if("punctuated"===r&&"sequence"===n){if("comma"!==e[0].contentNodes[0].role)return 1!==e[0].contentNodes.length||"vbar"!==e[0].contentNodes[0].role&&"colon"!==e[0].contentNodes[0].role?void 0:(t.role="set extended",void c.getInstance().setExtension_(t));t.role="set collection"}}setExtension_(t){const e=t.childNodes[0].childNodes[0];e&&"infixop"===e.type&&1===e.contentNodes.length&&s.isMembership(e.contentNodes[0])&&(e.addAnnotation("set","intensional"),e.contentNodes[0].addAnnotation("set","intensional"))}getPunctuationInRow_(t){if(t.length<=1)return t;const e=t=>{const e=t.type;return"punctuation"===e||"text"===e||"operator"===e||"relation"===e},r=l.partitionNodes(t,(function(r){if(!s.isPunctuation(r))return!1;if(s.isPunctuation(r)&&!s.isRole(r,"ellipsis"))return!0;const n=t.indexOf(r);if(0===n)return!t[1]||!e(t[1]);const o=t[n-1];if(n===t.length-1)return!e(o);const i=t[n+1];return!e(o)||!e(i)}));if(0===r.rel.length)return t;const n=[];let o=r.comp.shift();o.length>0&&n.push(c.getInstance().row(o));let i=0;for(;r.comp.length>0;)n.push(r.rel[i++]),o=r.comp.shift(),o.length>0&&n.push(c.getInstance().row(o));return[c.getInstance().punctuatedNode_(n,r.rel)]}punctuatedNode_(t,e){const r=c.getInstance().factory_.makeBranchNode("punctuated",t,e);if(e.length===t.length){const t=e[0].role;if("unknown"!==t&&e.every((function(e){return e.role===t})))return r.role=t,r}return s.singlePunctAtPosition(t,e,0)?r.role="startpunct":s.singlePunctAtPosition(t,e,t.length-1)?r.role="endpunct":e.every((t=>s.isRole(t,"dummy")))?r.role="text":e.every((t=>s.isRole(t,"space")))?r.role="space":r.role="sequence",r}dummyNode_(t){const e=c.getInstance().factory_.makeMultipleContentNodes(t.length-1,o.invisibleComma());return e.forEach((function(t){t.role="dummy"})),c.getInstance().punctuatedNode_(t,e)}accentRole_(t,e){if(!s.isAccent(t))return!1;const r=t.textContent,n=o.lookupSecondary("bar",r)||o.lookupSecondary("tilde",r)||t.role;return t.role="underscore"===e?"underaccent":"overaccent",t.addAnnotation("accent",n),!0}accentNode_(t,e,r,n,o){const i=(e=e.slice(0,n+1))[1],a=e[2];let s;if(!o&&a&&(s=c.getInstance().factory_.makeBranchNode("subscript",[t,i],[]),s.role="subsup",e=[s,a],r="superscript"),o){const n=c.getInstance().accentRole_(i,r);if(a){c.getInstance().accentRole_(a,"overscore")&&!n?(s=c.getInstance().factory_.makeBranchNode("overscore",[t,a],[]),e=[s,i],r="underscore"):(s=c.getInstance().factory_.makeBranchNode("underscore",[t,i],[]),e=[s,a],r="overscore"),s.role="underover"}}return c.getInstance().makeLimitNode_(t,e,s,r)}makeLimitNode_(t,e,r,n){if("limupper"===n&&"limlower"===t.type)return t.childNodes.push(e[1]),e[1].parent=t,t.type="limboth",t;if("limlower"===n&&"limupper"===t.type)return t.childNodes.splice(1,-1,e[1]),e[1].parent=t,t.type="limboth",t;const o=c.getInstance().factory_.makeBranchNode(n,e,[]),i=s.isEmbellished(t);return r&&(r.embellished=i),o.embellished=i,o.role=t.role,o}getFunctionsInRow_(t,e){const r=e||[];if(0===t.length)return r;const n=t.shift(),o=c.classifyFunction_(n,t);if(!o)return r.push(n),c.getInstance().getFunctionsInRow_(t,r);const i=c.getInstance().getFunctionsInRow_(t,[]),a=c.getInstance().getFunctionArgs_(n,i,o);return r.concat(a)}getFunctionArgs_(t,e,r){let n,o,i;switch(r){case"integral":{const r=c.getInstance().getIntegralArgs_(e);if(!r.intvar&&!r.integrand.length)return r.rest.unshift(t),r.rest;const n=c.getInstance().row(r.integrand);return i=c.getInstance().integralNode_(t,n,r.intvar),r.rest.unshift(i),r.rest}case"prefix":if(e[0]&&"fenced"===e[0].type){const r=e.shift();return s.isNeutralFence(r)||(r.role="leftright"),i=c.getInstance().functionNode_(t,r),e.unshift(i),e}if(n=l.sliceNodes(e,s.isPrefixFunctionBoundary),n.head.length)o=c.getInstance().row(n.head),n.div&&n.tail.unshift(n.div);else{if(!n.div||!s.isType(n.div,"appl"))return e.unshift(t),e;o=n.div}return i=c.getInstance().functionNode_(t,o),n.tail.unshift(i),n.tail;case"bigop":return n=l.sliceNodes(e,s.isBigOpBoundary),n.head.length?(o=c.getInstance().row(n.head),i=c.getInstance().bigOpNode_(t,o),n.div&&n.tail.unshift(n.div),n.tail.unshift(i),n.tail):(e.unshift(t),e);default:{if(0===e.length)return[t];const r=e[0];return"fenced"===r.type&&!s.isNeutralFence(r)&&s.isSimpleFunctionScope(r)?(r.role="leftright",c.propagateFunctionRole_(t,"simple function"),i=c.getInstance().functionNode_(t,e.shift()),e.unshift(i),e):(e.unshift(t),e)}}}getIntegralArgs_(t,e=[]){if(0===t.length)return{integrand:e,intvar:null,rest:t};const r=t[0];if(s.isGeneralFunctionBoundary(r))return{integrand:e,intvar:null,rest:t};if(s.isIntegralDxBoundarySingle(r))return r.role="integral",{integrand:e,intvar:r,rest:t.slice(1)};if(t[1]&&s.isIntegralDxBoundary(r,t[1])){const n=c.getInstance().prefixNode_(t[1],[r]);return n.role="integral",{integrand:e,intvar:n,rest:t.slice(2)}}return e.push(t.shift()),c.getInstance().getIntegralArgs_(t,e)}functionNode_(t,e){const r=c.getInstance().factory_.makeContentNode(o.functionApplication()),n=c.getInstance().funcAppls[t.id];n&&(r.mathmlTree=n.mathmlTree,r.mathml=n.mathml,r.annotation=n.annotation,r.attributes=n.attributes,delete c.getInstance().funcAppls[t.id]),r.type="punctuation",r.role="application";const i=c.getFunctionOp_(t,(function(t){return s.isType(t,"function")||s.isType(t,"identifier")&&s.isRole(t,"simple function")}));return c.getInstance().functionalNode_("appl",[t,e],i,[r])}bigOpNode_(t,e){const r=c.getFunctionOp_(t,(t=>s.isType(t,"largeop")));return c.getInstance().functionalNode_("bigop",[t,e],r,[])}integralNode_(t,e,r){e=e||c.getInstance().factory_.makeEmptyNode(),r=r||c.getInstance().factory_.makeEmptyNode();const n=c.getFunctionOp_(t,(t=>s.isType(t,"largeop")));return c.getInstance().functionalNode_("integral",[t,e,r],n,[])}functionalNode_(t,e,r,n){const o=e[0];let i;r&&(i=r.parent,n.push(r));const a=c.getInstance().factory_.makeBranchNode(t,e,n);return a.role=o.role,i&&(r.parent=i),a}fractionNode_(t,e){const r=c.getInstance().factory_.makeBranchNode("fraction",[t,e],[]);return r.role=r.childNodes.every((function(t){return s.isType(t,"number")&&s.isRole(t,"integer")}))?"vulgar":r.childNodes.every(s.isPureUnit)?"unit":"division",i.run("propagateSimpleFunction",r)}scriptNode_(t,e,r){let n;switch(t.length){case 0:n=c.getInstance().factory_.makeEmptyNode();break;case 1:if(n=t[0],r)return n;break;default:n=c.getInstance().dummyNode_(t)}return n.role=e,n}findNestedRow_(t,e,r,o){if(r>3)return null;for(let i,a=0;i=t[a];a++){const t=n.tagName(i);if("MSPACE"!==t){if("MROW"===t)return c.getInstance().findNestedRow_(n.toArray(i.childNodes),e,r+1,o);if(c.findSemantics(i,e,o))return i}}return null}}e.default=c,c.FENCE_TO_PUNCT_={metric:"metric",neutral:"vbar",open:"openfence",close:"closefence"},c.MML_TO_LIMIT_={MSUB:{type:"limlower",length:1},MUNDER:{type:"limlower",length:1},MSUP:{type:"limupper",length:1},MOVER:{type:"limupper",length:1},MSUBSUP:{type:"limboth",length:2},MUNDEROVER:{type:"limboth",length:2}},c.MML_TO_BOUNDS_={MSUB:{type:"subscript",length:1,accent:!1},MSUP:{type:"superscript",length:1,accent:!1},MSUBSUP:{type:"subscript",length:2,accent:!1},MUNDER:{type:"underscore",length:1,accent:!0},MOVER:{type:"overscore",length:1,accent:!0},MUNDEROVER:{type:"underscore",length:2,accent:!0}},c.CLASSIFY_FUNCTION_={integral:"integral",sum:"bigop","prefix function":"prefix","limit function":"prefix","simple function":"prefix","composed function":"prefix"},c.MATHJAX_FONTS={"-tex-caligraphic":"caligraphic","-tex-caligraphic-bold":"caligraphic-bold","-tex-calligraphic":"caligraphic","-tex-calligraphic-bold":"caligraphic-bold","-tex-oldstyle":"oldstyle","-tex-oldstyle-bold":"oldstyle-bold","-tex-mathit":"italic"}},5656:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.SemanticSkeleton=void 0;const n=r(707),o=r(5274),i=r(2298);class a{constructor(t){this.parents=null,this.levelsMap=null,t=0===t?t:t||[],this.array=t}static fromTree(t){return a.fromNode(t.root)}static fromNode(t){return new a(a.fromNode_(t))}static fromString(t){return new a(a.fromString_(t))}static simpleCollapseStructure(t){return"number"==typeof t}static contentCollapseStructure(t){return!!t&&!a.simpleCollapseStructure(t)&&"c"===t[0]}static interleaveIds(t,e){return n.interleaveLists(a.collapsedLeafs(t),a.collapsedLeafs(e))}static collapsedLeafs(...t){return t.reduce(((t,e)=>{return t.concat((r=e,a.simpleCollapseStructure(r)?[r]:(r=r,a.contentCollapseStructure(r[1])?r.slice(2):r.slice(1))));var r}),[])}static fromStructure(t,e){return new a(a.tree_(t,e.root))}static combineContentChildren(t,e,r){switch(t.type){case"relseq":case"infixop":case"multirel":return n.interleaveLists(r,e);case"prefixop":return e.concat(r);case"postfixop":return r.concat(e);case"fenced":return r.unshift(e[0]),r.push(e[1]),r;case"appl":return[r[0],e[0],r[1]];case"root":return[r[1],r[0]];case"row":case"line":return e.length&&r.unshift(e[0]),r;default:return r}}static makeSexp_(t){return a.simpleCollapseStructure(t)?t.toString():a.contentCollapseStructure(t)?"(c "+t.slice(1).map(a.makeSexp_).join(" ")+")":"("+t.map(a.makeSexp_).join(" ")+")"}static fromString_(t){let e=t.replace(/\(/g,"[");return e=e.replace(/\)/g,"]"),e=e.replace(/ /g,","),e=e.replace(/c/g,'"c"'),JSON.parse(e)}static fromNode_(t){if(!t)return[];const e=t.contentNodes;let r;e.length&&(r=e.map(a.fromNode_),r.unshift("c"));const n=t.childNodes;if(!n.length)return e.length?[t.id,r]:t.id;const o=n.map(a.fromNode_);return e.length&&o.unshift(r),o.unshift(t.id),o}static tree_(t,e){if(!e)return[];if(!e.childNodes.length)return e.id;const r=e.id,n=[r],s=o.evalXPath(`.//self::*[@${i.Attribute.ID}=${r}]`,t)[0],l=a.combineContentChildren(e,e.contentNodes.map((function(t){return t})),e.childNodes.map((function(t){return t})));s&&a.addOwns_(s,l);for(let e,r=0;e=l[r];r++)n.push(a.tree_(t,e));return n}static addOwns_(t,e){const r=t.getAttribute(i.Attribute.COLLAPSED),n=r?a.realLeafs_(a.fromString(r).array):e.map((t=>t.id));t.setAttribute(i.Attribute.OWNS,n.join(" "))}static realLeafs_(t){if(a.simpleCollapseStructure(t))return[t];if(a.contentCollapseStructure(t))return[];t=t;let e=[];for(let r=1;r<t.length;r++)e=e.concat(a.realLeafs_(t[r]));return e}populate(){this.parents&&this.levelsMap||(this.parents={},this.levelsMap={},this.populate_(this.array,this.array,[]))}toString(){return a.makeSexp_(this.array)}populate_(t,e,r){if(a.simpleCollapseStructure(t))return t=t,this.levelsMap[t]=e,void(this.parents[t]=t===r[0]?r.slice(1):r);const n=a.contentCollapseStructure(t)?t.slice(1):t,o=[n[0]].concat(r);for(let e=0,r=n.length;e<r;e++){const r=n[e];this.populate_(r,t,o)}}isRoot(t){return t===this.levelsMap[t][0]}directChildren(t){if(!this.isRoot(t))return[];return this.levelsMap[t].slice(1).map((t=>a.simpleCollapseStructure(t)?t:a.contentCollapseStructure(t)?t[1]:t[0]))}subtreeNodes(t){if(!this.isRoot(t))return[];const e=(t,r)=>{a.simpleCollapseStructure(t)?r.push(t):(t=t,a.contentCollapseStructure(t)&&(t=t.slice(1)),t.forEach((t=>e(t,r))))},r=this.levelsMap[t],n=[];return e(r.slice(1),n),n}}e.SemanticSkeleton=a},7075:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.SemanticTree=void 0;const n=r(5740),o=r(7630),i=r(9265),a=r(7228),s=r(5952),l=r(5609);r(94);class c{constructor(t){this.mathml=t,this.parser=new a.SemanticMathml,this.root=this.parser.parse(t),this.collator=this.parser.getFactory().leafMap.collateMeaning();const e=this.collator.newDefault();e&&(this.parser=new a.SemanticMathml,this.parser.getFactory().defaultMap=e,this.root=this.parser.parse(t)),u.visit(this.root,{}),(0,o.annotate)(this.root)}static empty(){const t=n.parseInput("<math/>"),e=new c(t);return e.mathml=t,e}static fromNode(t,e){const r=c.empty();return r.root=t,e&&(r.mathml=e),r}static fromRoot(t,e){let r=t;for(;r.parent;)r=r.parent;const n=c.fromNode(r);return e&&(n.mathml=e),n}static fromXml(t){const e=c.empty();return t.childNodes[0]&&(e.root=s.SemanticNode.fromXml(t.childNodes[0])),e}xml(t){const e=n.parseInput("<stree></stree>"),r=this.root.xml(e.ownerDocument,t);return e.appendChild(r),e}toString(t){return n.serializeXml(this.xml(t))}formatXml(t){const e=this.toString(t);return n.formatXml(e)}displayTree(){this.root.displayTree()}replaceNode(t,e){const r=t.parent;r?r.replaceChild(t,e):this.root=e}toJson(){const t={};return t.stree=this.root.toJson(),t}}e.SemanticTree=c;const u=new i.SemanticVisitor("general","unit",((t,e)=>{if("infixop"===t.type&&("multiplication"===t.role||"implicit"===t.role)){const e=t.childNodes;e.length&&(l.isPureUnit(e[0])||l.isUnitCounter(e[0]))&&t.childNodes.slice(1).every(l.isPureUnit)&&(t.role="unit")}return!1}))},4795:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.partitionNodes=e.sliceNodes=e.getEmbellishedInner=e.addAttributes=e.isZeroLength=e.purgeNodes=e.isOrphanedGlyph=e.hasDisplayTag=e.hasEmptyTag=e.hasIgnoreTag=e.hasLeafTag=e.hasMathTag=e.directSpeechKeys=e.DISPLAYTAGS=e.EMPTYTAGS=e.IGNORETAGS=e.LEAFTAGS=void 0;const n=r(5740);function o(t){return!!t&&-1!==e.LEAFTAGS.indexOf(n.tagName(t))}function i(t,e,r){r&&t.reverse();const n=[];for(let o,i=0;o=t[i];i++){if(e(o))return r?{head:t.slice(i+1).reverse(),div:o,tail:n.reverse()}:{head:n,div:o,tail:t.slice(i+1)};n.push(o)}return r?{head:[],div:null,tail:n.reverse()}:{head:n,div:null,tail:[]}}e.LEAFTAGS=["MO","MI","MN","MTEXT","MS","MSPACE"],e.IGNORETAGS=["MERROR","MPHANTOM","MALIGNGROUP","MALIGNMARK","MPRESCRIPTS","ANNOTATION","ANNOTATION-XML"],e.EMPTYTAGS=["MATH","MROW","MPADDED","MACTION","NONE","MSTYLE","SEMANTICS"],e.DISPLAYTAGS=["MROOT","MSQRT"],e.directSpeechKeys=["aria-label","exact-speech","alt"],e.hasMathTag=function(t){return!!t&&"MATH"===n.tagName(t)},e.hasLeafTag=o,e.hasIgnoreTag=function(t){return!!t&&-1!==e.IGNORETAGS.indexOf(n.tagName(t))},e.hasEmptyTag=function(t){return!!t&&-1!==e.EMPTYTAGS.indexOf(n.tagName(t))},e.hasDisplayTag=function(t){return!!t&&-1!==e.DISPLAYTAGS.indexOf(n.tagName(t))},e.isOrphanedGlyph=function(t){return!!t&&"MGLYPH"===n.tagName(t)&&!o(t.parentNode)},e.purgeNodes=function(t){const r=[];for(let o,i=0;o=t[i];i++){if(o.nodeType!==n.NodeType.ELEMENT_NODE)continue;const t=n.tagName(o);-1===e.IGNORETAGS.indexOf(t)&&(-1!==e.EMPTYTAGS.indexOf(t)&&0===o.childNodes.length||r.push(o))}return r},e.isZeroLength=function(t){if(!t)return!1;if(-1!==["negativeveryverythinmathspace","negativeverythinmathspace","negativethinmathspace","negativemediummathspace","negativethickmathspace","negativeverythickmathspace","negativeveryverythickmathspace"].indexOf(t))return!0;const e=t.match(/[0-9.]+/);return!!e&&0===parseFloat(e[0])},e.addAttributes=function(t,r){if(r.hasAttributes()){const n=r.attributes;for(let r=n.length-1;r>=0;r--){const o=n[r].name;o.match(/^ext/)&&(t.attributes[o]=n[r].value,t.nobreaking=!0),-1!==e.directSpeechKeys.indexOf(o)&&(t.attributes["ext-speech"]=n[r].value,t.nobreaking=!0),o.match(/texclass$/)&&(t.attributes.texclass=n[r].value),"href"===o&&(t.attributes.href=n[r].value,t.nobreaking=!0)}}},e.getEmbellishedInner=function t(e){return e&&e.embellished&&e.childNodes.length>0?t(e.childNodes[0]):e},e.sliceNodes=i,e.partitionNodes=function(t,e){let r=t;const n=[],o=[];let a=null;do{a=i(r,e),o.push(a.head),n.push(a.div),r=a.tail}while(a.div);return n.pop(),{rel:n,comp:o}}},6278:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.AbstractSpeechGenerator=void 0;const n=r(6828),o=r(2298),i=r(1214),a=r(9543);e.AbstractSpeechGenerator=class{constructor(){this.modality=o.addPrefix("speech"),this.rebuilt_=null,this.options_={}}getRebuilt(){return this.rebuilt_}setRebuilt(t){this.rebuilt_=t}setOptions(t){this.options_=t||{},this.modality=o.addPrefix(this.options_.modality||"speech")}getOptions(){return this.options_}start(){}end(){}generateSpeech(t,e){return this.rebuilt_||(this.rebuilt_=new i.RebuildStree(e)),(0,n.setup)(this.options_),a.computeMarkup(this.getRebuilt().xml)}}},1452:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.AdhocSpeechGenerator=void 0;const n=r(6278);class o extends n.AbstractSpeechGenerator{getSpeech(t,e){const r=this.generateSpeech(t,e);return t.setAttribute(this.modality,r),r}}e.AdhocSpeechGenerator=o},5152:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.ColorGenerator=void 0;const n=r(2298),o=r(8396),i=r(1214),a=r(1204),s=r(6278);class l extends s.AbstractSpeechGenerator{constructor(){super(...arguments),this.modality=(0,n.addPrefix)("foreground"),this.contrast=new o.ContrastPicker}static visitStree_(t,e,r){if(t.childNodes.length){if(t.contentNodes.length&&("punctuated"===t.type&&t.contentNodes.forEach((t=>r[t.id]=!0)),"implicit"!==t.role&&e.push(t.contentNodes.map((t=>t.id)))),t.childNodes.length){if("implicit"===t.role){const n=[];let o=[];for(const e of t.childNodes){const t=[];l.visitStree_(e,t,r),t.length<=2&&n.push(t.shift()),o=o.concat(t)}return e.push(n),void o.forEach((t=>e.push(t)))}t.childNodes.forEach((t=>l.visitStree_(t,e,r)))}}else r[t.id]||e.push(t.id)}getSpeech(t,e){return a.getAttribute(t,this.modality)}generateSpeech(t,e){return this.getRebuilt()||this.setRebuilt(new i.RebuildStree(t)),this.colorLeaves_(t),a.getAttribute(t,this.modality)}colorLeaves_(t){const e=[];l.visitStree_(this.getRebuilt().streeRoot,e,{});for(const r of e){const e=this.contrast.generate();let n=!1;n=Array.isArray(r)?r.map((r=>this.colorLeave_(t,r,e))).reduce(((t,e)=>t||e),!1):this.colorLeave_(t,r.toString(),e),n&&this.contrast.increment()}}colorLeave_(t,e,r){const n=a.getBySemanticId(t,e);return!!n&&(n.setAttribute(this.modality,r),!0)}}e.ColorGenerator=l},6604:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.DirectSpeechGenerator=void 0;const n=r(1204),o=r(6278);class i extends o.AbstractSpeechGenerator{getSpeech(t,e){return n.getAttribute(t,this.modality)}}e.DirectSpeechGenerator=i},3123:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.DummySpeechGenerator=void 0;const n=r(6278);class o extends n.AbstractSpeechGenerator{getSpeech(t,e){return""}}e.DummySpeechGenerator=o},5858:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.NodeSpeechGenerator=void 0;const n=r(1204),o=r(4598);class i extends o.TreeSpeechGenerator{getSpeech(t,e){return super.getSpeech(t,e),n.getAttribute(t,this.modality)}}e.NodeSpeechGenerator=i},9552:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.generatorMapping_=e.generator=void 0;const n=r(1452),o=r(5152),i=r(6604),a=r(3123),s=r(5858),l=r(597),c=r(4598);e.generator=function(t){return(e.generatorMapping_[t]||e.generatorMapping_.Direct)()},e.generatorMapping_={Adhoc:()=>new n.AdhocSpeechGenerator,Color:()=>new o.ColorGenerator,Direct:()=>new i.DirectSpeechGenerator,Dummy:()=>new a.DummySpeechGenerator,Node:()=>new s.NodeSpeechGenerator,Summary:()=>new l.SummarySpeechGenerator,Tree:()=>new c.TreeSpeechGenerator}},9543:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.computeSummary_=e.retrieveSummary=e.connectAllMactions=e.connectMactions=e.nodeAtPosition_=e.computePrefix_=e.retrievePrefix=e.addPrefix=e.addModality=e.addSpeech=e.recomputeMarkup=e.computeMarkup=e.recomputeSpeech=e.computeSpeech=void 0;const n=r(8290),o=r(5740),i=r(5274),a=r(2298),s=r(2362),l=r(7075),c=r(1204);function u(t){return s.SpeechRuleEngine.getInstance().evaluateNode(t)}function p(t){return u(l.SemanticTree.fromNode(t).xml())}function h(t){const e=p(t);return n.markup(e)}function d(t){const e=f(t);return n.markup(e)}function f(t){const e=l.SemanticTree.fromRoot(t),r=i.evalXPath('.//*[@id="'+t.id+'"]',e.xml());let n=r[0];return r.length>1&&(n=m(t,r)||n),n?s.SpeechRuleEngine.getInstance().runInSetting({modality:"prefix",domain:"default",style:"default",strict:!0,speech:!0},(function(){return s.SpeechRuleEngine.getInstance().evaluateNode(n)})):[]}function m(t,e){const r=e[0];if(!t.parent)return r;const n=[];for(;t;)n.push(t.id),t=t.parent;const o=function(t,e){for(;e.length&&e.shift().toString()===t.getAttribute("id")&&t.parentNode&&t.parentNode.parentNode;)t=t.parentNode.parentNode;return!e.length};for(let t,r=0;t=e[r];r++)if(o(t,n.slice()))return t;return r}function y(t){return t?s.SpeechRuleEngine.getInstance().runInSetting({modality:"summary",strict:!1,speech:!0},(function(){return s.SpeechRuleEngine.getInstance().evaluateNode(t)})):[]}e.computeSpeech=u,e.recomputeSpeech=p,e.computeMarkup=function(t){const e=u(t);return n.markup(e)},e.recomputeMarkup=h,e.addSpeech=function(t,e,r){const i=o.querySelectorAllByAttrValue(r,"id",e.id.toString())[0],s=i?n.markup(u(i)):h(e);t.setAttribute(a.Attribute.SPEECH,s)},e.addModality=function(t,e,r){const n=h(e);t.setAttribute(r,n)},e.addPrefix=function(t,e){const r=d(e);r&&t.setAttribute(a.Attribute.PREFIX,r)},e.retrievePrefix=d,e.computePrefix_=f,e.nodeAtPosition_=m,e.connectMactions=function(t,e,r){const n=o.querySelectorAll(e,"maction");for(let e,i=0;e=n[i];i++){const n=e.getAttribute("id"),i=o.querySelectorAllByAttrValue(t,"id",n)[0];if(!i)continue;const s=e.childNodes[1],l=s.getAttribute(a.Attribute.ID);let u=c.getBySemanticId(t,l);if(u&&"dummy"!==u.getAttribute(a.Attribute.TYPE))continue;if(u=i.childNodes[0],u.getAttribute("sre-highlighter-added"))continue;const p=s.getAttribute(a.Attribute.PARENT);p&&u.setAttribute(a.Attribute.PARENT,p),u.setAttribute(a.Attribute.TYPE,"dummy"),u.setAttribute(a.Attribute.ID,l);o.querySelectorAllByAttrValue(r,"id",l)[0].setAttribute("alternative",l)}},e.connectAllMactions=function(t,e){const r=o.querySelectorAll(t,"maction");for(let t,n=0;t=r[n];n++){const r=t.childNodes[1].getAttribute(a.Attribute.ID);o.querySelectorAllByAttrValue(e,"id",r)[0].setAttribute("alternative",r)}},e.retrieveSummary=function(t){const e=y(t);return n.markup(e)},e.computeSummary_=y},597:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.SummarySpeechGenerator=void 0;const n=r(6278),o=r(9543);class i extends n.AbstractSpeechGenerator{getSpeech(t,e){return o.connectAllMactions(e,this.getRebuilt().xml),this.generateSpeech(t,e)}}e.SummarySpeechGenerator=i},4598:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.TreeSpeechGenerator=void 0;const n=r(2298),o=r(1204),i=r(6278),a=r(9543);class s extends i.AbstractSpeechGenerator{getSpeech(t,e){const r=this.generateSpeech(t,e),i=this.getRebuilt().nodeDict;for(const r in i){const s=i[r],l=o.getBySemanticId(e,r),c=o.getBySemanticId(t,r);l&&c&&(this.modality&&this.modality!==n.Attribute.SPEECH?a.addModality(c,s,this.modality):a.addSpeech(c,s,this.getRebuilt().xml),this.modality===n.Attribute.SPEECH&&a.addPrefix(c,s))}return r}}e.TreeSpeechGenerator=s},313:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.INTERVALS=e.makeLetter=e.numberRules=e.alphabetRules=e.getFont=e.makeInterval=e.generate=e.makeDomains_=e.Domains_=e.Base=e.Embellish=e.Font=void 0;const n=r(5897),o=r(7491),i=r(4356),a=r(2536),s=r(2780);var l,c,u;function p(){const t=i.LOCALE.ALPHABETS,r=(t,e)=>{const r={};return Object.keys(t).forEach((t=>r[t]=!0)),Object.keys(e).forEach((t=>r[t]=!0)),Object.keys(r)};e.Domains_.small=r(t.smallPrefix,t.letterTrans),e.Domains_.capital=r(t.capPrefix,t.letterTrans),e.Domains_.digit=r(t.digitPrefix,t.digitTrans)}function h(t){const e=t.toString(16).toUpperCase();return e.length>3?e:("000"+e).slice(-4)}function d([t,e],r){const n=parseInt(t,16),o=parseInt(e,16),i=[];for(let t=n;t<=o;t++){let e=h(t);!1!==r[e]&&(e=r[e]||e,i.push(e))}return i}function f(t){const e="normal"===t||"fullwidth"===t?"":i.LOCALE.MESSAGES.font[t]||i.LOCALE.MESSAGES.embellish[t]||"";return(0,a.localeFontCombiner)(e)}function m(t,r,n,o,a,s){const l=f(o);for(let o,c,u,p=0;o=t[p],c=r[p],u=n[p];p++){const t=s?i.LOCALE.ALPHABETS.capPrefix:i.LOCALE.ALPHABETS.smallPrefix,r=s?e.Domains_.capital:e.Domains_.small;g(l.combiner,o,c,u,l.font,t,a,i.LOCALE.ALPHABETS.letterTrans,r)}}function y(t,r,n,o,a){const s=f(n);for(let n,l,c=0;n=t[c],l=r[c];c++){const t=i.LOCALE.ALPHABETS.digitPrefix,r=c+a;g(s.combiner,n,l,r,s.font,t,o,i.LOCALE.ALPHABETS.digitTrans,e.Domains_.digit)}}function g(t,e,r,n,o,i,a,l,c){for(let u,p=0;u=c[p];p++){const c=u in l?l[u]:l.default,p=u in 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smartPreferences(t,e){const r=c.getLocalePreferences()[e];if(!r)return[];const n=t.explorers.speech,i=c.relevantPreferences(n.walker.getFocus().getSemanticPrimary()),a=o.DOMAIN_TO_STYLES.clearspeak;return[{type:"radio",content:"No Preferences",id:"clearspeak-default",variable:"speechRules"},{type:"radio",content:"Current Preferences",id:"clearspeak-"+a,variable:"speechRules"},{type:"rule"},{type:"label",content:"Preferences for "+i},{type:"rule"}].concat(r[i].map((function(t){const e=t.split("_");return{type:"radio",content:e[1],id:"clearspeak-"+c.addPreference(a,e[0],e[1]),variable:"speechRules"}})))}static relevantPreferences(t){const e=f[t.type];return e&&(e[t.role]||e[""])||"ImpliedTimes"}static findPreference(t,e){if("default"===t)return c.AUTO;return c.fromPreference(t)[e]||c.AUTO}static addPreference(t,e,r){if("default"===t)return e+"_"+r;const n=c.fromPreference(t);return n[e]=r,c.toPreference(n)}static getLocalePreferences_(t){const e={};for(const r in 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p extends a.DefaultComparator{constructor(t,e){super(t,e),this.preference=t instanceof c?t.preference:{}}match(t){if(!(t instanceof c))return super.match(t);if("default"===t.getComponents()[a.Axis.STYLE])return!0;const e=Object.keys(t.preference);for(let r,n=0;r=e[n];n++)if(this.preference[r]!==t.preference[r])return!1;return!0}compare(t,e){const r=super.compare(t,e);if(0!==r)return r;const n=t instanceof c,o=e instanceof c;if(!n&&o)return 1;if(n&&!o)return-1;if(!n&&!o)return 0;const i=Object.keys(t.preference).length,a=Object.keys(e.preference).length;return i>a?-1:i<a?1:0}}e.Comparator=p;class h extends a.DynamicCstrParser{constructor(){super([a.Axis.LOCALE,a.Axis.MODALITY,a.Axis.DOMAIN,a.Axis.STYLE])}parse(t){const e=super.parse(t);let r=e.getValue(a.Axis.STYLE);const n=e.getValue(a.Axis.LOCALE),o=e.getValue(a.Axis.MODALITY);let s={};return r!==i.DynamicCstr.DEFAULT_VALUE&&(s=this.fromPreference(r),r=this.toPreference(s)),new c({locale:n,modality:o,domain:"clearspeak",style:r},s)}fromPreference(t){return c.fromPreference(t)}toPreference(t){return c.toPreference(t)}}e.Parser=h;const d=[["AbsoluteValue","fenced","neutral","metric"],["Bar","overscore","overaccent"],["Caps","identifier","latinletter"],["CombinationPermutation","appl","unknown"],["Ellipses","punctuation","ellipsis"],["Exponent","superscript",""],["Fraction","fraction",""],["Functions","appl","simple function"],["ImpliedTimes","operator","implicit"],["Log","appl","prefix 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n=r(1676),o=r(365),i=r(9912),a=r(1378),s=r(8437),l=r(7283);e.ClearspeakRules=function(){l.addStore(n.DynamicCstr.BASE_LOCALE+".speech.clearspeak","",{CTFpauseSeparator:o.pauseSeparator,CTFnodeCounter:i.nodeCounter,CTFcontentIterator:o.contentIterator,CSFvulgarFraction:s.vulgarFraction,CQFvulgarFractionSmall:i.isSmallVulgarFraction,CQFcellsSimple:i.allCellsSimple,CSFordinalExponent:i.ordinalExponent,CSFwordOrdinal:i.wordOrdinal,CQFmatchingFences:i.matchingFences,CSFnestingDepth:i.nestingDepth,CQFfencedArguments:i.fencedArguments,CQFsimpleArguments:i.simpleArguments,CQFspaceoutNumber:a.spaceoutNumber})}},9912:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.wordOrdinal=e.layoutFactor_=e.fencedFactor_=e.simpleFactor_=e.simpleArguments=e.fencedArguments=e.insertNesting=e.matchingFences=e.nestingDepth=e.NESTING_DEPTH=e.ordinalExponent=e.allTextLastContent_=e.isUnitExpression=e.isSmallVulgarFraction=e.allCellsSimple=e.allIndices_=e.isInteger_=e.simpleCell_=e.simpleNode=e.hasPreference=e.isSimpleFraction_=e.isSimpleNumber_=e.isNumber_=e.isLetter_=e.isSimple_=e.isSimpleLetters_=e.isSimpleDegree_=e.isSimpleNegative_=e.isSimpleFunction_=e.isSimpleExpression=e.nodeCounter=void 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n>1&&n<=e?[t]:[]}},6922:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.implicitIterator=e.relationIterator=e.propagateNumber=e.checkParent_=e.NUMBER_INHIBITORS_=e.NUMBER_PROPAGATORS_=e.enlargeFence=e.indexRadical=e.closingRadical=e.openingRadical=e.radicalNestingDepth=e.nestedRadical=e.overBevelledFraction=e.overFraction=e.closingFraction=e.openingFraction=void 0;const n=r(7052),o=r(5740),i=r(5274),a=r(2105),s=r(5897),l=r(7630),c=r(9265),u=r(4356),p=r(1378);function h(t,e){const r=d(t);return 1===r?e:new Array(r).join(u.LOCALE.MESSAGES.MS.NESTED)+e}function d(t,e){const r=e||0;return t.parentNode?d(t.parentNode,"root"===t.tagName||"sqrt"===t.tagName?r+1:r):r}function f(t){const e="\u2820";if(1===t.length)return e+t;const r=t.split("");return r.every((function(t){return"\u2833"===t}))?e+r.join(e):t.slice(0,-1)+e+t.slice(-1)}function m(t,r){const n=t.parent;if(!n)return!1;const o=n.type;return-1!==e.NUMBER_PROPAGATORS_.indexOf(o)||"prefixop"===o&&"negative"===n.role&&!r.script||"prefixop"===o&&"geometry"===n.role||!("punctuated"!==o||r.enclosed&&"text"!==n.role)}function y(t,r){return t.childNodes.length?(-1!==e.NUMBER_INHIBITORS_.indexOf(t.type)&&(r.script=!0),"fenced"===t.type?(r.number=!1,r.enclosed=!0,["",r]):(m(t,r)&&(r.number=!0,r.enclosed=!1),["",r])):(m(t,r)&&(r.number=!0,r.script=!1,r.enclosed=!1),[r.number?"number":"",{number:!1,enclosed:r.enclosed,script:r.script}])}e.openingFraction=function(t){const e=p.fractionNestingDepth(t);return new Array(e).join(u.LOCALE.MESSAGES.MS.FRACTION_REPEAT)+u.LOCALE.MESSAGES.MS.FRACTION_START},e.closingFraction=function(t){const e=p.fractionNestingDepth(t);return new Array(e).join(u.LOCALE.MESSAGES.MS.FRACTION_REPEAT)+u.LOCALE.MESSAGES.MS.FRACTION_END},e.overFraction=function(t){const e=p.fractionNestingDepth(t);return new 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l.concat(c&&u&&"space"===s.getAttribute("role")?[n.AuditoryDescription.create({text:"\u2800"},{})]:[])}}},8437:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.ordinalPosition=e.vulgarFraction=e.wordCounter=e.ordinalCounter=void 0;const n=r(9536),o=r(5740),i=r(4356),a=r(4977);e.ordinalCounter=function(t,e){let r=0;return function(){return i.LOCALE.NUMBERS.numericOrdinal(++r)+" "+e}},e.wordCounter=function(t,e){let r=0;return function(){return i.LOCALE.NUMBERS.numberToOrdinal(++r,!1)+" "+e}},e.vulgarFraction=function(t){const e=(0,a.convertVulgarFraction)(t,i.LOCALE.MESSAGES.MS.FRAC_OVER);return e.convertible&&e.enumerator&&e.denominator?[new n.Span(i.LOCALE.NUMBERS.numberToWords(e.enumerator),{extid:t.childNodes[0].childNodes[0].getAttribute("extid"),separator:""}),new n.Span(i.LOCALE.NUMBERS.vulgarSep,{separator:""}),new n.Span(i.LOCALE.NUMBERS.numberToOrdinal(e.denominator,1!==e.enumerator),{extid:t.childNodes[0].childNodes[1].getAttribute("extid")})]:[new n.Span(e.content||"",{extid:t.getAttribute("extid")})]},e.ordinalPosition=function(t){const e=o.toArray(t.parentNode.childNodes);return i.LOCALE.NUMBERS.numericOrdinal(e.indexOf(t)+1).toString()}},9284:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.BrailleRules=e.OtherRules=e.PrefixRules=void 0;const 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n=r(7052),o=r(8290),i=r(5740),a=r(4440),s=r(6828),l=r(8496),c=r(2298),u=r(4356),p=r(2105),h=r(5656),d=r(9552),f=r(9543),m=r(8504),y=r(7730),g=r(1214),b=r(179),v=r(1204),_=r(5274);class S{constructor(t,e,r,n){this.node=t,this.generator=e,this.highlighter=r,this.modifier=!1,this.keyMapping=new Map([[l.KeyCode.UP,this.up.bind(this)],[l.KeyCode.DOWN,this.down.bind(this)],[l.KeyCode.RIGHT,this.right.bind(this)],[l.KeyCode.LEFT,this.left.bind(this)],[l.KeyCode.TAB,this.repeat.bind(this)],[l.KeyCode.DASH,this.expand.bind(this)],[l.KeyCode.SPACE,this.depth.bind(this)],[l.KeyCode.HOME,this.home.bind(this)],[l.KeyCode.X,this.summary.bind(this)],[l.KeyCode.Z,this.detail.bind(this)],[l.KeyCode.V,this.virtualize.bind(this)],[l.KeyCode.P,this.previous.bind(this)],[l.KeyCode.U,this.undo.bind(this)],[l.KeyCode.LESS,this.previousRules.bind(this)],[l.KeyCode.GREATER,this.nextRules.bind(this)]]),this.cursors=[],this.xml_=null,this.rebuilt_=null,this.focus_=null,this.active_=!1,this.node.id?this.id=this.node.id:this.node.hasAttribute(S.SRE_ID_ATTR)?this.id=this.node.getAttribute(S.SRE_ID_ATTR):(this.node.setAttribute(S.SRE_ID_ATTR,S.ID_COUNTER.toString()),this.id=S.ID_COUNTER++),this.rootNode=v.getSemanticRoot(t),this.rootId=this.rootNode.getAttribute(c.Attribute.ID),this.xmlString_=n,this.moved=b.WalkerMoves.ENTER}getXml(){return 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g.RebuildStree(this.getXml()),this.rootId=this.rebuilt_.stree.root.id.toString(),this.generator.setRebuilt(this.rebuilt_),this.skeleton=h.SemanticSkeleton.fromTree(this.rebuilt_.stree),this.skeleton.populate(),this.focus_=this.singletonFocus(this.rootId),this.levels=this.initLevels(),f.connectMactions(this.node,this.getXml(),this.rebuilt_.xml)}previousLevel(){const t=this.getFocus().getDomPrimary();return t?v.getAttribute(t,c.Attribute.PARENT):this.getFocus().getSemanticPrimary().parent.id.toString()}nextLevel(){const t=this.getFocus().getDomPrimary();let e,r;if(t){e=v.splitAttribute(v.getAttribute(t,c.Attribute.CHILDREN)),r=v.splitAttribute(v.getAttribute(t,c.Attribute.CONTENT));const n=v.getAttribute(t,c.Attribute.TYPE),o=v.getAttribute(t,c.Attribute.ROLE);return this.combineContentChildren(n,o,r,e)}const n=t=>t.id.toString(),o=this.getRebuilt().nodeDict[this.primaryId()];return e=o.childNodes.map(n),r=o.contentNodes.map(n),0===e.length?[]:this.combineContentChildren(o.type,o.role,r,e)}singletonFocus(t){this.getRebuilt();const e=this.retrieveVisuals(t);return this.focusFromId(t,e)}retrieveVisuals(t){if(!this.skeleton)return[t];const e=parseInt(t,10),r=this.skeleton.subtreeNodes(e);if(!r.length)return[t];r.unshift(e);const n={},o=[];_.updateEvaluator(this.getXml());for(const t of r)n[t]||(o.push(t.toString()),n[t]=!0,this.subtreeIds(t,n));return o}subtreeIds(t,e){const r=_.evalXPath(`//*[@data-semantic-id="${t}"]`,this.getXml());_.evalXPath("*//@data-semantic-id",r[0]).forEach((t=>e[parseInt(t.textContent,10)]=!0))}focusFromId(t,e){return y.Focus.factory(t,e,this.getRebuilt(),this.node)}summary(){return this.moved=this.isSpeech()?b.WalkerMoves.SUMMARY:b.WalkerMoves.REPEAT,this.getFocus().clone()}detail(){return this.moved=this.isSpeech()?b.WalkerMoves.DETAIL:b.WalkerMoves.REPEAT,this.getFocus().clone()}specialMove(){return null}virtualize(t){return this.cursors.push({focus:this.getFocus(),levels:this.levels,undo:t||!this.cursors.length}),this.levels=this.levels.clone(),this.getFocus().clone()}previous(){const t=this.cursors.pop();return t?(this.levels=t.levels,t.focus):this.getFocus()}undo(){let t;do{t=this.cursors.pop()}while(t&&!t.undo);return t?(this.levels=t.levels,t.focus):this.getFocus()}update(t){this.generator.setOptions(t),(0,s.setup)(t).then((()=>d.generator("Tree").getSpeech(this.node,this.getXml())))}nextRules(){const t=this.generator.getOptions();return"speech"!==t.modality?this.getFocus():(a.DOMAIN_TO_STYLES[t.domain]=t.style,t.domain="mathspeak"===t.domain?"clearspeak":"mathspeak",t.style=a.DOMAIN_TO_STYLES[t.domain],this.update(t),this.moved=b.WalkerMoves.REPEAT,this.getFocus().clone())}nextStyle(t,e){if("mathspeak"===t){const t=["default","brief","sbrief"],r=t.indexOf(e);return-1===r?e:r>=t.length-1?t[0]:t[r+1]}if("clearspeak"===t){const t=m.ClearspeakPreferences.getLocalePreferences().en;if(!t)return"default";const r=m.ClearspeakPreferences.relevantPreferences(this.getFocus().getSemanticPrimary()),n=m.ClearspeakPreferences.findPreference(e,r),o=t[r].map((function(t){return t.split("_")[1]})),i=o.indexOf(n);if(-1===i)return e;const a=i>=o.length-1?o[0]:o[i+1];return m.ClearspeakPreferences.addPreference(e,r,a)}return e}previousRules(){const t=this.generator.getOptions();return"speech"!==t.modality?this.getFocus():(t.style=this.nextStyle(t.domain,t.style),this.update(t),this.moved=b.WalkerMoves.REPEAT,this.getFocus().clone())}refocus(){let t,e=this.getFocus();for(;!e.getNodes().length;){t=this.levels.peek();const r=this.up();if(!r)break;this.setFocus(r),e=this.getFocus(!0)}this.levels.push(t),this.setFocus(e)}toggleActive_(){this.active_=!this.active_}mergePrefix_(t,e=[]){const r=this.isSpeech()?this.prefix_():"";r&&t.unshift(r);const n=this.isSpeech()?this.postfix_():"";return n&&t.push(n),o.finalize(o.merge(e.concat(t)))}prefix_(){const t=this.getFocus().getDomNodes(),e=this.getFocus().getSemanticNodes();return t[0]?v.getAttribute(t[0],c.Attribute.PREFIX):f.retrievePrefix(e[0])}postfix_(){const t=this.getFocus().getDomNodes();return t[0]?v.getAttribute(t[0],c.Attribute.POSTFIX):""}depth_(){const t=p.Grammar.getInstance().getParameter("depth");p.Grammar.getInstance().setParameter("depth",!0);const e=this.getFocus().getDomPrimary(),r=this.expandable(e)?u.LOCALE.MESSAGES.navigate.EXPANDABLE:this.collapsible(e)?u.LOCALE.MESSAGES.navigate.COLLAPSIBLE:"",i=u.LOCALE.MESSAGES.navigate.LEVEL+" "+this.getDepth(),a=this.getFocus().getSemanticNodes(),s=f.retrievePrefix(a[0]),l=[new n.AuditoryDescription({text:i,personality:{}}),new n.AuditoryDescription({text:s,personality:{}}),new n.AuditoryDescription({text:r,personality:{}})];return p.Grammar.getInstance().setParameter("depth",t),o.finalize(o.markup(l))}actionable_(t){const e=null==t?void 0:t.parentNode;return e&&this.highlighter.isMactionNode(e)?e:null}summary_(){const t=this.getFocus().getSemanticPrimary().id.toString(),e=this.getRebuilt().xml.getAttribute("id")===t?this.getRebuilt().xml:i.querySelectorAllByAttrValue(this.getRebuilt().xml,"id",t)[0],r=f.retrieveSummary(e);return this.mergePrefix_([r])}detail_(){const t=this.getFocus().getSemanticPrimary().id.toString(),e=this.getRebuilt().xml.getAttribute("id")===t?this.getRebuilt().xml:i.querySelectorAllByAttrValue(this.getRebuilt().xml,"id",t)[0],r=e.getAttribute("alternative");e.removeAttribute("alternative");const n=f.computeMarkup(e),o=this.mergePrefix_([n]);return e.setAttribute("alternative",r),o}}e.AbstractWalker=S,S.ID_COUNTER=0,S.SRE_ID_ATTR="sre-explorer-id"},162:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.DummyWalker=void 0;const n=r(3284);class o extends n.AbstractWalker{up(){return null}down(){return null}left(){return null}right(){return null}repeat(){return null}depth(){return null}home(){return null}getDepth(){return 0}initLevels(){return null}combineContentChildren(t,e,r,n){return[]}findFocusOnLevel(t){return null}}e.DummyWalker=o},7730:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.Focus=void 0;const n=r(1204);class o{constructor(t,e){this.nodes=t,this.primary=e,this.domNodes=[],this.domPrimary_=null,this.allNodes=[]}static factory(t,e,r,i){const a=t=>n.getBySemanticId(i,t),s=r.nodeDict,l=a(t),c=e.map(a),u=e.map((function(t){return s[t]})),p=new o(u,s[t]);return p.domNodes=c,p.domPrimary_=l,p.allNodes=o.generateAllVisibleNodes_(e,c,s,i),p}static generateAllVisibleNodes_(t,e,r,i){const a=t=>n.getBySemanticId(i,t);let s=[];for(let n=0,l=t.length;n<l;n++){if(e[n]){s.push(e[n]);continue}const l=r[t[n]];if(!l)continue;const c=l.childNodes.map((function(t){return t.id.toString()})),u=c.map(a);s=s.concat(o.generateAllVisibleNodes_(c,u,r,i))}return s}getSemanticPrimary(){return this.primary}getSemanticNodes(){return this.nodes}getNodes(){return this.allNodes}getDomNodes(){return this.domNodes}getDomPrimary(){return this.domPrimary_}toString(){return"Primary:"+this.domPrimary_+" Nodes:"+this.domNodes}clone(){const t=new o(this.nodes,this.primary);return t.domNodes=this.domNodes,t.domPrimary_=this.domPrimary_,t.allNodes=this.allNodes,t}}e.Focus=o},9797:function(t,e){Object.defineProperty(e,"__esModule",{value:!0}),e.Levels=void 0;class r{constructor(){this.level_=[]}push(t){this.level_.push(t)}pop(){return this.level_.pop()}peek(){return this.level_[this.level_.length-1]||null}indexOf(t){const e=this.peek();return e?e.indexOf(t):null}find(t){const e=this.peek();if(!e)return null;for(let r=0,n=e.length;r<n;r++)if(t(e[r]))return e[r];return null}get(t){const e=this.peek();return!e||t<0||t>=e.length?null:e[t]}depth(){return this.level_.length}clone(){const t=new r;return t.level_=this.level_.slice(0),t}toString(){let t="";for(let e,r=0;e=this.level_[r];r++)t+="\n"+e.map((function(t){return t.toString()}));return t}}e.Levels=r},1214:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.RebuildStree=void 0;const n=r(5740),o=r(2298),i=r(3588),a=r(6537),s=r(3308),l=r(5656),c=r(7075),u=r(4795),p=r(1204);class h{constructor(t){this.mathml=t,this.factory=new a.SemanticNodeFactory,this.nodeDict={},this.mmlRoot=p.getSemanticRoot(t),this.streeRoot=this.assembleTree(this.mmlRoot),this.stree=c.SemanticTree.fromNode(this.streeRoot,this.mathml),this.xml=this.stree.xml(),s.default.getInstance().setNodeFactory(this.factory)}static addAttributes(t,e,r){r&&1===e.childNodes.length&&e.childNodes[0].nodeType!==n.NodeType.TEXT_NODE&&u.addAttributes(t,e.childNodes[0]),u.addAttributes(t,e)}static textContent(t,e,r){if(!r&&e.textContent)return void(t.textContent=e.textContent);const n=p.splitAttribute(p.getAttribute(e,o.Attribute.OPERATOR));n.length>1&&(t.textContent=n[1])}static isPunctuated(t){return!l.SemanticSkeleton.simpleCollapseStructure(t)&&t[1]&&l.SemanticSkeleton.contentCollapseStructure(t[1])}getTree(){return this.stree}assembleTree(t){const e=this.makeNode(t),r=p.splitAttribute(p.getAttribute(t,o.Attribute.CHILDREN)),n=p.splitAttribute(p.getAttribute(t,o.Attribute.CONTENT));if(h.addAttributes(e,t,!(r.length||n.length)),0===n.length&&0===r.length)return h.textContent(e,t),e;if(n.length>0){const t=p.getBySemanticId(this.mathml,n[0]);t&&h.textContent(e,t,!0)}e.contentNodes=n.map((t=>this.setParent(t,e))),e.childNodes=r.map((t=>this.setParent(t,e)));const i=p.getAttribute(t,o.Attribute.COLLAPSED);return i?this.postProcess(e,i):e}makeNode(t){const e=p.getAttribute(t,o.Attribute.TYPE),r=p.getAttribute(t,o.Attribute.ROLE),n=p.getAttribute(t,o.Attribute.FONT),i=p.getAttribute(t,o.Attribute.ANNOTATION)||"",a=p.getAttribute(t,o.Attribute.ID),s=p.getAttribute(t,o.Attribute.EMBELLISHED),l=p.getAttribute(t,o.Attribute.FENCEPOINTER),c=this.createNode(parseInt(a,10));return c.type=e,c.role=r,c.font=n||"unknown",c.parseAnnotation(i),l&&(c.fencePointer=l),s&&(c.embellished=s),c}makePunctuation(t){const e=this.createNode(t);return e.updateContent((0,i.invisibleComma)()),e.role="dummy",e}makePunctuated(t,e,r){const n=this.createNode(e[0]);n.type="punctuated",n.embellished=t.embellished,n.fencePointer=t.fencePointer,n.role=r;const o=e.splice(1,1)[0].slice(1);n.contentNodes=o.map(this.makePunctuation.bind(this)),this.collapsedChildren_(e)}makeEmpty(t,e,r){const n=this.createNode(e);n.type="empty",n.embellished=t.embellished,n.fencePointer=t.fencePointer,n.role=r}makeIndex(t,e,r){if(h.isPunctuated(e))return this.makePunctuated(t,e,r),void(e=e[0]);l.SemanticSkeleton.simpleCollapseStructure(e)&&!this.nodeDict[e.toString()]&&this.makeEmpty(t,e,r)}postProcess(t,e){const r=l.SemanticSkeleton.fromString(e).array;if("subsup"===t.type){const e=this.createNode(r[1][0]);return e.type="subscript",e.role="subsup",t.type="superscript",e.embellished=t.embellished,e.fencePointer=t.fencePointer,this.makeIndex(t,r[1][2],"rightsub"),this.makeIndex(t,r[2],"rightsuper"),this.collapsedChildren_(r),t}if("subscript"===t.type)return this.makeIndex(t,r[2],"rightsub"),this.collapsedChildren_(r),t;if("superscript"===t.type)return this.makeIndex(t,r[2],"rightsuper"),this.collapsedChildren_(r),t;if("tensor"===t.type)return this.makeIndex(t,r[2],"leftsub"),this.makeIndex(t,r[3],"leftsuper"),this.makeIndex(t,r[4],"rightsub"),this.makeIndex(t,r[5],"rightsuper"),this.collapsedChildren_(r),t;if("punctuated"===t.type){if(h.isPunctuated(r)){const e=r.splice(1,1)[0].slice(1);t.contentNodes=e.map(this.makePunctuation.bind(this))}return t}if("underover"===t.type){const e=this.createNode(r[1][0]);return"overaccent"===t.childNodes[1].role?(e.type="overscore",t.type="underscore"):(e.type="underscore",t.type="overscore"),e.role="underover",e.embellished=t.embellished,e.fencePointer=t.fencePointer,this.collapsedChildren_(r),t}return t}createNode(t){const e=this.factory.makeNode(t);return this.nodeDict[t.toString()]=e,e}collapsedChildren_(t){const e=t=>{const r=this.nodeDict[t[0]];r.childNodes=[];for(let n=1,o=t.length;n<o;n++){const o=t[n];r.childNodes.push(l.SemanticSkeleton.simpleCollapseStructure(o)?this.nodeDict[o]:e(o))}return r};e(t)}setParent(t,e){const r=p.getBySemanticId(this.mathml,t),n=this.assembleTree(r);return n.parent=e,n}}e.RebuildStree=h},6295:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.SemanticWalker=void 0;const n=r(3284),o=r(9797);class i extends n.AbstractWalker{constructor(t,e,r,n){super(t,e,r,n),this.node=t,this.generator=e,this.highlighter=r,this.levels=null,this.restoreState()}initLevels(){const t=new o.Levels;return t.push([this.getFocus()]),t}up(){super.up();const t=this.previousLevel();if(!t)return null;this.levels.pop();return this.levels.find((function(e){return e.getSemanticNodes().some((function(e){return e.id.toString()===t}))}))}down(){super.down();const t=this.nextLevel();return 0===t.length?null:(this.levels.push(t),t[0])}combineContentChildren(t,e,r,n){switch(t){case"relseq":case"infixop":case"multirel":return this.makePairList(n,r);case"prefixop":return[this.focusFromId(n[0],r.concat(n))];case"postfixop":return[this.focusFromId(n[0],n.concat(r))];case"matrix":case"vector":case"fenced":return[this.focusFromId(n[0],[r[0],n[0],r[1]])];case"cases":return[this.focusFromId(n[0],[r[0],n[0]])];case"punctuated":return"text"===e?n.map(this.singletonFocus.bind(this)):n.length===r.length?r.map(this.singletonFocus.bind(this)):this.combinePunctuations(n,r,[],[]);case"appl":return[this.focusFromId(n[0],[n[0],r[0]]),this.singletonFocus(n[1])];case"root":return[this.singletonFocus(n[1]),this.singletonFocus(n[0])];default:return n.map(this.singletonFocus.bind(this))}}combinePunctuations(t,e,r,n){if(0===t.length)return n;const o=t.shift(),i=e.shift();return o===i?(r.push(i),this.combinePunctuations(t,e,r,n)):(e.unshift(i),r.push(o),t.length===e.length?(n.push(this.focusFromId(o,r.concat(e))),n):(n.push(this.focusFromId(o,r)),this.combinePunctuations(t,e,[],n)))}makePairList(t,e){if(0===t.length)return[];if(1===t.length)return[this.singletonFocus(t[0])];const r=[this.singletonFocus(t.shift())];for(let n=0,o=t.length;n<o;n++)r.push(this.focusFromId(t[n],[e[n],t[n]]));return r}left(){super.left();const t=this.levels.indexOf(this.getFocus());if(null===t)return null;const e=this.levels.get(t-1);return e||null}right(){super.right();const t=this.levels.indexOf(this.getFocus());if(null===t)return null;const e=this.levels.get(t+1);return e||null}findFocusOnLevel(t){return this.levels.find((e=>e.getSemanticPrimary().id===t))}}e.SemanticWalker=i},9806:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.SyntaxWalker=void 0;const n=r(707),o=r(3284),i=r(9797);class a extends o.AbstractWalker{constructor(t,e,r,n){super(t,e,r,n),this.node=t,this.generator=e,this.highlighter=r,this.levels=null,this.restoreState()}initLevels(){const t=new i.Levels;return t.push([this.primaryId()]),t}up(){super.up();const t=this.previousLevel();return t?(this.levels.pop(),this.singletonFocus(t)):null}down(){super.down();const t=this.nextLevel();if(0===t.length)return null;const e=this.singletonFocus(t[0]);return e&&this.levels.push(t),e}combineContentChildren(t,e,r,o){switch(t){case"relseq":case"infixop":case"multirel":return(0,n.interleaveLists)(o,r);case"prefixop":return r.concat(o);case"postfixop":return o.concat(r);case"matrix":case"vector":case"fenced":return o.unshift(r[0]),o.push(r[1]),o;case"cases":return o.unshift(r[0]),o;case"punctuated":return"text"===e?(0,n.interleaveLists)(o,r):o;case"appl":return[o[0],r[0],o[1]];case"root":return[o[1],o[0]];default:return o}}left(){super.left();const t=this.levels.indexOf(this.primaryId());if(null===t)return null;const e=this.levels.get(t-1);return e?this.singletonFocus(e):null}right(){super.right();const t=this.levels.indexOf(this.primaryId());if(null===t)return null;const e=this.levels.get(t+1);return e?this.singletonFocus(e):null}findFocusOnLevel(t){return this.singletonFocus(t.toString())}focusDomNodes(){return[this.getFocus().getDomPrimary()]}focusSemanticNodes(){return[this.getFocus().getSemanticPrimary()]}}e.SyntaxWalker=a},1799:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.TableWalker=void 0;const n=r(5740),o=r(8496),i=r(9806),a=r(179);class s extends i.SyntaxWalker{constructor(t,e,r,n){super(t,e,r,n),this.node=t,this.generator=e,this.highlighter=r,this.firstJump=null,this.key_=null,this.row_=0,this.currentTable_=null,this.keyMapping.set(o.KeyCode.ZERO,this.jumpCell.bind(this)),this.keyMapping.set(o.KeyCode.ONE,this.jumpCell.bind(this)),this.keyMapping.set(o.KeyCode.TWO,this.jumpCell.bind(this)),this.keyMapping.set(o.KeyCode.THREE,this.jumpCell.bind(this)),this.keyMapping.set(o.KeyCode.FOUR,this.jumpCell.bind(this)),this.keyMapping.set(o.KeyCode.FIVE,this.jumpCell.bind(this)),this.keyMapping.set(o.KeyCode.SIX,this.jumpCell.bind(this)),this.keyMapping.set(o.KeyCode.SEVEN,this.jumpCell.bind(this)),this.keyMapping.set(o.KeyCode.EIGHT,this.jumpCell.bind(this)),this.keyMapping.set(o.KeyCode.NINE,this.jumpCell.bind(this))}move(t){this.key_=t;const e=super.move(t);return this.modifier=!1,e}up(){return this.moved=a.WalkerMoves.UP,this.eligibleCell_()?this.verticalMove_(!1):super.up()}down(){return this.moved=a.WalkerMoves.DOWN,this.eligibleCell_()?this.verticalMove_(!0):super.down()}jumpCell(){if(!this.isInTable_()||null===this.key_)return this.getFocus();if(this.moved===a.WalkerMoves.ROW){this.moved=a.WalkerMoves.CELL;const t=this.key_-o.KeyCode.ZERO;return this.isLegalJump_(this.row_,t)?this.jumpCell_(this.row_,t):this.getFocus()}const t=this.key_-o.KeyCode.ZERO;return t>this.currentTable_.childNodes.length?this.getFocus():(this.row_=t,this.moved=a.WalkerMoves.ROW,this.getFocus().clone())}undo(){const t=super.undo();return t===this.firstJump&&(this.firstJump=null),t}eligibleCell_(){const t=this.getFocus().getSemanticPrimary();return this.modifier&&"cell"===t.type&&-1!==s.ELIGIBLE_CELL_ROLES.indexOf(t.role)}verticalMove_(t){const e=this.previousLevel();if(!e)return null;const r=this.getFocus(),n=this.levels.indexOf(this.primaryId()),o=this.levels.pop(),i=this.levels.indexOf(e),a=this.levels.get(t?i+1:i-1);if(!a)return this.levels.push(o),null;this.setFocus(this.singletonFocus(a));const s=this.nextLevel();return s[n]?(this.levels.push(s),this.singletonFocus(s[n])):(this.setFocus(r),this.levels.push(o),null)}jumpCell_(t,e){this.firstJump?this.virtualize(!1):(this.firstJump=this.getFocus(),this.virtualize(!0));const r=this.currentTable_.id.toString();let n;do{n=this.levels.pop()}while(-1===n.indexOf(r));this.levels.push(n),this.setFocus(this.singletonFocus(r)),this.levels.push(this.nextLevel());const o=this.currentTable_.childNodes[t-1];return this.setFocus(this.singletonFocus(o.id.toString())),this.levels.push(this.nextLevel()),this.singletonFocus(o.childNodes[e-1].id.toString())}isLegalJump_(t,e){const r=n.querySelectorAllByAttrValue(this.getRebuilt().xml,"id",this.currentTable_.id.toString())[0];if(!r||r.hasAttribute("alternative"))return!1;const o=this.currentTable_.childNodes[t-1];if(!o)return!1;const i=n.querySelectorAllByAttrValue(r,"id",o.id.toString())[0];return!(!i||i.hasAttribute("alternative"))&&!(!o||!o.childNodes[e-1])}isInTable_(){let t=this.getFocus().getSemanticPrimary();for(;t;){if(-1!==s.ELIGIBLE_TABLE_TYPES.indexOf(t.type))return this.currentTable_=t,!0;t=t.parent}return!1}}e.TableWalker=s,s.ELIGIBLE_CELL_ROLES=["determinant","rowvector","binomial","squarematrix","multiline","matrix","vector","cases","table"],s.ELIGIBLE_TABLE_TYPES=["multiline","matrix","vector","cases","table"]},179:function(t,e){Object.defineProperty(e,"__esModule",{value:!0}),e.WalkerState=e.WalkerMoves=void 0,function(t){t.UP="up",t.DOWN="down",t.LEFT="left",t.RIGHT="right",t.REPEAT="repeat",t.DEPTH="depth",t.ENTER="enter",t.EXPAND="expand",t.HOME="home",t.SUMMARY="summary",t.DETAIL="detail",t.ROW="row",t.CELL="cell"}(e.WalkerMoves||(e.WalkerMoves={}));class r{static resetState(t){delete r.STATE[t]}static setState(t,e){r.STATE[t]=e}static getState(t){return r.STATE[t]}}e.WalkerState=r,r.STATE={}},3362:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.walkerMapping_=e.walker=void 0;const n=r(162),o=r(6295),i=r(9806),a=r(1799);e.walker=function(t,r,n,o,i){return(e.walkerMapping_[t.toLowerCase()]||e.walkerMapping_.dummy)(r,n,o,i)},e.walkerMapping_={dummy:(t,e,r,o)=>new n.DummyWalker(t,e,r,o),semantic:(t,e,r,n)=>new o.SemanticWalker(t,e,r,n),syntax:(t,e,r,n)=>new i.SyntaxWalker(t,e,r,n),table:(t,e,r,n)=>new a.TableWalker(t,e,r,n)}},1204:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.getBySemanticId=e.getSemanticRoot=e.getAttribute=e.splitAttribute=void 0;const n=r(5740),o=r(2298);e.splitAttribute=function(t){return t?t.split(/,/):[]},e.getAttribute=function(t,e){return t.getAttribute(e)},e.getSemanticRoot=function(t){if(t.hasAttribute(o.Attribute.TYPE)&&!t.hasAttribute(o.Attribute.PARENT))return t;const e=n.querySelectorAllByAttr(t,o.Attribute.TYPE);for(let 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<header id="title-block-header">
<h1 class="title" style="text-align:center">Trivial Relocatability For
C++26</h1>
<h3 class="subtitle" style="text-align:center">Proposal to safely
relocate objects in memory</h3>
<table style="border:none;float:right">
  <tr>
    <td>Document #:</td>
    <td>P2786R12</td>
  </tr>
  <tr>
    <td>Date:</td>
    <td><!-- $TimeStamp$ -->
2025-02-10 22:54 CET<!-- $ --></td>
  </tr>
  <tr>
    <td style="vertical-align:top">Project:</td>
    <td>Programming Language C++</td>
  </tr>
  <tr>
    <td style="vertical-align:top">Audience:</td>
    <td>
      CWG, LWG<br>
    </td>
  </tr>
  <tr>
    <td style="vertical-align:top">Reply-to:</td>
    <td>
      Mungo Gill<br>&lt;<a href="mailto:mgill83@bloomberg.net" class="email">mgill83@bloomberg.net</a>&gt;<br>
      Joshua Berne<br>&lt;<a href="mailto:jberne4@bloomberg.net" class="email">jberne4@bloomberg.net</a>&gt;<br>
      Corentin Jabot<br>&lt;<a href="mailto:corentinjabot@gmail.com" class="email">corentinjabot@gmail.com</a>&gt;<br>
      Pablo Halpern<br>&lt;<a href="mailto:phalpern@halpernwightsoftware.com" class="email">phalpern@halpernwightsoftware.com</a>&gt;<br>
      Lori Hughes<br>&lt;<a href="mailto:lori@lorihughes.com" class="email">lori@lorihughes.com</a>&gt;<br>
    </td>
  </tr>
</table>
</header>
<div style="clear:both">
<div id="TOC" role="doc-toc">
<h1 id="toctitle">Contents</h1>
<ul>
<li><a href="#abstract" id="toc-abstract"><span class="toc-section-number">1</span> Abstract<span></span></a></li>
<li><a href="#rev.hist" id="toc-rev.hist"><span class="toc-section-number">2</span> Revision History<span></span></a>
<ul>
<li><a href="#r12-february-2025-mid-hagenberg" id="toc-r12-february-2025-mid-hagenberg">R12: February 2025
(mid-Hagenberg)<span></span></a></li>
<li><a href="#r11-december-2024-post-wrocław-mailing" id="toc-r11-december-2024-post-wrocław-mailing">R11: December 2024
(post-Wrocław mailing)<span></span></a></li>
<li><a href="#r10-november-2024-wrocław-meeting-lewg" id="toc-r10-november-2024-wrocław-meeting-lewg">R10: November 2024
(Wrocław meeting, LEWG)<span></span></a></li>
<li><a href="#r9-november-2024-wrocław-meeting-ewg" id="toc-r9-november-2024-wrocław-meeting-ewg">R9: November 2024 (Wrocław
meeting, EWG)<span></span></a></li>
<li><a href="#r8-october-2024-pre-wrocław-mailing" id="toc-r8-october-2024-pre-wrocław-mailing">R8: October 2024
(pre-Wrocław mailing)<span></span></a></li>
<li><a href="#r7-september-2024-midterm-mailing" id="toc-r7-september-2024-midterm-mailing">R7: September 2024 (midterm
mailing)<span></span></a></li>
<li><a href="#r16-january-2023-april-2024" id="toc-r16-january-2023-april-2024">R1–6: January 2023 – April
2024<span></span></a></li>
</ul></li>
<li><a href="#proposal.status" id="toc-proposal.status"><span class="toc-section-number">3</span> Proposal Status<span></span></a>
<ul>
<li><a href="#class-property-specifier-keywords" id="toc-class-property-specifier-keywords"><span class="toc-section-number">3.1</span> Class-property specifier
keywords<span></span></a></li>
<li><a href="#low-level-memory-management-library-functions" id="toc-low-level-memory-management-library-functions"><span class="toc-section-number">3.2</span> Low-level memory-management
Library functions<span></span></a></li>
<li><a href="#consumer-library-interface" id="toc-consumer-library-interface"><span class="toc-section-number">3.3</span> Consumer Library
interface<span></span></a></li>
<li><a href="#library-traits-for-relocatability-and-replaceability" id="toc-library-traits-for-relocatability-and-replaceability"><span class="toc-section-number">3.4</span> Library Traits for relocatability
and replaceability<span></span></a></li>
</ul></li>
<li><a href="#open.issues" id="toc-open.issues"><span class="toc-section-number">4</span> Open Issues as of
R11<span></span></a>
<ul>
<li><a href="#keyword-selection" id="toc-keyword-selection"><span class="toc-section-number">4.1</span> Keyword
selection<span></span></a></li>
<li><a href="#low-level-interface" id="toc-low-level-interface"><span class="toc-section-number">4.2</span> Low-level
interface<span></span></a></li>
<li><a href="#consumer-interface" id="toc-consumer-interface"><span class="toc-section-number">4.3</span> Consumer
interface<span></span></a></li>
<li><a href="#is_nothrow_relocatable-trait" id="toc-is_nothrow_relocatable-trait"><span class="toc-section-number">4.4</span>
<code class="sourceCode cpp">is_nothrow_relocatable</code>
trait<span></span></a></li>
</ul></li>
<li><a href="#doc.conventions" id="toc-doc.conventions"><span class="toc-section-number">5</span> Document
Conventions<span></span></a>
<ul>
<li><a href="#typography" id="toc-typography"><span class="toc-section-number">5.1</span> Typography<span></span></a></li>
<li><a href="#definitions" id="toc-definitions"><span class="toc-section-number">5.2</span> Definitions<span></span></a></li>
<li><a href="#core-language-additions" id="toc-core-language-additions"><span class="toc-section-number">5.3</span> Core-language
additions<span></span></a></li>
<li><a href="#library.additions" id="toc-library.additions"><span class="toc-section-number">5.4</span> Library
additions<span></span></a></li>
</ul></li>
<li><a href="#introduction" id="toc-introduction"><span class="toc-section-number">6</span> Introduction<span></span></a></li>
<li><a href="#basic.ideas" id="toc-basic.ideas"><span class="toc-section-number">7</span> Basic Ideas<span></span></a>
<ul>
<li><a href="#trivial-relocatability" id="toc-trivial-relocatability"><span class="toc-section-number">7.1</span> Trivial
relocatability<span></span></a></li>
<li><a href="#replaceability" id="toc-replaceability"><span class="toc-section-number">7.2</span>
Replaceability<span></span></a></li>
<li><a href="#examples-of-types-having-neither-one-or-both-properties" id="toc-examples-of-types-having-neither-one-or-both-properties"><span class="toc-section-number">7.3</span> Examples of types having neither,
one, or both properties<span></span></a></li>
<li><a href="#independent-features" id="toc-independent-features"><span class="toc-section-number">7.4</span> Independent
features<span></span></a></li>
</ul></li>
<li><a href="#technical-background" id="toc-technical-background"><span class="toc-section-number">8</span> Technical
Background<span></span></a></li>
<li><a href="#basic-design-principles" id="toc-basic-design-principles"><span class="toc-section-number">9</span> Basic Design
Principles<span></span></a>
<ul>
<li><a href="#create-a-feature-for-users-not-just-the-standard-library" id="toc-create-a-feature-for-users-not-just-the-standard-library"><span class="toc-section-number">9.1</span> Create a feature for users, not
just the Standard Library<span></span></a></li>
<li><a href="#a-formal-specification-is-built-around-object-lifetimes" id="toc-a-formal-specification-is-built-around-object-lifetimes"><span class="toc-section-number">9.2</span> A formal specification is built
around object lifetimes<span></span></a></li>
<li><a href="#behavior-must-be-reliable" id="toc-behavior-must-be-reliable"><span class="toc-section-number">9.3</span> Behavior must be
reliable<span></span></a></li>
<li><a href="#guard-against-accidental-undefined-behavior" id="toc-guard-against-accidental-undefined-behavior"><span class="toc-section-number">9.4</span> Guard against accidental undefined
behavior<span></span></a></li>
</ul></li>
<li><a href="#core-proposal" id="toc-core-proposal"><span class="toc-section-number">10</span> Core Proposal<span></span></a>
<ul>
<li><a href="#trivial-relocatability-1" id="toc-trivial-relocatability-1"><span class="toc-section-number">10.1</span> Trivial
relocatability<span></span></a></li>
<li><a href="#replaceability-1" id="toc-replaceability-1"><span class="toc-section-number">10.2</span>
Replaceability<span></span></a></li>
<li><a href="#not-optimizing-stdswap" id="toc-not-optimizing-stdswap"><span class="toc-section-number">10.3</span> (Not) Optimizing
<code class="sourceCode cpp">std<span class="op">::</span>swap</code><span></span></a></li>
</ul></li>
<li><a href="#simple-worked-examples" id="toc-simple-worked-examples"><span class="toc-section-number">11</span> Simple Worked
Examples<span></span></a>
<ul>
<li><a href="#exposition-only-classes" id="toc-exposition-only-classes"><span class="toc-section-number">11.1</span> Exposition-only
classes<span></span></a></li>
<li><a href="#rule-of-zero" id="toc-rule-of-zero"><span class="toc-section-number">11.2</span> Rule of
zero<span></span></a></li>
<li><a href="#impact-of-destructors" id="toc-impact-of-destructors"><span class="toc-section-number">11.3</span> Impact of
destructors<span></span></a></li>
<li><a href="#impact-of-move-constructors" id="toc-impact-of-move-constructors"><span class="toc-section-number">11.4</span> Impact of move
constructors<span></span></a></li>
</ul></li>
<li><a href="#plans-for-library-update" id="toc-plans-for-library-update"><span class="toc-section-number">12</span> Plans for Library
Update<span></span></a>
<ul>
<li><a href="#immediate-updates" id="toc-immediate-updates"><span class="toc-section-number">12.1</span> Immediate
updates<span></span></a></li>
<li><a href="#abi-concerns" id="toc-abi-concerns"><span class="toc-section-number">12.2</span> ABI
concerns<span></span></a></li>
<li><a href="#specific-follow-ups" id="toc-specific-follow-ups"><span class="toc-section-number">12.3</span> Specific
follow-ups<span></span></a></li>
</ul></li>
<li><a href="#use-cases" id="toc-use-cases"><span class="toc-section-number">13</span> Use Cases<span></span></a>
<ul>
<li><a href="#optimizing-stdvector-at-run-time" id="toc-optimizing-stdvector-at-run-time"><span class="toc-section-number">13.1</span> Optimizing
<code class="sourceCode cpp">std<span class="op">::</span>vector</code>
at run time<span></span></a></li>
<li><a href="#optimizing-stdoptional-to-be-trivially-relocatable-and-replaceable" id="toc-optimizing-stdoptional-to-be-trivially-relocatable-and-replaceable"><span class="toc-section-number">13.2</span> Optimizing <code class="sourceCode cpp">std<span class="op">::</span>optional</code> to
be trivially relocatable and replaceable<span></span></a></li>
</ul></li>
<li><a href="#implementation" id="toc-implementation"><span class="toc-section-number">14</span> Implementation
Experience<span></span></a></li>
<li><a href="#faq." id="toc-faq."><span class="toc-section-number">15</span> FAQ<span></span></a>
<ul>
<li><a href="#is-void-trivially-relocatable" id="toc-is-void-trivially-relocatable"><span class="toc-section-number">15.1</span> Is
<code class="sourceCode cpp"><span class="dt">void</span></code>
trivially relocatable?<span></span></a></li>
<li><a href="#are-reference-types-trivially-relocatable" id="toc-are-reference-types-trivially-relocatable"><span class="toc-section-number">15.2</span> Are reference types trivially
relocatable?<span></span></a></li>
<li><a href="#why-can-a-class-with-a-reference-member-be-trivially-relocatable" id="toc-why-can-a-class-with-a-reference-member-be-trivially-relocatable"><span class="toc-section-number">15.3</span> Why can a class with a reference
member be trivially relocatable?<span></span></a></li>
<li><a href="#are-cv-qualified-types-notably-const-types-trivially-relocatable" id="toc-are-cv-qualified-types-notably-const-types-trivially-relocatable"><span class="toc-section-number">15.4</span> Are <em>cv</em>-qualified types,
notably
<code class="sourceCode cpp"><span class="kw">const</span></code> types,
trivially relocatable?<span></span></a></li>
<li><a href="#can-const-qualified-types-be-passed-to-trivially_relocate" id="toc-can-const-qualified-types-be-passed-to-trivially_relocate"><span class="toc-section-number">15.5</span> Can
<code class="sourceCode cpp"><span class="kw">const</span></code>-qualified
types be passed to
<code class="sourceCode cpp">trivially_relocate</code>?<span></span></a></li>
<li><a href="#can-types-that-are-not-implicit-lifetime-types-be-trivially-relocatable" id="toc-can-types-that-are-not-implicit-lifetime-types-be-trivially-relocatable"><span class="toc-section-number">15.6</span> Can types that are not
implicit-lifetime types be trivially relocatable?<span></span></a></li>
<li><a href="#faq.virt.bases" id="toc-faq.virt.bases"><span class="toc-section-number">15.7</span> Why are virtual base classes not
trivially relocatable?<span></span></a></li>
<li><a href="#what-happens-if-a-relocate-operation-throws" id="toc-what-happens-if-a-relocate-operation-throws"><span class="toc-section-number">15.8</span> What happens if a relocate
operation throws?<span></span></a></li>
<li><a href="#why-do-deleted-special-members-inhibit-implicit-trivial-relocatability" id="toc-why-do-deleted-special-members-inhibit-implicit-trivial-relocatability"><span class="toc-section-number">15.9</span> Why do deleted special members
inhibit implicit trivial relocatability?<span></span></a></li>
<li><a href="#can-the-compiler-transform-argument-passing-with-trivial-relocation" id="toc-can-the-compiler-transform-argument-passing-with-trivial-relocation"><span class="toc-section-number">15.10</span> Can the compiler transform
argument passing with trivial relocation?<span></span></a></li>
<li><a href="#can-the-standard-library-containers-use-this-new-feature-internally" id="toc-can-the-standard-library-containers-use-this-new-feature-internally"><span class="toc-section-number">15.11</span> Can the Standard Library
containers use this new feature internally?<span></span></a></li>
<li><a href="#do-implementations-need-to-mark-classes-trivially_relocatable_if_eligible-to-benefit" id="toc-do-implementations-need-to-mark-classes-trivially_relocatable_if_eligible-to-benefit"><span class="toc-section-number">15.12</span> Do implementations need to mark
classes
<code class="sourceCode cpp">trivially_relocatable_if_eligible</code> to
benefit?<span></span></a></li>
<li><a href="#can-i-mark-as-trivially-relocatable-a-type-that-is-not-replaceable" id="toc-can-i-mark-as-trivially-relocatable-a-type-that-is-not-replaceable"><span class="toc-section-number">15.13</span> Can I mark as trivially
relocatable a type that is not replaceable?<span></span></a></li>
<li><a href="#can-i-mark-a-type-as-replaceable-but-not-trivially-relocatable" id="toc-can-i-mark-a-type-as-replaceable-but-not-trivially-relocatable"><span class="toc-section-number">15.14</span> Can I mark a type as replaceable
but not trivially relocatable?<span></span></a></li>
<li><a href="#what-happened-to-the-predicates-for-the-contextual-keywords" id="toc-what-happened-to-the-predicates-for-the-contextual-keywords"><span class="toc-section-number">15.15</span> What happened to the predicates
for the contextual keywords?<span></span></a></li>
<li><a href="#why-is-copy-replacement-unsupported" id="toc-why-is-copy-replacement-unsupported"><span class="toc-section-number">15.16</span> Why is copy-replacement
unsupported?<span></span></a></li>
<li><a href="#why-is-marking-a-class-that-can-never-be-trivially-relocatable-not-ill-formed" id="toc-why-is-marking-a-class-that-can-never-be-trivially-relocatable-not-ill-formed"><span class="toc-section-number">15.17</span> Why is marking a class that can
<em>never</em> be trivially relocatable not
ill-formed?<span></span></a></li>
<li><a href="#why-is-there-no-is_trivially_replaceable-trait" id="toc-why-is-there-no-is_trivially_replaceable-trait"><span class="toc-section-number">15.18</span> Why is there no
<code class="sourceCode cpp">is_trivially_replaceable</code>
trait?<span></span></a></li>
<li><a href="#is-it-ub-to-mark-a-nonconforming-type-as-trivially-relocatable" id="toc-is-it-ub-to-mark-a-nonconforming-type-as-trivially-relocatable"><span class="toc-section-number">15.19</span> Is it UB to mark a nonconforming
type as trivially relocatable?<span></span></a></li>
<li><a href="#is-it-ub-to-mark-a-nonconforming-type-as-replaceable" id="toc-is-it-ub-to-mark-a-nonconforming-type-as-replaceable"><span class="toc-section-number">15.20</span> Is it UB to mark a nonconforming
type as replaceable?<span></span></a></li>
<li><a href="#why-does-replaceability-not-require-trivial-relocatability" id="toc-why-does-replaceability-not-require-trivial-relocatability"><span class="toc-section-number">15.21</span> Why does replaceability not
require trivial relocatability?<span></span></a></li>
<li><a href="#why-does-trivial-relocation-support-const-data-members-but-replacement-does-not" id="toc-why-does-trivial-relocation-support-const-data-members-but-replacement-does-not"><span class="toc-section-number">15.22</span> Why does trivial relocation
support
<code class="sourceCode cpp"><span class="kw">const</span></code> data
members, but replacement does not?<span></span></a></li>
<li><a href="#why-does-library.class.props-explicitly-call-out-permission-to-use-the-contextual-keywords" id="toc-why-does-library.class.props-explicitly-call-out-permission-to-use-the-contextual-keywords"><span class="toc-section-number">15.23</span> Why does [library.class.props]
explicitly call out permission to use the contextual
keywords?<span></span></a></li>
<li><a href="#why-are-classes-with-virtual-base-classes-replaceable-what-does-that-even-mean" id="toc-why-are-classes-with-virtual-base-classes-replaceable-what-does-that-even-mean"><span class="toc-section-number">15.24</span> Why are classes with virtual
base classes “replaceable”? What does that even
mean?<span></span></a></li>
</ul></li>
<li><a href="#illustrative-examples" id="toc-illustrative-examples"><span class="toc-section-number">16</span> Illustrative
Examples<span></span></a>
<ul>
<li><a href="#unconstrained-vector" id="toc-unconstrained-vector"><span class="toc-section-number">16.1</span> Unconstrained
vector<span></span></a></li>
<li><a href="#standard-vector" id="toc-standard-vector"><span class="toc-section-number">16.2</span> Standard
vector<span></span></a></li>
<li><a href="#conforming-implementation-of-a-trivially-relocatable-stdoptional" id="toc-conforming-implementation-of-a-trivially-relocatable-stdoptional"><span class="toc-section-number">16.3</span> Conforming implementation of a
trivially relocatable <code class="sourceCode cpp">std<span class="op">::</span>optional</code><span></span></a></li>
<li><a href="#c26-implementation-using-internal-array" id="toc-c26-implementation-using-internal-array"><span class="toc-section-number">16.4</span> C++26 implementation using
internal array<span></span></a></li>
</ul></li>
<li><a href="#proposed-wording" id="toc-proposed-wording"><span class="toc-section-number">17</span> Proposed Wording<span></span></a>
<ul>
<li><a href="#add-new-identifiers-with-a-special-meaning" id="toc-add-new-identifiers-with-a-special-meaning"><span class="toc-section-number">17.1</span> Add new identifiers with a
special meaning<span></span></a></li>
<li><a href="#specify-trivially-relocatable-types" id="toc-specify-trivially-relocatable-types"><span class="toc-section-number">17.2</span> Specify trivially relocatable
types<span></span></a></li>
<li><a href="#address-trivial-relocation-of-lambdas" id="toc-address-trivial-relocation-of-lambdas"><span class="toc-section-number">17.3</span> Address trivial relocation of
lambdas<span></span></a></li>
<li><a href="#update-grammar-to-support-_if_eligible-contextual-keywords" id="toc-update-grammar-to-support-_if_eligible-contextual-keywords"><span class="toc-section-number">17.4</span> Update grammar to support
<code class="sourceCode cpp">_if_eligible</code> contextual
keywords<span></span></a></li>
<li><a href="#specification-for-trivially-relocatable-classes" id="toc-specification-for-trivially-relocatable-classes"><span class="toc-section-number">17.5</span> Specification for trivially
relocatable classes<span></span></a></li>
<li><a href="#add-feature-macros" id="toc-add-feature-macros"><span class="toc-section-number">17.6</span> Add feature
macros<span></span></a></li>
<li><a href="#library-wording" id="toc-library-wording"><span class="toc-section-number">17.7</span> Library
wording<span></span></a></li>
<li><a href="#add-new-type-traits" id="toc-add-new-type-traits"><span class="toc-section-number">17.8</span> Add new type
traits<span></span></a></li>
<li><a href="#specify-the-compiler-magic-functions" id="toc-specify-the-compiler-magic-functions"><span class="toc-section-number">17.9</span> Specify the compiler-magic
functions<span></span></a></li>
</ul></li>
<li><a href="#acknowledgements" id="toc-acknowledgements"><span class="toc-section-number">18</span>
Acknowledgements<span></span></a></li>
<li><a href="#bibliography" id="toc-bibliography"><span class="toc-section-number">19</span> References<span></span></a></li>
</ul>
</div>
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<h1 data-number="1" id="abstract"><span class="header-section-number">1</span> Abstract<a href="#abstract" class="self-link"></a></h1>
<p>Many types in C++ cannot be trivially moved or destroyed but do
support trivially moving an object from one location to another by
copying its bits — an operation known as <em>trivial relocation</em>.
Some types even support bitwise swapping, which requires replacing the
objects passed to the <code class="sourceCode cpp">swap</code> function,
without violating any object invariants. Optimizing containers to take
advantage of this property of a type is already in widespread use
throughout the industry but is undefined behavior as far as the language
is concerned. This paper provides a mechanism to annotate types as
having the appropriate properties to be eligible for these
optimizations, along with library interfaces to make use of them in a
well-defined manner.</p>
<h1 data-number="2" id="rev.hist"><span class="header-section-number">2</span> Revision History<a href="#rev.hist" class="self-link"></a></h1>
<h2 class="unnumbered" id="r12-february-2025-mid-hagenberg">R12:
February 2025 (mid-Hagenberg)<a href="#r12-february-2025-mid-hagenberg" class="self-link"></a></h2>
<ul>
<li><p>We removed the single-object
<code class="sourceCode cpp">trivially_relocate_at</code> function
(retaining the bulk
<code class="sourceCode cpp">trivially_relocate</code> function), per
LEWG vote in 2025-01-14 telecom.</p></li>
<li><p>LEWG forwarded the library portion of this paper to LWG in their
2025-01-14 telecom.</p></li>
<li><p>We renamed
<code class="sourceCode cpp">memberwise_trivially_relocatable</code> to
<code class="sourceCode cpp">trivially_relocatable_if_eligible</code>
and renamed <code class="sourceCode cpp">memberwise_replaceable</code>
to <code class="sourceCode cpp">replaceable_if_eligible</code> per EWG
vote on 2025-02-10 in Hagenberg.</p></li>
<li><p>EWG forwarded the language portion of this paper to CWG in the
first session on 2025-02-10 in Hagenberg.</p></li>
</ul>
<!-- PGH: "Wroc\l{}aw" does not render correctly in HTML, so reverting all references to "Wrocław". -->
<h2 class="unnumbered" id="r11-december-2024-post-wrocław-mailing">R11:
December 2024 (post-Wrocław mailing)<a href="#r11-december-2024-post-wrocław-mailing" class="self-link"></a></h2>
<p><em>R11 is the third of three revisions in the post-Wrocław
mailing.</em></p>
<p>Although there was some support for each of changes made between R9
and R10 and although those changes were intended to <em>increase</em>
consensus, some of those changes appeared to <em>decrease</em> consensus
in the forwarding poll.</p>
<ul>
<li><p>The shortened keywords, despite being the most popular in an LEWG
bikeshed poll, resulted in several strongly opposed votes in the
forwarding poll because, as Nico Josuttis put it, “This group has to
stop giving different semantics the same name.” The lesson we took from
that discussion is that keyword names need rationale and should
<em>not</em> be subject to “bikeshed” discussions. R11 reverts the
keywords to those approved by EWG in R9 but leaves keyword naming as an
open issue. Alternatives are presented along with a set of principles,
including the one articulated by Nico, for choosing reasonable
keywords.</p></li>
<li><p>A number of people expressed discomfort with forwarding the
low-level interface without knowing the shape of a standard
consumer-level interface. R11 restores the consumer-level
<code class="sourceCode cpp">relocate</code> algorithm present in R9 but
leaves the choice of consumer-level interface as an open issue, citing
an alternative interface described in <span class="citation" data-cites="P3516R0">[<a href="https://isocpp.org/files/papers/P3516R0.html" role="doc-biblioref">P3516R0</a>]</span> (unpublished as of this
writing).</p></li>
<li><p>The removal of
<code class="sourceCode cpp">swap_value_representations</code>
<em>did</em> increase consensus, so it has also been omitted from
R11.</p></li>
</ul>
<p>In brief, the changes from R10 to R11 are as described below.</p>
<ul>
<li><p>Added a new <a href="#proposal.status">Proposal Status</a>
section that includes a brief summary of the proposal and remaining open
issues</p></li>
<li><p>Added a new <a href="#open.issues">Open Issues</a> section with
recommended resolutions and possible polls</p></li>
<li><p>Restored the keywords to the R9 versions, as approved by
EWG</p></li>
<li><p>Added a low-level
<code class="sourceCode cpp">trivially_relocate_at</code> interface to
relocate a single object</p></li>
<li><p>Restored the consumer-level
<code class="sourceCode cpp">relocate</code> algorithm that was present
in R9</p></li>
<li><p>Added a
<code class="sourceCode cpp">is_nothrow_relocatable</code>
trait</p></li>
</ul>
<h2 class="unnumbered" id="r10-november-2024-wrocław-meeting-lewg">R10:
November 2024 (Wrocław meeting, LEWG)<a href="#r10-november-2024-wrocław-meeting-lewg" class="self-link"></a></h2>
<p><em>R10 is the second of three revisions in the post-Wrocław
mailing.</em></p>
<p>The R10 revision, containing changes made after EWG review in
Wrocław, was presented to LEWG on Wednesday afternoon during the Wrocław
meeting. With the exception of the keyword changes, the R10 revision
contains no language changes and would not, therefore, affect CWG
review.</p>
<p>There was some concern that the keywords approved by EWG and the
consumer interface described in R9 would create some opposition in LEWG.
Since the paper is mostly intended to address a language feature, the
library interface was trimmed back to a minimal set of language-support
features, and the keywords were shortened, though the new keywords were
expected to be discussed and voted on before being finalized.</p>
<ul>
<li><p>Changed keywords from
<code class="sourceCode cpp">memberwise_trivially_relocatable</code> and
<code class="sourceCode cpp">memberwise_replceable</code> to
<code class="sourceCode cpp">trivially_relocatable</code> and
<code class="sourceCode cpp">replceable</code></p></li>
<li><p>Reduced scope to minimal set of features</p>
<ul>
<li>Removed the consumer-level, non-trivial,
<code class="sourceCode cpp">relocate</code> algorithm</li>
<li>Removed the
<code class="sourceCode cpp">swap_value_representations</code> function
template</li>
<li>Deferred
<code class="sourceCode cpp">std<span class="op">::</span>swap</code>
optimizations to <code class="sourceCode cpp">QoI</code></li>
</ul></li>
<li><p>Editorial changes to sync with the technical changes above</p>
<ul>
<li>Removed all content referring to
<code class="sourceCode cpp">swap_value_repesentations</code> and
<code class="sourceCode cpp">relocate</code></li>
<li>Removed most remaining content talking about
<code class="sourceCode cpp">swap</code></li>
<li>Removed Library support for nontrivial relocation</li>
<li>Added rationale for how <code class="sourceCode cpp">swap</code> can
be optimized with just this simplified paper</li>
<li>Removed FAQ entries that were no longer relevant</li>
<li>Added a section on future Consumer APIs</li>
</ul></li>
</ul>
<p><span class="citation" data-cites="P2786R10">[<a href="https://wg21.link/p2786r10" role="doc-biblioref">P2786R10</a>]</span> failed to reach consensus to
forward in LEWG in Wrocław.</p>
<h2 class="unnumbered" id="r9-november-2024-wrocław-meeting-ewg">R9:
November 2024 (Wrocław meeting, EWG)<a href="#r9-november-2024-wrocław-meeting-ewg" class="self-link"></a></h2>
<p><em>R9 is the first of three revisions in the post-Wrocław
mailing.</em></p>
<p>The R9 revision was discussed in EWG on the Monday of the Wrocław
meeting. It differs from the pre-meeting mailing in having more examples
and correcting a few, noncontroversial technical issues. <span class="citation" data-cites="P2786R9">[<a href="https://wg21.link/p2786r9" role="doc-biblioref">P2786R9</a>]</span> was forwarded by EWG to Core
and LWG.</p>
<ul>
<li>Added missing precondition to
<code class="sourceCode cpp">trivially_relocate</code> and
<code class="sourceCode cpp">relocate</code></li>
<li>Added an extensive set of worked examples to demonstrate primitive
functionality</li>
<li>Added more FAQ entries prompted by reflector discussion</li>
<li>Fixed core wording
<ul>
<li>Types with deleted destructors can no longer be trivially
relocatable or replaceable.</li>
<li>To be <em>eligible for replacement</em>, a class must have an
<em>eligible</em> constructor and assignment operator.</li>
</ul></li>
<li>New wording for
<code class="sourceCode cpp">swap_value_representations</code></li>
<li>New discussion of contextual keyword renaming</li>
</ul>
<h2 class="unnumbered" id="r8-october-2024-pre-wrocław-mailing">R8:
October 2024 (pre-Wrocław mailing)<a href="#r8-october-2024-pre-wrocław-mailing" class="self-link"></a></h2>
<ul>
<li>Extracted <a href="#doc.conventions">Document Conventions</a> to
above the <a href="#introduction">Introduction</a></li>
<li>Added <a href="#basic.ideas">Basic Ideas</a>, a higher-level
introduction to the new features</li>
<li>Listed example types for the different type categories defined by
this paper</li>
<li>Corrected implementation of several example functions</li>
<li>Extended the FAQ
<ul>
<li>What happens if a relocate operation throws?</li>
<li>Why is there no
<code class="sourceCode cpp">is_trivially_replaceable</code> trait?</li>
<li>Is it UB to mark a nonconforming type as trivially relocatable?</li>
<li>Is it UB to mark a nonconforming type as replaceable?</li>
</ul></li>
<li>Explained how to apply the new features to optimize vectors</li>
</ul>
<h2 class="unnumbered" id="r7-september-2024-midterm-mailing">R7:
September 2024 (midterm mailing)<a href="#r7-september-2024-midterm-mailing" class="self-link"></a></h2>
<ul>
<li>Significant redrafting since <span class="citation" data-cites="P2786R6">[<a href="https://wg21.link/p2786r6" role="doc-biblioref">P2786R6</a>]</span> to better address EWG and LEWG
concerns</li>
<li>Simplified presentation and discussion of trivial relocatability
(for detailed history, consult <span class="citation" data-cites="P2786R6">[<a href="https://wg21.link/p2786r6" role="doc-biblioref">P2786R6</a>]</span>)</li>
<li>Integrated discussion of <code class="sourceCode cpp">swap</code>;
the present paper supersedes <span class="citation" data-cites="P3239R0">[<a href="https://wg21.link/p3239r0" role="doc-biblioref">P3239R0</a>]</span></li>
<li>Behavior changes since <span class="citation" data-cites="P2786R6">[<a href="https://wg21.link/p2786r6" role="doc-biblioref">P2786R6</a>]</span>
<ul>
<li>User-provided move assignment now prevents a type from being
implicitly trivially relocatable</li>
<li>The contextual keyword
<ul>
<li>gets a new name,
<code class="sourceCode cpp">memberwise_trivially_relocatable</code>, to
better reflect revised semantics</li>
<li>is opt-in only</li>
<li>deduces relocatability on bases and members</li>
</ul></li>
<li>No predicate follows the contextual keyword, so no mechanism for
opting out is present</li>
<li>A new <code class="sourceCode cpp">relocate</code> function
additionally supports nontrivial types and constant evaluation</li>
</ul></li>
<li>Behavior changes since <span class="citation" data-cites="P3239R0">[<a href="https://wg21.link/p3239r0" role="doc-biblioref">P3239R0</a>]</span>
<ul>
<li>Clarifies that trivial swappability is based on being replaceable
and trivially relocatable</li>
<li>Proposes a new contextual keyword,
<code class="sourceCode cpp">memberwise_replaceable</code></li>
<li>Proposes optimizing
<code class="sourceCode cpp">std<span class="op">::</span>swap</code>,
using the new properties, and the
<code class="sourceCode cpp">swap_value_representations</code>
function</li>
</ul></li>
</ul>
<h2 class="unnumbered" id="r16-january-2023-april-2024">R1–6: January
2023 – April 2024<a href="#r16-january-2023-april-2024" class="self-link"></a></h2>
<p>Early versions of this paper were careful to include comparison and
contrast with other papers in this space. That progress is archived by
<span class="citation" data-cites="P2786R6">[<a href="https://wg21.link/p2786r6" role="doc-biblioref">P2786R6</a>]</span>.</p>
<p>The evolution groups requested a clean draft that presents just our
proposal and integrates our follow-up papers such that a single coherent
design is presented, and revision R7 is the original response to that
request.</p>
<h1 data-number="3" id="proposal.status"><span class="header-section-number">3</span> Proposal Status<a href="#proposal.status" class="self-link"></a></h1>
<p>P2786R12 was forwarded by both EWG and LEWG to their respective
wording groups.</p>
<p>The language portion of this proposal was reviewed by EWG and
forwarded to CWG and LEWG during the November 2024 Wrocław meeting.
Since then, we have asked EWG to reconsider the keyword names (see <a href="#keyword-selection">Keyword selection</a>). EWG did reconsider the
keyword names and forwarded the paper with revised names at the
2025-02-10 session of the Hagenberg meeting.</p>
<p>The library portion of this proposal did not reach consensus in
Wrocław but was later forwarded by LEWG (with changes) to LWG during the
2025-01-14 telecom.</p>
<p>The short summary of the proposal, presented in the following
subsections, has only enough detail to focus discussion on the open
issues as of <span class="citation" data-cites="P2786R11">[<a href="https://wg21.link/p2786r11" role="doc-biblioref">P2786R11</a>]</span>. This brief recap is intended
for those already familiar with the concepts, terminology, and semantics
described in the rest of the paper; readers new to this proposal should
continue from the <a href="#doc.conventions">Document Conventions</a>
section. Since R11, all open issues have been addressed by the
appropriate evolution groups. Each issue lists its resolution at the
end.</p>
<h2 data-number="3.1" id="class-property-specifier-keywords"><span class="header-section-number">3.1</span> Class-property specifier
keywords<a href="#class-property-specifier-keywords" class="self-link"></a></h2>
<p>Two new <em>class-property-specifier</em>s (formerly
<em>class-virt-specifier</em>) are added to the Core language as
contextual keywords that appear in a class definition after the class
name, i.e., in the same syntactic position as
<code class="sourceCode cpp"><span class="kw">final</span></code>:</p>
<blockquote>
<p><code class="sourceCode cpp">memberwise_trivially_relocatable</code></p>
</blockquote>
<p>and</p>
<blockquote>
<p><code class="sourceCode cpp">memberwise_replaceable</code></p>
</blockquote>
<p><strong>R11 Open Issue</strong>: These keyword names are fairly long
yet not particularly descriptive of their semantics; see the <a href="#keyword-selection">Keyword selection</a> section.</p>
<p><strong>EWG Resolution</strong>: Renamed
<code class="sourceCode cpp">memberwise_trivially_relocatable</code> to
<code class="sourceCode cpp">trivially_relocatable_if_eligible</code>
and renamed <code class="sourceCode cpp">memberwise_replaceable</code>
to <code class="sourceCode cpp">replaceable_if_eligible</code>.</p>
<h2 data-number="3.2" id="low-level-memory-management-library-functions"><span class="header-section-number">3.2</span> Low-level memory-management
Library functions<a href="#low-level-memory-management-library-functions" class="self-link"></a></h2>
<p>Two functions are added to the memory management library:</p>
<blockquote>
<div class="line-block"><code class="sourceCode cpp"><span class="kw">template</span> <span class="op">&lt;</span><span class="kw">class</span> T<span class="op">&gt;</span></code><br />
    <code class="sourceCode cpp">T<span class="op">*</span> trivially_relocate_at<span class="op">(</span>T<span class="op">*</span> location, T<span class="op">*</span> from<span class="op">)</span>;</code></div>
</blockquote>
<p>to relocate a single item, and</p>
<blockquote>
<div class="line-block"><code class="sourceCode cpp"><span class="kw">template</span> <span class="op">&lt;</span><span class="kw">class</span> T<span class="op">&gt;</span></code><br />
    <code class="sourceCode cpp">T<span class="op">*</span> trivially_relocate<span class="op">(</span>T<span class="op">*</span> first, T<span class="op">*</span> last, T<span class="op">*</span> result<span class="op">)</span>;</code></div>
</blockquote>
<p>to relocate a contiguous sequence of items.</p>
<p><strong>R11 Open Issue</strong>: Because these are low-level
interfaces, only one is technically needed since one can be written in
terms of the other, but they have different safety, usability, and
efficiency trade-offs. See the <a href="#low-level-interface">Low-level
interface</a> section.</p>
<p><strong>LEWG Resolution</strong>: The single-object
<code class="sourceCode cpp">trivially_relocate_at</code> function was
removed. No change was made to the bulk
<code class="sourceCode cpp">trivially_relocate</code> function.</p>
<h2 data-number="3.3" id="consumer-library-interface"><span class="header-section-number">3.3</span> Consumer Library interface<a href="#consumer-library-interface" class="self-link"></a></h2>
<p>Many types that are not trivially relocatable can still be relocated
via move and destroy. By providing a higher-level function that performs
relocation by whichever mechanism is available and efficient for a given
type, relocation is made more convenient and more forethoughtful of
future forms of relocation. The proposed
<code class="sourceCode cpp">relocate</code> algorithm is available in a
<code class="sourceCode cpp"><span class="kw">constexpr</span></code>
context, unlike the low-level functions described above:</p>
<blockquote>
<div class="line-block"><code class="sourceCode cpp"><span class="kw">template</span> <span class="op">&lt;</span><span class="kw">class</span> T<span class="op">&gt;</span></code><br />
    <code class="sourceCode cpp"><span class="kw">constexpr</span> T<span class="op">*</span> relocate<span class="op">(</span>T<span class="op">*</span> first, T<span class="op">*</span> last, T<span class="op">*</span> result<span class="op">)</span>;</code></div>
</blockquote>
<p><strong>R11 Open Issue</strong>: <span class="citation" data-cites="P3516R0">[<a href="https://isocpp.org/files/papers/P3516R0.html" role="doc-biblioref">P3516R0</a>]</span>, which was not complete as of
this writing, presents a different consumer interface. See the <a href="#consumer-interface">Consumer interface</a> section. </p>
<p><strong>LEWG Resolution</strong>: No changes were made to the
proposed feature. <span class="citation" data-cites="P3516R0">[<a href="https://isocpp.org/files/papers/P3516R0.html" role="doc-biblioref">P3516R0</a>]</span> is still forthcoming and will
be discussed separately.</p>
<h2 data-number="3.4" id="library-traits-for-relocatability-and-replaceability"><span class="header-section-number">3.4</span> Library Traits for
relocatability and replaceability<a href="#library-traits-for-relocatability-and-replaceability" class="self-link"></a></h2>
<p>Three new traits are added to the Standard Library:</p>
<blockquote>
<div class="line-block"><code class="sourceCode cpp">is_trivially_relocatable<span class="op">&lt;</span>T<span class="op">&gt;</span></code><br />
<code class="sourceCode cpp">is_replaceable<span class="op">&lt;</span>T<span class="op">&gt;</span></code><br />
<code class="sourceCode cpp">is_nothrow_relocatable<span class="op">&lt;</span>T<span class="op">&gt;</span></code></div>
</blockquote>
<p>The last trait does not appear in previous revisions of this paper.
It was added because some people, including the authors of this paper,
believed it necessary to be able to concisely ask the question of
whether <code class="sourceCode cpp">relocate</code> can be invoked
safely. The value of this trait is equal to <code class="sourceCode cpp">is_nothrow_move_constructible_v<span class="op">&lt;</span>T<span class="op">&gt;</span> <span class="op">||</span> is_trivially_relocatable_v<span class="op">&lt;</span>T<span class="op">&gt;</span></code>
today, but its definition can be expanded in the future to include other
relocation methods. Code that uses this trait rather than directly
querying the other two traits would thus automatically benefit from
evolving support for relocation.</p>
<p><strong>R11 Open Issue</strong>: If relocation is inherently a
nothrow operation, then <code class="sourceCode cpp">nothrow</code> in
the trait name is redundant. See the <a href="#is_nothrow_relocatable-trait"><code class="sourceCode cpp">is_nothrow_relocatable</code>
trait</a> section.</p>
<p><strong>LEWG Resolution</strong>: No changes were made to the
proposed feature; this new trait was retained, and its name was
unchanged.</p>
<h1 data-number="4" id="open.issues"><span class="header-section-number">4</span> Open Issues as of R11<a href="#open.issues" class="self-link"></a></h1>
<p><strong>2025-02-10 UPDATE</strong>: EWG and LEWG have resolved all
open issues and forwarded this paper (P2786R12) to CWG and LWG. The
now-closed open issues are listed here for historical review and to
provide background on their resolution.</p>
<h2 data-number="4.1" id="keyword-selection"><span class="header-section-number">4.1</span> Keyword selection<a href="#keyword-selection" class="self-link"></a></h2>
<p>The keywords
<code class="sourceCode cpp">memberwise_trivially_relocatable</code> and
<code class="sourceCode cpp">memberwise_replaceable</code> are workable
but not very descriptive of their actual function, especially in the
case of replaceability. In both cases, the keyword doesn’t actually
establish the property in question but indicates that the property will
be deduced for the class if and only if it holds for all subobjects.</p>
<p>In trying to select better keywords, we applied the following four
principles.</p>
<ol type="1">
<li>Do not choose a keyword that strongly implies a property unless it
actually establishes that property.</li>
<li>Verbosity is acceptable within limits.</li>
<li>The keywords shouldn’t imply something radically different than
intended.</li>
<li>Relocatability and replaceability are orthogonal concepts; we need
not follow the same naming convention for both.</li>
</ol>
<p>Some people will object to principle 2 because they don’t want class
declarations to extend past the rightmost column of their display.
However, a <em>class-property-specifier</em> like
<code class="sourceCode cpp"><span class="kw">final</span></code> is an
elegant way to add properties to a class, and we can envision having a
rich set of such properties, as other languages do, in the future. Thus,
the list of properties will soon not fit on the same line as the class
name (as templated base classes often don’t already), and we should get
used to listing the properties, however long their names, on separate
lines:</p>
<div class="sourceCode" id="cb1"><pre class="sourceCode default"><code class="sourceCode default"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a>class X</span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a>  memberwise_trivially_relocatable</span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a>  memberwise_replaceable</span>
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a>  final</span>
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a>  chocolate_flavored</span>
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a>  unemployed</span>
<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a>{</span>
<span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a>  // ...</span>
<span id="cb1-9"><a href="#cb1-9" aria-hidden="true" tabindex="-1"></a>};</span></code></pre></div>
<p>The following keywords conform to the principles above.</p>
<ul>
<li><p><code class="sourceCode cpp">memberwise_trivially_relocatable</code>
and <code class="sourceCode cpp">memberwise_replaceable</code>: The
status-quo keywords, though not precise, do not run afoul of our
principles, although
<code class="sourceCode cpp">memberwise_replaceable</code> might be
considered misleading since replacement is not performed member by
member.</p></li>
<li><p><code class="sourceCode cpp">memberwise_relocatable</code>:
Although the keyword cannot establish triviality, it <em>can</em> claim
that the class can be relocated by relocating each member. If all the
class’s subobjects are trivially relocatable, it follows that the class
as a whole would be. On the downside, this paper has no provision for
memberwise nontrivial relocation, though such a capability is envisioned
for the future. Replaceability has no such equivalent.</p></li>
<li><p><code class="sourceCode cpp">trivially_relocatable_if_eligible</code>
and <code class="sourceCode cpp">replaceable_if_eligible</code>: These
keywords say exactly what is meant. Though they are somewhat long, at 33
and 23 characters, respectively, they are each only one character longer
than the status-quo keywords.</p></li>
</ul>
<p>The following keywords were ruled out based on the principles listed
above.</p>
<ul>
<li><p><code class="sourceCode cpp">trivially_relocatable</code> and
<code class="sourceCode cpp">replaceable</code>: Both violate principle
1 because neither property is guaranteed by the use of the keyword;
i.e., <code class="sourceCode cpp">is_trivially_relocatable_v<span class="op">&lt;</span>T<span class="op">&gt;</span></code>
can be <code class="sourceCode cpp"><span class="kw">false</span></code>
even if the keyword is used in the declaration of
<code class="sourceCode cpp">T</code>.</p></li>
<li><p><code class="sourceCode cpp">try_trivial_relocatable</code> and
<code class="sourceCode cpp">try_replaceable</code>: Both violate
principle 3 because “try” implies some relationship to
exceptions.</p></li>
</ul>
<p>In addition, the prefixes
<code class="sourceCode cpp">tentatively_</code>,
<code class="sourceCode cpp">provisionally_</code>, and
<code class="sourceCode cpp">conditionally_</code> were ruled out
because, though adhering to the principles, they are less descriptive
than the <code class="sourceCode cpp">_if_eligible</code> suffix,
despite being the same length or longer.</p>
<ol type="1">
<li><p>Change
<code class="sourceCode cpp">memberwise_trivially_relocatable</code> to
<code class="sourceCode cpp">memberwise_relocatable</code>. The authors
of this paper are in favor of this name change.</p></li>
<li><p>Change <code class="sourceCode cpp">memberwise_replaceable</code>
to <code class="sourceCode cpp">replaceable_if_eligible</code>. If poll
1 fails to reach consensus, also change
<code class="sourceCode cpp">memberwise_trivially_relocatable</code> to
<code class="sourceCode cpp">trivially_relocatable_if_eligible</code>.
Some authors of this paper are in favor of this name change; the rest
are neutral.</p></li>
</ol>
<p><strong>EWG Poll Results</strong>: Consensus to change
<code class="sourceCode cpp">memberwise_replaceable</code> to
<code class="sourceCode cpp">replaceable_if_eligible</code> and to
change
<code class="sourceCode cpp">memberwise_trivially_relocatable</code> to
<code class="sourceCode cpp">trivially_relocatable_if_eligible</code>.</p>
<p>The first poll was not taken since discussion indicated little
support for choosing a keyword based on unspecified future features. The
two polls below were conducted to choose between
<code class="sourceCode cpp">trivially_relocatable_if_eligible</code>
and <code class="sourceCode cpp">permit_trivially_relocatability</code>.
The consensus was clearly in favor of the former.</p>
<p>Poll: p2786r11 change
<code class="sourceCode cpp">memberwise_trivially_relocatable</code> to
<code class="sourceCode cpp">trivially_relocatable_if_eligible</code>
and <code class="sourceCode cpp">memberwise_replaceable</code> to
replaceable_if_eligible, and proceed as previously approved to CWG for
C++26.</p>
<table>
<thead>
<tr class="header">
<th><div style="text-align:center">
<strong>SF</strong>
</div></th>
<th><div style="text-align:center">
<strong>F</strong>
</div></th>
<th><div style="text-align:center">
<strong>N</strong>
</div></th>
<th><div style="text-align:center">
<strong>A</strong>
</div></th>
<th><div style="text-align:center">
<strong>SA</strong>
</div></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>19</td>
<td>26</td>
<td>7</td>
<td>4</td>
<td>1</td>
</tr>
</tbody>
</table>
<p>Poll: p2786r11 change
<code class="sourceCode cpp">memberwise_trivially_relocatable</code> to
<code class="sourceCode cpp">permit_trivial_relocatability</code> and
<code class="sourceCode cpp">memberwise_replaceable</code> to
<code class="sourceCode cpp">permit_replaceability</code>, and proceed
as previously approved to CWG for C++26.</p>
<table>
<thead>
<tr class="header">
<th><div style="text-align:center">
<strong>SF</strong>
</div></th>
<th><div style="text-align:center">
<strong>F</strong>
</div></th>
<th><div style="text-align:center">
<strong>N</strong>
</div></th>
<th><div style="text-align:center">
<strong>A</strong>
</div></th>
<th><div style="text-align:center">
<strong>SA</strong>
</div></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>5</td>
<td>15</td>
<td>20</td>
<td>13</td>
<td>3</td>
</tr>
</tbody>
</table>
<h2 data-number="4.2" id="low-level-interface"><span class="header-section-number">4.2</span> Low-level interface<a href="#low-level-interface" class="self-link"></a></h2>
<p>The original low-level library interface was the three-parameter,
contiguous-sequence-based
<code class="sourceCode cpp">trivially_relocate</code> algorithm. This
algorithm was a drop-in replacement for
<code class="sourceCode cpp">memmove</code>, which is how many existing
libraries achieve trivial relocation, albeit by relying on undefined
behavior.</p>
<p>At the November 2024 meeting in Wrocław, LEWG voted to change to a
low-level interface that relocates just one object at a time. The
rationale was that such an interface was more natural for the
lowest-level interface. The authors opposed this change, arguing that
the real use case for trivial relocation was bulk relocation and that
the single-object interface would be more dangerous, allowing
programmers to easily create undefined behavior by relocating a single
object with dynamic type different from its static type or relocating
out of a variable with automatic storage duration, with no obvious
marker (such as pointer arithmetic or a cast) indicating that the
programmer is performing a dangerous operation.</p>
<p>The R11 wording included both interfaces, with the new,
single-object, interface renamed to
<code class="sourceCode cpp">trivially_relocate_at</code>, as preferred
by its advocates. The original interface is still included because
<code class="sourceCode cpp">trivially_relocate</code> was the primitive
interface approved by EWG, and the authors were, therefore, unaware that
they would need to defend it in LEWG and thus had not prepared a clear
and compelling argument. In addition, new technical information has cast
doubt on the wisdom of removing this
<code class="sourceCode cpp">memmove</code>-like interface.</p>
<p>The arguments in favor of the contiguous-sequence-based
<code class="sourceCode cpp">trivially_relocate</code> and against the
single-object <code class="sourceCode cpp">trivially_relocate_at</code>
are as follows.</p>
<ul>
<li><p><code class="sourceCode cpp">trivially_relocate</code> has field
experience. It is a drop-in replacement for
<code class="sourceCode cpp">memmove</code>, which has been used
extensively in multiple libraries.
<code class="sourceCode cpp">trivially_relocate_at</code> has no such
field experience.</p></li>
<li><p>Experimentation has shown that a loop calling
<code class="sourceCode cpp">trivially_relocate_at</code> will not be
optimized into a single <code class="sourceCode cpp">memmove</code>-like
operation. Thus, for the typical use case of bulk relocation,
<code class="sourceCode cpp">trivially_relocate_at</code> is not fit for
purpose and cannot be adapted using a simple wrapper. Regardless of
one’s interface preference, we should not standardize something that
cannot be used for its most common function, nor should we — when we
have an alternative that works well today — standardize something based
on a hope that compilers will improve in one specific area.</p></li>
<li><p>Arrays are naturally a homogeneous collection of complete
objects. A single object passed to
<code class="sourceCode cpp">trivially_relocate_at</code> might be a
base class subobject. The result of trivially relocating such a
subobject is much worse than slicing since the virtual table of the
relocated object will incorrectly be that of the derived class.</p></li>
<li><p>If the array-based
<code class="sourceCode cpp">trivially_relocate</code> <em>is</em> used
to relocate a single object, the needed pointer arithmetic is apparent
in code review:</p></li>
</ul>
<div class="sourceCode" id="cb2"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a>    Thing x;  <span class="co">// automatic variable; should not be relocated!</span></span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a>    trivially_relocate<span class="op">(&amp;</span>x, <span class="op">&amp;</span>x <span class="op">+</span> <span class="dv">1</span>, dest_p<span class="op">)</span>;  <span class="co">// dangerous and suspicious</span></span>
<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a>    trivially_relocate_at<span class="op">(</span>dest_p, <span class="op">&amp;</span>x<span class="op">)</span>;       <span class="co">// less suspicious but equally dangerous</span></span></code></pre></div>
<ul>
<li>Although situations do exist by which a single object might be
relocated, such situations are the exception and yield much less
performance benefit than bulk relocation. If a user discovers a need to
frequently relocate a single object, they can easily implement a
single-object trivial-relocation function as a wrapper around the
array-based version.</li>
</ul>
<p>Ultimately, both interfaces are low-level footguns intended for
expert use, and the status quo in this paper is to include both. The
authors’ position, however, is that
<code class="sourceCode cpp">trivially_relocate_at</code>, compared to
the bulk <code class="sourceCode cpp">trivially_relocate</code>
algorithm, is more dangerous, is more difficult to use correctly, and
provides very little in terms of optimization.</p>
<p><strong>Recommended Poll</strong> (for LEWG): Remove single-object
<code class="sourceCode cpp">trivially_relocate_at</code>. The authors
of this paper are in favor of removal.</p>
<p><strong>LEWG Poll Results</strong>: Census for removing
<code class="sourceCode cpp">trivially_relocate_at</code> and preserving
<code class="sourceCode cpp">trivially_relocate</code>.</p>
<p>POLL: Remove the single object version as suggested in P2786R11:</p>
<div class="line-block"><code class="sourceCode cpp"><span class="kw">template</span> <span class="op">&lt;</span><span class="kw">class</span> T<span class="op">&gt;</span></code><br />
    <code class="sourceCode cpp">T<span class="op">*</span> trivially_relocate_at<span class="op">(</span>T<span class="op">*</span> location, T<span class="op">*</span> source<span class="op">)</span>;</code></div>
<table>
<thead>
<tr class="header">
<th><div style="text-align:center">
<strong>SF</strong>
</div></th>
<th><div style="text-align:center">
<strong>F</strong>
</div></th>
<th><div style="text-align:center">
<strong>N</strong>
</div></th>
<th><div style="text-align:center">
<strong>A</strong>
</div></th>
<th><div style="text-align:center">
<strong>SA</strong>
</div></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>2</td>
<td>9</td>
<td>9</td>
<td>1</td>
<td>0</td>
</tr>
</tbody>
</table>
<p>POLL: Remove the bulk version as suggested in P2786R11:</p>
<div class="line-block"><code class="sourceCode cpp"><span class="kw">template</span> <span class="op">&lt;</span><span class="kw">class</span> T<span class="op">&gt;</span></code><br />
    <code class="sourceCode cpp">T<span class="op">*</span> trivially_relocate<span class="op">(</span>T<span class="op">*</span> first, T<span class="op">*</span> last, T<span class="op">*</span> result<span class="op">)</span>;</code></div>
<table>
<thead>
<tr class="header">
<th><div style="text-align:center">
<strong>SF</strong>
</div></th>
<th><div style="text-align:center">
<strong>F</strong>
</div></th>
<th><div style="text-align:center">
<strong>N</strong>
</div></th>
<th><div style="text-align:center">
<strong>A</strong>
</div></th>
<th><div style="text-align:center">
<strong>SA</strong>
</div></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>1</td>
<td>1</td>
<td>2</td>
<td>8</td>
<td>9</td>
</tr>
</tbody>
</table>
<h2 data-number="4.3" id="consumer-interface"><span class="header-section-number">4.3</span> Consumer interface<a href="#consumer-interface" class="self-link"></a></h2>
<p>The consumer-level <code class="sourceCode cpp">relocate</code>
function was included in R9 but removed in R10 with the thought that a
different consumer-level interface, more similar to the existing <code class="sourceCode cpp">uninitialized_<span class="op">*</span></code>
algorithms, would be better and that we could increase consensus by
reducing the interface to its low-level bare minimum. Unfortunately,
several members of LEWG considered this paper incomplete and were
uncomfortable approving the low-level interface without knowing what the
consumer-level interface would look like, especially since the low-level
interface cannot be used in a
<code class="sourceCode cpp"><span class="kw">constexpr</span></code>
context.</p>
<p>In the Wrocław meeting, members of LEWG expressed interest in
modeling a consumer interface on the <code class="sourceCode cpp">uninitailized_<span class="op">*</span></code>
functions already in the Standard. As of this writing, no complete
proposal has been put forth for the shape of this interface, although
Louis Dionne appears to be working on a paper, <span class="citation" data-cites="P3516R0">[<a href="https://isocpp.org/files/papers/P3516R0.html" role="doc-biblioref">P3516R0</a>]</span>, that provides the requested
<code class="sourceCode cpp">uninitialized_relocate</code> interface,
compatible with but independent of <em>trivial</em> relocation. The
authors of this paper are uncomfortable with the interface proposed in
P3516R0 for the reasons listed below. The original
<code class="sourceCode cpp">relocate</code> interface has been restored
in R11 of this paper, not to prejudice the discussion of future
alternatives but to provide a simple and proven interface that allows
P2786 to move forward.</p>
<p>Our concerns with modeling the interface after
<code class="sourceCode cpp">uninitialized_copy</code> and its ilk are
as follows.</p>
<ul>
<li><p>The generality afforded by an iterator (as opposed to pointer)
interface is dangerous, overly complicated, and not useful. We see no
use case for noncontiguous iterators that wouldn’t leave some container
in an undestructible state. Further, most input-only iterators would
yield UB if used with these interfaces.</p></li>
<li><p>Louis’s draft interface is large (ten new functions and
overloads), yet most of it is not well motivated. Moreover, even
existing <code class="sourceCode cpp">uninitialized_<span class="op">*</span></code>
interfaces (as recently expanded) are poorly motivated and not useful,
e.g., within allocator-aware containers.</p></li>
</ul>
<p><strong>Suggested process</strong>: Louis’s paper is not published.
The Standard would not be broken if both interfaces
(<code class="sourceCode cpp">relocate</code> and
<code class="sourceCode cpp">uninitialized_relocate</code>) were adopted
(though the redundancy would be strange). Rather than hold up P2786 or
vote something incomplete into the working paper, we suggest that we
uncouple the progress of P2786 from P3516 by forwarding P2786 with the
<code class="sourceCode cpp">relocate</code> function template in place.
If LEWG ultimately decides that P3516 is a better direction, a future
revision of P3516 — one that replaces
<code class="sourceCode cpp">relocate</code> with an
<code class="sourceCode cpp">uninitialized_relocate</code> that takes
advantage of trivial relocation — can be adopted, and we will work
collegially with Louis to make that happen.</p>
<p><strong>No poll was needed, and none was taken by LEWG.</strong></p>
<h2 data-number="4.4" id="is_nothrow_relocatable-trait"><span class="header-section-number">4.4</span>
<code class="sourceCode cpp">is_nothrow_relocatable</code> trait<a href="#is_nothrow_relocatable-trait" class="self-link"></a></h2>
<p>The <code class="sourceCode cpp">is_nothrow_relocatable_v<span class="op">&lt;</span>T<span class="op">&gt;</span></code>
is <code class="sourceCode cpp"><span class="kw">true</span></code> if
<code class="sourceCode cpp">T</code> can be relocated either via
trivial relocation or via a nothrow move constructor and destructor. We
assert that relocation is <em>inherently</em> a no-fail (and, therefore,
nothrow) operation, so the “nothrow” in the trait name is arguably
redundant.</p>
<p>The arguments for keeping “nothrow” are as follows.</p>
<ul>
<li><p>The name is consistent with other traits, such as
<code class="sourceCode cpp">is_nothrow_move_constructible</code>.</p></li>
<li><p>If relocation is later discovered to not be inherently
nonthrowing, the trait would be well named and would admit the
possibility of an <code class="sourceCode cpp">is_relocatable</code>
trait that does not imply a nothrow operation.</p></li>
</ul>
<p>The argument for removing “nothrow” is as follows.</p>
<ul>
<li>“Nothrow” implies that relocation might be throwing though we
believe it must never be such.</li>
</ul>
<p><strong>Possible Poll</strong> (for LEWG): Rename
<code class="sourceCode cpp">is_nothrow_relocatable</code> to
<code class="sourceCode cpp">is_relocatable</code>. The authors of this
paper are neutral on this name change.</p>
<p><strong>LEWG Poll Results</strong>: Retain this trait with the
current name.</p>
<p>POLL: Remove is_nothrow_relocatable trait from P2786R11.</p>
<table>
<thead>
<tr class="header">
<th><div style="text-align:center">
<strong>SF</strong>
</div></th>
<th><div style="text-align:center">
<strong>F</strong>
</div></th>
<th><div style="text-align:center">
<strong>N</strong>
</div></th>
<th><div style="text-align:center">
<strong>A</strong>
</div></th>
<th><div style="text-align:center">
<strong>SA</strong>
</div></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>1</td>
<td>1</td>
<td>0</td>
<td>10</td>
<td>3</td>
</tr>
</tbody>
</table>
<p>POLL: Rename is_nothrow_relocatable into is_relocatable in
P2786R11.</p>
<p>Outcome: No objection to unanimous dissent. The name stays as is in
the paper:
<code class="sourceCode cpp">is_nothrow_relocatable</code>.</p>
<h1 data-number="5" id="doc.conventions"><span class="header-section-number">5</span> Document Conventions<a href="#doc.conventions" class="self-link"></a></h1>
<h2 data-number="5.1" id="typography"><span class="header-section-number">5.1</span> Typography<a href="#typography" class="self-link"></a></h2>
<p>Throughout this paper, a <strong>bold typeface</strong> will be used
for terms defined herein and <strong><em>bold italicized
typeface</em></strong> for terms of art defined herein; the proposed
wording, however, will use the conventions of the Standard.</p>
<h2 data-number="5.2" id="definitions"><span class="header-section-number">5.2</span> Definitions<a href="#definitions" class="self-link"></a></h2>
<p>We define a <strong>relocation operation</strong> of a source object
as one that ends the lifetime of that object and starts the lifetime of
a new object at a new location. Importantly, the destructor is not
necessarily run by a <strong>relocation operation</strong>. For types in
which move construction and destruction are supported, a relocation can
be accomplished by constructing an object in the new location from an
xvalue referring to the source object, followed by invoking the
destructor of the source object.</p>
<p>We define a <strong>trivial relocation operation</strong> as a
<strong>relocation operation</strong> accomplished by performing a
bitwise copy of its <em>object representation</em> to a new memory
location that ends the lifetime of that source object — just as if that
(source) object’s storage were used by another object (<span>6.7.4
<a href="https://wg21.link/N4993#basic.life">[basic.life]</a><a href="#fn1" class="footnote-ref" id="fnref1" role="doc-noteref"><sup>1</sup></a></span>p5) — and starts the life of a
new object at the new location. Importantly, nothing else is done to the
source object; in particular, <em>its destructor is not run</em>. This
operation will typically be semantically equivalent to a nontrivial
<strong>relocation operation</strong> performed via move construction
and destruction (though exceptions, while not encouraged, are not
expressly forbidden).</p>
<p>We define <strong>replacement</strong> of a target object by a source
object as destroying the target object immediately followed by move
construction into the location of the target object from the source
object. For many types, this operation is semantically equivalent to a
move-assignment operation from the source object to the target
object.</p>
<!-- AJM 2024/10/15:
  These two subsections feel redundant with Basic Ideas, but also define the
  following terms:

* trivially relocatable type
* trivially relocatable class
* trivially relocatable
* replaceable type
* replaceable class
* replaceable
* replaceability
* trivial relocatability
  -->
<h2 data-number="5.3" id="core-language-additions"><span class="header-section-number">5.3</span> Core-language additions<a href="#core-language-additions" class="self-link"></a></h2>
<p>We propose a new Core-language definition for a <strong><em>trivially
relocatable type</em></strong>. This new definition is inspired by the
recursive nature and handling of special member functions used in the
definition of a <em>trivially copyable</em> type. A
<strong><em>trivially relocatable type</em></strong> is a scalar type, a
<strong><em>trivially relocatable class</em></strong>, an array of such
types, or a cv-qualified version of such a type. A class will be
implicitly <strong><em>trivially relocatable</em></strong> if all its
bases and members are <strong><em>trivially relocatable</em></strong>
and none of its eligible special member functions are user provided; a
contextual keyword will signify that a class might still be
<strong><em>trivially relocatable</em></strong> even if it has
user-provided special member functions.</p>
<p>We similarly propose a new Core-language definition for a
<strong><em>replaceable type</em></strong> in which a class will be a
<strong><em>replaceable class</em></strong> if all its bases and members
are <strong><em>replaceable</em></strong> and none of its relevant
special member functions are user provided; a contextual keyword will
signify that a class might still be a <strong><em>replaceable
class</em></strong>, even if it has those user-provided special member
functions.</p>
<p>Because <strong>replaceability</strong> is explicitly about the
equivalence of assignment with destruction followed by construction, we
do not decide that a type is <em>implicitly</em>
<strong><em>replaceable</em></strong> when the special member functions
selected for those operations are user provided.</p>
<h2 data-number="5.4" id="library.additions"><span class="header-section-number">5.4</span> Library additions<a href="#library.additions" class="self-link"></a></h2>
<p>The Standard Library APIs to support <strong>trivial
relocation</strong> and <strong>replaceability</strong> comprise</p>
<ul>
<li>a type trait to detect <strong>trivial relocatability</strong></li>
<li>a function, <code class="sourceCode cpp">trivially_relocate</code>,
that performs relocation on a range of objects by moving their bytes
(similarly to <code class="sourceCode cpp">memmove</code>) while
starting the lifetime of the destination objects and ending the lifetime
of the source objects</li>
<li>a user-facing function,
<code class="sourceCode cpp">relocate</code>, that emulates relocation
by using the move-and-destroy idiom for types that are not
<strong><em>trivially relocatable</em></strong> and delegates to
<code class="sourceCode cpp">trivially_relocate</code> for types that
are <strong><em>trivially relocatable</em></strong></li>
<li>a type trait to detect nothrow <strong>relocatability</strong>,
i.e., whether a type can be used with
<code class="sourceCode cpp">relocate</code></li>
<li>a type trait to detect <strong>replaceability</strong></li>
</ul>
<p>To support common use cases, both
<code class="sourceCode cpp">trivially_relocate</code> and
<code class="sourceCode cpp">relocate</code> are specified to support
overlapping ranges.</p>
<p>Finally, we propose modifications to Standard Library wording to
describe when Standard Library types are allowed and expected to have
various properties, including <strong>trivial relocatability</strong>
and <strong>replaceability</strong>.</p>
<h1 data-number="6" id="introduction"><span class="header-section-number">6</span> Introduction<a href="#introduction" class="self-link"></a></h1>
<p>Containers in C++, in particular those like
<code class="sourceCode cpp">std<span class="op">::</span>vector</code>
and
<code class="sourceCode cpp">std<span class="op">::</span>deque</code>
that manage objects within a range of continuous storage, live and die
by the efficiency with which they can move objects around. One of the
most common fundamental steps in many of the operations these types
perform is that of relocation — taking an element at one location in
memory and creating a new element at a different location in memory with
the same value and then destroying that original value.</p>
<p>Many frequently used libraries have long recognized that, for many
types, the two nontrivial steps of move construction and destruction
often combine into a single operation that can be accomplished by a
simple bitwise copy followed by discarding the source object instead of
evaluating its destructor. Much of the work a move constructor might do
to the source object, such as setting pointers to owned data to
<code class="sourceCode cpp"><span class="kw">nullptr</span></code>, is
done only to make sure the destructor that will eventually run knows
that no data is present that it is still responsible for freeing. By
taking advantage of the knowledge that certain types can be relocated by
simply copying bits, complex operations that can involve the invocation
of many user-provided special members functions can be replaced by
single calls to <code class="sourceCode cpp">memcpy</code>, realizing
huge benefits in performance.</p>
<p>The problem, of course, is that moving objects in this fashion that
are not trivially copyable violates the C++ object model and is
undefined behavior. In this paper, we propose a mechanism to fix that
problem.</p>
<ul>
<li>Types with no user-provided special member functions are identified
as <strong><em>trivially relocatable</em></strong> based on whether
their bases and nonstatic data members are <strong><em>trivially
relocatable</em></strong>.</li>
<li>Users are able to further identify those types whose user-provided
special member functions compound into a trivial operation by marking
those types with a new class specifier,
<code class="sourceCode cpp">trivially_relocatable_if_eligible</code>.</li>
<li>The Standard Library then provides a tool to safely perform
<strong>trivial relocation</strong> operations.</li>
</ul>
<p>A more subtle problem occurs where developers want to apply
optimizations based on <strong>trivial relocation</strong>, but their
code was previously taking advantage of library APIs to assume that
assignment and destroy-then-construct were interchangeable operations.
For types that do not support that property, switching to
<code class="sourceCode cpp">trivially_relocate</code>, which emulates
move construction, will behave differently than code optimized to use
assignment instead. This property — that we name
<strong>replaceability</strong> — of a type is not programmatically
detectable today. For a frequently mentioned example, the C++ Standard
Library specification for
<code class="sourceCode cpp">std<span class="op">::</span>vector</code>
insert and erase operations allows implementers to relocate elements
using assignment, assuming but not requiring that all stored types are
<strong><em>replaceable</em></strong>; for an implementation using
assignment to relocate elements in these operations to start using
<strong>trivial relocation</strong> instead — an otherwise valid
transformation — would be an observable change of behavior unless the
implementation could make a compile-time test to verify that the element
type is not only <strong><em>trivially relocatable</em></strong>, but
also <strong><em>replaceable</em></strong>.</p>
<p>To incorporate this concept of <strong>replaceability</strong> into
the language, we propose further additional changes.</p>
<ul>
<li>Types are implicitly recursively
<strong><em>replaceable</em></strong> if all their members and bases are
<strong><em>replaceable</em></strong>.</li>
<li>Through the use of the
<code class="sourceCode cpp">replaceable_if_eligible</code> specifier on
a class, users can specify that their user-provided constructors,
destructors, and assignment operators still satisfy the appropriate
equivalence specified by being <strong><em>replaceable</em></strong> as
long as all members and bases also have this property.</li>
</ul>
<p>Put together, we hope this proposal provides a complete picture of
how to incorporate into the C++ Standard, in a comprehensible and
effective manner, bitwise operations that are already performed by many
libraries in the industry.</p>
<h1 data-number="7" id="basic.ideas"><span class="header-section-number">7</span> Basic Ideas<a href="#basic.ideas" class="self-link"></a></h1>
<p>This paper introduces two new complementary but independent notions
into C++.</p>
<h2 data-number="7.1" id="trivial-relocatability"><span class="header-section-number">7.1</span> Trivial relocatability<a href="#trivial-relocatability" class="self-link"></a></h2>
<p>Relocation is the act of moving an object and all its nested
subobjects from one memory location to another. This result is typically
achieved by calling the move constructor to make a new object at the new
location followed by calling the destructor of the original object to
end its lifetime.</p>
<p>A type is <strong><em>trivially relocatable</em></strong> if it can
be relocated by copying the bytes of its <em>object representation</em>
from the old location to the new and the lifetime of the original object
can be ended <em>without</em> running its destructor. However, C++
object lifetimes do not currently permit types (with the exception of
those few types that meet the strict requirements of trivial
copyability) to be relocated by means of byte copying (<strong>trivial
relocation</strong>).</p>
<p>If the object model were to allow it, most C++ types could safely be
trivially relocated. The two known exceptions are types that maintain an
internal pointer to a data member and types that register their presence
in an external registry that must point back to the object.</p>
<p>This paper proposes adding</p>
<ul>
<li>a Core-language definition for <strong><em>trivially relocatable
types</em></strong></li>
<li>a way to explicitly mark types <strong><em>trivially
relocatable</em></strong> when that cannot be deduced by a compiler</li>
<li>a type trait to report whether a type is <strong><em>trivially
relocatable</em></strong></li>
<li>a “compiler-magic” function to perform <strong>trivial
relocation</strong>, respecting object lifetimes</li>
<li>a user-facing <code class="sourceCode cpp">relocate</code> function
that can be safely used with types that are not <strong><em>trivially
relocatable</em></strong></li>
<li>a type trait to report whether a type is nothrow-relocatable</li>
</ul>
<p>The equivalent of <strong>trivial relocation</strong> has been used
for decades with code that has relied on compilers not reacting to the
use of undefined behavior when bitwise copying nontrivial types, even
though such copies violate C++ object lifetime rules.</p>
<h2 data-number="7.2" id="replaceability"><span class="header-section-number">7.2</span> Replaceability<a href="#replaceability" class="self-link"></a></h2>
<p><strong>Replaceability</strong> is a semantic property of a type,
where move assignment is isomorphic to destroy then move-construct. Just
like in <strong>trivial relocatability</strong>, a compiler cannot
deduce whether a type is <strong><em>replaceable</em></strong> if the
user provides a move-assignment operator, move constructor, or
destructor without extra guidance from the user.</p>
<p>In many cases, a library would like to require or assume
<strong>replaceability</strong>, such as for moving elements around a
<code class="sourceCode cpp">std<span class="op">::</span>vector</code>
when inserting or erasing elements.</p>
<p>This paper proposes adding</p>
<ul>
<li>a Core-language definition for <strong><em>replaceable
types</em></strong></li>
<li>a way to mark types as <strong><em>replaceable</em></strong> if the
compiler cannot deduce that property</li>
<li>a type trait to report whether a type is
<strong><em>replaceable</em></strong></li>
</ul>
<p>Note that no part of the language requires types to be
<strong><em>replaceable</em></strong>; this feature is purely to allow
users to mark their types with a property that many libraries seek to
exploit.</p>
<h2 data-number="7.3" id="examples-of-types-having-neither-one-or-both-properties"><span class="header-section-number">7.3</span> Examples of types having
neither, one, or both properties<a href="#examples-of-types-having-neither-one-or-both-properties" class="self-link"></a></h2>
<p>In the following table, let <code class="sourceCode cpp">list1</code>
be an implementation of
<code class="sourceCode cpp">std<span class="op">::</span>list</code>
whose sentinel node is part of the container’s footprint and
<code class="sourceCode cpp">list2</code> be an implementation of
<code class="sourceCode cpp">std<span class="op">::</span>list</code>
whose a sentinel node is allocated on the heap. Also, let
<code class="sourceCode cpp">string1</code> be an implementation of
<code class="sourceCode cpp">std<span class="op">::</span>string</code>
that may contain a pointer to its own small-string buffer and
<code class="sourceCode cpp">string2</code> be an implementation of
<code class="sourceCode cpp">std<span class="op">::</span>string</code>
that will never point to itself. These examples are described in more
detail in the subsequent subsections.</p>
<table>
<colgroup>
<col style="width: 40%" />
<col style="width: 35%" />
<col style="width: 24%" />
</colgroup>
<thead>
<tr class="header">
<th></th>
<th style="text-align: left;"><div style="text-align:center">
<strong>Not replaceable</strong>
</div></th>
<th style="text-align: left;"><div style="text-align:center">
<strong>Replaceable</strong>
</div></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td><strong>Not trivially relocatable</strong></td>
<td style="text-align: left;"><code class="sourceCode cpp">pmr<span class="op">::</span>list1<span class="op">&lt;</span>T<span class="op">&gt;</span></code><br />
<code class="sourceCode cpp">tuple<span class="op">&lt;</span>pmr<span class="op">::</span>string1<span class="op">&gt;</span></code><br />
<code class="sourceCode cpp">pair<span class="op">&lt;</span><span class="dt">int</span>, <span class="kw">const</span> string1<span class="op">&gt;</span></code></td>
<td style="text-align: left;"><code class="sourceCode cpp">list1<span class="op">&lt;</span>T<span class="op">&gt;</span></code><br />
<code class="sourceCode cpp">string1</code></td>
</tr>
<tr class="even">
<td><strong>Trivially relocatable</strong></td>
<td style="text-align: left;"><code class="sourceCode cpp">tuple<span class="op">&lt;</span>T<span class="op">&amp;&gt;</span></code><br />
<code class="sourceCode cpp">pmr<span class="op">::</span>vector<span class="op">&lt;</span>T<span class="op">&gt;</span></code><br />
<code class="sourceCode cpp">pmr<span class="op">::</span>list2<span class="op">&lt;</span>T<span class="op">&gt;</span></code></td>
<td style="text-align: left;"><code class="sourceCode cpp">shared_ptr<span class="op">&lt;</span>T<span class="op">&gt;</span></code><br />
<code class="sourceCode cpp">future<span class="op">&lt;</span>T<span class="op">&gt;</span></code><br />
<code class="sourceCode cpp">vector<span class="op">&lt;</span>T<span class="op">&gt;</span></code><br />
<code class="sourceCode cpp">string2</code><br />
<code class="sourceCode cpp">list2<span class="op">&lt;</span>T<span class="op">&gt;</span></code><br />
<code class="sourceCode cpp">tuple<span class="op">&lt;</span>vector<span class="op">&lt;</span>T<span class="op">&gt;&gt;</span></code></td>
</tr>
</tbody>
</table>
<h3 data-number="7.3.1" id="examples-of-trivially-relocatable-and-replaceable-types"><span class="header-section-number">7.3.1</span> Examples of trivially
relocatable and replaceable types<a href="#examples-of-trivially-relocatable-and-replaceable-types" class="self-link"></a></h3>
<p>If we assume the default template arguments, we would expect the
following Standard Library types to be both <strong><em>trivially
relocatable</em></strong> and <strong><em>replaceable</em></strong>:</p>
<ul>
<li><code class="sourceCode cpp">std<span class="op">::</span>shared_ptr</code></li>
<li><code class="sourceCode cpp">std<span class="op">::</span>future</code></li>
<li><code class="sourceCode cpp">std<span class="op">::</span>vector</code></li>
</ul>
<p>We would expect the following types to be both <strong><em>trivially
relocatable</em></strong> and <strong><em>replaceable</em></strong> if
all their template arguments are both <strong><em>trivially
relocatable</em></strong> and <strong><em>replaceable</em></strong>:</p>
<ul>
<li><code class="sourceCode cpp">std<span class="op">::</span>pair</code></li>
<li><code class="sourceCode cpp">std<span class="op">::</span>tuple</code></li>
</ul>
<h3 data-number="7.3.2" id="examples-of-trivially-relocatable-types-that-are-not-replaceable"><span class="header-section-number">7.3.2</span> Examples of trivially
relocatable types that are <em>not</em> replaceable<a href="#examples-of-trivially-relocatable-types-that-are-not-replaceable" class="self-link"></a></h3>
<p>A variety of types, while <strong><em>trivially
relocatable</em></strong>, do not maintain the invariants of
<strong>replaceability</strong>:</p>
<ul>
<li><code class="sourceCode cpp">std<span class="op">::</span>tuple<span class="op">&lt;</span>T <span class="op">&amp;&gt;</span></code></li>
<li><code class="sourceCode cpp">std<span class="op">::</span>pmr</code>
containers (because <code class="sourceCode cpp">pmr</code> allocators
do not propagate on assignment)</li>
<li>Any class with a trivially-relocatable
<code class="sourceCode cpp"><span class="kw">const</span></code> data
member</li>
</ul>
<p>In many contexts, relocation of such types is desirable, especially
in user-defined data structures beyond the reach of the Standard
Library.</p>
<h3 data-number="7.3.3" id="examples-of-replaceable-types-that-are-not-trivially-relocatable"><span class="header-section-number">7.3.3</span> Examples of replaceable types
that are not <em>trivially</em> relocatable<a href="#examples-of-replaceable-types-that-are-not-trivially-relocatable" class="self-link"></a></h3>
<p>Any object directly or indirectly containing pointers to itself would
not be trivially relocatable but can certainly be replaceable. Examples
include</p>
<ul>
<li><p>Implementations of <code class="sourceCode cpp">std<span class="op">::</span>basic_string</code>
that may contain a pointer to its own small-string buffer
(<code class="sourceCode cpp">string1</code>)</p></li>
<li><p>Implementations of
<code class="sourceCode cpp">std<span class="op">::</span>list</code>
that do not allocate a sentinel node
(<code class="sourceCode cpp">list1</code>); the first and last nodes of
such an implementation typically point back to the container object
itself</p></li>
<li><p>Containers supporting iterators that point back to the container,
typically for detecting iterator invalidation during debugging</p></li>
</ul>
<p>This category of types would meet preconditions for algorithms in
which the semantics of <strong>replaceability</strong> are important,
and they might be enforced by the equivalent of Mandates, Constraints,
or Preconditions in users’ libraries.</p>
<h3 data-number="7.3.4" id="examples-of-standard-library-types-that-must-defer-to-the-implementation"><span class="header-section-number">7.3.4</span> Examples of Standard Library
types that must defer to the implementation<a href="#examples-of-standard-library-types-that-must-defer-to-the-implementation" class="self-link"></a></h3>
<p>We would expect the quality of implementation would decide whether
the following types are <strong><em>trivially relocatable</em></strong>
<em>and</em> <strong><em>replaceable</em></strong> or are just
<strong><em>replaceable</em></strong>:</p>
<ul>
<li><code class="sourceCode cpp">std<span class="op">::</span>basic_string</code>,
depending on whether the short string optimization maintains an internal
pointer (<code class="sourceCode cpp">string1</code>
vs. <code class="sourceCode cpp">string2</code>).</li>
<li><code class="sourceCode cpp">std<span class="op">::</span>list</code>,
depending on whether the sentinel node is a nonstatic data member
(<code class="sourceCode cpp">list1</code>
vs. <code class="sourceCode cpp">list2</code>)</li>
</ul>
<h2 data-number="7.4" id="independent-features"><span class="header-section-number">7.4</span> Independent features<a href="#independent-features" class="self-link"></a></h2>
<p>From the variety of types and usage examples above, we see that while
<strong>trivial relocation</strong> and <strong>replacement</strong> are
often used together, each has important use cases and neither can be
built on top of the other.</p>
<h1 data-number="8" id="technical-background"><span class="header-section-number">8</span> Technical Background<a href="#technical-background" class="self-link"></a></h1>
<p>Some very specific uses of terminology from the C++ Standard are
important to understand when reading this proposal and are quickly
summarized here.</p>
<p>For decades, C++ developers have been optimizing low-level data
structures, such as their own
<code class="sourceCode cpp">vector</code>-like types, by byte-wise
copying objects from one location to another, even though doing so is
often UB; see earlier papers<a href="#fn2" class="footnote-ref" id="fnref2" role="doc-noteref"><sup>2</sup></a> for rationale.</p>
<p>Earlier revisions of this paper initially proposed language and
library extensions, termed <strong>trivial relocation</strong>, to make
writing such code well defined and was forwarded to Core where it
received a strong review that challenged our assumptions about copying
bytes. From the perspective of the C++ abstract machine, we should not
be making assumptions about in-memory representations — that is the
compiler’s job — and should limit ourselves to copying the <em>object
representation</em>, leaving the compiler itself to optimize copying and
moving the object representations using efficient memory-copying
operations.</p>
<p>The Core review in Tokyo 2024 proceeded in parallel to the LEWG
review at the same meeting, which subsequently sent the proposal back to
EWG, asking for a more complete handling of bitwise operations, notably
optimizations for byte-wise swaps. Subsequent feedback, given that
<code class="sourceCode cpp">swap</code> cannot rely on <strong>trivial
relocation</strong> lest it corrupt a potentially overlapped member
subobject, was that the full details of
<code class="sourceCode cpp">swap</code> are best left to the Library
and compiler to work out for themselves and that supplying the two
traits for <strong>trivial relocatability</strong> and for
<strong>replaceability</strong> is sufficient for them to make
progress.</p>
<p>Polls in LEWG in Wrocław 2024 indicated that the fundamental
primitive should be an API to relocate a single object at a time,
leaving relocating ranges to a higher-level consumer API to be
separately proposed in follow-up papers. Further consideration as well
as compiler benchmarks indicate that single-object <strong>trivial
relocation</strong> has few uses cases, cannot be optimized efficiently
by current compilers, and fails to achieve the important goal of being a
drop-in substitute for <code class="sourceCode cpp">memmove</code>. In
deference to the LEWG poll, the single-object primitive was retained,
but the contiguous-sequence primitive was also restored.</p>
<!-- \addcontentsline{toc}{section}{\protect\pagebreak} -->
<h1 data-number="9" id="basic-design-principles"><span class="header-section-number">9</span> Basic Design Principles<a href="#basic-design-principles" class="self-link"></a></h1>
<h2 data-number="9.1" id="create-a-feature-for-users-not-just-the-standard-library"><span class="header-section-number">9.1</span> Create a feature for users, not
just the Standard Library<a href="#create-a-feature-for-users-not-just-the-standard-library" class="self-link"></a></h2>
<p>Efficient implementation of many data structures often needs a means
to efficiently move and exchange objects that those data structures are
managing, especially for data structures that manage their elements in
contiguous storage or in some other location that is not a node at the
end of a pointer.</p>
<p>We note that such object manipulation is also a sharp tool that is
not initially expected to see much use other than optimizing the
internal management of data structures. While this paper focuses on
supplying the essential building blocks of <strong>trivial
relocation</strong>, we defer the design of a more usable consumer API
to follow-up papers that can debate their varied merits and
trade-offs.</p>
<h2 data-number="9.2" id="a-formal-specification-is-built-around-object-lifetimes"><span class="header-section-number">9.2</span> A formal specification is built
around object lifetimes<a href="#a-formal-specification-is-built-around-object-lifetimes" class="self-link"></a></h2>
<p>C++ has a well-specified object model that is important to
optimizers, sanitizers, and analysis tools alike. Such tools must reason
about object lifetimes and, importantly, minimize the doubt created for
developers regarding that reasoning leading to false positives or false
negatives when seeking to optimize or alert users.</p>
<h2 data-number="9.3" id="behavior-must-be-reliable"><span class="header-section-number">9.3</span> Behavior must be reliable<a href="#behavior-must-be-reliable" class="self-link"></a></h2>
<p>No freedom for quality of implementation (QoI) in semantics is an
important quality that builds on the well-specified object model.</p>
<h2 data-number="9.4" id="guard-against-accidental-undefined-behavior"><span class="header-section-number">9.4</span> Guard against accidental
undefined behavior<a href="#guard-against-accidental-undefined-behavior" class="self-link"></a></h2>
<p>The new Library APIs support only types that would produce
well-defined behavior. The specification prefers <em>Mandates</em>
clauses to <em>Constraints:</em> clauses since SFINAE behavior carries
no expected benefit and is likely to produce error messages with less
useful information.</p>
<h1 data-number="10" id="core-proposal"><span class="header-section-number">10</span> Core Proposal<a href="#core-proposal" class="self-link"></a></h1>
<p>Our core proposal comprises two parts: <strong>trivial
relocation</strong> and <strong>replaceability</strong>, including
Standard Library primitives that are necessary for well-defined use of
each feature. <strong>Trivial relocation</strong> is a technique already
widely used in the industry, and <strong>replaceability</strong> is a
more novel property that is exploited directly by optimizing library
code based on its availability.</p>
<h2 data-number="10.1" id="trivial-relocatability-1"><span class="header-section-number">10.1</span> Trivial relocatability<a href="#trivial-relocatability-1" class="self-link"></a></h2>
<p>To ensure that libraries taking advantage of the
<strong><em>trivially relocatable</em></strong> semantic do not
introduce undefined behavior, the model of lifetimes for objects must be
extended to allow for relocation of <strong><em>trivially relocatable
types</em></strong>. Since the compiler cannot know if a specific
<code class="sourceCode cpp">memcpy</code> or
<code class="sourceCode cpp">memmove</code> call is intended to
duplicate (or to move) an object, we propose introducing a new function
template, <code class="sourceCode cpp">std<span class="op">::</span>trivially_relocate</code>,
that is restricted to <strong><em>trivially relocatable
types</em></strong>. The purpose of the new function template is to
efficiently move the <em>object representation</em>, typically with a
call to <code class="sourceCode cpp">memmove</code> or
<code class="sourceCode cpp">memcpy</code> while signifying to the
compiler (and other analysis tools) that the lifetime of the new objects
has begun — similar to calling
<code class="sourceCode cpp">start_lifetime_as</code> on the destination
locations — and that the lifetime of the original objects has ended
(without running destructors).</p>
<p>This design deliberately puts all compiler-magic and Core-language
interaction dealing with the object lifetimes into a single place,
rather than into a number of different
<code class="sourceCode cpp">relocate</code>-related overloads. Note
that users are not permitted to copy the bytes to perform a relocation
themselves, unlike with trivial copyability, although byte copies would
continue to work for trivially copyable types.</p>
<h3 data-number="10.1.1" id="new-type-category-trivially-relocatable"><span class="header-section-number">10.1.1</span> New type category: Trivially
relocatable<a href="#new-type-category-trivially-relocatable" class="self-link"></a></h3>
<p>To better integrate language support, we further propose that the
language can detect types as <strong><em>trivially
relocatable</em></strong> where all their bases and nonstatic data
members are, in turn, <strong><em>trivially relocatable</em></strong>:
The constructor selected for construction from a single rvalue of the
same type is neither user provided nor deleted, the same applies for the
assignment operator for rvalues, and their destructor is neither user
provided nor deleted. Conceptually, this definition combines the rules
we would follow if there was a new user-definable special member
function for relocation <em>and</em> when that operation would be
trivial.</p>
<p>Note that our notion of relocation relies on being semantically
equivalent to move construction of the target followed by destruction of
the source. Even though it is not involved in this definition, we still
consider assignment operations when deciding if a type is
<em>implicitly</em> <strong><em>trivially relocatable</em></strong> for
the same reasons that we consider assignment when deciding if a type
should have an implicitly declared move constructor; any existing type
with a particular set of user-provided special member functions should
not begin to have new operations considered valid for it if those
operations might subvert expectations due to compiling with a new
language Standard.</p>
<h3 data-number="10.1.2" id="new-keyword-and-explicit-rule"><span class="header-section-number">10.1.2</span> New keyword and explicit
rule<a href="#new-keyword-and-explicit-rule" class="self-link"></a></h3>
<p>Without an opt-in mechanism, the only types that would be implicitly
<strong><em>trivially relocatable</em></strong> would be those that are
already trivially copyable, an important yet relatively small subset of
the full universe of types in C++. To enable <strong>trivial
relocatability</strong> on the many more interesting types that have
nontrivial special member functions, explicitly marking such types must
be possible. This marking is needed for only user-defined class types
(including unions); hence, we propose adding a new contextual keyword,
<code class="sourceCode cpp">trivially_relocatable_if_eligible</code>,
as part of the class definition, similar to how
<code class="sourceCode cpp"><span class="kw">final</span></code>
applies to classes:</p>
<div class="sourceCode" id="cb3"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> X;                                      <span class="co">// Forward declaration does not admit `final`.</span></span>
<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> X <span class="kw">final</span> <span class="op">{}</span>;                             <span class="co">// Class definition admits `final`.</span></span>
<span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> Y trivially_relocatable_if_eligible <span class="op">{}</span>; <span class="co">// New contextual keyword, placed like `final`.</span></span></code></pre></div>
<p>We propose one new contextual keyword,
<code class="sourceCode cpp">trivially_relocatable_if_eligible</code>,
that can be placed in a class-head (on a class definition) to indicate
that a type’s special operations do nothing that would violate the
implicit rule that would make a type <strong><em>trivially
relocatable</em></strong>.</p>
<p>By means of the
<code class="sourceCode cpp">trivially_relocatable_if_eligible</code>
specification, a class will be determined to be <strong><em>trivially
relocatable</em></strong> if, according to the implicit rules for a
<strong><em>trivially relocatable class</em></strong>, the class would
be <strong><em>trivially relocatable</em></strong> if the presence of
user-declared special member functions were ignored.</p>
<p>Users considering whether to apply this keyword to a given type that
has user-provided special member functions must simply inspect their
move constructor and destructor and decide if, when applied together as
part of a relocate operation, they have no net effect. Common examples
include many types.</p>
<ul>
<li>For a resource-owning type, such as <code class="sourceCode cpp">std<span class="op">::</span>unique_ptr</code>,
the newly constructed object will have the same bits as the source
object, the source object will have its pointer member set to
<code class="sourceCode cpp"><span class="kw">nullptr</span></code>, and
the source object destructor will do nothing because, by the time it
runs, that member will be
<code class="sourceCode cpp"><span class="kw">nullptr</span></code>.
Simply copying the bytes and discarding the source object achieves the
same semantic effect.</li>
<li>A reference-counting type, however, might increment a count by one
when constructing the target object and then decrement that same count
by one when destroying the source object. Combining these operations
clarifies that the constructor and destructor negate one another.</li>
</ul>
<h3 data-number="10.1.3" id="core.relocate_trait"><span class="header-section-number">10.1.3</span> New type trait:
<code class="sourceCode cpp">is_trivially_relocatable</code><a href="#core.relocate_trait" class="self-link"></a></h3>
<p>To expose the <strong>relocatability</strong> property of a type to
library functions seeking to provide appropriate optimizations, we
propose a new trait, <code class="sourceCode cpp">std<span class="op">::</span>is_trivially_relocatable<span class="op">&lt;</span>T<span class="op">&gt;</span></code>,
which enables the detection of <strong>trivial </strong>:</p>
<div class="sourceCode" id="cb4"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a><span class="kw">template</span><span class="op">&lt;</span> <span class="kw">class</span> T <span class="op">&gt;</span></span>
<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> is_trivially_relocatable;</span>
<span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb4-4"><a href="#cb4-4" aria-hidden="true" tabindex="-1"></a><span class="kw">template</span><span class="op">&lt;</span> <span class="kw">class</span> T <span class="op">&gt;</span></span>
<span id="cb4-5"><a href="#cb4-5" aria-hidden="true" tabindex="-1"></a><span class="kw">constexpr</span> <span class="dt">bool</span> is_trivially_relocatable_v <span class="op">=</span> is_trivially_relocatable<span class="op">&lt;</span>T<span class="op">&gt;::</span>value;</span></code></pre></div>
<p>The <code class="sourceCode cpp">std<span class="op">::</span>is_trivially_relocatable<span class="op">&lt;</span>T<span class="op">&gt;</span></code>
trait has a base characteristic of <code class="sourceCode cpp">std<span class="op">::</span>true_type</code> if
<code class="sourceCode cpp">T</code> is <strong><em>trivially
relocatable</em></strong> and has <code class="sourceCode cpp">std<span class="op">::</span>false_type</code>
otherwise.</p>
<p>Note that the <code class="sourceCode cpp">std<span class="op">::</span>is_trivially_relocatable</code>
trait reflects the underlying property that a type has, and like all
similar traits in the Standard Library, it must not be <em>user
specializable</em>. Compilers themselves are expected to determine this
property internally and should not introduce a library dependency such
as by instantiating this type trait.</p>
<p>We expect that the <code class="sourceCode cpp">std<span class="op">::</span>is_trivially_relocatable</code>
trait shall be implemented through a compiler intrinsic, much like <code class="sourceCode cpp">std<span class="op">::</span>is_trivially_copyable</code>,
so the compiler can use that intrinsic when the language semantics
require <strong>trivial relocatability</strong>, rather than requiring
actual instantiation (and knowledge) of the Standard Library trait. The
trait must always agree with the intrinsic since users do <em>not</em>
have permission to specialize standard type traits (unless explicitly
granted permission for a specific trait).</p>
<p>We see no particular need to separately detect whether a type has
attempted to make itself <strong><em>trivially relocatable</em></strong>
with the
<code class="sourceCode cpp">trivially_relocatable_if_eligible</code>
token or by leaning on the implicit definition.</p>
<h3 data-number="10.1.4" id="core.relocate_function"><span class="header-section-number">10.1.4</span> New primitive function:
<code class="sourceCode cpp">trivially_relocate</code><a href="#core.relocate_function" class="self-link"></a></h3>
<p>As stated in <a href="#library.additions">“Library additions,”</a> we
are proposing a new function template,
<code class="sourceCode cpp">trivially_relocate</code>, that is the
primitive entry point into the core magic that tracks and manages object
lifetimes in the abstract machine:</p>
<div class="sourceCode" id="cb5"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="kw">template</span> <span class="op">&lt;</span><span class="kw">class</span> T<span class="op">&gt;</span></span>
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a>T<span class="op">*</span> trivially_relocate<span class="op">(</span>T<span class="op">*</span> first, T<span class="op">*</span> last, T<span class="op">*</span> result<span class="op">)</span></span>
<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a><span class="op">{</span></span>
<span id="cb5-4"><a href="#cb5-4" aria-hidden="true" tabindex="-1"></a>  <span class="kw">static_assert</span><span class="op">(</span> is_trivially_relocatable_v<span class="op">&lt;</span>T<span class="op">&gt;</span> <span class="op">&amp;&amp;</span> <span class="op">!</span>is_const_v<span class="op">&lt;</span>T<span class="op">&gt;</span> <span class="op">)</span>;</span>
<span id="cb5-5"><a href="#cb5-5" aria-hidden="true" tabindex="-1"></a>  <span class="co">// ... (platform-provided implementation)</span></span>
<span id="cb5-6"><a href="#cb5-6" aria-hidden="true" tabindex="-1"></a><span class="op">}</span></span></code></pre></div>
<p>This function template <em>mandates</em> that <code class="sourceCode cpp">is_trivially_relocatable_v<span class="op">&lt;</span>T<span class="op">&gt;</span> <span class="op">&amp;&amp;</span> <span class="op">!</span>is_const_v<span class="op">&lt;</span>T<span class="op">&gt;</span></code>
is <code class="sourceCode cpp"><span class="kw">true</span></code> and
has a <em>precondition</em> that any objects nested within the source
objects are also <strong><em>trivially relocatable</em></strong>.</p>
<p>Its postcondition is that the new objects — and all their nested
subobjects — at the destination addresses have the same object
representations as the objects — and their corresponding nested
subobjects — originally at the source locations; the lifetimes of the
source objects and their subobjects have ended without running any
destructors or other clean-up code.</p>
<p>On most platforms, this template is functionally equivalent to</p>
<blockquote>
<p><code class="sourceCode cpp">memmove<span class="op">(</span>result, first, last <span class="op">-</span> first<span class="op">)</span>;</code></p>
</blockquote>
<p>However, unlike <code class="sourceCode cpp">memmove</code> on its
own, this function template is restricted to <strong><em>trivially
relocatable types</em></strong> rather than to implicit lifetime
types.</p>
<p>Note that this function has the nofail guarantee and can never throw
an exception, yet it is not marked as
<code class="sourceCode cpp"><span class="kw">noexcept</span></code>,
following the principles of the Lakos Rule, which can be summarized as,
“If a function has a narrow contract, then, unless that function is
likely to be used in conjunction with the
<code class="sourceCode cpp"><span class="kw">noexcept</span></code>
operator, the exception specification should be left to the library as
QoI.”</p>
<p>In addition to performing
<code class="sourceCode cpp">memmove</code>, the function also has the
following two important effects that matter to the abstract machine but
have no apparent physical effect (i.e., these effects do not change bits
in memory), much like
<code class="sourceCode cpp">std<span class="op">::</span>launder</code>.</p>
<ol type="1">
<li><p>The function ends the lifetime of the source objects. This ending
of the objects’ lifetimes means that attempting to access those objects
or attempting to run their destructor will be <em>undefined
behavior</em>.
<!-- lah: note to self: ajm is using italics here for emphasis; "it should be scary." --></p></li>
<li><p>The function begins the lifetime of the result objects. If those
objects or any of their nested subobjects are unions, they have the same
active elements as the corresponding unions in the original
objects.</p></li>
</ol>
<p>The current library-level mechanism to start the lifetime of an
object without invoking a constructor is <code class="sourceCode cpp">std<span class="op">::</span>start_lifetime_as</code>,
a function that works for only implicit lifetime types that must have
trivial default constructors. <strong><em>Trivially relocatable
types</em></strong>, however, include a much wider range of types,
including many that establish and maintain invariants in their special
member functions and thus cannot be implicit lifetime types.</p>
<p>A tool for ending lifetimes is similarly unavailable in the Standard
Library today. This task can be accomplished by reusing the storage of
an object, but that requires modifications of some sort.</p>
<p>The <code class="sourceCode cpp">trivially_relocate</code> function,
therefore, is interacting with the abstract machine in ways that are not
currently available. Importantly, for many of the types we are concerned
with (e.g.,
<code class="sourceCode cpp">std<span class="op">::</span>vector</code>,
<code class="sourceCode cpp">std<span class="op">::</span>unique_ptr</code>,
and so on), the component steps of the <strong>relocation
operation</strong> are decidedly not trivial, so we are compelled to
make this primitive function responsible for the needed compiler
magic.</p>
<p>To remove the need for a larger family of functions and avoid overly
limiting cases in which <strong>trivial relocation</strong> might be
applied, the <code class="sourceCode cpp">trivially_relocate</code>
function is intended to support overlapping source and destination
ranges, just like <code class="sourceCode cpp">memmove</code>. If the
ranges are overlapping, the implementation must take care around the
management of the lifetime of objects relocated out of or into the
overlap.</p>
<h3 data-number="10.1.5" id="new-library-function-stdrelocate"><span class="header-section-number">10.1.5</span> New library function: <code class="sourceCode cpp">std<span class="op">::</span>relocate</code><a href="#new-library-function-stdrelocate" class="self-link"></a></h3>
<p>The function <code class="sourceCode cpp">trivially_relocate</code>
is a sharp tool that requires compiler magic to implement, and the user
must write an alternative code path for types that are not
<strong><em>trivially relocatable</em></strong>. General relocation that
supports both trivial and nontrivial relocation is, however, a subtle
and tedious function to implement correctly, and we do not want to force
all users to reimplement this function.</p>
<p>Therefore, we propose an additional user-friendly, general-purpose
relocation function, <code class="sourceCode cpp">std<span class="op">::</span>relocate</code>,
that will use <code class="sourceCode cpp">trivially_relocate</code> for
<strong><em>trivially relocatable types</em></strong> and otherwise
<strong>relocate</strong> elements by calling the move constructor to
move each object, followed by their destructor. This function must
correctly order its moves to support overlapping ranges, just like
<code class="sourceCode cpp">trivially_relocate</code>.</p>
<p>In addition, <code class="sourceCode cpp">std<span class="op">::</span>relocate</code> is
<code class="sourceCode cpp"><span class="kw">constexpr</span></code> to
support easy implementation of
<code class="sourceCode cpp"><span class="kw">constexpr</span></code>
containers like
<code class="sourceCode cpp">std<span class="op">::</span>vector</code>.
Adding such support means that in addition to checking whether a type is
<strong><em>trivially relocatable</em></strong> before calling
<code class="sourceCode cpp">trivially_relocate</code>, we must also
have an <code class="sourceCode cpp"><span class="cf">if</span> <span class="kw">consteval</span></code>
path that does <em>not</em> call
<code class="sourceCode cpp">trivially_relocate</code> during constant
evaluation:</p>
<div class="sourceCode" id="cb6"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="kw">template</span> <span class="op">&lt;</span><span class="kw">class</span> T<span class="op">&gt;</span></span>
<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a><span class="kw">constexpr</span></span>
<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a>T<span class="op">*</span> relocate<span class="op">(</span>T<span class="op">*</span> first, T<span class="op">*</span> last, T<span class="op">*</span> result<span class="op">)</span></span>
<span id="cb6-4"><a href="#cb6-4" aria-hidden="true" tabindex="-1"></a><span class="op">{</span></span>
<span id="cb6-5"><a href="#cb6-5" aria-hidden="true" tabindex="-1"></a>  <span class="kw">static_assert</span><span class="op">(</span>is_trivially_relocatable_v<span class="op">&lt;</span>T<span class="op">&gt;</span></span>
<span id="cb6-6"><a href="#cb6-6" aria-hidden="true" tabindex="-1"></a>               <span class="op">||</span> is_nothrow_move_constructible_v<span class="op">&lt;</span>T<span class="op">&gt;)</span>;</span>
<span id="cb6-7"><a href="#cb6-7" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb6-8"><a href="#cb6-8" aria-hidden="true" tabindex="-1"></a>  <span class="co">// When relocating to the same location or an empty range, do nothing.</span></span>
<span id="cb6-9"><a href="#cb6-9" aria-hidden="true" tabindex="-1"></a>  <span class="cf">if</span> <span class="op">(</span>first <span class="op">==</span> result<span class="op">)</span> <span class="cf">return</span> last;</span>
<span id="cb6-10"><a href="#cb6-10" aria-hidden="true" tabindex="-1"></a>  <span class="cf">if</span> <span class="op">(</span>first <span class="op">==</span> last<span class="op">)</span> <span class="cf">return</span> result;</span>
<span id="cb6-11"><a href="#cb6-11" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb6-12"><a href="#cb6-12" aria-hidden="true" tabindex="-1"></a>  <span class="co">// Then, if we are not evaluating at compile time and the type supports</span></span>
<span id="cb6-13"><a href="#cb6-13" aria-hidden="true" tabindex="-1"></a>  <span class="co">// trivial relocation, delegate to `trivially_relocate`.</span></span>
<span id="cb6-14"><a href="#cb6-14" aria-hidden="true" tabindex="-1"></a>  <span class="cf">if</span> <span class="op">!</span> <span class="kw">consteval</span> <span class="op">{</span></span>
<span id="cb6-15"><a href="#cb6-15" aria-hidden="true" tabindex="-1"></a>    <span class="cf">if</span> <span class="kw">constexpr</span> <span class="op">(</span>is_trivially_relocatable_v<span class="op">&lt;</span>T<span class="op">&gt;)</span> <span class="op">{</span></span>
<span id="cb6-16"><a href="#cb6-16" aria-hidden="true" tabindex="-1"></a>      <span class="cf">return</span> trivially_relocate<span class="op">(</span>first, last, result<span class="op">)</span>;</span>
<span id="cb6-17"><a href="#cb6-17" aria-hidden="true" tabindex="-1"></a>    <span class="op">}</span></span>
<span id="cb6-18"><a href="#cb6-18" aria-hidden="true" tabindex="-1"></a>  <span class="op">}</span></span>
<span id="cb6-19"><a href="#cb6-19" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb6-20"><a href="#cb6-20" aria-hidden="true" tabindex="-1"></a>  <span class="cf">if</span> <span class="kw">constexpr</span> <span class="op">(</span>is_move_constructible_v<span class="op">&lt;</span>T<span class="op">&gt;)</span> <span class="op">{</span></span>
<span id="cb6-21"><a href="#cb6-21" aria-hidden="true" tabindex="-1"></a>    <span class="co">// For nontrivial relocatable types or any time during constant</span></span>
<span id="cb6-22"><a href="#cb6-22" aria-hidden="true" tabindex="-1"></a>    <span class="co">// evaluation, we must detect overlapping ranges and act accordingly,</span></span>
<span id="cb6-23"><a href="#cb6-23" aria-hidden="true" tabindex="-1"></a>    <span class="co">// which can be done only if the type is movable.  Note that trivially</span></span>
<span id="cb6-24"><a href="#cb6-24" aria-hidden="true" tabindex="-1"></a>    <span class="co">// relocatable types are allowed to have throwing move constructors, and</span></span>
<span id="cb6-25"><a href="#cb6-25" aria-hidden="true" tabindex="-1"></a>    <span class="co">// any throwing move that occurs in this branch will cause constant</span></span>
<span id="cb6-26"><a href="#cb6-26" aria-hidden="true" tabindex="-1"></a>    <span class="co">// evaluation to fail.</span></span>
<span id="cb6-27"><a href="#cb6-27" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb6-28"><a href="#cb6-28" aria-hidden="true" tabindex="-1"></a>    <span class="cf">if</span> <span class="op">!</span> <span class="kw">consteval</span> <span class="op">{</span></span>
<span id="cb6-29"><a href="#cb6-29" aria-hidden="true" tabindex="-1"></a>      <span class="co">// At run time, when there is no overlap, we can, using other Standard</span></span>
<span id="cb6-30"><a href="#cb6-30" aria-hidden="true" tabindex="-1"></a>      <span class="co">// Library algorithms, do all moves at once followed by all destructions.</span></span>
<span id="cb6-31"><a href="#cb6-31" aria-hidden="true" tabindex="-1"></a>      <span class="cf">if</span> <span class="op">(</span>less<span class="op">{}(</span>last,result<span class="op">)</span> <span class="op">||</span> less<span class="op">{}(</span>result <span class="op">+</span> <span class="op">(</span>last<span class="op">-</span>first<span class="op">)</span>, first<span class="op">))</span> <span class="op">{</span></span>
<span id="cb6-32"><a href="#cb6-32" aria-hidden="true" tabindex="-1"></a>        T<span class="op">*</span> result <span class="op">=</span> uninitialized_move<span class="op">(</span>first, last, result<span class="op">)</span>;</span>
<span id="cb6-33"><a href="#cb6-33" aria-hidden="true" tabindex="-1"></a>        destroy<span class="op">(</span>first,last<span class="op">)</span>;</span>
<span id="cb6-34"><a href="#cb6-34" aria-hidden="true" tabindex="-1"></a>        <span class="cf">return</span> result;</span>
<span id="cb6-35"><a href="#cb6-35" aria-hidden="true" tabindex="-1"></a>      <span class="op">}</span></span>
<span id="cb6-36"><a href="#cb6-36" aria-hidden="true" tabindex="-1"></a>    <span class="op">}</span></span>
<span id="cb6-37"><a href="#cb6-37" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb6-38"><a href="#cb6-38" aria-hidden="true" tabindex="-1"></a>    <span class="cf">if</span> <span class="op">(</span>less<span class="op">{}(</span>result,first<span class="op">)</span> <span class="op">||</span> less<span class="op">{}(</span>last,result<span class="op">))</span> <span class="op">{</span></span>
<span id="cb6-39"><a href="#cb6-39" aria-hidden="true" tabindex="-1"></a>      <span class="co">// Any move to a lower address in memory or any nonoverlapping move can be</span></span>
<span id="cb6-40"><a href="#cb6-40" aria-hidden="true" tabindex="-1"></a>      <span class="co">// done by iterating forward through the range.</span></span>
<span id="cb6-41"><a href="#cb6-41" aria-hidden="true" tabindex="-1"></a>      T<span class="op">*</span> next <span class="op">=</span> first;</span>
<span id="cb6-42"><a href="#cb6-42" aria-hidden="true" tabindex="-1"></a>      T<span class="op">*</span> dest <span class="op">=</span> result;</span>
<span id="cb6-43"><a href="#cb6-43" aria-hidden="true" tabindex="-1"></a>      <span class="cf">while</span> <span class="op">(</span>next <span class="op">!=</span> last<span class="op">)</span> <span class="op">{</span></span>
<span id="cb6-44"><a href="#cb6-44" aria-hidden="true" tabindex="-1"></a>        <span class="op">::</span><span class="kw">new</span><span class="op">(</span>dest<span class="op">)</span> T<span class="op">(</span>move<span class="op">(*</span>next<span class="op">))</span>;</span>
<span id="cb6-45"><a href="#cb6-45" aria-hidden="true" tabindex="-1"></a>        next<span class="op">-&gt;~</span>T<span class="op">()</span>;</span>
<span id="cb6-46"><a href="#cb6-46" aria-hidden="true" tabindex="-1"></a>        <span class="op">++</span>next; <span class="op">++</span>dest;</span>
<span id="cb6-47"><a href="#cb6-47" aria-hidden="true" tabindex="-1"></a>      <span class="op">}</span></span>
<span id="cb6-48"><a href="#cb6-48" aria-hidden="true" tabindex="-1"></a>    <span class="op">}</span></span>
<span id="cb6-49"><a href="#cb6-49" aria-hidden="true" tabindex="-1"></a>    <span class="cf">else</span> <span class="op">{</span></span>
<span id="cb6-50"><a href="#cb6-50" aria-hidden="true" tabindex="-1"></a>      <span class="co">// When moving to a higher address that overlaps, we must go backward through</span></span>
<span id="cb6-51"><a href="#cb6-51" aria-hidden="true" tabindex="-1"></a>      <span class="co">// the range.</span></span>
<span id="cb6-52"><a href="#cb6-52" aria-hidden="true" tabindex="-1"></a>      T<span class="op">*</span> next <span class="op">=</span> last;</span>
<span id="cb6-53"><a href="#cb6-53" aria-hidden="true" tabindex="-1"></a>      T<span class="op">*</span> dest <span class="op">=</span> result <span class="op">+</span> <span class="op">(</span>last<span class="op">-</span>first<span class="op">)</span>;</span>
<span id="cb6-54"><a href="#cb6-54" aria-hidden="true" tabindex="-1"></a>      <span class="cf">while</span> <span class="op">(</span>next <span class="op">!=</span> first<span class="op">)</span> <span class="op">{</span></span>
<span id="cb6-55"><a href="#cb6-55" aria-hidden="true" tabindex="-1"></a>        <span class="op">--</span>next;  <span class="op">--</span>dest;</span>
<span id="cb6-56"><a href="#cb6-56" aria-hidden="true" tabindex="-1"></a>        <span class="op">::</span><span class="kw">new</span><span class="op">(</span>dest<span class="op">)</span> T<span class="op">(</span>move<span class="op">(*</span>next<span class="op">))</span>;</span>
<span id="cb6-57"><a href="#cb6-57" aria-hidden="true" tabindex="-1"></a>        next<span class="op">-&gt;~</span>T<span class="op">()</span>;</span>
<span id="cb6-58"><a href="#cb6-58" aria-hidden="true" tabindex="-1"></a>      <span class="op">}</span></span>
<span id="cb6-59"><a href="#cb6-59" aria-hidden="true" tabindex="-1"></a>    <span class="op">}</span></span>
<span id="cb6-60"><a href="#cb6-60" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb6-61"><a href="#cb6-61" aria-hidden="true" tabindex="-1"></a>    <span class="cf">return</span> result <span class="op">+</span> <span class="op">(</span>last<span class="op">-</span>first<span class="op">)</span>;</span>
<span id="cb6-62"><a href="#cb6-62" aria-hidden="true" tabindex="-1"></a>  <span class="op">}</span></span>
<span id="cb6-63"><a href="#cb6-63" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb6-64"><a href="#cb6-64" aria-hidden="true" tabindex="-1"></a>  <span class="co">// The only way to reach this point is during constant evaluation where type `T`</span></span>
<span id="cb6-65"><a href="#cb6-65" aria-hidden="true" tabindex="-1"></a>  <span class="co">// is trivially relocatable but not move constructible.  Such cases are not supported,</span></span>
<span id="cb6-66"><a href="#cb6-66" aria-hidden="true" tabindex="-1"></a>  <span class="co">// so we mark this branch as unreachable.</span></span>
<span id="cb6-67"><a href="#cb6-67" aria-hidden="true" tabindex="-1"></a>  unreachable<span class="op">()</span>;</span>
<span id="cb6-68"><a href="#cb6-68" aria-hidden="true" tabindex="-1"></a><span class="op">}</span></span></code></pre></div>
<p>Note that <span class="citation" data-cites="P3516R0">[<a href="https://isocpp.org/files/papers/P3516R0.html" role="doc-biblioref">P3516R0</a>]</span> presents
<code class="sourceCode cpp">uninitialized_relocate</code> and
<code class="sourceCode cpp">uninitialize_relocate_backward</code>
templates that provide a different —larger but more general— alternative
interface, providing similar functionality to the
<code class="sourceCode cpp">relocate</code> function template.</p>
<h2 data-number="10.2" id="replaceability-1"><span class="header-section-number">10.2</span> Replaceability<a href="#replaceability-1" class="self-link"></a></h2>
<p>In addition to <strong>trivial relocation</strong>, we introduce the
orthogonal notion of <strong>replaceability</strong>. An object of type
<code class="sourceCode cpp">T</code> is
<strong><em>replaceable</em></strong> by an object of type
<code class="sourceCode cpp">U</code> if destroying the object of type
<code class="sourceCode cpp">T</code> and reconstructing an object of
type <code class="sourceCode cpp">T</code> in its place from an xvalue
of type <code class="sourceCode cpp">U</code> is equivalent to assigning
to the original object of type <code class="sourceCode cpp">T</code>
with an xvalue of type <code class="sourceCode cpp">U</code>. Note that
<strong>replacement</strong> updates an object’s value, so
<code class="sourceCode cpp"><span class="kw">const</span></code>-qualified
objects are never <strong><em>replaceable</em></strong>.</p>
<p><strong>Replaceability</strong> is an important property when we want
to transform <strong>relocation</strong> into assignment or vice versa.
Containers such as
<code class="sourceCode cpp">std<span class="op">::</span>vector</code>
already make a general assumption that all types are
<strong><em>replaceable</em></strong>, but other functions, such as
<code class="sourceCode cpp">std<span class="op">::</span>swap</code>,
do not make such an assumption, so we provide a mechanism to identify
those types that provide guarantees by using this new property.</p>
<h3 data-number="10.2.1" id="new-type-category-replaceable-type"><span class="header-section-number">10.2.1</span> New type category:
Replaceable type<a href="#new-type-category-replaceable-type" class="self-link"></a></h3>
<p>A type <code class="sourceCode cpp">T</code> is a
<strong><em>replaceable type</em></strong> if every object of type
<code class="sourceCode cpp">T</code> is
<strong><em>replaceable</em></strong> by every other object of type
<code class="sourceCode cpp">T</code>. Note that <strong><em>replaceable
types</em></strong> must be object types; function types, reference
types, and
<code class="sourceCode cpp"><span class="dt">void</span></code> are
never <strong><em>replaceable</em></strong>.</p>
<p>A cv-unqualified type <code class="sourceCode cpp">T</code> will
implicitly be a <strong><em>replaceable type</em></strong> if all its
bases and nonstatic members are <strong><em>replaceable
types</em></strong> and if it has no user-provided move constructor,
move-assignment operator, nor destructor.</p>
<h3 data-number="10.2.2" id="new-keyword-and-explicit-rule-1"><span class="header-section-number">10.2.2</span> New keyword and explicit
rule<a href="#new-keyword-and-explicit-rule-1" class="self-link"></a></h3>
<p>To enable <strong>replaceability</strong> to be useful for classes
with user-provided special member functions, explicitly marking class
(including union) types as potentially
<strong><em>replaceable</em></strong> must be possible (just like for
<strong><em>trivially relocatable types</em></strong>). To that end, we
propose adding a new contextual keyword,
<code class="sourceCode cpp">replaceable_if_eligible</code>, as part of
the class definition (mirroring the design of
<code class="sourceCode cpp">trivially_relocatable_if_eligible</code>).</p>
<div class="sourceCode" id="cb7"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> X;                           <span class="co">// Forward declaration does not admit `final`.</span></span>
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> X <span class="kw">final</span> <span class="op">{}</span>;                  <span class="co">// Class definition admits `final`.</span></span>
<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> Y trivially_relocatable_if_eligible <span class="op">{}</span>;  <span class="co">// New contextual keyword is placed like `final`.</span></span>
<span id="cb7-4"><a href="#cb7-4" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> Z replaceable_if_eligible <span class="op">{}</span>;            <span class="co">// New contextual keyword is placed like `final`.</span></span></code></pre></div>
<p>A class can be marked with both
<code class="sourceCode cpp">trivially_relocatable_if_eligible</code>
and <code class="sourceCode cpp">replaceable_if_eligible</code>; we
expect many uses of
<code class="sourceCode cpp">replaceable_if_eligible</code> to also
require
<code class="sourceCode cpp">trivially_relocatable_if_eligible</code>.</p>
<h3 data-number="10.2.3" id="new-type-trait-is_replaceable"><span class="header-section-number">10.2.3</span> New type trait:
<code class="sourceCode cpp">is_replaceable</code><a href="#new-type-trait-is_replaceable" class="self-link"></a></h3>
<p>To expose the <strong>replaceability</strong> property of a type to
library functions seeking to provide appropriate optimizations, we
propose a new trait, <code class="sourceCode cpp">std<span class="op">::</span>is_replaceable<span class="op">&lt;</span>T<span class="op">&gt;</span></code>,
that enables the detection of <strong><em>replaceable
types</em></strong>:</p>
<div class="sourceCode" id="cb8"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a><span class="kw">template</span><span class="op">&lt;</span> <span class="kw">class</span> T <span class="op">&gt;</span></span>
<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> is_replaceable;</span>
<span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb8-4"><a href="#cb8-4" aria-hidden="true" tabindex="-1"></a><span class="kw">template</span><span class="op">&lt;</span> <span class="kw">class</span> T <span class="op">&gt;</span></span>
<span id="cb8-5"><a href="#cb8-5" aria-hidden="true" tabindex="-1"></a><span class="kw">constexpr</span> <span class="dt">bool</span> is_replaceable_v <span class="op">=</span> is_replaceable<span class="op">&lt;</span>T<span class="op">&gt;::</span>value;</span></code></pre></div>
<p>The <code class="sourceCode cpp">std<span class="op">::</span>is_replaceable<span class="op">&lt;</span>T<span class="op">&gt;</span></code>
trait has a base characteristic of <code class="sourceCode cpp">std<span class="op">::</span>true_type</code> if
<code class="sourceCode cpp">T</code> is
<strong><em>replaceable</em></strong> and <code class="sourceCode cpp">std<span class="op">::</span>false_type</code>
otherwise.</p>
<p>Note that the <code class="sourceCode cpp">std<span class="op">::</span>is_replaceable</code>
trait reflects the underlying property that a type has, and like all
similar traits in the Standard Library, it must not be <em>user
specializable</em>. Compilers themselves are expected to determine this
property internally and should not introduce a library dependency such
as by instantiating this type trait.</p>
<h2 data-number="10.3" id="not-optimizing-stdswap"><span class="header-section-number">10.3</span> (Not) Optimizing
<code class="sourceCode cpp">std<span class="op">::</span>swap</code><a href="#not-optimizing-stdswap" class="self-link"></a></h2>
<p><code class="sourceCode cpp">std<span class="op">::</span>swap</code>
usage differs significantly from <strong>trivial relocation</strong> in
several ways.
<code class="sourceCode cpp">std<span class="op">::</span>swap</code> is
an existing well-specified function with a wide contract, and it starts
and ends with two valid objects and cannot end the lifetimes of either
without vastly changing its current expected behavior; users will have
no well-defined way to implement a safe, general purpose, byte-wise
<code class="sourceCode cpp">swap</code>. However, Standard Library
implementations are not constrained by simple things like undefined
behavior, so vendors will remain free to provide such optimizations as a
QoI feature that relies on
<code class="sourceCode cpp">is_trivially_relocatable</code> and
<code class="sourceCode cpp">is_replaceable</code> to spot candidate
types; the implementation would still need to rely on compiler
intrinsics to avoid the dangers inherent in nontransparent
<strong>replacement</strong>, but techniques to evade this problem are
known.</p>
<p>Note that revisions R7–9 of this paper included extensive work to
guarantee a byte-wise <code class="sourceCode cpp">swap</code>, but
ultimately those extensions were deemed complex, distracting, and
nonessential. They might return in a follow-up paper if this paper
(P2786) is adopted.</p>
<h3 data-number="10.3.1" id="untyped-nested-subobjects"><span class="header-section-number">10.3.1</span> Untyped nested subobjects<a href="#untyped-nested-subobjects" class="self-link"></a></h3>
<p>A complete object can store a variety of nested subobjects, the
obvious case being all its member subobjects, yet nested subobjects can
be created in other ways too. For example, if a class has a nonstatic
data member that is an array of
<code class="sourceCode cpp">std<span class="op">::</span>byte</code>, a
nested subobject with dynamic storage duration can be created in that
storage.</p>
<p>When an object is relocated, all its nested subobjects, including
those of dynamic storage duration stashed in member arrays, must be
relocated too.</p>
<h1 data-number="11" id="simple-worked-examples"><span class="header-section-number">11</span> Simple Worked Examples<a href="#simple-worked-examples" class="self-link"></a></h1>
<p>To help dispel confusion and misunderstanding, we present a variety
of simple classes that illustrate most of the concerns regarding whether
a type will be <strong><em>trivially relocatable</em></strong>,
<strong><em>replaceable</em></strong>, neither, or both. For reference,
we will also note whether such types are trivially copyable as well.</p>
<h2 data-number="11.1" id="exposition-only-classes"><span class="header-section-number">11.1</span> Exposition-only classes<a href="#exposition-only-classes" class="self-link"></a></h2>
<p>The following exposition-only classes have their semantics defined by
their documentation comments. They are used throughout the rest of this
section to illustrate the interaction of the proposed new facilities
with both implicit and explicit deduction of the new properties with a
relevant variety of data members.</p>
<div class="sourceCode" id="cb9"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> Empty <span class="op">{}</span>;</span>
<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb9-3"><a href="#cb9-3" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span>    is_trivially_copyable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb9-4"><a href="#cb9-4" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span>    is_trivially_relocatable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb9-5"><a href="#cb9-5" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span>    is_replaceable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb9-6"><a href="#cb9-6" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb9-7"><a href="#cb9-7" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb9-8"><a href="#cb9-8" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> <em>Non-Trivial</em> <span class="op">{</span></span>
<span id="cb9-9"><a href="#cb9-9" aria-hidden="true" tabindex="-1"></a>   <span class="co">// Implementation details are elided.</span></span>
<span id="cb9-10"><a href="#cb9-10" aria-hidden="true" tabindex="-1"></a>   <span class="co">// <em>Non-Trivial</em> is neither trivially copyable, trivially relocatable, nor replaceable.</span></span>
<span id="cb9-11"><a href="#cb9-11" aria-hidden="true" tabindex="-1"></a><span class="op">]</span>;</span>
<span id="cb9-12"><a href="#cb9-12" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb9-13"><a href="#cb9-13" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span><span class="kw">not</span> is_trivially_copyable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb9-14"><a href="#cb9-14" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span><span class="kw">not</span> is_trivially_relocatable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb9-15"><a href="#cb9-15" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span><span class="kw">not</span> is_replaceable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb9-16"><a href="#cb9-16" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb9-17"><a href="#cb9-17" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb9-18"><a href="#cb9-18" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> Immobile <span class="op">{</span></span>
<span id="cb9-19"><a href="#cb9-19" aria-hidden="true" tabindex="-1"></a>   Immobile<span class="op">(</span>Immobile<span class="op">&amp;&amp;)</span> <span class="op">=</span> <span class="kw">delete</span>;</span>
<span id="cb9-20"><a href="#cb9-20" aria-hidden="true" tabindex="-1"></a>   Immobile<span class="op">&amp;</span> <span class="kw">operator</span><span class="op">=(</span>Immobile<span class="op">&amp;&amp;)</span> <span class="op">=</span> <span class="kw">delete</span>;</span>
<span id="cb9-21"><a href="#cb9-21" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb9-22"><a href="#cb9-22" aria-hidden="true" tabindex="-1"></a>   Immobile<span class="op">()</span> <span class="op">=</span> <span class="cf">default</span>;</span>
<span id="cb9-23"><a href="#cb9-23" aria-hidden="true" tabindex="-1"></a><span class="op">}</span>;</span>
<span id="cb9-24"><a href="#cb9-24" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb9-25"><a href="#cb9-25" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span><span class="kw">not</span> is_trivially_copyable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb9-26"><a href="#cb9-26" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span>    is_trivially_relocatable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb9-27"><a href="#cb9-27" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span><span class="kw">not</span> is_replaceable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span></code></pre></div>
<h2 data-number="11.2" id="rule-of-zero"><span class="header-section-number">11.2</span> Rule of zero<a href="#rule-of-zero" class="self-link"></a></h2>
<div class="sourceCode" id="cb10"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> X<span class="op">{}</span>;</span>
<span id="cb10-2"><a href="#cb10-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb10-3"><a href="#cb10-3" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span>    is_trivially_copyable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb10-4"><a href="#cb10-4" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span>    is_trivially_relocatable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb10-5"><a href="#cb10-5" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span>    is_replaceable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span></code></pre></div>
<div class="sourceCode" id="cb11"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> X <span class="op">:</span> Empty <span class="op">{}</span>;</span>
<span id="cb11-2"><a href="#cb11-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb11-3"><a href="#cb11-3" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span>    is_trivially_copyable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb11-4"><a href="#cb11-4" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span>    is_trivially_relocatable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb11-5"><a href="#cb11-5" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span>    is_replaceable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span></code></pre></div>
<div class="sourceCode" id="cb12"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> X <span class="op">:</span> <span class="kw">virtual</span> Empty <span class="op">{}</span>;</span>
<span id="cb12-2"><a href="#cb12-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb12-3"><a href="#cb12-3" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span><span class="kw">not</span> is_trivially_copyable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb12-4"><a href="#cb12-4" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span><span class="kw">not</span> is_trivially_relocatable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb12-5"><a href="#cb12-5" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span>    is_replaceable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;         <span class="co">// Replaceable types can have virtual bases.</span></span></code></pre></div>
<div class="sourceCode" id="cb13"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> X trivially_relocatable_if_eligible <span class="op">:</span> <span class="kw">virtual</span> Empty <span class="op">{}</span>;</span>
<span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb13-3"><a href="#cb13-3" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span><span class="kw">not</span> is_trivially_copyable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb13-4"><a href="#cb13-4" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span><span class="kw">not</span> is_trivially_relocatable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;  <span class="co">// Trivially reloctable types never have</span></span>
<span id="cb13-5"><a href="#cb13-5" aria-hidden="true" tabindex="-1"></a>                                                   <span class="co">// virtual bases.</span></span>
<span id="cb13-6"><a href="#cb13-6" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span>    is_replaceable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span></code></pre></div>
<div class="sourceCode" id="cb14"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> X <span class="op">{</span></span>
<span id="cb14-2"><a href="#cb14-2" aria-hidden="true" tabindex="-1"></a>   <em>Non-Trivial</em> data;</span>
<span id="cb14-3"><a href="#cb14-3" aria-hidden="true" tabindex="-1"></a><span class="op">}</span>;</span>
<span id="cb14-4"><a href="#cb14-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb14-5"><a href="#cb14-5" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span><span class="kw">not</span> is_trivially_copyable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb14-6"><a href="#cb14-6" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span><span class="kw">not</span> is_trivially_relocatable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb14-7"><a href="#cb14-7" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span><span class="kw">not</span> is_replaceable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span></code></pre></div>
<h2 data-number="11.3" id="impact-of-destructors"><span class="header-section-number">11.3</span> Impact of destructors<a href="#impact-of-destructors" class="self-link"></a></h2>
<div class="sourceCode" id="cb15"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> X <span class="op">{</span></span>
<span id="cb15-2"><a href="#cb15-2" aria-hidden="true" tabindex="-1"></a>   <span class="op">~</span>X<span class="op">()</span> <span class="op">=</span> <span class="cf">default</span>;</span>
<span id="cb15-3"><a href="#cb15-3" aria-hidden="true" tabindex="-1"></a><span class="op">}</span>;</span>
<span id="cb15-4"><a href="#cb15-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb15-5"><a href="#cb15-5" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span>    is_trivially_copyable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb15-6"><a href="#cb15-6" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span>    is_trivially_relocatable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb15-7"><a href="#cb15-7" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span>    is_replaceable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span></code></pre></div>
<div class="sourceCode" id="cb16"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb16-1"><a href="#cb16-1" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> X <span class="op">{</span></span>
<span id="cb16-2"><a href="#cb16-2" aria-hidden="true" tabindex="-1"></a>   <span class="op">~</span>X<span class="op">()</span>;</span>
<span id="cb16-3"><a href="#cb16-3" aria-hidden="true" tabindex="-1"></a><span class="op">}</span>;</span>
<span id="cb16-4"><a href="#cb16-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb16-5"><a href="#cb16-5" aria-hidden="true" tabindex="-1"></a>X<span class="op">::~</span>X<span class="op">()</span> <span class="op">=</span> <span class="cf">default</span>;</span>
<span id="cb16-6"><a href="#cb16-6" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb16-7"><a href="#cb16-7" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span><span class="kw">not</span> is_trivially_copyable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb16-8"><a href="#cb16-8" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span><span class="kw">not</span> is_trivially_relocatable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb16-9"><a href="#cb16-9" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span><span class="kw">not</span> is_replaceable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span></code></pre></div>
<div class="sourceCode" id="cb17"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb17-1"><a href="#cb17-1" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> X <span class="op">{</span></span>
<span id="cb17-2"><a href="#cb17-2" aria-hidden="true" tabindex="-1"></a>   <span class="kw">virtual</span> <span class="op">~</span>X<span class="op">()</span> <span class="op">=</span> <span class="cf">default</span>;</span>
<span id="cb17-3"><a href="#cb17-3" aria-hidden="true" tabindex="-1"></a><span class="op">}</span>;</span>
<span id="cb17-4"><a href="#cb17-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb17-5"><a href="#cb17-5" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span><span class="kw">not</span> is_trivially_copyable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb17-6"><a href="#cb17-6" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span><span class="kw">not</span> is_trivially_relocatable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb17-7"><a href="#cb17-7" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span><span class="kw">not</span> is_replaceable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span></code></pre></div>
<div class="sourceCode" id="cb18"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> X <span class="op">{</span></span>
<span id="cb18-2"><a href="#cb18-2" aria-hidden="true" tabindex="-1"></a>   <span class="op">~</span>X<span class="op">()</span> <span class="op">=</span> <span class="kw">delete</span>;</span>
<span id="cb18-3"><a href="#cb18-3" aria-hidden="true" tabindex="-1"></a><span class="op">}</span>;</span>
<span id="cb18-4"><a href="#cb18-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb18-5"><a href="#cb18-5" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span><span class="kw">not</span> is_trivially_copyable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb18-6"><a href="#cb18-6" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span><span class="kw">not</span> is_trivially_relocatable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb18-7"><a href="#cb18-7" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span><span class="kw">not</span> is_replaceable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span></code></pre></div>
<h2 data-number="11.4" id="impact-of-move-constructors"><span class="header-section-number">11.4</span> Impact of move constructors<a href="#impact-of-move-constructors" class="self-link"></a></h2>
<div class="sourceCode" id="cb19"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb19-1"><a href="#cb19-1" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> X <span class="op">{</span></span>
<span id="cb19-2"><a href="#cb19-2" aria-hidden="true" tabindex="-1"></a>   X<span class="op">(</span>X<span class="op">&amp;&amp;)</span> <span class="op">=</span> <span class="cf">default</span>;</span>
<span id="cb19-3"><a href="#cb19-3" aria-hidden="true" tabindex="-1"></a><span class="op">}</span>;</span>
<span id="cb19-4"><a href="#cb19-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb19-5"><a href="#cb19-5" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span>    is_trivially_copyable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb19-6"><a href="#cb19-6" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span>    is_trivially_relocatable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb19-7"><a href="#cb19-7" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span>    is_replaceable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span></code></pre></div>
<div class="sourceCode" id="cb20"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb20-1"><a href="#cb20-1" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> X <span class="op">{</span></span>
<span id="cb20-2"><a href="#cb20-2" aria-hidden="true" tabindex="-1"></a>   X<span class="op">(</span>X<span class="op">&amp;&amp;)</span>;</span>
<span id="cb20-3"><a href="#cb20-3" aria-hidden="true" tabindex="-1"></a><span class="op">}</span>;</span>
<span id="cb20-4"><a href="#cb20-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb20-5"><a href="#cb20-5" aria-hidden="true" tabindex="-1"></a>X<span class="op">::</span>X<span class="op">(</span>X<span class="op">&amp;&amp;)</span> <span class="op">=</span> <span class="cf">default</span>;</span>
<span id="cb20-6"><a href="#cb20-6" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb20-7"><a href="#cb20-7" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span><span class="kw">not</span> is_trivially_copyable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb20-8"><a href="#cb20-8" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span><span class="kw">not</span> is_trivially_relocatable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb20-9"><a href="#cb20-9" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span><span class="kw">not</span> is_replaceable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span></code></pre></div>
<p>Note: This class has an implicitly deleted copy constructor and an
implicitly deleted copy-assignment operator.</p>
<div class="sourceCode" id="cb21"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb21-1"><a href="#cb21-1" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> X <span class="op">{</span></span>
<span id="cb21-2"><a href="#cb21-2" aria-hidden="true" tabindex="-1"></a>   X<span class="op">(</span>X<span class="op">&amp;&amp;)</span> <span class="op">=</span> <span class="kw">delete</span>;</span>
<span id="cb21-3"><a href="#cb21-3" aria-hidden="true" tabindex="-1"></a><span class="op">}</span>;</span>
<span id="cb21-4"><a href="#cb21-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb21-5"><a href="#cb21-5" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span><span class="kw">not</span> is_trivially_copyable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb21-6"><a href="#cb21-6" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span><span class="kw">not</span> is_trivially_relocatable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span>
<span id="cb21-7"><a href="#cb21-7" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span><span class="kw">not</span> is_replaceable_v<span class="op">&lt;</span>X<span class="op">&gt;)</span>;</span></code></pre></div>
<h1 data-number="12" id="plans-for-library-update"><span class="header-section-number">12</span> Plans for Library Update<a href="#plans-for-library-update" class="self-link"></a></h1>
<p>We plan to enable the adoption of these new features in follow-up
papers targeting LEWG.</p>
<h2 data-number="12.1" id="immediate-updates"><span class="header-section-number">12.1</span> Immediate updates<a href="#immediate-updates" class="self-link"></a></h2>
<p>In addition to specifying the type traits and Library functions that
enable the facilities, we should update the Library frontmatter to
indicate whether and how the Library is allowed to use these features to
enhance their QoI.</p>
<p>Clearly, under the as-if rule, the Library immediately gets
permission to optimize algorithms and functions for
<strong><em>trivially relocatable</em></strong> and
<strong><em>replaceable</em></strong> types where such optimizations are
not observable. For example,
<code class="sourceCode cpp">std<span class="op">::</span>vector</code>
could optimize many of its operations for such types, given a suitable
allocator, such as the default <code class="sourceCode cpp">std<span class="op">::</span>allocator</code>. No
updates to the Library specification are needed for these optimizations,
and follow-up papers that suggest changing specifications to allow such
optimizations that <em>would</em> be observable should be properly
directed to LEWG.</p>
<!-- cj: TBD Are we actually saying anything here? -->
<p>The other category of interest is whether Library types themselves
can — or should — be <strong><em>trivially relocatable</em></strong> or
<strong><em>replaceable</em></strong>. For example, any implementation
of
<code class="sourceCode cpp">std<span class="op">::</span>vector</code>
should be able to satisfy the requirements to be both
<strong><em>trivially relocatable</em></strong> and
<strong><em>replaceable</em></strong> for any element type as long as
its allocator has those properties; we might want to mandate that
<code class="sourceCode cpp">std<span class="op">::</span>vector</code>
is relocatable and/or <strong><em>replaceable</em></strong> in such
cases. Conversely, in the two common implementation strategies for
<code class="sourceCode cpp">std<span class="op">::</span>list</code>,
the <em>sentinel node</em> is either dynamically allocated or stored
directly in the footprint of the
<code class="sourceCode cpp">list</code>. The dynamic node case is
always <strong><em>trivially relocatable</em></strong> and
<strong><em>replaceable</em></strong>, but the in-place representation
is neither; however, the in-place representation is
<em>nothrow-movable</em>, whereas the dynamic case must allocate a new
node, which can potentially throw. In both cases,
<strong>relocation</strong> will never throw, but different trade-offs
must be considered when choosing an implementation strategy, and such
cases are almost always better left for implementation QoI (especially
since ABI concerns might require consideration).</p>
<p>When granting permission for implementations to use keywords that are
in addition to those specified by the C++ Standard, we have taken two
approaches that we will term the
<code class="sourceCode cpp"><span class="kw">noexcept</span></code>
approach and the
<code class="sourceCode cpp"><span class="kw">constexpr</span></code>
approach. In the
<code class="sourceCode cpp"><span class="kw">noexcept</span></code>
approach, an implementation is granted permission to add
<code class="sourceCode cpp"><span class="kw">noexcept</span></code>
specifications to functions as long as those specifications do not
invalidate other aspects of the function contract; i.e., an exception
specification cannot be added to a virtual function or to a function
that is specified to throw exceptions. Conversely, the
<code class="sourceCode cpp"><span class="kw">constexpr</span></code>
approach disallows adding
<code class="sourceCode cpp"><span class="kw">constexpr</span></code> to
a function that is not declared as
<code class="sourceCode cpp"><span class="kw">constexpr</span></code> in
the C++ Standard.</p>
<p>For the purposes of this paper, we believe the minimal necessary
specification should use the
<code class="sourceCode cpp"><span class="kw">noexcept</span></code>
approach, and we propose the appropriate wording to say so. That choice
will allow implementations to experiment with the feature and then
provide clear recommendations for specific cases as follow-up LEWG
papers.</p>
<h2 data-number="12.2" id="abi-concerns"><span class="header-section-number">12.2</span> ABI concerns<a href="#abi-concerns" class="self-link"></a></h2>
<p>We believe no ABI concerns exist for libraries applying these new
features throughout the Standard Library, even as unspecified QoI
improvements.</p>
<p>The name-mangling of a type should not depend on whether it is either
<strong><em>trivially relocatable</em></strong> or
<strong><em>replaceable</em></strong>. While these properties can be
determined through type traits, by definition of being a new feature, no
existing code will be SFINAE-enabled on these traits. Updating the
internal layout of any Standard Library type to accommodate
optimizations using these traits should be unnecessary.</p>
<p>The main concern might be adding constraints to
implementation-specific functions used to dispatch to optimized
algorithms, such as when growing a vector. In these cases, to avoid
introducing new mangled names that would affect link compatibility,
<code class="sourceCode cpp"><span class="cf">if</span> <span class="kw">constexpr</span></code>
within the dispatching function could be used to enable a fully
link-compatible library.</p>
<p>One situation that should be called out is when a library wants to
adopt an optimization with an observable behavior change, such as
relocating a nonreplaceable type where previously assignment was used.
The same concerns would arise as with any other change of unspecified
behavior or even a typical bug fix, and library vendors might choose to
be conservative and postpone making those QoI changes.</p>
<h2 data-number="12.3" id="specific-follow-ups"><span class="header-section-number">12.3</span> Specific follow-ups<a href="#specific-follow-ups" class="self-link"></a></h2>
<p>In a follow-up paper, we intended to propose adding a new
specification element, <em>Class properties</em>, for any specification
related to class properties <span>11.2
<a href="https://wg21.link/N4993#class.prop">[class.prop]</a></span>.
The Standard Library already makes some effort to specify whether a
class must be trivially copyable, standard layout, and so on, and we
believe tracking such specification would be more maintainable with a
consistent presentation and using a consistent form.</p>
<p>Once we have a <em>Class properties</em> element, we can then review
all Library classes and decide whether to specify the
<strong>trivial-relocatability</strong> behavior for that class, which
might be conditional on its template arguments if it is a class
template. We might also deliberately defer specifying behavior to allow
for implementations making different choices, such as node-based
containers allocating their end node vs. storing the pointers in the
container’s object representation.</p>
<p>Finally, once we have an easy way to document class properties, we
might consider making stronger guarantees on existing Library components
where such specification would be useful, e.g., clarifying which types
are implicit lifetime.</p>
<p>We would propose moving the specification for the following
properties in this new element</p>
<ul>
<li><em>Trivially Copyable</em></li>
<li><em>Standard Layout</em></li>
<li><em>Implicit Lifetime</em></li>
<li><em>Structural</em></li>
<li><em>Aggregate</em></li>
<li><em>Empty</em></li>
<li><em>Bitmask</em></li>
</ul>
<p>along with the two new properties specified in this paper</p>
<ul>
<li><strong><em>Trivially Relocatable</em></strong></li>
<li><strong><em>Replaceable</em></strong></li>
</ul>
<p>The following clauses in the Standard Library specification would
then include additional notes regarding this new element and updated
specification:</p>
<ul>
<li><span>16.3.2.4
<a href="https://wg21.link/N4993#structure.specifications">[structure.specifications]</a></span>
— class properties as well as invariants</li>
<li><span>16.3.3.3.5
<a href="https://wg21.link/N4993#customization.point.object">[customization.point.object]</a></span>
— might be mildly reformulated with the new specification element</li>
<li><span>16.3.3.6
<a href="https://wg21.link/N4993#objects.within.classes">[objects.within.classes]</a></span>
— might be constraining which members may be added</li>
</ul>
<!-- \addcontentsline{toc}{section}{\protect\pagebreak} -->
<h1 data-number="13" id="use-cases"><span class="header-section-number">13</span> Use Cases<a href="#use-cases" class="self-link"></a></h1>
<h2 data-number="13.1" id="optimizing-stdvector-at-run-time"><span class="header-section-number">13.1</span> Optimizing
<code class="sourceCode cpp">std<span class="op">::</span>vector</code>
at run time<a href="#optimizing-stdvector-at-run-time" class="self-link"></a></h2>
<p><code class="sourceCode cpp">std<span class="op">::</span>vector</code>
can optimize moving elements into a new buffer by relying strictly on
<strong>trivial relocation</strong> when the allocator does not
implement <code class="sourceCode cpp">construct</code> and
<code class="sourceCode cpp">destroy</code>. A library paper targeting
the broader issue of optimizing containers for allocators that use the
<code class="sourceCode cpp">construct</code> and
<code class="sourceCode cpp">destroy</code> customization points will
follow since that is a concern for more than just <strong>trivial
relocation</strong>.</p>
<p>We find that the current specification allows for <strong>trivial
relocation</strong> on <code class="sourceCode cpp">insert</code> and
<code class="sourceCode cpp">erase</code>, although that use might
produce a change of semantics that implementations using assignment
prefer to avoid. Hence, we will leave the choice to implementers and
their interpretation of the specification.</p>
<p>We expect to provide a Library-specific paper to address the
semantics of inserting into and erasing from a
<code class="sourceCode cpp">std<span class="op">::</span>vector</code>
that is independent of <strong>trivial relocation</strong> concerns and
that leans heavily into <strong>replaceability</strong>.</p>
<h2 data-number="13.2" id="optimizing-stdoptional-to-be-trivially-relocatable-and-replaceable"><span class="header-section-number">13.2</span> Optimizing <code class="sourceCode cpp">std<span class="op">::</span>optional</code> to
be trivially relocatable and replaceable<a href="#optimizing-stdoptional-to-be-trivially-relocatable-and-replaceable" class="self-link"></a></h2>
<p>If <code class="sourceCode cpp">std<span class="op">::</span>optional</code> is
implemented with a variant member (anonymous union) and a boolean flag
to indicate if the <code class="sourceCode cpp">optional</code> is
engaged, then memberwise determination of both <strong>trivial
relocatability</strong> and <strong>replaceability</strong> will produce
the correct property. Typical usage might be something like the
following example, which clearly shows that any
<code class="sourceCode cpp">optional</code> implementation is going to
provide implementations of all the special member functions and thus
require use of both contextual keywords.</p>
<table>
<thead>
<tr class="header">
<th><div style="text-align:center">
<strong>Original</strong>
</div></th>
<th><div style="text-align:center">
<strong>Optimized</strong>
</div></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td><div>

<div class="sourceCode" id="cb22"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb22-1"><a href="#cb22-1" aria-hidden="true" tabindex="-1"></a><span class="kw">template</span> <span class="op">&lt;</span><span class="kw">class</span> T<span class="op">&gt;</span></span>
<span id="cb22-2"><a href="#cb22-2" aria-hidden="true" tabindex="-1"></a><span class="kw">class</span> optional <span class="op">{</span></span>
<span id="cb22-3"><a href="#cb22-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb22-4"><a href="#cb22-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb22-5"><a href="#cb22-5" aria-hidden="true" tabindex="-1"></a>   <span class="kw">union</span> <span class="op">{</span></span>
<span id="cb22-6"><a href="#cb22-6" aria-hidden="true" tabindex="-1"></a>      T d_object;</span>
<span id="cb22-7"><a href="#cb22-7" aria-hidden="true" tabindex="-1"></a>   <span class="op">}</span>;</span>
<span id="cb22-8"><a href="#cb22-8" aria-hidden="true" tabindex="-1"></a>   <span class="dt">bool</span> d_engaged<span class="op">{</span><span class="kw">false</span><span class="op">}</span>;</span>
<span id="cb22-9"><a href="#cb22-9" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb22-10"><a href="#cb22-10" aria-hidden="true" tabindex="-1"></a><span class="kw">public</span><span class="op">:</span></span>
<span id="cb22-11"><a href="#cb22-11" aria-hidden="true" tabindex="-1"></a>   <span class="kw">using</span> value_type <span class="op">=</span> T;</span>
<span id="cb22-12"><a href="#cb22-12" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb22-13"><a href="#cb22-13" aria-hidden="true" tabindex="-1"></a>   <span class="op">...</span></span>
<span id="cb22-14"><a href="#cb22-14" aria-hidden="true" tabindex="-1"></a><span class="op">}</span>;</span></code></pre></div>

</div></td>
<td><div>

<div class="sourceCode" id="cb23"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb23-1"><a href="#cb23-1" aria-hidden="true" tabindex="-1"></a><span class="kw">template</span> <span class="op">&lt;</span><span class="kw">class</span> T<span class="op">&gt;</span></span>
<span id="cb23-2"><a href="#cb23-2" aria-hidden="true" tabindex="-1"></a><span class="kw">class</span> optional</span>
<span id="cb23-3"><a href="#cb23-3" aria-hidden="true" tabindex="-1"></a>      <span class="add" style="color: #006e28"><ins>trivially_relocatable_if_eligible</ins></span></span>
<span id="cb23-4"><a href="#cb23-4" aria-hidden="true" tabindex="-1"></a>      <span class="add" style="color: #006e28"><ins>replaceable_if_eligible</ins></span> <span class="op">{</span></span>
<span id="cb23-5"><a href="#cb23-5" aria-hidden="true" tabindex="-1"></a>   <span class="kw">union</span> <span class="op">{</span></span>
<span id="cb23-6"><a href="#cb23-6" aria-hidden="true" tabindex="-1"></a>      T d_object;</span>
<span id="cb23-7"><a href="#cb23-7" aria-hidden="true" tabindex="-1"></a>   <span class="op">}</span>;</span>
<span id="cb23-8"><a href="#cb23-8" aria-hidden="true" tabindex="-1"></a>   <span class="dt">bool</span> d_engaged<span class="op">{</span><span class="kw">false</span><span class="op">}</span>;</span>
<span id="cb23-9"><a href="#cb23-9" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb23-10"><a href="#cb23-10" aria-hidden="true" tabindex="-1"></a><span class="kw">public</span><span class="op">:</span></span>
<span id="cb23-11"><a href="#cb23-11" aria-hidden="true" tabindex="-1"></a>   <span class="kw">using</span> value_type <span class="op">=</span> T;</span>
<span id="cb23-12"><a href="#cb23-12" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb23-13"><a href="#cb23-13" aria-hidden="true" tabindex="-1"></a>   <span class="op">...</span></span>
<span id="cb23-14"><a href="#cb23-14" aria-hidden="true" tabindex="-1"></a><span class="op">}</span>;</span></code></pre></div>

</div></td>
</tr>
</tbody>
</table>
<p>Note that to support the
<code class="sourceCode cpp"><span class="kw">constexpr</span></code>
operations required by the Standard, a union-based implementation is the
only known way to conform. However, if we were not concerned about
<code class="sourceCode cpp"><span class="kw">constexpr</span></code>
evaluations, then we might choose to store our active element in an
array of bytes. Unfortunately, adding the
<code class="sourceCode cpp">trivially_relocatable_if_eligible</code> or
<code class="sourceCode cpp">replaceable_if_eligible</code> properties
to the class definition will give our class that same property —
<em>even when the array member is used as storage for a type
<strong><em>without</em></strong> those properties</em> — since an array
of <code class="sourceCode cpp">std<span class="op">::</span>byte</code>
is both <strong><em>trivially relocatable</em></strong> and
<strong><em>replaceable</em></strong>.</p>
<p>This problem can be resolved in several ways, but the key is to
include a data member that is <em>conditionally</em>
<strong><em>trivially relocatable</em></strong> or
<strong><em>replaceable</em></strong>. This resolution is most easily
achieved by adding, to the class, an empty data member that ideally can
preserve the object layout and ABI.</p>
<div class="sourceCode" id="cb24"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb24-1"><a href="#cb24-1" aria-hidden="true" tabindex="-1"></a><span class="kw">template</span> <span class="op">&lt;</span><span class="dt">bool</span> <span class="op">=</span> <span class="kw">true</span><span class="op">&gt;</span></span>
<span id="cb24-2"><a href="#cb24-2" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> OptionallyRelocatable <span class="op">{}</span>;</span>
<span id="cb24-3"><a href="#cb24-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb24-4"><a href="#cb24-4" aria-hidden="true" tabindex="-1"></a><span class="kw">template</span> <span class="op">&lt;&gt;</span></span>
<span id="cb24-5"><a href="#cb24-5" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> OptionallyRelocatable<span class="op">&lt;</span><span class="kw">false</span><span class="op">&gt;</span> <span class="op">{</span></span>
<span id="cb24-6"><a href="#cb24-6" aria-hidden="true" tabindex="-1"></a>    <span class="op">~</span>OptionallyRelocatable<span class="op">(){}</span></span>
<span id="cb24-7"><a href="#cb24-7" aria-hidden="true" tabindex="-1"></a><span class="op">}</span>;</span>
<span id="cb24-8"><a href="#cb24-8" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb24-9"><a href="#cb24-9" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span> std<span class="op">::</span>is_trivially_relocatable_v<span class="op">&lt;</span>OptionallyRelocatable<span class="op">&lt;&gt;&gt;)</span>;</span>
<span id="cb24-10"><a href="#cb24-10" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(!</span>std<span class="op">::</span>is_trivially_relocatable_v<span class="op">&lt;</span>OptionallyRelocatable<span class="op">&lt;</span><span class="kw">false</span><span class="op">&gt;&gt;)</span>;</span>
<span id="cb24-11"><a href="#cb24-11" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb24-12"><a href="#cb24-12" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span> std<span class="op">::</span>is_replaceable_v<span class="op">&lt;</span>OptionallyRelocatable<span class="op">&lt;&gt;&gt;)</span>;</span>
<span id="cb24-13"><a href="#cb24-13" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(!</span>std<span class="op">::</span>is_replaceable_v<span class="op">&lt;</span>OptionallyRelocatable<span class="op">&lt;</span><span class="kw">false</span><span class="op">&gt;&gt;)</span>;</span></code></pre></div>
<table>
<thead>
<tr class="header">
<th><div style="text-align:center">
<strong>Original</strong>
</div></th>
<th><div style="text-align:center">
<strong>Optimized</strong>
</div></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td><div>

<div class="sourceCode" id="cb25"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb25-1"><a href="#cb25-1" aria-hidden="true" tabindex="-1"></a><span class="kw">template</span> <span class="op">&lt;</span><span class="kw">class</span> T<span class="op">&gt;</span></span>
<span id="cb25-2"><a href="#cb25-2" aria-hidden="true" tabindex="-1"></a><span class="kw">class</span> optional <span class="op">{</span></span>
<span id="cb25-3"><a href="#cb25-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb25-4"><a href="#cb25-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb25-5"><a href="#cb25-5" aria-hidden="true" tabindex="-1"></a>   <span class="kw">alignas</span> <span class="op">(</span>T<span class="op">)</span></span>
<span id="cb25-6"><a href="#cb25-6" aria-hidden="true" tabindex="-1"></a>   std<span class="op">::</span>byte d_object<span class="op">[</span><span class="kw">sizeof</span> <span class="op">(</span>T<span class="op">)]</span>;</span>
<span id="cb25-7"><a href="#cb25-7" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb25-8"><a href="#cb25-8" aria-hidden="true" tabindex="-1"></a>   <span class="dt">bool</span>      d_engaged<span class="op">{</span><span class="kw">false</span><span class="op">}</span>;</span>
<span id="cb25-9"><a href="#cb25-9" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb25-10"><a href="#cb25-10" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb25-11"><a href="#cb25-11" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb25-12"><a href="#cb25-12" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb25-13"><a href="#cb25-13" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb25-14"><a href="#cb25-14" aria-hidden="true" tabindex="-1"></a><span class="kw">public</span><span class="op">:</span></span>
<span id="cb25-15"><a href="#cb25-15" aria-hidden="true" tabindex="-1"></a>   <span class="kw">using</span> value_type <span class="op">=</span> T;</span>
<span id="cb25-16"><a href="#cb25-16" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb25-17"><a href="#cb25-17" aria-hidden="true" tabindex="-1"></a>   <span class="op">...</span></span>
<span id="cb25-18"><a href="#cb25-18" aria-hidden="true" tabindex="-1"></a><span class="op">}</span>;</span></code></pre></div>

</div></td>
<td><div>

<div class="sourceCode" id="cb26"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb26-1"><a href="#cb26-1" aria-hidden="true" tabindex="-1"></a><span class="kw">template</span> <span class="op">&lt;</span><span class="kw">class</span> T<span class="op">&gt;</span></span>
<span id="cb26-2"><a href="#cb26-2" aria-hidden="true" tabindex="-1"></a><span class="kw">class</span> optional</span>
<span id="cb26-3"><a href="#cb26-3" aria-hidden="true" tabindex="-1"></a>      <span class="add" style="color: #006e28"><ins>trivially_relocatable_if_eligible</ins></span></span>
<span id="cb26-4"><a href="#cb26-4" aria-hidden="true" tabindex="-1"></a>      <span class="add" style="color: #006e28"><ins>replaceable_if_eligible</ins></span> <span class="op">{</span></span>
<span id="cb26-5"><a href="#cb26-5" aria-hidden="true" tabindex="-1"></a>   <span class="kw">alignas</span> <span class="op">(</span>T<span class="op">)</span></span>
<span id="cb26-6"><a href="#cb26-6" aria-hidden="true" tabindex="-1"></a>   std<span class="op">::</span>byte d_object<span class="op">[</span><span class="kw">sizeof</span> <span class="op">(</span>T<span class="op">)]</span>;</span>
<span id="cb26-7"><a href="#cb26-7" aria-hidden="true" tabindex="-1"></a>   <span class="kw">union</span> <span class="op">{</span></span>
<span id="cb26-8"><a href="#cb26-8" aria-hidden="true" tabindex="-1"></a>      <span class="dt">bool</span>   d_engaged<span class="op">{</span><span class="kw">false</span><span class="op">}</span>;</span>
<span id="cb26-9"><a href="#cb26-9" aria-hidden="true" tabindex="-1"></a>      <span class="add" style="color: #006e28"><ins>OptionallyRelocatable&lt;</ins></span></span>
<span id="cb26-10"><a href="#cb26-10" aria-hidden="true" tabindex="-1"></a>         <span class="add" style="color: #006e28"><ins>std::is_trivially_relocatable_v&lt;T&gt;</ins></span></span>
<span id="cb26-11"><a href="#cb26-11" aria-hidden="true" tabindex="-1"></a>      <span class="add" style="color: #006e28"><ins>&amp;&amp;
std::is_replaceable_v&lt;T&gt;&gt; _;</ins></span></span>
<span id="cb26-12"><a href="#cb26-12" aria-hidden="true" tabindex="-1"></a>   <span class="op">}</span>;</span>
<span id="cb26-13"><a href="#cb26-13" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb26-14"><a href="#cb26-14" aria-hidden="true" tabindex="-1"></a><span class="kw">public</span><span class="op">:</span></span>
<span id="cb26-15"><a href="#cb26-15" aria-hidden="true" tabindex="-1"></a>   <span class="kw">using</span> value_type <span class="op">=</span> T;</span>
<span id="cb26-16"><a href="#cb26-16" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb26-17"><a href="#cb26-17" aria-hidden="true" tabindex="-1"></a>   <span class="op">...</span></span>
<span id="cb26-18"><a href="#cb26-18" aria-hidden="true" tabindex="-1"></a><span class="op">}</span>;</span></code></pre></div>

</div></td>
</tr>
</tbody>
</table>
<p>Note that in the above implementation, even though we have made a
<code class="sourceCode cpp"><span class="kw">union</span></code> to
contain our empty conditionally relocatable object, the
<code class="sourceCode cpp">d_engaged</code> member will always be
active. A similar conditional <strong><em>replaceable</em></strong>
object would have the same implementation and be simple to add as
well.</p>
<h1 data-number="14" id="implementation"><span class="header-section-number">14</span> Implementation Experience<a href="#implementation" class="self-link"></a></h1>
<p>An implementation of the R9 version of this proposal is available as
a fork of Clang and can also be accessed on <a href="https://compiler-explorer.com/z/5jMa4394n">Compiler Explorer</a>.
We have not yet updated that implementation to relocate a single object
at a time.</p>
<p>In addition to the handling of the new keywords and class properties,
the implementation relies on built-in type traits for
<code class="sourceCode cpp">is_trivially_relocatable</code> and
<code class="sourceCode cpp">is_replaceable</code>, which are not
different than other type traits of the same nature.</p>
<p>Our Clang implementation of
<code class="sourceCode cpp">trivial_relocate</code> is implemented in
terms of <code class="sourceCode cpp">memcpy</code>. We did not add the
necessary machinery to end and start lifetimes since that task is
unsupported by the Clang front end and the LLVM optimizer (a known
deficiency of LLVM rather than with our implementation). In general,
starting and ending lifetimes requires an implementation to add some
optimization fences so that optimizers that perform type-based alias
analysis are not overly eager and inappropriately prune all code that
depends on the new object lifetimes. Either way, adding such fences to
an implementation that supports
<code class="sourceCode cpp">start_lifetime_as</code> would present no
notable challenges. We have not explored whether sanitizers would need
to be made aware of these function semantics.</p>
<p>Note that Clang already supports the notion of <strong><em>trivially
relocatable types</em></strong> in production, although with no opt-in
mechanism. This property is used in the implementation of
<code class="sourceCode cpp">std<span class="op">::</span>vector</code>
in libc++ (once again demonstrating an industry need for this feature,
as well as deployment experience with very similar ideas).</p>
<p>Clang also offers a <code class="sourceCode cpp"><span class="op">[[</span><span class="ex">clang::trivial_abi</span><span class="op">]]</span></code>
type attribute that allows a type to be passed in registers when its
destructor/constructor pair can be replaced by a
<code class="sourceCode cpp">memcpy</code>. Types with that attribute
can be passed in a register, which affects calling convention, and
therefore ABI.</p>
<h1 data-number="15" id="faq."><span class="header-section-number">15</span> FAQ<a href="#faq." class="self-link"></a></h1>
<h2 data-number="15.1" id="is-void-trivially-relocatable"><span class="header-section-number">15.1</span> Is
<code class="sourceCode cpp"><span class="dt">void</span></code>
trivially relocatable?<a href="#is-void-trivially-relocatable" class="self-link"></a></h2>
<p>No, nor is it trivially copyable.</p>
<h2 data-number="15.2" id="are-reference-types-trivially-relocatable"><span class="header-section-number">15.2</span> Are reference types trivially
relocatable?<a href="#are-reference-types-trivially-relocatable" class="self-link"></a></h2>
<p>No, nor are they trivially copyable.</p>
<p>Taking the address of a reference to pass it to
<code class="sourceCode cpp">trivially_relocate</code> is not possible.
How the compiler implements references is entirely unspecified and might
not need physical storage if the reference never leaves a local scope.
Asking about copying or relocating a naked reference, rather than the
entity it refers to, is not meaningful, so these trivial properties are
<code class="sourceCode cpp"><span class="kw">false</span></code>.</p>
<h2 data-number="15.3" id="why-can-a-class-with-a-reference-member-be-trivially-relocatable"><span class="header-section-number">15.3</span> Why can a class with a
reference member be trivially relocatable?<a href="#why-can-a-class-with-a-reference-member-be-trivially-relocatable" class="self-link"></a></h2>
<p>A class with a reference member can be <strong><em>trivially
relocatable</em></strong> for the same reason such a class can be
trivially copyable. Strictly speaking, reference members are not
nonstatic data members, and we cannot create a pointer-to-data-member to
one; they deliberately escape the relevant wording by not appearing in
the list of disallowed entities, despite not being trivially copyable or
<strong><em>trivially relocatable</em></strong> as a distinct type in
their own right. This wording is subtle and can entrap the unwary but
has been standard practice for many years.</p>
<h2 data-number="15.4" id="are-cv-qualified-types-notably-const-types-trivially-relocatable"><span class="header-section-number">15.4</span> Are <em>cv</em>-qualified
types, notably
<code class="sourceCode cpp"><span class="kw">const</span></code> types,
trivially relocatable?<a href="#are-cv-qualified-types-notably-const-types-trivially-relocatable" class="self-link"></a></h2>
<p>Yes, if the unqualified type is <strong><em>trivially
relocatable</em></strong>.</p>
<h2 data-number="15.5" id="can-const-qualified-types-be-passed-to-trivially_relocate"><span class="header-section-number">15.5</span> Can
<code class="sourceCode cpp"><span class="kw">const</span></code>-qualified
types be passed to
<code class="sourceCode cpp">trivially_relocate</code>?<a href="#can-const-qualified-types-be-passed-to-trivially_relocate" class="self-link"></a></h2>
<p>No. While
<code class="sourceCode cpp"><span class="kw">const</span></code>-qualified
types are <strong><em>trivially relocatable</em></strong> and thus do
not inhibit the <strong>trivial relocatability</strong> of a wrapping
type, they are typically not safe to <strong>relocate</strong> due to
leaving behind a dead object that cannot be replaced using well-defined
behavior. Hence, the
<code class="sourceCode cpp">trivially_relocate</code> function is
constrained to exclude
<code class="sourceCode cpp"><span class="kw">const</span></code>-qualified
types. This exclusion can be skirted using
<code class="sourceCode cpp"><span class="kw">const_cast</span></code>
if doing so would not introduce undefined behavior.</p>
<h2 data-number="15.6" id="can-types-that-are-not-implicit-lifetime-types-be-trivially-relocatable"><span class="header-section-number">15.6</span> Can types that are not
implicit-lifetime types be trivially relocatable?<a href="#can-types-that-are-not-implicit-lifetime-types-be-trivially-relocatable" class="self-link"></a></h2>
<p>Yes, and our experience tells us to expect the majority of types,
even those that own resources and have nontrivial move constructors and
destructors, to still be <strong><em>trivially
relocatable</em></strong>.</p>
<h2 data-number="15.7" id="faq.virt.bases"><span class="header-section-number">15.7</span> Why are virtual base classes
not trivially relocatable?<a href="#faq.virt.bases" class="self-link"></a></h2>
<p>Because they are not trivially copyable and because the
implementation of virtual base classes on some platforms involves an
internal pointer, virtual base classes are not <strong><em>trivially
relocatable</em></strong>.</p>
<p>We believe that implementing virtual bases such that trivial
copyability and relocatability would not be a concern is possible since
all the needed data for indirection could be stored as offsets instead
of direct pointers. However, whether all implementations could use such
a layout or are able to switch to such a layout is unclear. Forcing this
support might also require an ABI break.</p>
<p>In our opinion, this low-level behavior should be kept consistent
across platforms, rather than left as an unspecified QoI concern, since
our current experience has not yet turned up a usage of virtual base
classes that would also benefit from this feature.</p>
<p>We would be happy to remove this restriction, but consistency must be
maintained with the corresponding restriction on trivially copyable. If
no current ABIs are affected, we might consider normatively allowing —
or even encouraging — such an implementation (for both trivialities) as
conditionally supported behavior on platforms that would not incur an
ABI break.</p>
<p>Note that no issues occur with virtual functions since virtual
function-table implementations do not take a pointer back into the
class, so the vtable pointer can be safely relocated.</p>
<h2 data-number="15.8" id="what-happens-if-a-relocate-operation-throws"><span class="header-section-number">15.8</span> What happens if a relocate
operation throws?<a href="#what-happens-if-a-relocate-operation-throws" class="self-link"></a></h2>
<p><strong>Relocation operations</strong> must be no-fail, so they do
not permit exceptions; if a relocate operation were allowed to fail,
whether the failed state had 0, 1, 2, or more valid objects would be
unknowable, essentially leaving the program in an undefined state that
cannot be cleaned up correctly, which is a significant problem with
objects holding resources like a locked mutex.</p>
<p>Our proposal makes clear that <code class="sourceCode cpp">std<span class="op">::</span>trivial_relocate</code>
cannot fail, and the nontrivial implementation of
<code class="sourceCode cpp">relocate</code> mandates that the object
type is <em>nothrow</em> move constructible. Hence, neither of our
operations can fail by throwing an exception.</p>
<h2 data-number="15.9" id="why-do-deleted-special-members-inhibit-implicit-trivial-relocatability"><span class="header-section-number">15.9</span> Why do deleted special members
inhibit implicit trivial relocatability?<a href="#why-do-deleted-special-members-inhibit-implicit-trivial-relocatability" class="self-link"></a></h2>
<p>Initially, we considered allowing <strong>trivial relocation</strong>
of types with these special members functions deleted, based on a notion
that we have been familiar with since C++17 when <em>mandatory copy
elision</em> started propagating noncopyable and nonmovable return
values. However, relocation is not the same as copy elision, so
objections arose to the idea that, when a user deliberately removes an
operation, we should not <em>silently</em> re-enable it via a backdoor
method. Note that this inhibition changes only the default, preventing
accidental relocation of noncopyable or nonmovable types for which
<strong>relocatability</strong> was neither considered nor intended; if
<strong>trivial relocatability</strong> is desired, such classes can be
made explicitly <strong><em>trivially relocatable</em></strong> by means
of the
<code class="sourceCode cpp">trivially_relocatable_if_eligible</code>
keyword.</p>
<p>This design also follows that of the Core language for trivial
copyability, which was changed by <span class="citation" data-cites="CWG1734">[<a href="https://wg21.link/cwg1734" role="doc-biblioref">CWG1734</a>]</span> to exclude types that deleted
all copying operations and which landed in C++17.</p>
<h2 data-number="15.10" id="can-the-compiler-transform-argument-passing-with-trivial-relocation"><span class="header-section-number">15.10</span> Can the compiler transform
argument passing with trivial relocation?<a href="#can-the-compiler-transform-argument-passing-with-trivial-relocation" class="self-link"></a></h2>
<p>As currently specified, we do not yet enable such support. We believe
that this could be accomplished with the appropriate allowances (which
already exist for trivially copyable types), but significant work in
platform ABIs would be needed to make this happen, similar to what is
needed to support Clang’s <code class="sourceCode cpp"><span class="op">[[</span><span class="at">trivial_abi</span><span class="op">]]</span></code>
attribute.</p>
<p>To enable bitwise parameter passing, such as through registers, for
<strong><em>trivially relocatable types</em></strong>, we would need to
enable the compiler to freely create extra instances of our objects when
passing arguments and return results from functions, which would then
enable a compiler to pass the data itself via a register. Importantly
and unlike for trivially copyable types (which have trivial
destructors), major changes would be needed to ensure that the receiver
of the final object is aware that it is now responsible for destruction
of that object since currently the creator of parameters is responsible
for their destruction on many ABIs.</p>
<p>A separate proposal for argument passing by relocation was offered in
<span class="citation" data-cites="P2839R0">[<a href="https://wg21.link/p2839r0" role="doc-biblioref">P2839R0</a>]</span> but was not reviewed favorably
on its initial presentation to EWG.</p>
<h2 data-number="15.11" id="can-the-standard-library-containers-use-this-new-feature-internally"><span class="header-section-number">15.11</span> Can the Standard Library
containers use this new feature internally?<a href="#can-the-standard-library-containers-use-this-new-feature-internally" class="self-link"></a></h2>
<!--
  mg:  Do we want to mention `swap_value_representations` in this FAQ answer?
  jmb: nah
  -->
<p>Yes, where the current specification is permitted to use move
construction to <strong>relocate</strong> an object (e.g., when growing
or when moving objects within a
<code class="sourceCode cpp">vector</code>), this feature can be used
instead for <strong><em>trivially relocatable types</em></strong>.</p>
<p>A common misconception implies that
<code class="sourceCode cpp">vector</code> is required to use assignment
when inserting into or erasing from a
<code class="sourceCode cpp">vector</code> (other than at the back).
This requirement is not, however, explicitly specified in the Standard.
The misunderstanding stems from a number of places, which are addressed
individually in the subsections below.</p>
<p>However, even if an implementation is <em>allowed</em> to switch from
assignment to relocation for arbitrary <strong><em>trivially
relocatable</em></strong> types, it would likely choose to do so for
only such types that are also <strong><em>replaceable</em></strong> to
avoid silently changing behavior for customers relying on such
types.</p>
<h3 data-number="15.11.1" id="complexity-constraints"><span class="header-section-number">15.11.1</span> Complexity constraints<a href="#complexity-constraints" class="self-link"></a></h3>
<p>The first source of this misunderstanding is that people incorrectly
consider the requirement to be implied from (<span>23.3.11.5
<a href="https://wg21.link/N4993#vector.modifiers">[vector.modifiers]</a></span>p5),
which states for <code class="sourceCode cpp">vector<span class="op">::</span>erase</code>:</p>
<blockquote>
<p><em>Complexity:</em> The destructor of
<code class="sourceCode cpp">T</code> is called the number of times
equal to the number of the elements erased, but the assignment operator
of <code class="sourceCode cpp">T</code> is called the number of times
equal to the number of elements in the
<code class="sourceCode cpp">vector</code> after the erased
elements.</p>
</blockquote>
<p>This complexity existed in C++98, and the only revision has been a
change in C++11 where the text “assignment operator” was updated to
“move assignment operator.” Note that <code class="sourceCode cpp">vector<span class="op">::</span>insert</code> has
no such complexity requirement; it is specified only for the <code class="sourceCode cpp">vector<span class="op">::</span>erase</code>
operation.</p>
<p>The misconception also comes from the following sentence in
(<span>16.3.2.4
<a href="https://wg21.link/N4993#structure.specifications">[structure.specifications]</a></span>p7):</p>
<blockquote>
<p>Complexity requirements specified in the library clauses are upper
bounds, and implementations that provide better complexity guarantees
meet the requirements.</p>
</blockquote>
<p>This statement is <em>not</em>, therefore, a mandate from the
Standard that calls to <code class="sourceCode cpp">vector<span class="op">::</span>erase</code>
shall use the assignment operator as long as the implementation performs
as well as or better than the specified complexity. Given that the
<code class="sourceCode cpp">trivially_relocate</code> function as
specified in this paper is guaranteed to perform a copy of bytes of the
object representation, it must outperform the complexity requirement,
and the Standard, therefore, permits implementations to use the
<code class="sourceCode cpp">trivially_relocate</code> function for
<code class="sourceCode cpp">vector<span class="op">::</span>erase</code>
operations.</p>
<h3 data-number="15.11.2" id="precondition-specifications"><span class="header-section-number">15.11.2</span> Precondition
specifications<a href="#precondition-specifications" class="self-link"></a></h3>
<p>The second source of this misunderstanding stems from phrases such as
the following in(<span>23.2.4
<a href="https://wg21.link/N4993#sequence.reqmts">[sequence.reqmts]</a></span>p29):</p>
<blockquote>
<p><strong><code class="sourceCode cpp">a<span class="op">.</span>insert<span class="op">(</span>p, rv<span class="op">)</span></code></strong></p>
<p>Preconditions: <code class="sourceCode cpp">T</code> is
<em>Cpp17MoveInsertable</em> into <code class="sourceCode cpp">X</code>.
For <code class="sourceCode cpp">vector</code> and
<code class="sourceCode cpp">deque</code>,
<code class="sourceCode cpp">T</code> is also
<em>Cpp17MoveAssignable</em>.</p>
<p>Effects: Inserts a copy of <code class="sourceCode cpp">rv</code>
before <code class="sourceCode cpp">p</code>.</p>
</blockquote>
<p>Although this specification requires that statements of the form
<code class="sourceCode cpp">t <span class="op">=</span> rv</code> be
well-formed, it does <em>not</em> impose any limitations on
implementations to use assignment when moving objects around
internally.</p>
<p>Although the requirement that a type be <em>Cpp17CopyAssignable</em>
or <em>Cpp17MoveAssignable</em> does impose semantic requirements on the
assignment operator(s), the requirements are vague and specified in
terms of a notion of “value” that is not defined in the Standard; see
(<span>16.4.4.2
<a href="https://wg21.link/N4993#utility.arg.requirements">[utility.arg.requirements]</a></span>tab:cpp17.moveassignable).
This requirement was added in C++11 and has not been revisited since
then.</p>
<p>The above explanation refers to <code class="sourceCode cpp">vector<span class="op">::</span>insert<span class="op">(</span>p, rv<span class="op">)</span></code>,
but the same argument applies to similar preconditions on other member
functions. Observe that the postconditions are identical for all
sequence containers, including those, such as
<code class="sourceCode cpp">list</code>, that do not require
<em>Cpp17MoveAssignable</em> as a precondition.</p>
<h3 data-number="15.11.3" id="conclusion"><span class="header-section-number">15.11.3</span> Conclusion<a href="#conclusion" class="self-link"></a></h3>
<p>In other words, although most implementations of <code class="sourceCode cpp">vector<span class="op">::</span>erase</code> and
<code class="sourceCode cpp">vector<span class="op">::</span>insert</code>
currently use assignment, which is generally assumed the most efficient
approach currently available, implementations are under no obligation
whatsoever to do so. The various member functions of
<code class="sourceCode cpp">vector</code> guarantee only that values
will be moved around but grant implementations complete freedom as to
how that action should be performed, whether by means of (move)
assignment, (move) construction, or any other mechanism. Implementations
will, therefore, be permitted to perform this move by means of
<code class="sourceCode cpp">trivially_relocate</code> for types that
are <strong><em>trivially relocatable</em></strong>.</p>
<p>In fact, some implementations avoid using assignment for some
operations (for reasons of efficiency); see the linked examples for <a href="https://github.com/gcc-mirror/gcc/blob/e14c673ea9ab2eca5de4db91b478f0b5297ef321/libstdc%2B%2B-v3/include/bits/stl_uninitialized.h#L1111">GCC</a>
and <a href="https://github.com/llvm/llvm-project/blob/e33db249b53fb70dce62db3ebd82d42239bd1d9d/libcxx/include/__memory/uninitialized_algorithms.h#L623">LLVM</a>.</p>
<p>Note that all the comments above apply equally to
<code class="sourceCode cpp">deque</code> as well as to
<code class="sourceCode cpp">vector</code>.</p>
<p>Note also that this lack of a clear requirement exposes an existing
ambiguity for <code class="sourceCode cpp">vector<span class="op">::</span>insert</code> and
<code class="sourceCode cpp">vector<span class="op">::</span>erase</code>
operations where, for the contained type, move-assign plus destroy is
not equivalent to destroy plus move-construct. That ambiguity is an
issue that exists at the moment, and while we might address it with a
future, orthogonal proposal, a solution is not required for
<strong>trivial relocation</strong> as specified by this paper.
Similarly, we might choose to clarify the complexity and requirements
clauses above at some point in the future, but that clarification is not
required by this proposal and has been left for another time.</p>
<h2 data-number="15.12" id="do-implementations-need-to-mark-classes-trivially_relocatable_if_eligible-to-benefit"><span class="header-section-number">15.12</span> Do implementations need to
mark classes
<code class="sourceCode cpp">trivially_relocatable_if_eligible</code> to
benefit?<a href="#do-implementations-need-to-mark-classes-trivially_relocatable_if_eligible-to-benefit" class="self-link"></a></h2>
<p>No, although some classes will need to be annotated to qualify as
<strong><em>trivially relocatable</em></strong>. For example, the most
common implementations of
<code class="sourceCode cpp">std<span class="op">::</span>array</code>,
<code class="sourceCode cpp">std<span class="op">::</span>pair</code>,
and
<code class="sourceCode cpp">std<span class="op">::</span>tuple</code>
will be implicitly <strong><em>trivially relocatable</em></strong> if
all their members are <strong><em>trivially relocatable</em></strong>.
<code class="sourceCode cpp">std<span class="op">::</span>vector</code>
can safely be marked as <strong><em>trivially relocatable</em></strong>
if its allocator and pointer types are <strong><em>trivially
relocatable</em></strong>.
<code class="sourceCode cpp">std<span class="op">::</span>list</code>
might be marked as <strong><em>trivially relocatable</em></strong> if it
allocates its tail node but not if the tail node is embedded in the
object representation itself.</p>
<p>Once we establish a policy of how much we want to guarantee and how
much we want to leave open to implementer choice, a follow-up paper will
address desired guarantees for <strong>trivial relocatability</strong>
in the Standard Library.</p>
<h2 data-number="15.13" id="can-i-mark-as-trivially-relocatable-a-type-that-is-not-replaceable"><span class="header-section-number">15.13</span> Can I mark as trivially
relocatable a type that is not replaceable?<a href="#can-i-mark-as-trivially-relocatable-a-type-that-is-not-replaceable" class="self-link"></a></h2>
<p>Yes! For example, this would be appropriate for types having data
members that are references or using <code class="sourceCode cpp">std<span class="op">::</span>pmr<span class="op">::</span>polymorphic_allocator</code>
or any other type that does not propagate on
<code class="sourceCode cpp">swap</code>.</p>
<h2 data-number="15.14" id="can-i-mark-a-type-as-replaceable-but-not-trivially-relocatable"><span class="header-section-number">15.14</span> Can I mark a type as
replaceable but not trivially relocatable?<a href="#can-i-mark-a-type-as-replaceable-but-not-trivially-relocatable" class="self-link"></a></h2>
<p>Yes! This proposal does not offer any immediate advantages for doing
so, but we expect to build on <strong>replacement</strong> to optimize
other features, such as assignment, in the future.</p>
<h2 data-number="15.15" id="what-happened-to-the-predicates-for-the-contextual-keywords"><span class="header-section-number">15.15</span> What happened to the
predicates for the contextual keywords?<a href="#what-happened-to-the-predicates-for-the-contextual-keywords" class="self-link"></a></h2>
<p>An earlier version of this proposal included the option to add a
predicate following each of the new contextual keywords to activate or
inhibit their behavior. This feature was dropped for introducing too
much complexity, including a new vexing parse to resolve, and having
vague semantics when the predicate is
<code class="sourceCode cpp"><span class="kw">false</span></code> but
the implicit specification would have been
<code class="sourceCode cpp"><span class="kw">true</span></code>. Given
the rarity of such cases and the relative simplicity of the workaround
above, we chose to keep the core proposal as simple as possible,
following EWG guidance.</p>
<h2 data-number="15.16" id="why-is-copy-replacement-unsupported"><span class="header-section-number">15.16</span> Why is copy-replacement
unsupported?<a href="#why-is-copy-replacement-unsupported" class="self-link"></a></h2>
<p>In practice, only <strong>replaceability</strong> of objects of type
<code class="sourceCode cpp">T</code> from xvalues of type
<code class="sourceCode cpp">T</code> seems relevant to the operations
we are likely to optimize. We have, therefore, simplified the design to
focus solely on such <strong>replacement</strong> (which could be termed
move-replacement were we being pedantic) and not overcomplicate the
language or users’ lives by adding even more properties to consider.</p>
<h2 data-number="15.17" id="why-is-marking-a-class-that-can-never-be-trivially-relocatable-not-ill-formed"><span class="header-section-number">15.17</span> Why is marking a class that
can <em>never</em> be trivially relocatable not ill-formed?<a href="#why-is-marking-a-class-that-can-never-be-trivially-relocatable-not-ill-formed" class="self-link"></a></h2>
<p>A class with a virtual base class can never be <strong><em>trivially
relocatable</em></strong>, so why is adding the
<code class="sourceCode cpp">trivially_relocatable_if_eligible</code>
identifier to that class not ill-formed?</p>
<p>This case is still well-formed, but the class will indeed never be
<strong><em>trivially relocatable</em></strong>, and the type trait will
deterministically always return
<code class="sourceCode cpp"><span class="kw">false</span></code>.
However, this type might also be used as a base class or data member
when instantiating a class template, and we do not want to add
complexity by considering such special-case instantiations as
well-formed when the original case need not be marked as ill-formed.</p>
<p>However, the deterministic case of a direct virtual base class would
make for a useful compiler warning. The more general case of a data
member or nonvirtual base class not being relocatable (or
<strong><em>replaceable</em></strong>) is deliberately not an error
since we want to support different implementations of the same type that
have different properties; e.g., different implementations of
<code class="sourceCode cpp">std<span class="op">::</span>list</code>
choose different trade-offs on how to store the sentinel node marking
the end of the list, yet some of those choices are <strong><em>trivially
relocatable</em></strong> and some are not. We want to avoid the
inconsistency of deterministically flagging an error when compiling a
class with a
<code class="sourceCode cpp">std<span class="op">::</span>list</code>
data member in some Standard Library implementations and not in
others.</p>
<h2 data-number="15.18" id="why-is-there-no-is_trivially_replaceable-trait"><span class="header-section-number">15.18</span> Why is there no
<code class="sourceCode cpp">is_trivially_replaceable</code> trait?<a href="#why-is-there-no-is_trivially_replaceable-trait" class="self-link"></a></h2>
<p>A common use case is to require types that satisfy both <code class="sourceCode cpp">is_trivially_relocatable<span class="op">&lt;</span>T<span class="op">&gt;</span></code>
and <code class="sourceCode cpp">is_replaceable<span class="op">&lt;</span>T<span class="op">&gt;</span></code>.
We could consider whether this use case occurs frequently enough that
adding another trait that is the logical conjunction of the two would be
valuable.</p>
<p>We opted to omit this trait from our proposal since such a trait is
not primitive to the Core-language design of this paper and could easily
be added as an amendment in an LEWG follow-up paper well within the
timeframe of C++26 if desired.</p>
<p>The lack of a core type category named <em>trivially replaceable</em>
is another reason to defer to a follow-up paper, and we would be
consuming that potential for future vocabulary for a pure Library
extension. Making that choice before advancing this paper is
unnecessary.</p>
<p>Finally, we must recognize that a type that is both
<strong><em>trivially relocatable</em></strong> and
<strong><em>replaceable</em></strong> does not have a <em>trivial</em>
replacement operation. The functionality that such a type enables is to
turn a rotate or shift operation into a bitwise one without a change in
semantics compared to using assignment for such an operation, but no
single <strong>replacement</strong> operation is a bitwise one since
that would fail to free resources owned by the original object in the
target location.</p>
<h2 data-number="15.19" id="is-it-ub-to-mark-a-nonconforming-type-as-trivially-relocatable"><span class="header-section-number">15.19</span> Is it UB to mark a
nonconforming type as trivially relocatable?<a href="#is-it-ub-to-mark-a-nonconforming-type-as-trivially-relocatable" class="self-link"></a></h2>
<p>First, the compiler has no way to validate that our class’s
constructors and destructor do not maintain an invariant that is not
relocatable, so the compiler will trust us and enable the type trait.
This in itself is not UB, but UB will likely follow when some library
code makes a transformation that causes our invariant, such as an
internal pointer, to no longer hold. Such UB will occur in the
subsequent library call, not in the class definition.</p>
<h2 data-number="15.20" id="is-it-ub-to-mark-a-nonconforming-type-as-replaceable"><span class="header-section-number">15.20</span> Is it UB to mark a
nonconforming type as replaceable?<a href="#is-it-ub-to-mark-a-nonconforming-type-as-replaceable" class="self-link"></a></h2>
<p>Just as erroneously marking a type as <strong><em>trivially
relocatable</em></strong> can lead to undefined behavior in library
calls, so can marking a type as <strong><em>replaceable</em></strong>.
However, where <strong>replaceability</strong> is used as a constraint
without <strong>trivial relocation</strong>, there remain reasonable
implementations that do not incur UB. For example, if operations are
logged, then the act of writing to a log is typically an observable side
effect. Library code that transforms between assignment and
destroy-then-construct will have an observable change of behavior, such
as the suggested logging, but such changes do not in themselves
constitute undefined behavior. The creator of the affected class must
decide whether a change of such logging behavior would be problematic
and then choose whether to mark their type as
<strong><em>replaceable</em></strong>.</p>
<h2 data-number="15.21" id="why-does-replaceability-not-require-trivial-relocatability"><span class="header-section-number">15.21</span> Why does replaceability not
require trivial relocatability?<a href="#why-does-replaceability-not-require-trivial-relocatability" class="self-link"></a></h2>
<p>While all specified uses of
<code class="sourceCode cpp">is_replaceable</code> in this proposal
require that the type be both <strong><em>replaceable</em></strong> and
<strong><em>trivially relocatable</em></strong>, the principle
underpinning <strong>replaceability</strong> — i.e., a consistent
definition for constructors, destructor, and assignment operators — is
highly relevant in a variety of places in the Standard Library. We
anticipate this distinct trait being useful to Library implementations
today, and we expect to see wider adoption in the Standard Library
specification once the trait becomes available. For example,
<code class="sourceCode cpp">std<span class="op">::</span>vector</code>
expects — but does not require — that its members be
<strong><em>replaceable</em></strong> to efficiently switch to
assignment rather than destroy/construct when replacing its elements
during an insert or erase operation. Motivating examples for why we
might want to address this design are found in <span class="citation" data-cites="P2959R0">[<a href="https://wg21.link/p2959r0" role="doc-biblioref">P2959R0</a>]</span>, although the specification of
<strong>replaceability</strong> in this paper is now the preferred
direction rather than the suggestions proposed in that paper.</p>
<h2 data-number="15.22" id="why-does-trivial-relocation-support-const-data-members-but-replacement-does-not"><span class="header-section-number">15.22</span> Why does trivial relocation
support
<code class="sourceCode cpp"><span class="kw">const</span></code> data
members, but replacement does not?<a href="#why-does-trivial-relocation-support-const-data-members-but-replacement-does-not" class="self-link"></a></h2>
<p>Relocation creates new objects and can safely copy
<code class="sourceCode cpp"><span class="kw">const</span></code>
members. <strong>Replacement</strong> overwrites the data in the
replaced object, which cannot — and should not — replace
<code class="sourceCode cpp"><span class="kw">const</span></code>
data.</p>
<h2 data-number="15.23" id="why-does-library.class.props-explicitly-call-out-permission-to-use-the-contextual-keywords"><span class="header-section-number">15.23</span> Why does
[library.class.props] explicitly call out permission to use the
contextual keywords?<a href="#why-does-library.class.props-explicitly-call-out-permission-to-use-the-contextual-keywords" class="self-link"></a></h2>
<p>For the same reason we explicitly grant permission to add
<code class="sourceCode cpp"><span class="kw">noexcept</span></code> to
function declarations, even before the exception specification entered
the type system, and for the same reasons that implementations cannot
experiment with marking functions as
<code class="sourceCode cpp"><span class="kw">constexpr</span></code>
due to the observable nature with a (deliberate) lack of explicit
permission.
<!-- lah: note to self: not a complete sentence but allow. --></p>
<h2 data-number="15.24" id="why-are-classes-with-virtual-base-classes-replaceable-what-does-that-even-mean"><span class="header-section-number">15.24</span> Why are classes with virtual
base classes “replaceable”? What does that even mean?<a href="#why-are-classes-with-virtual-base-classes-replaceable-what-does-that-even-mean" class="self-link"></a></h2>
<p>Classes with virtual bases might be
<strong><em>replaceable</em></strong> but will never be
<strong><em>trivially relocatable</em></strong>; just as with trivial
copyability, we cannot, at this point, restrict implementations from
using implementation strategies for virtual bases that require having
self-referential pointers (instead of offsets) that would be invalid if
simply copied to a new object.</p>
<p>On the other hand, <strong>replaceability</strong> is a relationship
between a type’s constructor, destructor, and assignment operator, all
of which are applicable to reason about even for a type with a virtual
base class.</p>
<p>In practice, we expect <strong>replaceability</strong> to come into
play most often once types like
<code class="sourceCode cpp">std<span class="op">::</span>vector</code>
start to prefer relocation (even if not trivial) and use
<strong>replacement</strong> (and assignment operators) only for types
that declare, by being <strong><em>replaceable</em></strong>, that such
a strategy is viable. Not allowing such freedom for a vector of objects
with virtual base classes would be counterproductive.</p>
<h1 data-number="16" id="illustrative-examples"><span class="header-section-number">16</span> Illustrative Examples<a href="#illustrative-examples" class="self-link"></a></h1>
<h2 data-number="16.1" id="unconstrained-vector"><span class="header-section-number">16.1</span> Unconstrained vector<a href="#unconstrained-vector" class="self-link"></a></h2>
<p>Let us consider the case of a user-written container, similar to
<code class="sourceCode cpp">std<span class="op">::</span>vector</code>.
Since <code class="sourceCode cpp">std<span class="op">::</span>relocate</code> is a
nofail function that exploits <strong>trivial relocation</strong> where
it is available, we have to consider only two kinds of elements:</p>
<ul>
<li>Types that are either <strong><em>trivially
relocatable</em></strong> or no-throw move constructible</li>
<li>All other types</li>
</ul>
<p>An alternative summary of these two kinds are</p>
<ul>
<li>types that can be safely relocated</li>
<li>types that cannot be safely relocated</li>
</ul>
<p>The first case to optimize is relocating elements when the current
capacity is exceeded by an insert operation. In this case, we clearly
can simply relocate for those element types that are safely relocatable
and must manually move-construct the second category, accounting for a
possible thrown exception on move.</p>
<p>The next operation to consider is erasing an element. In this
scenario, we will destroy the requested element(s) and then, for types
that can be safely relocated,
<code class="sourceCode cpp">relocate</code> the tail of the vector to
the lower address since <code class="sourceCode cpp">relocate</code> is
nofail and supports overlapping ranges. For the second category of
types, we must perform the manual relocation and clear the remains of
the tail if an exception is thrown.</p>
<p>The final operation to consider is an insertion in the middle of this
vector. Here, the first thing we do, assuming capacity is not exceeded,
is relocate all elements from the insertion point up by a distance to
allow all the new elements to be inserted. Then we construct all the new
elements, which is a potentially throwing operation. If an exception
<em>is</em> thrown, we have several options for our custom vector. For
the strong exception safety guarantee, we can destroy the newly inserted
items and then safely relocate the original elements back in place since
<code class="sourceCode cpp">relocate</code> is a nofail operation.
Alternatively, we provide the basic guarantee by destroying the old tail
— and potentially the newly inserted items — before adjusting the
vector’s size, or maybe we could even clear the whole vector.</p>
<p>Note that all these operations use only <strong>trivial
relocation</strong> and never call for
<strong>replaceability</strong>.</p>
<h2 data-number="16.2" id="standard-vector"><span class="header-section-number">16.2</span> Standard vector<a href="#standard-vector" class="self-link"></a></h2>
<p>When we add the constraints that the Standard imposes on
<code class="sourceCode cpp">std<span class="op">::</span>vector</code>,
we find that <strong>replaceability</strong> becomes a useful property.
For both insertion and erasure, the Standard likes to assume that
elements are <strong><em>replaceable</em></strong>, i.e., assignment is
interchangeable with destroy-then-move-construct. Within that guarantee,
the Standard Library vector can use relocation per our custom vector
example, but for types that are relocatable but not
<strong><em>replaceable</em></strong>, matters become more complicated.
That topic will be the subject of a separate paper specific to vector,
which is necessary regardless of whether we support relocation in C++26.
Having the ability to detect <strong><em>replaceable</em></strong> types
would be extremely helpful for that follow-up paper.</p>
<h2 data-number="16.3" id="conforming-implementation-of-a-trivially-relocatable-stdoptional"><span class="header-section-number">16.3</span> Conforming implementation of a
trivially relocatable <code class="sourceCode cpp">std<span class="op">::</span>optional</code><a href="#conforming-implementation-of-a-trivially-relocatable-stdoptional" class="self-link"></a></h2>
<p>The following implementation of
<code class="sourceCode cpp">optional</code> satisfies the C++ Standard
specification for the members that it implements and provides a minimal
test driver. This implementation uses the new feature macro to ensure
that the code compiles with both C++23 and C++26 and is
<strong><em>trivially relocatable</em></strong> if and only if its
element type is <strong><em>trivially relocatable</em></strong>.</p>
<p>To implement the
<code class="sourceCode cpp"><span class="kw">constexpr</span></code>
members, the implementation is required to use a union to represent its
internal state when engaged<a href="#fn3" class="footnote-ref" id="fnref3" role="doc-noteref"><sup>3</sup></a>:</p>
<div class="sourceCode" id="cb27"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb27-1"><a href="#cb27-1" aria-hidden="true" tabindex="-1"></a><span class="pp">#include </span><span class="im">&lt;cassert&gt;</span></span>
<span id="cb27-2"><a href="#cb27-2" aria-hidden="true" tabindex="-1"></a><span class="pp">#include </span><span class="im">&lt;iostream&gt;</span></span>
<span id="cb27-3"><a href="#cb27-3" aria-hidden="true" tabindex="-1"></a><span class="pp">#include </span><span class="im">&lt;memory&gt;</span></span>
<span id="cb27-4"><a href="#cb27-4" aria-hidden="true" tabindex="-1"></a><span class="pp">#include </span><span class="im">&lt;new&gt;</span></span>
<span id="cb27-5"><a href="#cb27-5" aria-hidden="true" tabindex="-1"></a><span class="pp">#include </span><span class="im">&lt;type_traits&gt;</span></span>
<span id="cb27-6"><a href="#cb27-6" aria-hidden="true" tabindex="-1"></a><span class="pp">#include </span><span class="im">&lt;utility&gt;</span></span>
<span id="cb27-7"><a href="#cb27-7" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb27-8"><a href="#cb27-8" aria-hidden="true" tabindex="-1"></a><span class="kw">template</span> <span class="op">&lt;</span><span class="kw">class</span> T<span class="op">&gt;</span></span>
<span id="cb27-9"><a href="#cb27-9" aria-hidden="true" tabindex="-1"></a><span class="kw">class</span> optional</span>
<span id="cb27-10"><a href="#cb27-10" aria-hidden="true" tabindex="-1"></a>      <span class="add" style="color: #006e28"><ins>trivially_relocatable_if_eligible</ins></span></span>
<span id="cb27-11"><a href="#cb27-11" aria-hidden="true" tabindex="-1"></a>      <span class="add" style="color: #006e28"><ins>replaceable_if_eligible</ins></span></span>
<span id="cb27-12"><a href="#cb27-12" aria-hidden="true" tabindex="-1"></a><span class="op">{</span></span>
<span id="cb27-13"><a href="#cb27-13" aria-hidden="true" tabindex="-1"></a>   <span class="kw">union</span> <span class="op">{</span></span>
<span id="cb27-14"><a href="#cb27-14" aria-hidden="true" tabindex="-1"></a>      T d_object;</span>
<span id="cb27-15"><a href="#cb27-15" aria-hidden="true" tabindex="-1"></a>   <span class="op">}</span>;</span>
<span id="cb27-16"><a href="#cb27-16" aria-hidden="true" tabindex="-1"></a>   <span class="dt">bool</span>      d_engaged<span class="op">{</span><span class="kw">false</span><span class="op">}</span>;</span>
<span id="cb27-17"><a href="#cb27-17" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb27-18"><a href="#cb27-18" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> T <span class="kw">const</span> <span class="op">*</span> address<span class="op">()</span> <span class="kw">const</span> <span class="kw">noexcept</span></span>
<span id="cb27-19"><a href="#cb27-19" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span> <span class="cf">return</span> <span class="op">::</span>std<span class="op">::</span>addressof<span class="op">(</span>d_object<span class="op">)</span>; <span class="op">}</span>;</span>
<span id="cb27-20"><a href="#cb27-20" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb27-21"><a href="#cb27-21" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> T       <span class="op">*</span> address<span class="op">()</span>       <span class="kw">noexcept</span></span>
<span id="cb27-22"><a href="#cb27-22" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span> <span class="cf">return</span> <span class="op">::</span>std<span class="op">::</span>addressof<span class="op">(</span>d_object<span class="op">)</span>; <span class="op">}</span>;</span>
<span id="cb27-23"><a href="#cb27-23" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb27-24"><a href="#cb27-24" aria-hidden="true" tabindex="-1"></a>   <span class="kw">template</span><span class="op">&lt;</span><span class="kw">class</span><span class="op">...</span> Args<span class="op">&gt;</span></span>
<span id="cb27-25"><a href="#cb27-25" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> <span class="dt">void</span> do_emplace<span class="op">(</span>Args<span class="op">&amp;&amp;...</span> args<span class="op">)</span> <span class="op">{</span></span>
<span id="cb27-26"><a href="#cb27-26" aria-hidden="true" tabindex="-1"></a>      <span class="op">::</span><span class="kw">new</span><span class="op">(</span>address<span class="op">())</span> T<span class="op">(</span>std<span class="op">::</span>forward<span class="op">&lt;</span>Args<span class="op">&gt;(</span>args<span class="op">)...)</span>;</span>
<span id="cb27-27"><a href="#cb27-27" aria-hidden="true" tabindex="-1"></a>      d_engaged <span class="op">=</span> <span class="kw">true</span>;</span>
<span id="cb27-28"><a href="#cb27-28" aria-hidden="true" tabindex="-1"></a>   <span class="op">}</span></span>
<span id="cb27-29"><a href="#cb27-29" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb27-30"><a href="#cb27-30" aria-hidden="true" tabindex="-1"></a><span class="kw">public</span><span class="op">:</span></span>
<span id="cb27-31"><a href="#cb27-31" aria-hidden="true" tabindex="-1"></a>   <span class="kw">using</span> value_type <span class="op">=</span> T;</span>
<span id="cb27-32"><a href="#cb27-32" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb27-33"><a href="#cb27-33" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> optional<span class="op">()</span> <span class="kw">noexcept</span> <span class="op">{}</span></span>
<span id="cb27-34"><a href="#cb27-34" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb27-35"><a href="#cb27-35" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> optional<span class="op">(</span>optional <span class="kw">const</span> <span class="op">&amp;</span> other<span class="op">)</span></span>
<span id="cb27-36"><a href="#cb27-36" aria-hidden="true" tabindex="-1"></a>   <span class="op">:</span> d_engaged<span class="op">{</span>other<span class="op">.</span>d_engaged<span class="op">}</span> <span class="op">{</span></span>
<span id="cb27-37"><a href="#cb27-37" aria-hidden="true" tabindex="-1"></a>      <span class="cf">if</span> <span class="op">(</span>d_engaged<span class="op">)</span> <span class="op">{</span></span>
<span id="cb27-38"><a href="#cb27-38" aria-hidden="true" tabindex="-1"></a>        <span class="op">::</span><span class="kw">new</span><span class="op">(</span>address<span class="op">())</span> T<span class="op">(</span> other<span class="op">.</span>value<span class="op">()</span> <span class="op">)</span>;</span>
<span id="cb27-39"><a href="#cb27-39" aria-hidden="true" tabindex="-1"></a>      <span class="op">}</span></span>
<span id="cb27-40"><a href="#cb27-40" aria-hidden="true" tabindex="-1"></a>   <span class="op">}</span></span>
<span id="cb27-41"><a href="#cb27-41" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb27-42"><a href="#cb27-42" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> optional<span class="op">(</span>optional<span class="op">&amp;&amp;</span> other<span class="op">)</span></span>
<span id="cb27-43"><a href="#cb27-43" aria-hidden="true" tabindex="-1"></a>       <span class="kw">noexcept</span><span class="op">(</span>std<span class="op">::</span>is_nothrow_move_constructible_v<span class="op">&lt;</span>T<span class="op">&gt;)</span></span>
<span id="cb27-44"><a href="#cb27-44" aria-hidden="true" tabindex="-1"></a>   <span class="op">:</span> d_engaged<span class="op">{</span>other<span class="op">.</span>d_engaged<span class="op">}</span></span>
<span id="cb27-45"><a href="#cb27-45" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span></span>
<span id="cb27-46"><a href="#cb27-46" aria-hidden="true" tabindex="-1"></a>      <span class="cf">if</span> <span class="op">(</span>d_engaged<span class="op">)</span> <span class="op">{</span></span>
<span id="cb27-47"><a href="#cb27-47" aria-hidden="true" tabindex="-1"></a>        <span class="op">::</span><span class="kw">new</span><span class="op">(</span>address<span class="op">())</span> T<span class="op">(</span> std<span class="op">::</span>move<span class="op">(</span>other<span class="op">).</span>value<span class="op">()</span> <span class="op">)</span>;</span>
<span id="cb27-48"><a href="#cb27-48" aria-hidden="true" tabindex="-1"></a>      <span class="op">}</span></span>
<span id="cb27-49"><a href="#cb27-49" aria-hidden="true" tabindex="-1"></a>   <span class="op">}</span></span>
<span id="cb27-50"><a href="#cb27-50" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb27-51"><a href="#cb27-51" aria-hidden="true" tabindex="-1"></a>   <span class="kw">template</span><span class="op">&lt;</span><span class="kw">class</span> U <span class="op">=</span> T<span class="op">&gt;</span></span>
<span id="cb27-52"><a href="#cb27-52" aria-hidden="true" tabindex="-1"></a>      <span class="kw">requires</span> <span class="op">(</span>std<span class="op">::</span>is_constructible_v<span class="op">&lt;</span>T, U<span class="op">&gt;</span></span>
<span id="cb27-53"><a href="#cb27-53" aria-hidden="true" tabindex="-1"></a>            <span class="op">&amp;&amp;</span> <span class="op">!</span>std<span class="op">::</span>is_same_v<span class="op">&lt;</span>std<span class="op">::</span>remove_cvref_t<span class="op">&lt;</span>U<span class="op">&gt;</span>, optional<span class="op">&gt;)</span></span>
<span id="cb27-54"><a href="#cb27-54" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span></span>
<span id="cb27-55"><a href="#cb27-55" aria-hidden="true" tabindex="-1"></a>   <span class="kw">explicit</span><span class="op">(!</span>std<span class="op">::</span>is_convertible_v<span class="op">&lt;</span>U, T<span class="op">&gt;)</span></span>
<span id="cb27-56"><a href="#cb27-56" aria-hidden="true" tabindex="-1"></a>   optional<span class="op">(</span>U<span class="op">&amp;&amp;</span> arg<span class="op">)</span> <span class="op">{</span></span>
<span id="cb27-57"><a href="#cb27-57" aria-hidden="true" tabindex="-1"></a>      do_emplace<span class="op">(</span> std<span class="op">::</span>forward<span class="op">&lt;</span>U<span class="op">&gt;(</span>arg<span class="op">)</span> <span class="op">)</span>;</span>
<span id="cb27-58"><a href="#cb27-58" aria-hidden="true" tabindex="-1"></a>   <span class="op">}</span></span>
<span id="cb27-59"><a href="#cb27-59" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb27-60"><a href="#cb27-60" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> <span class="op">~</span>optional<span class="op">()</span> <span class="op">{</span></span>
<span id="cb27-61"><a href="#cb27-61" aria-hidden="true" tabindex="-1"></a>      <span class="add" style="color: #006e28"><ins>static_assert(std::is_replaceable_v&lt;optional&gt;
== std::is_replaceable_v&lt;T&gt;);</ins></span></span>
<span id="cb27-62"><a href="#cb27-62" aria-hidden="true" tabindex="-1"></a>      <span class="add" style="color: #006e28"><ins>static_assert(</ins></span></span>
<span id="cb27-63"><a href="#cb27-63" aria-hidden="true" tabindex="-1"></a>         <span class="add" style="color: #006e28"><ins>std::is_trivially_relocatable_v&lt;optional&gt;
== std::is_trivially_relocatable_v&lt;T&gt;);</ins></span></span>
<span id="cb27-64"><a href="#cb27-64" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb27-65"><a href="#cb27-65" aria-hidden="true" tabindex="-1"></a>      <span class="cf">if</span> <span class="op">(</span>d_engaged<span class="op">)</span> <span class="op">{</span></span>
<span id="cb27-66"><a href="#cb27-66" aria-hidden="true" tabindex="-1"></a>         d_object<span class="op">.~</span>T<span class="op">()</span>;</span>
<span id="cb27-67"><a href="#cb27-67" aria-hidden="true" tabindex="-1"></a>      <span class="op">}</span></span>
<span id="cb27-68"><a href="#cb27-68" aria-hidden="true" tabindex="-1"></a>   <span class="op">}</span></span>
<span id="cb27-69"><a href="#cb27-69" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb27-70"><a href="#cb27-70" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> optional<span class="op">&amp;</span> <span class="kw">operator</span><span class="op">=(</span>optional <span class="kw">const</span> <span class="op">&amp;</span> rhs<span class="op">)</span>;</span>
<span id="cb27-71"><a href="#cb27-71" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb27-72"><a href="#cb27-72" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> optional<span class="op">&amp;</span> <span class="kw">operator</span><span class="op">=(</span>optional <span class="op">&amp;&amp;</span> rhs<span class="op">)</span></span>
<span id="cb27-73"><a href="#cb27-73" aria-hidden="true" tabindex="-1"></a>             <span class="kw">noexcept</span><span class="op">(</span>std<span class="op">::</span>is_nothrow_move_assignable_v<span class="op">&lt;</span>T<span class="op">&gt;</span></span>
<span id="cb27-74"><a href="#cb27-74" aria-hidden="true" tabindex="-1"></a>                   <span class="op">&amp;&amp;</span> std<span class="op">::</span>is_nothrow_move_constructible_v<span class="op">&lt;</span>T<span class="op">&gt;)</span> <span class="op">{</span></span>
<span id="cb27-75"><a href="#cb27-75" aria-hidden="true" tabindex="-1"></a>      std<span class="op">::</span>cout <span class="op">&lt;&lt;</span> <span class="st">&quot;Assignment</span><span class="sc">\n</span><span class="st">&quot;</span>;</span>
<span id="cb27-76"><a href="#cb27-76" aria-hidden="true" tabindex="-1"></a>      <span class="cf">if</span> <span class="op">(!</span>d_engaged<span class="op">)</span> <span class="op">{</span></span>
<span id="cb27-77"><a href="#cb27-77" aria-hidden="true" tabindex="-1"></a>        <span class="cf">if</span> <span class="op">(</span>rhs<span class="op">.</span>d_engaged<span class="op">)</span> <span class="op">{</span></span>
<span id="cb27-78"><a href="#cb27-78" aria-hidden="true" tabindex="-1"></a>           do_emplace<span class="op">(</span> std<span class="op">::</span>move<span class="op">(</span>rhs<span class="op">.</span>value<span class="op">())</span> <span class="op">)</span>;</span>
<span id="cb27-79"><a href="#cb27-79" aria-hidden="true" tabindex="-1"></a>        <span class="op">}</span></span>
<span id="cb27-80"><a href="#cb27-80" aria-hidden="true" tabindex="-1"></a>      <span class="op">}</span></span>
<span id="cb27-81"><a href="#cb27-81" aria-hidden="true" tabindex="-1"></a>      <span class="cf">else</span> <span class="cf">if</span> <span class="op">(!</span>rhs<span class="op">.</span>d_engaged<span class="op">)</span> <span class="op">{</span></span>
<span id="cb27-82"><a href="#cb27-82" aria-hidden="true" tabindex="-1"></a>         d_object<span class="op">.~</span>T<span class="op">()</span>;</span>
<span id="cb27-83"><a href="#cb27-83" aria-hidden="true" tabindex="-1"></a>         d_engaged <span class="op">=</span> <span class="kw">false</span>;</span>
<span id="cb27-84"><a href="#cb27-84" aria-hidden="true" tabindex="-1"></a>      <span class="op">}</span></span>
<span id="cb27-85"><a href="#cb27-85" aria-hidden="true" tabindex="-1"></a>      <span class="cf">else</span> <span class="op">{</span></span>
<span id="cb27-86"><a href="#cb27-86" aria-hidden="true" tabindex="-1"></a>        value<span class="op">()</span> <span class="op">=</span> rhs<span class="op">.</span>value<span class="op">()</span>;</span>
<span id="cb27-87"><a href="#cb27-87" aria-hidden="true" tabindex="-1"></a>      <span class="op">}</span></span>
<span id="cb27-88"><a href="#cb27-88" aria-hidden="true" tabindex="-1"></a>      <span class="cf">return</span> <span class="op">*</span><span class="kw">this</span>;</span>
<span id="cb27-89"><a href="#cb27-89" aria-hidden="true" tabindex="-1"></a>   <span class="op">}</span></span>
<span id="cb27-90"><a href="#cb27-90" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb27-91"><a href="#cb27-91" aria-hidden="true" tabindex="-1"></a>   <span class="kw">template</span><span class="op">&lt;</span><span class="kw">class</span> U <span class="op">=</span> T<span class="op">&gt;</span></span>
<span id="cb27-92"><a href="#cb27-92" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> optional<span class="op">&amp;</span> <span class="kw">operator</span><span class="op">=(</span>U <span class="op">&amp;&amp;</span> arg<span class="op">)</span> <span class="op">{</span></span>
<span id="cb27-93"><a href="#cb27-93" aria-hidden="true" tabindex="-1"></a>      std<span class="op">::</span>cout <span class="op">&lt;&lt;</span> <span class="st">&quot;Assignment</span><span class="sc">\n</span><span class="st">&quot;</span>;</span>
<span id="cb27-94"><a href="#cb27-94" aria-hidden="true" tabindex="-1"></a>      <span class="cf">if</span> <span class="op">(!</span>d_engaged<span class="op">)</span> <span class="op">{</span></span>
<span id="cb27-95"><a href="#cb27-95" aria-hidden="true" tabindex="-1"></a>        do_emplace<span class="op">(</span> std<span class="op">::</span>forward<span class="op">&lt;</span>U<span class="op">&gt;(</span>arg<span class="op">)</span> <span class="op">)</span>;</span>
<span id="cb27-96"><a href="#cb27-96" aria-hidden="true" tabindex="-1"></a>      <span class="op">}</span></span>
<span id="cb27-97"><a href="#cb27-97" aria-hidden="true" tabindex="-1"></a>      <span class="cf">else</span> <span class="op">{</span></span>
<span id="cb27-98"><a href="#cb27-98" aria-hidden="true" tabindex="-1"></a>         d_object <span class="op">=</span> std<span class="op">::</span>forward<span class="op">&lt;</span>U<span class="op">&gt;(</span>arg<span class="op">)</span>;</span>
<span id="cb27-99"><a href="#cb27-99" aria-hidden="true" tabindex="-1"></a>      <span class="op">}</span></span>
<span id="cb27-100"><a href="#cb27-100" aria-hidden="true" tabindex="-1"></a>      <span class="cf">return</span> <span class="op">*</span><span class="kw">this</span>;</span>
<span id="cb27-101"><a href="#cb27-101" aria-hidden="true" tabindex="-1"></a>   <span class="op">}</span></span>
<span id="cb27-102"><a href="#cb27-102" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb27-103"><a href="#cb27-103" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> T <span class="kw">const</span> <span class="op">*</span> <span class="kw">operator</span><span class="op">-&gt;()</span> <span class="kw">const</span>  <span class="kw">noexcept</span></span>
<span id="cb27-104"><a href="#cb27-104" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span> <span class="ot">assert</span><span class="op">(</span>d_engaged<span class="op">)</span>; <span class="cf">return</span> address<span class="op">()</span>; <span class="op">}</span></span>
<span id="cb27-105"><a href="#cb27-105" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb27-106"><a href="#cb27-106" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> T       <span class="op">*</span> <span class="kw">operator</span><span class="op">-&gt;()</span>        <span class="kw">noexcept</span></span>
<span id="cb27-107"><a href="#cb27-107" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span> <span class="ot">assert</span><span class="op">(</span>d_engaged<span class="op">)</span>; <span class="cf">return</span> address<span class="op">()</span>; <span class="op">}</span></span>
<span id="cb27-108"><a href="#cb27-108" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb27-109"><a href="#cb27-109" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> T <span class="kw">const</span> <span class="op">&amp;</span> <span class="kw">operator</span><span class="op">*()</span> <span class="kw">const</span> <span class="op">&amp;</span> <span class="kw">noexcept</span></span>
<span id="cb27-110"><a href="#cb27-110" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span> <span class="ot">assert</span><span class="op">(</span>d_engaged<span class="op">)</span>; <span class="cf">return</span> d_object; <span class="op">}</span></span>
<span id="cb27-111"><a href="#cb27-111" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> T       <span class="op">&amp;</span> <span class="kw">operator</span><span class="op">*()</span>       <span class="op">&amp;</span> <span class="kw">noexcept</span></span>
<span id="cb27-112"><a href="#cb27-112" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span> <span class="ot">assert</span><span class="op">(</span>d_engaged<span class="op">)</span>; <span class="cf">return</span> d_object; <span class="op">}</span></span>
<span id="cb27-113"><a href="#cb27-113" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> T      <span class="op">&amp;&amp;</span> <span class="kw">operator</span><span class="op">*()</span>      <span class="op">&amp;&amp;</span> <span class="kw">noexcept</span></span>
<span id="cb27-114"><a href="#cb27-114" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span> <span class="ot">assert</span><span class="op">(</span>d_engaged<span class="op">)</span>; <span class="cf">return</span> std<span class="op">::</span>move<span class="op">(</span>d_object<span class="op">)</span>; <span class="op">}</span></span>
<span id="cb27-115"><a href="#cb27-115" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> T <span class="kw">const</span><span class="op">&amp;&amp;</span> <span class="kw">operator</span><span class="op">*()</span> <span class="kw">const</span><span class="op">&amp;&amp;</span> <span class="kw">noexcept</span></span>
<span id="cb27-116"><a href="#cb27-116" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span> <span class="ot">assert</span><span class="op">(</span>d_engaged<span class="op">)</span>; <span class="cf">return</span> std<span class="op">::</span>move<span class="op">(</span>d_object<span class="op">)</span>; <span class="op">}</span></span>
<span id="cb27-117"><a href="#cb27-117" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb27-118"><a href="#cb27-118" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> <span class="kw">explicit</span> <span class="kw">operator</span> <span class="dt">bool</span><span class="op">()</span> <span class="kw">const</span> <span class="kw">noexcept</span></span>
<span id="cb27-119"><a href="#cb27-119" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span> <span class="cf">return</span> d_engaged; <span class="op">}</span></span>
<span id="cb27-120"><a href="#cb27-120" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> <span class="dt">bool</span>         has_value<span class="op">()</span> <span class="kw">const</span> <span class="kw">noexcept</span></span>
<span id="cb27-121"><a href="#cb27-121" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span> <span class="cf">return</span> d_engaged; <span class="op">}</span></span>
<span id="cb27-122"><a href="#cb27-122" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb27-123"><a href="#cb27-123" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> T <span class="kw">const</span> <span class="op">&amp;</span> value<span class="op">()</span> <span class="kw">const</span> <span class="op">&amp;</span></span>
<span id="cb27-124"><a href="#cb27-124" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span> <span class="ot">assert</span><span class="op">(</span>d_engaged<span class="op">)</span>; <span class="cf">return</span> d_object; <span class="op">}</span></span>
<span id="cb27-125"><a href="#cb27-125" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> T       <span class="op">&amp;</span> value<span class="op">()</span>       <span class="op">&amp;</span></span>
<span id="cb27-126"><a href="#cb27-126" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span> <span class="ot">assert</span><span class="op">(</span>d_engaged<span class="op">)</span>; <span class="cf">return</span> d_object; <span class="op">}</span></span>
<span id="cb27-127"><a href="#cb27-127" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> T      <span class="op">&amp;&amp;</span> value<span class="op">()</span>      <span class="op">&amp;&amp;</span></span>
<span id="cb27-128"><a href="#cb27-128" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span> <span class="ot">assert</span><span class="op">(</span>d_engaged<span class="op">)</span>; <span class="cf">return</span> std<span class="op">::</span>move<span class="op">(</span>d_object<span class="op">)</span>; <span class="op">}</span></span>
<span id="cb27-129"><a href="#cb27-129" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> T <span class="kw">const</span><span class="op">&amp;&amp;</span> value<span class="op">()</span> <span class="kw">const</span><span class="op">&amp;&amp;</span></span>
<span id="cb27-130"><a href="#cb27-130" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span> <span class="ot">assert</span><span class="op">(</span>d_engaged<span class="op">)</span>; <span class="cf">return</span> std<span class="op">::</span>move<span class="op">(</span>d_object<span class="op">)</span>; <span class="op">}</span></span>
<span id="cb27-131"><a href="#cb27-131" aria-hidden="true" tabindex="-1"></a><span class="op">}</span>;</span>
<span id="cb27-132"><a href="#cb27-132" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb27-133"><a href="#cb27-133" aria-hidden="true" tabindex="-1"></a><span class="kw">consteval</span> <span class="dt">int</span> number<span class="op">(</span><span class="dt">int</span> n<span class="op">)</span> <span class="op">{</span></span>
<span id="cb27-134"><a href="#cb27-134" aria-hidden="true" tabindex="-1"></a>   optional<span class="op">&lt;</span><span class="dt">int</span><span class="op">&gt;</span> x<span class="op">{</span>n<span class="op">}</span>;</span>
<span id="cb27-135"><a href="#cb27-135" aria-hidden="true" tabindex="-1"></a>   <span class="cf">return</span> x<span class="op">.</span>value<span class="op">()</span>;</span>
<span id="cb27-136"><a href="#cb27-136" aria-hidden="true" tabindex="-1"></a><span class="op">}</span></span>
<span id="cb27-137"><a href="#cb27-137" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb27-138"><a href="#cb27-138" aria-hidden="true" tabindex="-1"></a><span class="dt">int</span> a<span class="op">[</span>number<span class="op">(</span><span class="dv">5</span><span class="bu">u</span><span class="er">z</span><span class="op">)]</span>;</span>
<span id="cb27-139"><a href="#cb27-139" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb27-140"><a href="#cb27-140" aria-hidden="true" tabindex="-1"></a><span class="dt">int</span> main<span class="op">()</span> <span class="op">{</span></span>
<span id="cb27-141"><a href="#cb27-141" aria-hidden="true" tabindex="-1"></a>   optional<span class="op">&lt;</span><span class="dt">int</span><span class="op">&gt;</span> x;</span>
<span id="cb27-142"><a href="#cb27-142" aria-hidden="true" tabindex="-1"></a>   <span class="ot">assert</span><span class="op">(!</span>x<span class="op">)</span>;</span>
<span id="cb27-143"><a href="#cb27-143" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb27-144"><a href="#cb27-144" aria-hidden="true" tabindex="-1"></a>   std<span class="op">::</span>cout <span class="op">&lt;&lt;</span> <span class="st">&quot;Assignments to x</span><span class="sc">\n</span><span class="st">&quot;</span>;</span>
<span id="cb27-145"><a href="#cb27-145" aria-hidden="true" tabindex="-1"></a>   x <span class="op">=</span> <span class="dv">3</span>;</span>
<span id="cb27-146"><a href="#cb27-146" aria-hidden="true" tabindex="-1"></a>   <span class="kw">auto</span> y <span class="op">=</span> x;</span>
<span id="cb27-147"><a href="#cb27-147" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb27-148"><a href="#cb27-148" aria-hidden="true" tabindex="-1"></a>   x <span class="op">=</span> <span class="dv">4</span>;</span>
<span id="cb27-149"><a href="#cb27-149" aria-hidden="true" tabindex="-1"></a>   std<span class="op">::</span>cout <span class="op">&lt;&lt;</span> <span class="st">&quot;swap x</span><span class="sc">\n</span><span class="st">&quot;</span>;</span>
<span id="cb27-150"><a href="#cb27-150" aria-hidden="true" tabindex="-1"></a>   std<span class="op">::</span>swap<span class="op">(</span>x, y<span class="op">)</span>;</span>
<span id="cb27-151"><a href="#cb27-151" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb27-152"><a href="#cb27-152" aria-hidden="true" tabindex="-1"></a>   <span class="ot">assert</span><span class="op">(</span><span class="dv">3</span> <span class="op">==</span> <span class="op">*</span>x<span class="op">)</span>;</span>
<span id="cb27-153"><a href="#cb27-153" aria-hidden="true" tabindex="-1"></a>   <span class="ot">assert</span><span class="op">(</span><span class="dv">4</span> <span class="op">==</span> <span class="op">*</span>y<span class="op">)</span>;</span>
<span id="cb27-154"><a href="#cb27-154" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb27-155"><a href="#cb27-155" aria-hidden="true" tabindex="-1"></a>   optional<span class="op">&lt;</span>std<span class="op">::</span>shared_ptr<span class="op">&lt;</span><span class="dt">int</span><span class="op">&gt;&gt;</span> p1;</span>
<span id="cb27-156"><a href="#cb27-156" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb27-157"><a href="#cb27-157" aria-hidden="true" tabindex="-1"></a>   std<span class="op">::</span>cout <span class="op">&lt;&lt;</span> <span class="st">&quot;Assignments to p</span><span class="sc">\n</span><span class="st">&quot;</span>;</span>
<span id="cb27-158"><a href="#cb27-158" aria-hidden="true" tabindex="-1"></a>   p1 <span class="op">=</span> std<span class="op">::</span>make_shared<span class="op">&lt;</span><span class="dt">int</span><span class="op">&gt;(</span><span class="dv">3</span><span class="op">)</span>;</span>
<span id="cb27-159"><a href="#cb27-159" aria-hidden="true" tabindex="-1"></a>   <span class="kw">auto</span> p2 <span class="op">=</span> p1;</span>
<span id="cb27-160"><a href="#cb27-160" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb27-161"><a href="#cb27-161" aria-hidden="true" tabindex="-1"></a>   p2 <span class="op">=</span> std<span class="op">::</span>make_shared<span class="op">&lt;</span><span class="dt">int</span><span class="op">&gt;(</span><span class="dv">4</span><span class="op">)</span>;</span>
<span id="cb27-162"><a href="#cb27-162" aria-hidden="true" tabindex="-1"></a>   std<span class="op">::</span>cout <span class="op">&lt;&lt;</span> <span class="st">&quot;swap p</span><span class="sc">\n</span><span class="st">&quot;</span>;</span>
<span id="cb27-163"><a href="#cb27-163" aria-hidden="true" tabindex="-1"></a>   std<span class="op">::</span>swap<span class="op">(</span>p1, p2<span class="op">)</span>;</span>
<span id="cb27-164"><a href="#cb27-164" aria-hidden="true" tabindex="-1"></a><span class="op">}</span></span></code></pre></div>
<h2 data-number="16.4" id="c26-implementation-using-internal-array"><span class="header-section-number">16.4</span> C++26 implementation using
internal array<a href="#c26-implementation-using-internal-array" class="self-link"></a></h2>
<p>Using an internal array negates the ability to support
<code class="sourceCode cpp"><span class="kw">constexpr</span></code>,
but this implementation strategy is used frequently for similar types in
other libraries. Managing both <strong><em>trivially
relocatable</em></strong> and <strong><em>replaceable</em></strong>
properties with an empty member must be done with care since mistakenly
disabling both properties is easy to do when intending to disable only
one or the other.<a href="#fn4" class="footnote-ref" id="fnref4" role="doc-noteref"><sup>4</sup></a></p>
<div class="sourceCode" id="cb28"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb28-1"><a href="#cb28-1" aria-hidden="true" tabindex="-1"></a><span class="pp">#include </span><span class="im">&lt;cassert&gt;</span></span>
<span id="cb28-2"><a href="#cb28-2" aria-hidden="true" tabindex="-1"></a><span class="pp">#include </span><span class="im">&lt;cstddef&gt;</span></span>
<span id="cb28-3"><a href="#cb28-3" aria-hidden="true" tabindex="-1"></a><span class="pp">#include </span><span class="im">&lt;iostream&gt;</span></span>
<span id="cb28-4"><a href="#cb28-4" aria-hidden="true" tabindex="-1"></a><span class="pp">#include </span><span class="im">&lt;memory&gt;</span></span>
<span id="cb28-5"><a href="#cb28-5" aria-hidden="true" tabindex="-1"></a><span class="pp">#include </span><span class="im">&lt;new&gt;</span></span>
<span id="cb28-6"><a href="#cb28-6" aria-hidden="true" tabindex="-1"></a><span class="pp">#include </span><span class="im">&lt;type_traits&gt;</span></span>
<span id="cb28-7"><a href="#cb28-7" aria-hidden="true" tabindex="-1"></a><span class="pp">#include </span><span class="im">&lt;utility&gt;</span></span>
<span id="cb28-8"><a href="#cb28-8" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-9"><a href="#cb28-9" aria-hidden="true" tabindex="-1"></a><span class="kw">template</span> <span class="op">&lt;</span><span class="dt">bool</span> triviallyRelocatable,</span>
<span id="cb28-10"><a href="#cb28-10" aria-hidden="true" tabindex="-1"></a>          <span class="dt">bool</span> replaceable<span class="op">&gt;</span></span>
<span id="cb28-11"><a href="#cb28-11" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> ConditionalProperties <span class="op">{}</span>;</span>
<span id="cb28-12"><a href="#cb28-12" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-13"><a href="#cb28-13" aria-hidden="true" tabindex="-1"></a><span class="kw">template</span> <span class="op">&lt;&gt;</span></span>
<span id="cb28-14"><a href="#cb28-14" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> ConditionalProperties<span class="op">&lt;</span><span class="kw">false</span>,<span class="kw">true</span><span class="op">&gt;</span> replaceable_if_eligible <span class="op">{</span></span>
<span id="cb28-15"><a href="#cb28-15" aria-hidden="true" tabindex="-1"></a>    <span class="op">~</span>ConditionalProperties<span class="op">(){}</span></span>
<span id="cb28-16"><a href="#cb28-16" aria-hidden="true" tabindex="-1"></a><span class="op">}</span>;</span>
<span id="cb28-17"><a href="#cb28-17" aria-hidden="true" tabindex="-1"></a><span class="kw">template</span> <span class="op">&lt;&gt;</span></span>
<span id="cb28-18"><a href="#cb28-18" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> ConditionalProperties<span class="op">&lt;</span><span class="kw">true</span>,<span class="kw">false</span><span class="op">&gt;</span> trivially_relocatable_if_eligible <span class="op">{</span></span>
<span id="cb28-19"><a href="#cb28-19" aria-hidden="true" tabindex="-1"></a>    <span class="op">~</span>ConditionalProperties<span class="op">(){}</span></span>
<span id="cb28-20"><a href="#cb28-20" aria-hidden="true" tabindex="-1"></a><span class="op">}</span>;</span>
<span id="cb28-21"><a href="#cb28-21" aria-hidden="true" tabindex="-1"></a><span class="kw">template</span> <span class="op">&lt;&gt;</span></span>
<span id="cb28-22"><a href="#cb28-22" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> ConditionalProperties<span class="op">&lt;</span><span class="kw">false</span>,<span class="kw">false</span><span class="op">&gt;</span> <span class="op">{</span></span>
<span id="cb28-23"><a href="#cb28-23" aria-hidden="true" tabindex="-1"></a>    <span class="op">~</span>ConditionalProperties<span class="op">(){}</span></span>
<span id="cb28-24"><a href="#cb28-24" aria-hidden="true" tabindex="-1"></a><span class="op">}</span>;</span>
<span id="cb28-25"><a href="#cb28-25" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-26"><a href="#cb28-26" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span> std<span class="op">::</span>is_trivially_relocatable_v<span class="op">&lt;</span>ConditionalProperties<span class="op">&lt;</span><span class="kw">true</span>,<span class="kw">true</span><span class="op">&gt;&gt;)</span>;</span>
<span id="cb28-27"><a href="#cb28-27" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span> std<span class="op">::</span>is_trivially_relocatable_v<span class="op">&lt;</span>ConditionalProperties<span class="op">&lt;</span><span class="kw">true</span>,<span class="kw">false</span><span class="op">&gt;&gt;)</span>;</span>
<span id="cb28-28"><a href="#cb28-28" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(!</span>std<span class="op">::</span>is_trivially_relocatable_v<span class="op">&lt;</span>ConditionalProperties<span class="op">&lt;</span><span class="kw">false</span>,<span class="kw">true</span><span class="op">&gt;&gt;)</span>;</span>
<span id="cb28-29"><a href="#cb28-29" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(!</span>std<span class="op">::</span>is_trivially_relocatable_v<span class="op">&lt;</span>ConditionalProperties<span class="op">&lt;</span><span class="kw">false</span>,<span class="kw">false</span><span class="op">&gt;&gt;)</span>;</span>
<span id="cb28-30"><a href="#cb28-30" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-31"><a href="#cb28-31" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span> std<span class="op">::</span>is_replaceable_v<span class="op">&lt;</span>ConditionalProperties<span class="op">&lt;</span><span class="kw">true</span>,<span class="kw">true</span><span class="op">&gt;&gt;)</span>;</span>
<span id="cb28-32"><a href="#cb28-32" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(!</span>std<span class="op">::</span>is_replaceable_v<span class="op">&lt;</span>ConditionalProperties<span class="op">&lt;</span><span class="kw">true</span>,<span class="kw">false</span><span class="op">&gt;&gt;)</span>;</span>
<span id="cb28-33"><a href="#cb28-33" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(</span> std<span class="op">::</span>is_replaceable_v<span class="op">&lt;</span>ConditionalProperties<span class="op">&lt;</span><span class="kw">false</span>,<span class="kw">true</span><span class="op">&gt;&gt;)</span>;</span>
<span id="cb28-34"><a href="#cb28-34" aria-hidden="true" tabindex="-1"></a><span class="kw">static_assert</span><span class="op">(!</span>std<span class="op">::</span>is_replaceable_v<span class="op">&lt;</span>ConditionalProperties<span class="op">&lt;</span><span class="kw">false</span>,<span class="kw">false</span><span class="op">&gt;&gt;)</span>;</span>
<span id="cb28-35"><a href="#cb28-35" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-36"><a href="#cb28-36" aria-hidden="true" tabindex="-1"></a><span class="kw">template</span> <span class="op">&lt;</span><span class="kw">class</span> T<span class="op">&gt;</span></span>
<span id="cb28-37"><a href="#cb28-37" aria-hidden="true" tabindex="-1"></a><span class="kw">class</span> optional trivially_relocatable_if_eligible replaceable_if_eligible <span class="op">{</span></span>
<span id="cb28-38"><a href="#cb28-38" aria-hidden="true" tabindex="-1"></a>   <span class="kw">alignas</span> <span class="op">(</span>T<span class="op">)</span></span>
<span id="cb28-39"><a href="#cb28-39" aria-hidden="true" tabindex="-1"></a>   std<span class="op">::</span>byte d_object<span class="op">[</span><span class="kw">sizeof</span> <span class="op">(</span>T<span class="op">)]</span>;</span>
<span id="cb28-40"><a href="#cb28-40" aria-hidden="true" tabindex="-1"></a>   <span class="kw">union</span> <span class="op">{</span></span>
<span id="cb28-41"><a href="#cb28-41" aria-hidden="true" tabindex="-1"></a>      <span class="dt">bool</span>      d_engaged<span class="op">{</span><span class="kw">false</span><span class="op">}</span>;</span>
<span id="cb28-42"><a href="#cb28-42" aria-hidden="true" tabindex="-1"></a>      ConditionalProperties<span class="op">&lt;</span>std<span class="op">::</span>is_trivially_relocatable_v<span class="op">&lt;</span>T<span class="op">&gt;</span>,</span>
<span id="cb28-43"><a href="#cb28-43" aria-hidden="true" tabindex="-1"></a>                            std<span class="op">::</span>is_replaceable_v<span class="op">&lt;</span>T<span class="op">&gt;&gt;</span> enforce_properties;</span>
<span id="cb28-44"><a href="#cb28-44" aria-hidden="true" tabindex="-1"></a>   <span class="op">}</span>;</span>
<span id="cb28-45"><a href="#cb28-45" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-46"><a href="#cb28-46" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> T <span class="kw">const</span> <span class="op">*</span> address<span class="op">()</span> <span class="kw">const</span> <span class="kw">noexcept</span></span>
<span id="cb28-47"><a href="#cb28-47" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span> <span class="cf">return</span> <span class="kw">reinterpret_cast</span><span class="op">&lt;</span>T <span class="kw">const</span> <span class="op">*&gt;(</span>d_object<span class="op">)</span>; <span class="op">}</span>;</span>
<span id="cb28-48"><a href="#cb28-48" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> T       <span class="op">*</span> address<span class="op">()</span>       <span class="kw">noexcept</span></span>
<span id="cb28-49"><a href="#cb28-49" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span> <span class="cf">return</span> <span class="kw">reinterpret_cast</span><span class="op">&lt;</span>T       <span class="op">*&gt;(</span>d_object<span class="op">)</span>; <span class="op">}</span>;</span>
<span id="cb28-50"><a href="#cb28-50" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-51"><a href="#cb28-51" aria-hidden="true" tabindex="-1"></a><span class="kw">public</span><span class="op">:</span></span>
<span id="cb28-52"><a href="#cb28-52" aria-hidden="true" tabindex="-1"></a>   <span class="kw">using</span> value_type <span class="op">=</span> T;</span>
<span id="cb28-53"><a href="#cb28-53" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-54"><a href="#cb28-54" aria-hidden="true" tabindex="-1"></a>   <span class="co">// 22.5.3.2, constructors</span></span>
<span id="cb28-55"><a href="#cb28-55" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> optional<span class="op">()</span> <span class="kw">noexcept</span> <span class="op">=</span> <span class="cf">default</span>;</span>
<span id="cb28-56"><a href="#cb28-56" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-57"><a href="#cb28-57" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> optional<span class="op">(</span>optional <span class="kw">const</span> <span class="op">&amp;</span> other<span class="op">)</span> <span class="op">:</span> d_engaged<span class="op">{</span>other<span class="op">.</span>d_engaged<span class="op">}</span> <span class="op">{</span></span>
<span id="cb28-58"><a href="#cb28-58" aria-hidden="true" tabindex="-1"></a>      <span class="cf">if</span> <span class="op">(</span>d_engaged<span class="op">)</span> <span class="op">{</span></span>
<span id="cb28-59"><a href="#cb28-59" aria-hidden="true" tabindex="-1"></a>        <span class="op">::</span><span class="kw">new</span><span class="op">(</span>address<span class="op">())</span> T<span class="op">(</span> other<span class="op">.</span>value<span class="op">()</span> <span class="op">)</span>;</span>
<span id="cb28-60"><a href="#cb28-60" aria-hidden="true" tabindex="-1"></a>      <span class="op">}</span></span>
<span id="cb28-61"><a href="#cb28-61" aria-hidden="true" tabindex="-1"></a>   <span class="op">}</span></span>
<span id="cb28-62"><a href="#cb28-62" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-63"><a href="#cb28-63" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> optional<span class="op">(</span>optional<span class="op">&amp;&amp;</span> other<span class="op">)</span> <span class="kw">noexcept</span><span class="op">(</span>std<span class="op">::</span>is_nothrow_move_constructible_v<span class="op">&lt;</span>T<span class="op">&gt;)</span></span>
<span id="cb28-64"><a href="#cb28-64" aria-hidden="true" tabindex="-1"></a>   <span class="op">:</span> d_engaged<span class="op">{</span>other<span class="op">.</span>d_engaged<span class="op">}</span></span>
<span id="cb28-65"><a href="#cb28-65" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span></span>
<span id="cb28-66"><a href="#cb28-66" aria-hidden="true" tabindex="-1"></a>      <span class="cf">if</span> <span class="op">(</span>d_engaged<span class="op">)</span> <span class="op">{</span></span>
<span id="cb28-67"><a href="#cb28-67" aria-hidden="true" tabindex="-1"></a>        <span class="op">::</span><span class="kw">new</span><span class="op">(</span>address<span class="op">())</span> T<span class="op">(</span> std<span class="op">::</span>move<span class="op">(</span>other<span class="op">).</span>value<span class="op">()</span> <span class="op">)</span>;</span>
<span id="cb28-68"><a href="#cb28-68" aria-hidden="true" tabindex="-1"></a>      <span class="op">}</span></span>
<span id="cb28-69"><a href="#cb28-69" aria-hidden="true" tabindex="-1"></a>   <span class="op">}</span></span>
<span id="cb28-70"><a href="#cb28-70" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-71"><a href="#cb28-71" aria-hidden="true" tabindex="-1"></a>   <span class="kw">template</span><span class="op">&lt;</span><span class="kw">class</span> U <span class="op">=</span> T<span class="op">&gt;</span></span>
<span id="cb28-72"><a href="#cb28-72" aria-hidden="true" tabindex="-1"></a>      <span class="kw">requires</span> <span class="op">(</span>std<span class="op">::</span>is_constructible_v<span class="op">&lt;</span>T, U<span class="op">&gt;</span></span>
<span id="cb28-73"><a href="#cb28-73" aria-hidden="true" tabindex="-1"></a>            <span class="op">&amp;&amp;</span> <span class="op">!</span>std<span class="op">::</span>is_same_v<span class="op">&lt;</span>std<span class="op">::</span>remove_cvref_t<span class="op">&lt;</span>U<span class="op">&gt;</span>, optional<span class="op">&gt;)</span></span>
<span id="cb28-74"><a href="#cb28-74" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span></span>
<span id="cb28-75"><a href="#cb28-75" aria-hidden="true" tabindex="-1"></a>   <span class="kw">explicit</span><span class="op">(!</span>std<span class="op">::</span>is_convertible_v<span class="op">&lt;</span>U, T<span class="op">&gt;)</span></span>
<span id="cb28-76"><a href="#cb28-76" aria-hidden="true" tabindex="-1"></a>   optional<span class="op">(</span>U<span class="op">&amp;&amp;</span> arg<span class="op">)</span> <span class="op">{</span></span>
<span id="cb28-77"><a href="#cb28-77" aria-hidden="true" tabindex="-1"></a>      <span class="op">::</span><span class="kw">new</span><span class="op">(</span>address<span class="op">())</span> T<span class="op">(</span> std<span class="op">::</span>forward<span class="op">&lt;</span>U<span class="op">&gt;(</span>arg<span class="op">)</span> <span class="op">)</span>;</span>
<span id="cb28-78"><a href="#cb28-78" aria-hidden="true" tabindex="-1"></a>      d_engaged <span class="op">=</span> <span class="kw">true</span>;</span>
<span id="cb28-79"><a href="#cb28-79" aria-hidden="true" tabindex="-1"></a>   <span class="op">}</span></span>
<span id="cb28-80"><a href="#cb28-80" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-81"><a href="#cb28-81" aria-hidden="true" tabindex="-1"></a>   <span class="co">// 22.5.3.3, destructor</span></span>
<span id="cb28-82"><a href="#cb28-82" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> <span class="op">~</span>optional<span class="op">()</span> <span class="op">{</span></span>
<span id="cb28-83"><a href="#cb28-83" aria-hidden="true" tabindex="-1"></a>      <span class="kw">static_assert</span><span class="op">(</span>std<span class="op">::</span>is_trivially_relocatable_v<span class="op">&lt;</span>optional<span class="op">&gt;</span> <span class="op">==</span></span>
<span id="cb28-84"><a href="#cb28-84" aria-hidden="true" tabindex="-1"></a>                    std<span class="op">::</span>is_trivially_relocatable_v<span class="op">&lt;</span>T<span class="op">&gt;)</span>;</span>
<span id="cb28-85"><a href="#cb28-85" aria-hidden="true" tabindex="-1"></a>      <span class="kw">static_assert</span><span class="op">(</span>std<span class="op">::</span>is_replaceable_v<span class="op">&lt;</span>optional<span class="op">&gt;</span> <span class="op">==</span></span>
<span id="cb28-86"><a href="#cb28-86" aria-hidden="true" tabindex="-1"></a>                    std<span class="op">::</span>is_replaceable_v<span class="op">&lt;</span>T<span class="op">&gt;)</span>;</span>
<span id="cb28-87"><a href="#cb28-87" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-88"><a href="#cb28-88" aria-hidden="true" tabindex="-1"></a>      <span class="cf">if</span> <span class="op">(</span>d_engaged<span class="op">)</span> <span class="op">{</span></span>
<span id="cb28-89"><a href="#cb28-89" aria-hidden="true" tabindex="-1"></a>         address<span class="op">()-&gt;~</span>T<span class="op">()</span>;</span>
<span id="cb28-90"><a href="#cb28-90" aria-hidden="true" tabindex="-1"></a>      <span class="op">}</span></span>
<span id="cb28-91"><a href="#cb28-91" aria-hidden="true" tabindex="-1"></a>   <span class="op">}</span></span>
<span id="cb28-92"><a href="#cb28-92" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-93"><a href="#cb28-93" aria-hidden="true" tabindex="-1"></a>   <span class="co">// 22.5.3.4, assignment</span></span>
<span id="cb28-94"><a href="#cb28-94" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> optional<span class="op">&amp;</span> <span class="kw">operator</span><span class="op">=(</span>optional <span class="kw">const</span> <span class="op">&amp;</span> rhs<span class="op">)</span>;</span>
<span id="cb28-95"><a href="#cb28-95" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-96"><a href="#cb28-96" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> optional<span class="op">&amp;</span> <span class="kw">operator</span><span class="op">=(</span>optional <span class="op">&amp;&amp;</span> rhs<span class="op">)</span></span>
<span id="cb28-97"><a href="#cb28-97" aria-hidden="true" tabindex="-1"></a>     <span class="kw">noexcept</span><span class="op">(</span>std<span class="op">::</span>is_nothrow_move_assignable_v<span class="op">&lt;</span>T<span class="op">&gt;</span></span>
<span id="cb28-98"><a href="#cb28-98" aria-hidden="true" tabindex="-1"></a>           <span class="op">&amp;&amp;</span> std<span class="op">::</span>is_nothrow_move_constructible_v<span class="op">&lt;</span>T<span class="op">&gt;)</span></span>
<span id="cb28-99"><a href="#cb28-99" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span></span>
<span id="cb28-100"><a href="#cb28-100" aria-hidden="true" tabindex="-1"></a>      std<span class="op">::</span>cout <span class="op">&lt;&lt;</span> <span class="st">&quot;Assignment</span><span class="sc">\n</span><span class="st">&quot;</span>;</span>
<span id="cb28-101"><a href="#cb28-101" aria-hidden="true" tabindex="-1"></a>      <span class="cf">if</span> <span class="op">(!</span>d_engaged<span class="op">)</span> <span class="op">{</span></span>
<span id="cb28-102"><a href="#cb28-102" aria-hidden="true" tabindex="-1"></a>        <span class="cf">if</span> <span class="op">(</span>rhs<span class="op">.</span>d_engaged<span class="op">)</span> <span class="op">{</span></span>
<span id="cb28-103"><a href="#cb28-103" aria-hidden="true" tabindex="-1"></a>           <span class="op">::</span><span class="kw">new</span><span class="op">(</span>address<span class="op">())</span> T<span class="op">(</span> std<span class="op">::</span>move<span class="op">(</span>rhs<span class="op">.</span>value<span class="op">())</span> <span class="op">)</span>;</span>
<span id="cb28-104"><a href="#cb28-104" aria-hidden="true" tabindex="-1"></a>           rhs<span class="op">.</span>d_engaged <span class="op">=</span> <span class="kw">false</span>;</span>
<span id="cb28-105"><a href="#cb28-105" aria-hidden="true" tabindex="-1"></a>           d_engaged <span class="op">=</span> <span class="kw">true</span>;</span>
<span id="cb28-106"><a href="#cb28-106" aria-hidden="true" tabindex="-1"></a>        <span class="op">}</span></span>
<span id="cb28-107"><a href="#cb28-107" aria-hidden="true" tabindex="-1"></a>      <span class="op">}</span></span>
<span id="cb28-108"><a href="#cb28-108" aria-hidden="true" tabindex="-1"></a>      <span class="cf">else</span> <span class="cf">if</span> <span class="op">(!</span>rhs<span class="op">.</span>d_engaged<span class="op">)</span> <span class="op">{</span></span>
<span id="cb28-109"><a href="#cb28-109" aria-hidden="true" tabindex="-1"></a>         address<span class="op">()-&gt;~</span>T<span class="op">()</span>;</span>
<span id="cb28-110"><a href="#cb28-110" aria-hidden="true" tabindex="-1"></a>         d_engaged <span class="op">=</span> <span class="kw">false</span>;</span>
<span id="cb28-111"><a href="#cb28-111" aria-hidden="true" tabindex="-1"></a>      <span class="op">}</span></span>
<span id="cb28-112"><a href="#cb28-112" aria-hidden="true" tabindex="-1"></a>      <span class="cf">else</span> <span class="op">{</span></span>
<span id="cb28-113"><a href="#cb28-113" aria-hidden="true" tabindex="-1"></a>        value<span class="op">()</span> <span class="op">=</span> rhs<span class="op">.</span>value<span class="op">()</span>;</span>
<span id="cb28-114"><a href="#cb28-114" aria-hidden="true" tabindex="-1"></a>      <span class="op">}</span></span>
<span id="cb28-115"><a href="#cb28-115" aria-hidden="true" tabindex="-1"></a>      <span class="cf">return</span> <span class="op">*</span><span class="kw">this</span>;</span>
<span id="cb28-116"><a href="#cb28-116" aria-hidden="true" tabindex="-1"></a>   <span class="op">}</span></span>
<span id="cb28-117"><a href="#cb28-117" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-118"><a href="#cb28-118" aria-hidden="true" tabindex="-1"></a>   <span class="kw">template</span><span class="op">&lt;</span><span class="kw">class</span> U <span class="op">=</span> T<span class="op">&gt;</span></span>
<span id="cb28-119"><a href="#cb28-119" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> optional<span class="op">&amp;</span> <span class="kw">operator</span><span class="op">=(</span>U <span class="op">&amp;&amp;</span> arg<span class="op">)</span> <span class="op">{</span></span>
<span id="cb28-120"><a href="#cb28-120" aria-hidden="true" tabindex="-1"></a>      std<span class="op">::</span>cout <span class="op">&lt;&lt;</span> <span class="st">&quot;Assignment</span><span class="sc">\n</span><span class="st">&quot;</span>;</span>
<span id="cb28-121"><a href="#cb28-121" aria-hidden="true" tabindex="-1"></a>      <span class="cf">if</span> <span class="op">(!</span>d_engaged<span class="op">)</span> <span class="op">{</span></span>
<span id="cb28-122"><a href="#cb28-122" aria-hidden="true" tabindex="-1"></a>        <span class="op">::</span><span class="kw">new</span><span class="op">(</span>address<span class="op">())</span> T<span class="op">(</span> std<span class="op">::</span>forward<span class="op">&lt;</span>U<span class="op">&gt;(</span>arg<span class="op">)</span> <span class="op">)</span>;</span>
<span id="cb28-123"><a href="#cb28-123" aria-hidden="true" tabindex="-1"></a>        d_engaged <span class="op">=</span> <span class="kw">true</span>;</span>
<span id="cb28-124"><a href="#cb28-124" aria-hidden="true" tabindex="-1"></a>      <span class="op">}</span></span>
<span id="cb28-125"><a href="#cb28-125" aria-hidden="true" tabindex="-1"></a>      <span class="cf">else</span> <span class="op">{</span></span>
<span id="cb28-126"><a href="#cb28-126" aria-hidden="true" tabindex="-1"></a>         <span class="op">*</span>address<span class="op">()</span> <span class="op">=</span> std<span class="op">::</span>forward<span class="op">&lt;</span>U<span class="op">&gt;(</span>arg<span class="op">)</span>;</span>
<span id="cb28-127"><a href="#cb28-127" aria-hidden="true" tabindex="-1"></a>      <span class="op">}</span></span>
<span id="cb28-128"><a href="#cb28-128" aria-hidden="true" tabindex="-1"></a>      <span class="cf">return</span> <span class="op">*</span><span class="kw">this</span>;</span>
<span id="cb28-129"><a href="#cb28-129" aria-hidden="true" tabindex="-1"></a>   <span class="op">}</span></span>
<span id="cb28-130"><a href="#cb28-130" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-131"><a href="#cb28-131" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-132"><a href="#cb28-132" aria-hidden="true" tabindex="-1"></a>   <span class="co">// 22.5.3.7, observers</span></span>
<span id="cb28-133"><a href="#cb28-133" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> T <span class="kw">const</span> <span class="op">*</span> <span class="kw">operator</span><span class="op">-&gt;()</span> <span class="kw">const</span>  <span class="kw">noexcept</span></span>
<span id="cb28-134"><a href="#cb28-134" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span> <span class="ot">assert</span><span class="op">(</span>d_engaged<span class="op">)</span>; <span class="cf">return</span>  address<span class="op">()</span>; <span class="op">}</span></span>
<span id="cb28-135"><a href="#cb28-135" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> T       <span class="op">*</span> <span class="kw">operator</span><span class="op">-&gt;()</span>        <span class="kw">noexcept</span></span>
<span id="cb28-136"><a href="#cb28-136" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span> <span class="ot">assert</span><span class="op">(</span>d_engaged<span class="op">)</span>; <span class="cf">return</span>  address<span class="op">()</span>; <span class="op">}</span></span>
<span id="cb28-137"><a href="#cb28-137" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-138"><a href="#cb28-138" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> T <span class="kw">const</span> <span class="op">&amp;</span> <span class="kw">operator</span><span class="op">*()</span> <span class="kw">const</span> <span class="op">&amp;</span> <span class="kw">noexcept</span></span>
<span id="cb28-139"><a href="#cb28-139" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span> <span class="ot">assert</span><span class="op">(</span>d_engaged<span class="op">)</span>; <span class="cf">return</span> <span class="op">*</span>address<span class="op">()</span>; <span class="op">}</span></span>
<span id="cb28-140"><a href="#cb28-140" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> T       <span class="op">&amp;</span> <span class="kw">operator</span><span class="op">*()</span>       <span class="op">&amp;</span> <span class="kw">noexcept</span></span>
<span id="cb28-141"><a href="#cb28-141" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span> <span class="ot">assert</span><span class="op">(</span>d_engaged<span class="op">)</span>; <span class="cf">return</span> <span class="op">*</span>address<span class="op">()</span>; <span class="op">}</span></span>
<span id="cb28-142"><a href="#cb28-142" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> T      <span class="op">&amp;&amp;</span> <span class="kw">operator</span><span class="op">*()</span>      <span class="op">&amp;&amp;</span> <span class="kw">noexcept</span></span>
<span id="cb28-143"><a href="#cb28-143" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span> <span class="ot">assert</span><span class="op">(</span>d_engaged<span class="op">)</span>; <span class="cf">return</span> std<span class="op">::</span>move<span class="op">(*</span>address<span class="op">())</span>; <span class="op">}</span></span>
<span id="cb28-144"><a href="#cb28-144" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> T <span class="kw">const</span><span class="op">&amp;&amp;</span> <span class="kw">operator</span><span class="op">*()</span> <span class="kw">const</span><span class="op">&amp;&amp;</span> <span class="kw">noexcept</span></span>
<span id="cb28-145"><a href="#cb28-145" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span> <span class="ot">assert</span><span class="op">(</span>d_engaged<span class="op">)</span>; <span class="cf">return</span> std<span class="op">::</span>move<span class="op">(*</span>address<span class="op">())</span>; <span class="op">}</span></span>
<span id="cb28-146"><a href="#cb28-146" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-147"><a href="#cb28-147" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> <span class="kw">explicit</span> <span class="kw">operator</span> <span class="dt">bool</span><span class="op">()</span> <span class="kw">const</span> <span class="kw">noexcept</span></span>
<span id="cb28-148"><a href="#cb28-148" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span> <span class="cf">return</span> d_engaged; <span class="op">}</span></span>
<span id="cb28-149"><a href="#cb28-149" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> <span class="dt">bool</span>         has_value<span class="op">()</span> <span class="kw">const</span> <span class="kw">noexcept</span></span>
<span id="cb28-150"><a href="#cb28-150" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span> <span class="cf">return</span> d_engaged; <span class="op">}</span></span>
<span id="cb28-151"><a href="#cb28-151" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-152"><a href="#cb28-152" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> T <span class="kw">const</span> <span class="op">&amp;</span> value<span class="op">()</span> <span class="kw">const</span> <span class="op">&amp;</span></span>
<span id="cb28-153"><a href="#cb28-153" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span> <span class="ot">assert</span><span class="op">(</span>d_engaged<span class="op">)</span>; <span class="cf">return</span> <span class="op">*</span>address<span class="op">()</span>; <span class="op">}</span></span>
<span id="cb28-154"><a href="#cb28-154" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> T       <span class="op">&amp;</span> value<span class="op">()</span>       <span class="op">&amp;</span></span>
<span id="cb28-155"><a href="#cb28-155" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span> <span class="ot">assert</span><span class="op">(</span>d_engaged<span class="op">)</span>; <span class="cf">return</span> <span class="op">*</span>address<span class="op">()</span>; <span class="op">}</span></span>
<span id="cb28-156"><a href="#cb28-156" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> T      <span class="op">&amp;&amp;</span> value<span class="op">()</span>      <span class="op">&amp;&amp;</span></span>
<span id="cb28-157"><a href="#cb28-157" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span> <span class="ot">assert</span><span class="op">(</span>d_engaged<span class="op">)</span>; <span class="cf">return</span> std<span class="op">::</span>move<span class="op">(*</span>address<span class="op">())</span>; <span class="op">}</span></span>
<span id="cb28-158"><a href="#cb28-158" aria-hidden="true" tabindex="-1"></a>   <span class="kw">constexpr</span> T <span class="kw">const</span><span class="op">&amp;&amp;</span> value<span class="op">()</span> <span class="kw">const</span><span class="op">&amp;&amp;</span></span>
<span id="cb28-159"><a href="#cb28-159" aria-hidden="true" tabindex="-1"></a>   <span class="op">{</span> <span class="ot">assert</span><span class="op">(</span>d_engaged<span class="op">)</span>; <span class="cf">return</span> std<span class="op">::</span>move<span class="op">(*</span>address<span class="op">())</span>; <span class="op">}</span></span>
<span id="cb28-160"><a href="#cb28-160" aria-hidden="true" tabindex="-1"></a><span class="op">}</span>;</span>
<span id="cb28-161"><a href="#cb28-161" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-162"><a href="#cb28-162" aria-hidden="true" tabindex="-1"></a><span class="dt">int</span> main<span class="op">()</span> <span class="op">{</span></span>
<span id="cb28-163"><a href="#cb28-163" aria-hidden="true" tabindex="-1"></a>   optional<span class="op">&lt;</span><span class="dt">int</span><span class="op">&gt;</span> x;</span>
<span id="cb28-164"><a href="#cb28-164" aria-hidden="true" tabindex="-1"></a>   <span class="ot">assert</span><span class="op">(!</span>x<span class="op">)</span>;</span>
<span id="cb28-165"><a href="#cb28-165" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-166"><a href="#cb28-166" aria-hidden="true" tabindex="-1"></a>   std<span class="op">::</span>cout <span class="op">&lt;&lt;</span> <span class="st">&quot;Assignments to x</span><span class="sc">\n</span><span class="st">&quot;</span>;</span>
<span id="cb28-167"><a href="#cb28-167" aria-hidden="true" tabindex="-1"></a>   x <span class="op">=</span> <span class="dv">3</span>;</span>
<span id="cb28-168"><a href="#cb28-168" aria-hidden="true" tabindex="-1"></a>   <span class="kw">auto</span> y <span class="op">=</span> x;</span>
<span id="cb28-169"><a href="#cb28-169" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-170"><a href="#cb28-170" aria-hidden="true" tabindex="-1"></a>   x <span class="op">=</span> <span class="dv">4</span>;</span>
<span id="cb28-171"><a href="#cb28-171" aria-hidden="true" tabindex="-1"></a>   std<span class="op">::</span>cout <span class="op">&lt;&lt;</span> <span class="st">&quot;swap x</span><span class="sc">\n</span><span class="st">&quot;</span>;</span>
<span id="cb28-172"><a href="#cb28-172" aria-hidden="true" tabindex="-1"></a>   std<span class="op">::</span>swap<span class="op">(</span>x, y<span class="op">)</span>;</span>
<span id="cb28-173"><a href="#cb28-173" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-174"><a href="#cb28-174" aria-hidden="true" tabindex="-1"></a>   <span class="ot">assert</span><span class="op">(</span><span class="dv">3</span> <span class="op">==</span> <span class="op">*</span>x<span class="op">)</span>;</span>
<span id="cb28-175"><a href="#cb28-175" aria-hidden="true" tabindex="-1"></a>   <span class="ot">assert</span><span class="op">(</span><span class="dv">4</span> <span class="op">==</span> <span class="op">*</span>y<span class="op">)</span>;</span>
<span id="cb28-176"><a href="#cb28-176" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-177"><a href="#cb28-177" aria-hidden="true" tabindex="-1"></a>   optional<span class="op">&lt;</span>std<span class="op">::</span>shared_ptr<span class="op">&lt;</span><span class="dt">int</span><span class="op">&gt;&gt;</span> p1;</span>
<span id="cb28-178"><a href="#cb28-178" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-179"><a href="#cb28-179" aria-hidden="true" tabindex="-1"></a>   std<span class="op">::</span>cout <span class="op">&lt;&lt;</span> <span class="st">&quot;Assignments to p</span><span class="sc">\n</span><span class="st">&quot;</span>;</span>
<span id="cb28-180"><a href="#cb28-180" aria-hidden="true" tabindex="-1"></a>   p1 <span class="op">=</span> std<span class="op">::</span>make_shared<span class="op">&lt;</span><span class="dt">int</span><span class="op">&gt;(</span><span class="dv">3</span><span class="op">)</span>;</span>
<span id="cb28-181"><a href="#cb28-181" aria-hidden="true" tabindex="-1"></a>   <span class="kw">auto</span> p2 <span class="op">=</span> p1;</span>
<span id="cb28-182"><a href="#cb28-182" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-183"><a href="#cb28-183" aria-hidden="true" tabindex="-1"></a>   p2 <span class="op">=</span> std<span class="op">::</span>make_shared<span class="op">&lt;</span><span class="dt">int</span><span class="op">&gt;(</span><span class="dv">4</span><span class="op">)</span>;</span>
<span id="cb28-184"><a href="#cb28-184" aria-hidden="true" tabindex="-1"></a>   std<span class="op">::</span>cout <span class="op">&lt;&lt;</span> <span class="st">&quot;swap p</span><span class="sc">\n</span><span class="st">&quot;</span>;</span>
<span id="cb28-185"><a href="#cb28-185" aria-hidden="true" tabindex="-1"></a>   std<span class="op">::</span>swap<span class="op">(</span>p1, p2<span class="op">)</span>;</span>
<span id="cb28-186"><a href="#cb28-186" aria-hidden="true" tabindex="-1"></a><span class="op">}</span></span></code></pre></div>
<h1 data-number="17" id="proposed-wording"><span class="header-section-number">17</span> Proposed Wording<a href="#proposed-wording" class="self-link"></a></h1>
<p>Make the following changes to the C++ Working Draft. All wording is
relative to <span class="citation" data-cites="N4993">[<a href="https://wg21.link/n4993" role="doc-biblioref">N4993</a>]</span>,
the latest working draft at the time of writing.</p>
<h2 data-number="17.1" id="add-new-identifiers-with-a-special-meaning"><span class="header-section-number">17.1</span> Add new identifiers with a
special meaning<a href="#add-new-identifiers-with-a-special-meaning" class="self-link"></a></h2>
<h3 class="unnumbered" id="lex.name-identifiers"><span>5.11
<a href="https://wg21.link/N4993#lex.name">[lex.name]</a></span>
Identifiers<a href="#lex.name-identifiers" class="self-link"></a></h3>
<p>Table 4: Identifiers with special meaning [tab:lex.name.special]</p>
<table>
<colgroup>
<col style="width: 6%" />
<col style="width: 7%" />
<col style="width: 8%" />
<col style="width: 9%" />
<col style="width: 29%" />
<col style="width: 39%" />
</colgroup>
<tbody>
<tr class="odd">
<td><code class="sourceCode cpp"><span class="kw">final</span></code></td>
<td><code class="sourceCode cpp"><span class="kw">import</span></code></td>
<td><code class="sourceCode cpp"><span class="kw">module</span></code></td>
<td><code class="sourceCode cpp"><span class="kw">override</span></code></td>
<td><span class="add" style="color: #006e28"><ins><span><code class="sourceCode default">replaceable_if_eligible</code></span></ins></span></td>
<td><span class="add" style="color: #006e28"><ins><span><code class="sourceCode default">trivially_relocatable_if_eligible</code></span></ins></span></td>
</tr>
</tbody>
</table>
<h2 data-number="17.2" id="specify-trivially-relocatable-types"><span class="header-section-number">17.2</span> Specify trivially relocatable
types<a href="#specify-trivially-relocatable-types" class="self-link"></a></h2>
<p><strong>Editorial note:</strong> <em>We have separated each sentence
to improve clarity rather than trying to identify the definition of so
many terms as a single paragraph.</em></p>
<h3 class="unnumbered" id="basic.types.general-general"><span>6.8.1
<a href="https://wg21.link/N4993#basic.types.general">[basic.types.general]</a></span>
General<a href="#basic.types.general-general" class="self-link"></a></h3>
<p><span class="marginalizedparent"><a class="marginalized">9</a></span>
Arithmetic types (<span>6.8.2
<a href="https://wg21.link/N4993#basic.fundamental">[basic.fundamental]</a></span>),
enumeration types, pointer types, pointer-to-member types (<span>6.8.4
<a href="https://wg21.link/N4993#basic.compound">[basic.compound]</a></span>),
<code class="sourceCode cpp">std<span class="op">::</span>nullptr_t</code>,
and cv-qualified (<span>6.8.5
<a href="https://wg21.link/N4993#basic.type.qualifier">[basic.type.qualifier]</a></span>)
versions of these types are collectively called <em>scalar
types</em>.</p>
<p>Scalar types, trivially copyable class types (<span>11.2
<a href="https://wg21.link/N4993#class.prop">[class.prop]</a></span>),
arrays of such types, and cv-qualified versions of these types are
collectively called <em>trivially copyable types</em>.</p>
<p>Scalar types, trivial class types (<span>11.2
<a href="https://wg21.link/N4993#class.prop">[class.prop]</a></span>),
arrays of such types, and cv-qualified versions of these types are
collectively called <em>trivial types</em>.</p>
<p><span class="add" style="color: #006e28"><ins>Scalar types, trivially
relocatable class types (<span>11.2
<a href="https://wg21.link/N4993#class.prop">[class.prop]</a></span>),
arrays of such types, and cv-qualified versions of these types are
collectively called <em>trivially relocatable
types</em>.</ins></span></p>
<p><span class="add" style="color: #006e28"><ins>Scalar types,
replaceable class types (<span>11.2
<a href="https://wg21.link/N4993#class.prop">[class.prop]</a></span>),
and arrays of such types are collectively called <em>replaceable
types</em>.</ins></span></p>
<p>Scalar types, standard-layout class types (<span>11.2
<a href="https://wg21.link/N4993#class.prop">[class.prop]</a></span>),
arrays of such types, and cv-qualified versions of these types are
collectively called <em>standard-layout types</em>.</p>
<p>Scalar types, implicit-lifetime class types (<span>11.2
<a href="https://wg21.link/N4993#class.prop">[class.prop]</a></span>),
array types, and cv-qualified versions of these types are collectively
called <em>implicit-lifetime types</em>.</p>
<h2 data-number="17.3" id="address-trivial-relocation-of-lambdas"><span class="header-section-number">17.3</span> Address trivial relocation of
lambdas<a href="#address-trivial-relocation-of-lambdas" class="self-link"></a></h2>
<h3 class="unnumbered" id="expr.prim.lambda.closure-closure-types"><span>7.5.6.2
<a href="https://wg21.link/N4993#expr.prim.lambda.closure">[expr.prim.lambda.closure]</a></span>
Closure types<a href="#expr.prim.lambda.closure-closure-types" class="self-link"></a></h3>
<p><span class="marginalizedparent"><a class="marginalized">2</a></span>
The closure type is declared in the smallest block scope, class scope,
or namespace scope that contains the corresponding
<em>lambda-expression</em>.</p>
<p>[<em>Note 1:</em> This determines the set of namespaces and classes
associated with the closure type (<span>6.5.4
<a href="https://wg21.link/N4993#basic.lookup.argdep">[basic.lookup.argdep]</a></span>).
The parameter types of a <em>lambda-declarator</em> do not affect these
associated namespaces and classes. —<em>end note</em>]</p>
<p><span class="marginalizedparent"><a class="marginalized">3</a></span>
The closure type is not an aggregate type (<span>9.4.2
<a href="https://wg21.link/N4993#dcl.init.aggr">[dcl.init.aggr]</a></span>);
it is a structural type (<span>13.2
<a href="https://wg21.link/N4993#temp.param">[temp.param]</a></span>) if
and only if the lambda has no <em>lambda-capture</em>. An implementation
may define the closure type differently from what is described below
provided this does not alter the observable behavior of the program
other than by changing:</p>
<p><span class="marginalizedparent"><a class="marginalized">(3.1)</a></span> —
the size and/or alignment of the closure type,</p>
<p><span class="marginalizedparent"><a class="marginalized">(3.2)</a></span> —
whether the closure type is trivially copyable (<span>11.2
<a href="https://wg21.link/N4993#class.prop">[class.prop]</a></span>),
or</p>
<div class="add" style="color: #006e28">
<p><span class="marginalizedparent"><a class="marginalized">(3.x)</a></span> —
whether the closure type is trivially relocatable (<span>11.2
<a href="https://wg21.link/N4993#class.prop">[class.prop]</a></span>),
or</p>
</div>
<div class="add" style="color: #006e28">
<p><span class="marginalizedparent"><a class="marginalized">(3.y)</a></span> —
whether the closure type is replaceable (<span>11.2
<a href="https://wg21.link/N4993#class.prop">[class.prop]</a></span>),
or</p>
</div>
<p><span class="marginalizedparent"><a class="marginalized">(3.3)</a></span> —
whether the closure type is a standard-layout class (<span>11.2
<a href="https://wg21.link/N4993#class.prop">[class.prop]</a></span>).</p>
<p>An implementation shall not add members of rvalue reference type to
the closure type.</p>
<h2 data-number="17.4" id="update-grammar-to-support-_if_eligible-contextual-keywords"><span class="header-section-number">17.4</span> Update grammar to support
<code class="sourceCode cpp">_if_eligible</code> contextual keywords<a href="#update-grammar-to-support-_if_eligible-contextual-keywords" class="self-link"></a></h2>
<h3 class="unnumbered" id="class.pre-preamble"><span>11.1
<a href="https://wg21.link/N4993#class.pre">[class.pre]</a></span>
Preamble<a href="#class.pre-preamble" class="self-link"></a></h3>
<p><span class="marginalizedparent"><a class="marginalized">1</a></span>
A class is a type. Its name becomes a class-name (<span>11.3
<a href="https://wg21.link/N4993#class.name">[class.name]</a></span>)
within its scope.</p>
<div class="line-block">      <em>class-name</em> :<br />
              <em>identifier</em><br />
              <em>simple-template-id</em></div>
<p>A <em>class-specifier</em> or an <em>elaborated-type-specifier</em>
(<span>9.2.9.5
<a href="https://wg21.link/N4993#dcl.type.elab">[dcl.type.elab]</a></span>)
is used to make a <em>class-name</em>. An object of a class consists of
a (possibly empty) sequence of members and base class objects.</p>
<div class="line-block">      <em>class-specifier</em> :<br />
              <em>class-head</em>
<code class="sourceCode cpp"><span class="op">{</span></code>
<em>member-specification<sub>opt</sub></em>
<code class="sourceCode cpp"><span class="op">}</span></code><br />
<br />
      <em>class-head</em>:<br />
              <em>class-key</em>
<em>attribute-specifier-seq<sub>opt</sub></em> <em>class-head-name</em>
<em>class-<span class="rm" style="color: #bf0303"><del>virt</del></span><span class="add" style="color: #006e28"><ins>property</ins></span>-specifier<sub>opt</sub></em>
<em>base-clause<sub>opt</sub></em><br />
              <em>class-key</em>
<em>attribute-specifier-seq<sub>opt</sub></em>
<em>base-clause<sub>opt</sub></em><br />
<br />
      <em>class-head-name</em> :<br />
              <em>nested-name-specifier<sub>opt</sub></em>
<em>class-name</em><br />
<br />
      <span class="add" style="color: #006e28"><ins><em>class-property-specifier-seq</em>:</ins></span><br />
              <span class="add" style="color: #006e28"><ins><em>class-property-specifier</em>
<em>class-property-specifier-seq<sub>opt</sub></em></ins></span><br />
<br />
      <em>class-<span class="rm" style="color: #bf0303"><del>virt</del></span><span class="add" style="color: #006e28"><ins>property</ins></span>-specifier</em> :<br />
              <code class="sourceCode cpp"><span class="kw">final</span></code><br />
              <span class="add" style="color: #006e28"><ins><span><code class="sourceCode default">replaceable_if_eligible</code></span></ins></span><br />
              <span class="add" style="color: #006e28"><ins><span><code class="sourceCode default">trivially_relocatable_if_eligible</code></span></ins></span><br />
<br />
      <em>class-key</em> :<br />
              <code class="sourceCode cpp"><span class="kw">class</span></code><br />
              <code class="sourceCode cpp"><span class="kw">struct</span></code><br />
              <code class="sourceCode cpp"><span class="kw">union</span></code></div>
<p>A class declaration where the <em>class-name</em> in the
<em>class-head-name</em> is a <em>simple-template-id</em> shall be …</p>
<p><span class="marginalizedparent"><a class="marginalized">4</a></span>
[<em>Note 2:</em> The <em>class-key</em> determines whether the class is
a union (<span>11.5
<a href="https://wg21.link/N4993#class.union">[class.union]</a></span>)
and whether access is public or private by default (<span>11.8
<a href="https://wg21.link/N4993#class.access">[class.access]</a></span>).
A union holds the value of at most one data member at a time. —<em>end
note</em>]</p>
<div class="rm" style="color: #bf0303">
<p><span class="marginalizedparent"><a class="marginalized">5</a></span>
If a class is marked with the <em>class-virt-specifier</em>
<code class="sourceCode default">final</code> and it appears as a
<em>class-or-decltype</em> in a base-clause (<span>11.7
<a href="https://wg21.link/N4993#class.derived">[class.derived]</a></span>),
the program is ill-formed. Whenever a <em>class-key</em> is followed by
a <em>class-head-name</em>, the identifier
<code class="sourceCode default">final</code>, and a colon or left
brace, <code class="sourceCode default">final</code> is interpreted as a
<em>class-virt-specifier</em>.</p>
</div>
<div class="add" style="color: #006e28">
<p><span class="marginalizedparent"><a class="marginalized">5</a></span>
The same <em>class-property-specifier</em> shall not appear multiple
times within a single <em>class-property-specifier-seq</em>.</p>
<p>Whenever a <em>class-key</em> is followed by a
<em>class-head-name</em>, one of the identifiers
<code class="sourceCode default">final</code>,
<code class="sourceCode default">replaceable_if_eligible</code>, or
<code class="sourceCode default">trivially_relocatable_if_eligible</code>, and
a colon or left brace, the identifier is interpreted as a
<em>class-property-specifier</em>.</p>
</div>
<p>[<em>Example 2:</em></p>
<div class="sourceCode" id="cb29"><pre class="sourceCode default"><code class="sourceCode default"><span id="cb29-1"><a href="#cb29-1" aria-hidden="true" tabindex="-1"></a>struct A;</span>
<span id="cb29-2"><a href="#cb29-2" aria-hidden="true" tabindex="-1"></a>struct A final {}; // OK, definition of struct A,</span>
<span id="cb29-3"><a href="#cb29-3" aria-hidden="true" tabindex="-1"></a>                   // not value-initialization of variable final</span>
<span id="cb29-4"><a href="#cb29-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb29-5"><a href="#cb29-5" aria-hidden="true" tabindex="-1"></a>struct X {</span>
<span id="cb29-6"><a href="#cb29-6" aria-hidden="true" tabindex="-1"></a>  struct C { constexpr operator int() { return 5; } };</span>
<span id="cb29-7"><a href="#cb29-7" aria-hidden="true" tabindex="-1"></a>  struct B <span class="rm" style="color: #bf0303"><del>final</del></span><span class="add" style="color: #006e28"><ins>trivially_relocatable_if_eligible</ins></span> : C{};</span>
<span id="cb29-8"><a href="#cb29-8" aria-hidden="true" tabindex="-1"></a>                                   // OK, definition of nested class B,</span>
<span id="cb29-9"><a href="#cb29-9" aria-hidden="true" tabindex="-1"></a>                                   // not declaration of a bit-field</span>
<span id="cb29-10"><a href="#cb29-10" aria-hidden="true" tabindex="-1"></a>                                   // member <span class="rm" style="color: #bf0303"><del>final</del></span><span class="add" style="color: #006e28"><ins>trivially_relocatable_if_eligible</ins></span></span>
<span id="cb29-11"><a href="#cb29-11" aria-hidden="true" tabindex="-1"></a>};</span></code></pre></div>
<p>—<em>end example</em>]</p>
<div class="add" style="color: #006e28">
<p><span class="marginalizedparent"><a class="marginalized">u</a></span>
If a class is marked with the <em>class-property-specifier</em>
<code class="sourceCode default">final</code> and that class appears as
a <em>class-or-decltype</em> in a base-clause (<span>11.7
<a href="https://wg21.link/N4993#class.derived">[class.derived]</a></span>),
the program is ill-formed.</p>
</div>
<p><span class="marginalizedparent"><a class="marginalized">6</a></span>
[<em>Note 3:</em> Complete objects of class type have nonzero size. Base
class subobjects and members declared with the
<code class="sourceCode cpp">no_unique_address</code> attribute
(<span>9.12.12
<a href="https://wg21.link/N4993#dcl.attr.nouniqueaddr">[dcl.attr.nouniqueaddr]</a></span>)
are not so constrained. —<em>end note</em>]</p>
<h2 data-number="17.5" id="specification-for-trivially-relocatable-classes"><span class="header-section-number">17.5</span> Specification for trivially
relocatable classes<a href="#specification-for-trivially-relocatable-classes" class="self-link"></a></h2>
<blockquote>
<p><strong>Design note:</strong><br />
<em>Declaring a class as trivially relocatable is possible, by means
of</em> <em>the</em>
<code class="sourceCode cpp">trivially_relocatable_if_eligible</code>
<em>specifier, even if that class has</em> <em>user-provided special
members.</em> <em>Note that such a declaration is not permitted to break
the encapsulation of</em> <em>members or bases and allow for their
trivial relocation when they,</em> <em>themselves, are not trivially
relocatable.</em></p>
</blockquote>
<h3 class="unnumbered" id="class.prop-properties-of-classes"><span>11.2
<a href="https://wg21.link/N4993#class.prop">[class.prop]</a></span>
Properties of classes<a href="#class.prop-properties-of-classes" class="self-link"></a></h3>
<p><span class="marginalizedparent"><a class="marginalized">2</a></span>
A <em>trivial class</em> is a class that is trivially copyable and has
one or more eligible default constructors (<span>11.4.5.2
<a href="https://wg21.link/N4993#class.default.ctor">[class.default.ctor]</a></span>),
all of which are trivial.</p>
<p>[<em>Note 1:</em> In particular, a trivially copyable or trivial
class does not have virtual functions or virtual base classes. —<em>end
note</em>]</p>
<div class="add" style="color: #006e28">
<p><span class="marginalizedparent"><a class="marginalized">a</a></span>
A class is <em>eligible for trivial relocation</em> unless it has</p>
<ul>
<li>any virtual base classes, or</li>
<li>a base class that is not a trivially relocatable class, or</li>
<li>a non-static data member of a non-reference type that is not of a
trivially relocatable type, or</li>
<li>a deleted destructor.</li>
</ul>
<p><span class="marginalizedparent"><a class="marginalized">b</a></span>
A class C is <em>eligible for replacement</em> unless it has</p>
<ul>
<li>a base class that is not a replaceable class, or</li>
<li>a non-static data member that is not of a replaceable type,</li>
<li>no eligible constructor that would be selected when an object of
type <code class="sourceCode default">C</code> is direct-initialized
from an xvalue of type <code class="sourceCode default">C</code>,</li>
<li>no eligible assignment operator that would be selected when an
object of type <code class="sourceCode default">C</code> is assigned
from an xvalue of type <code class="sourceCode default">C</code>,</li>
<li>no destructor. </li>
</ul>
<p><span class="marginalizedparent"><a class="marginalized">c</a></span>
A class <code class="sourceCode default">C</code> is a <em>trivially
relocatable class</em> if it is eligible for trivial relocation and</p>
<ul>
<li>has the <code class="sourceCode default">trivially_relocatable_if_eligible</code>
<em>class-property-specifier</em>, or</li>
<li>is a union with no user-declared special member functions, or</li>
<li>satisfies all of the following:
<ul>
<li>when an object of type <code class="sourceCode default">C</code> is
direct-initialized from an xvalue of type
<code class="sourceCode default">C</code>, overload resolution would
select a constructor that is neither user-provided nor deleted, and</li>
<li>when an xvalue of type <code class="sourceCode default">C</code> is
assigned to an object of type <code class="sourceCode default">C</code>,
overload resolution would select an assignment operator that is neither
user-provided nor deleted, and</li>
<li>it has a destructor that is neither user-provided nor deleted.</li>
</ul></li>
</ul>
<p><span class="marginalizedparent"><a class="marginalized">d</a></span>
[<em>Note 2:</em> Accessibility of the special member functions is not
considered when establishing trivial relocatability. —<em>end
note</em>]</p>
<p><span class="marginalizedparent"><a class="marginalized">e</a></span>
[<em>Note 3:</em> A type with non-static data members that are
const-qualified or are references can be trivially relocatable. —<em>end
note</em>]</p>
<p><span class="marginalizedparent"><a class="marginalized">f</a></span>
[<em>Note 4:</em> Trivially copyable classes are trivially relocatable
unless they have deleted special members. —<em>end note</em>]</p>
<p><span class="marginalizedparent"><a class="marginalized">g</a></span>
A class <code class="sourceCode default">C</code> is a <em>replaceable
class</em> if it is eligible for replacement and</p>
<ul>
<li>has the
<code class="sourceCode default">replaceable_if_eligible</code>
<em>class-property-specifier</em>, or</li>
<li>is a union with no user-declared special member functions, or</li>
<li>satisfies all of the following:
<ul>
<li>when an object of type <code class="sourceCode default">C</code> is
direct-initialized from an xvalue of type
<code class="sourceCode default">C</code>, overload resolution would
select a constructor that is neither user-provided nor deleted, and</li>
<li>when an xvalue of type <code class="sourceCode default">C</code> is
assigned to an object of type <code class="sourceCode default">C</code>,
overload resolution would select an assignment operator that is neither
user-provided nor deleted, and</li>
<li>it has a destructor that is neither user-provided nor deleted.</li>
</ul></li>
</ul>
<p><span class="marginalizedparent"><a class="marginalized">h</a></span>
[<em>Note 5:</em> Accessibility of the special member functions is not
relevant. —<em>end note</em>]</p>
<p><span class="marginalizedparent"><a class="marginalized">i</a></span>
[<em>Note 6:</em> Trivially copyable classes are replaceable unless they
have deleted special members. —<em>end note</em>]</p>
</div>
<p><span class="marginalizedparent"><a class="marginalized">3</a></span>
A class <code class="sourceCode cpp">S</code> is a <em>standard-layout
class</em> if it:</p>
<p><span class="marginalizedparent"><a class="marginalized">(3.1)</a></span>
…</p>
<h2 data-number="17.6" id="add-feature-macros"><span class="header-section-number">17.6</span> Add feature macros<a href="#add-feature-macros" class="self-link"></a></h2>
<p>Add a
<code class="sourceCode cpp">__cpp_trivial_relocatability</code>
feature-test macro to the table in <span>15.11
<a href="https://wg21.link/N4993#cpp.predefined">[cpp.predefined]</a></span>,
set to the date of adoption.</p>
<p>…</p>
<h2 data-number="17.7" id="library-wording"><span class="header-section-number">17.7</span> Library wording<a href="#library-wording" class="self-link"></a></h2>
<blockquote>
<p><strong>Design note:</strong> <em>The first paragraph explicitly
captures the status quo that these class</em> <em>properties — the whole
set specified in <span>11.2
<a href="https://wg21.link/N4993#class.prop">[class.prop]</a></span> —
are</em> <em>deliberately left as a quality of implementation
feature.</em></p>
<p><em>The second paragraph addresses permission to add the new
annotation wherever</em> <em>an implementation might find it useful,
without being constrained by its</em> <em>absence from the library
specification, much like we grant permission to add</em>
<code class="sourceCode cpp"><span class="kw">noexcept</span></code>
<em>specifications to functions of the implementation’s choosing.</em>
<em>The specification really needs only the second paragraph, but adding
a</em> <em>section with the first paragraph gives us somewhere to hang
the wording.</em></p>
</blockquote>
<div class="add" style="color: #006e28">

<h3 class="unnumbered" id="x-properties-of-library-classes-library.class.props">16.4.6.X
Properties of library classes [library.class.props]<a href="#x-properties-of-library-classes-library.class.props" class="self-link"></a></h3>
<p><span class="marginalizedparent"><a class="marginalized">1</a></span>
Unless specifically stated, it is unspecified whether any class
described in Clause 17 through Clause 34 and Annex D is a trivial class,
a trivially copyable class, a trivially relocatable class, a
standard-layout class, or an implicit-lifetime class (<span>11.2
<a href="https://wg21.link/N4993#class.prop">[class.prop]</a></span>).</p>
</div>
<blockquote>
<p><strong>LWG Wording Note</strong>: The concepts of relocation and
replacement are described extensively in this paper but are not defined
in the wording. Describing the constraints on an implementation’s use of
<code class="sourceCode cpp">trivially_relocatable_if_eligible</code>
and <code class="sourceCode cpp">replaceable_if_eligible</code> is,
therefore, difficult. LWG might want to reword the blanket permissions
below.</p>
</blockquote>
<div class="add" style="color: #006e28">
<p><span class="marginalizedparent"><a class="marginalized">2</a></span>
An implementation may add the <em>class-property-specifier</em> <code class="sourceCode default">trivially_relocatable_if_eligible</code> to
any class for which trivial relocation would be semantically equivalent
to move-construction of the destination object followed by destruction
of the source object.</p>
<p><span class="marginalizedparent"><a class="marginalized">3</a></span>
An implementation may add the <em>class-property-specifier</em>
<code class="sourceCode default">replaceable_if_eligible</code> to any
class for which move assignment is semantically equivalent to destroying
the assigned-to object, then move-constructing a new object in its
place.</p>
</div>
<h2 data-number="17.8" id="add-new-type-traits"><span class="header-section-number">17.8</span> Add new type traits<a href="#add-new-type-traits" class="self-link"></a></h2>
<h3 class="unnumbered" id="meta.type.synop-header-type_traits-synopsis"><span>21.3.3
<a href="https://wg21.link/N4993#meta.type.synop">[meta.type.synop]</a></span>
Header <code class="sourceCode cpp"><span class="op">&lt;</span>type_traits<span class="op">&gt;</span></code>
synopsis<a href="#meta.type.synop-header-type_traits-synopsis" class="self-link"></a></h3>
<div class="add" style="color: #006e28">

<div class="sourceCode" id="cb30"><pre class="sourceCode default default"><code class="sourceCode default"><span id="cb30-1"><a href="#cb30-1" aria-hidden="true" tabindex="-1"></a>template&lt; class T &gt;</span>
<span id="cb30-2"><a href="#cb30-2" aria-hidden="true" tabindex="-1"></a>struct is_replaceable;</span>
<span id="cb30-3"><a href="#cb30-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb30-4"><a href="#cb30-4" aria-hidden="true" tabindex="-1"></a>template&lt; class T &gt;</span>
<span id="cb30-5"><a href="#cb30-5" aria-hidden="true" tabindex="-1"></a>struct is_trivially_relocatable;</span>
<span id="cb30-6"><a href="#cb30-6" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb30-7"><a href="#cb30-7" aria-hidden="true" tabindex="-1"></a>template&lt; class T &gt;</span>
<span id="cb30-8"><a href="#cb30-8" aria-hidden="true" tabindex="-1"></a>struct is_nothrow_relocatable;</span>
<span id="cb30-9"><a href="#cb30-9" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb30-10"><a href="#cb30-10" aria-hidden="true" tabindex="-1"></a>template&lt; class T &gt;</span>
<span id="cb30-11"><a href="#cb30-11" aria-hidden="true" tabindex="-1"></a>inline constexpr bool is_replaceable_v = is_replaceable&lt;T&gt;::value;</span>
<span id="cb30-12"><a href="#cb30-12" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb30-13"><a href="#cb30-13" aria-hidden="true" tabindex="-1"></a>template&lt; class T &gt;</span>
<span id="cb30-14"><a href="#cb30-14" aria-hidden="true" tabindex="-1"></a>inline constexpr bool is_trivially_relocatable_v = is_trivially_relocatable&lt;T&gt;::value;</span>
<span id="cb30-15"><a href="#cb30-15" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb30-16"><a href="#cb30-16" aria-hidden="true" tabindex="-1"></a>template&lt; class T &gt;</span>
<span id="cb30-17"><a href="#cb30-17" aria-hidden="true" tabindex="-1"></a>inline constexpr bool is_nothrow_relocatable_v = is_nothrow_relocatable&lt;T&gt;::value;</span></code></pre></div>

</div>
<h3 class="unnumbered" id="meta.unary.prop-type-properties"><span>21.3.5.4
<a href="https://wg21.link/N4993#meta.unary.prop">[meta.unary.prop]</a></span>
Type properties<a href="#meta.unary.prop-type-properties" class="self-link"></a></h3>
<div class="add" style="color: #006e28">

<table>
<colgroup>
<col style="width: 28%" />
<col style="width: 37%" />
<col style="width: 33%" />
</colgroup>
<thead>
<tr class="header">
<th><div style="text-align:center">
<strong>Template</strong>
</div></th>
<th><div style="text-align:center">
<strong>Condition</strong>
</div></th>
<th><div style="text-align:center">
<strong>Preconditions</strong>
</div></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td><code class="sourceCode default">template&lt;class T&gt; struct</code>
<code class="sourceCode default">is_replaceable;</code></td>
<td><code class="sourceCode default">T</code> is a replaceable type
(<span>6.8.1
<a href="https://wg21.link/N4993#basic.types.general">[basic.types.general]</a></span>)</td>
<td><code class="sourceCode default">remove_all_extents_t&lt;T&gt;</code>
shall be a complete type or <em>cv</em>
<code class="sourceCode default">void</code></td>
</tr>
<tr class="even">
<td><code class="sourceCode default">template&lt;class T&gt; struct</code>
<code class="sourceCode default">is_trivially_relocatable;</code></td>
<td><code class="sourceCode default">T</code> is a trivially relocatable
type (<span>6.8.1
<a href="https://wg21.link/N4993#basic.types.general">[basic.types.general]</a></span>)</td>
<td><code class="sourceCode default">remove_all_extents_t&lt;T&gt;</code>
shall be a complete type or <em>cv</em>
<code class="sourceCode default">void</code></td>
</tr>
<tr class="odd">
<td><code class="sourceCode default">template&lt;class T&gt; struct</code>
<code class="sourceCode default">is_nothrow_relocatable;</code></td>
<td><code class="sourceCode default">is_trivially_relocatable_v&lt;T&gt; ||</code>
<code class="sourceCode default">is_nothrow_move_constructible_v&lt;T&gt;</code></td>
<td><code class="sourceCode default">remove_all_extents_t&lt;T&gt;</code>
shall be a complete type or <em>cv</em>
<code class="sourceCode default">void</code></td>
</tr>
</tbody>
</table>

</div>
<h2 data-number="17.9" id="specify-the-compiler-magic-functions"><span class="header-section-number">17.9</span> Specify the compiler-magic
functions<a href="#specify-the-compiler-magic-functions" class="self-link"></a></h2>
<p>Add to the <code class="sourceCode cpp"><span class="op">&lt;</span>memory<span class="op">&gt;</span></code>
header synopsis in <span>20.2.2
<a href="https://wg21.link/N4993#memory.syn">[memory.syn]</a></span>p3.</p>
<h3 class="unnumbered" id="memory.syn-header-memory-synopsis"><span>20.2.2
<a href="https://wg21.link/N4993#memory.syn">[memory.syn]</a></span>
Header <code class="sourceCode cpp"><span class="op">&lt;</span>memory<span class="op">&gt;</span></code>
synopsis<a href="#memory.syn-header-memory-synopsis" class="self-link"></a></h3>
<!-- lah: All the "ng"s of "freestanding" extended outside the code box. -->
<!-- ajm: Undented all back by 2 spaces. Note preserved for future reference -->
<div class="sourceCode" id="cb31"><pre class="sourceCode default"><code class="sourceCode default"><span id="cb31-1"><a href="#cb31-1" aria-hidden="true" tabindex="-1"></a>// 20.2.6, explicit lifetime management</span>
<span id="cb31-2"><a href="#cb31-2" aria-hidden="true" tabindex="-1"></a>template&lt;class T&gt;</span>
<span id="cb31-3"><a href="#cb31-3" aria-hidden="true" tabindex="-1"></a>  T* start_lifetime_as(void* p) noexcept;                                     // freestanding</span>
<span id="cb31-4"><a href="#cb31-4" aria-hidden="true" tabindex="-1"></a>template&lt;class T&gt;</span>
<span id="cb31-5"><a href="#cb31-5" aria-hidden="true" tabindex="-1"></a>  const T* start_lifetime_as(const void* p) noexcept;                         // freestanding</span>
<span id="cb31-6"><a href="#cb31-6" aria-hidden="true" tabindex="-1"></a>template&lt;class T&gt;</span>
<span id="cb31-7"><a href="#cb31-7" aria-hidden="true" tabindex="-1"></a>  volatile T* start_lifetime_as(volatile void* p) noexcept;                   // freestanding</span>
<span id="cb31-8"><a href="#cb31-8" aria-hidden="true" tabindex="-1"></a>template&lt;class T&gt;</span>
<span id="cb31-9"><a href="#cb31-9" aria-hidden="true" tabindex="-1"></a>  const volatile T* start_lifetime_as(const volatile void* p) noexcept;       // freestanding</span>
<span id="cb31-10"><a href="#cb31-10" aria-hidden="true" tabindex="-1"></a>template&lt;class T&gt;</span>
<span id="cb31-11"><a href="#cb31-11" aria-hidden="true" tabindex="-1"></a>  T* start_lifetime_as_array(void* p, size_t n) noexcept;                     // freestanding</span>
<span id="cb31-12"><a href="#cb31-12" aria-hidden="true" tabindex="-1"></a>template&lt;class T&gt;</span>
<span id="cb31-13"><a href="#cb31-13" aria-hidden="true" tabindex="-1"></a>  const T* start_lifetime_as_array(const void* p, size_t n) noexcept;         // freestanding</span>
<span id="cb31-14"><a href="#cb31-14" aria-hidden="true" tabindex="-1"></a>template&lt;class T&gt;</span>
<span id="cb31-15"><a href="#cb31-15" aria-hidden="true" tabindex="-1"></a>  volatile T* start_lifetime_as_array(volatile void* p, size_t n) noexcept;   // freestanding</span>
<span id="cb31-16"><a href="#cb31-16" aria-hidden="true" tabindex="-1"></a>template&lt;class T&gt;</span>
<span id="cb31-17"><a href="#cb31-17" aria-hidden="true" tabindex="-1"></a>  const volatile T* start_lifetime_as_array(const volatile void* p,</span>
<span id="cb31-18"><a href="#cb31-18" aria-hidden="true" tabindex="-1"></a>                                            size_t n) noexcept;               // freestanding</span></code></pre></div>
<div class="add" style="color: #006e28">

<div class="sourceCode" id="cb32"><pre class="sourceCode default default"><code class="sourceCode default"><span id="cb32-1"><a href="#cb32-1" aria-hidden="true" tabindex="-1"></a>template &lt;class T&gt;</span>
<span id="cb32-2"><a href="#cb32-2" aria-hidden="true" tabindex="-1"></a>  T* trivially_relocate(T* first, T* last, T* result);                        // freestanding</span>
<span id="cb32-3"><a href="#cb32-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb32-4"><a href="#cb32-4" aria-hidden="true" tabindex="-1"></a>template &lt;class T&gt;</span>
<span id="cb32-5"><a href="#cb32-5" aria-hidden="true" tabindex="-1"></a>  constexpr T* relocate(T* first, T* last, T* result);                        // freestanding</span></code></pre></div>

</div>
<h3 class="unnumbered" id="obj.lifetime-explicit-lifetime-management"><span>20.2.6
<a href="https://wg21.link/N4993#obj.lifetime">[obj.lifetime]</a></span>
Explicit lifetime management<a href="#obj.lifetime-explicit-lifetime-management" class="self-link"></a></h3>
<div class="add" style="color: #006e28">

<div class="sourceCode" id="cb33"><pre class="sourceCode default default"><code class="sourceCode default"><span id="cb33-1"><a href="#cb33-1" aria-hidden="true" tabindex="-1"></a>template &lt;class T&gt;</span>
<span id="cb33-2"><a href="#cb33-2" aria-hidden="true" tabindex="-1"></a>  T* trivially_relocate(T* first, T* last, T* result);</span></code></pre></div>
<p><span class="marginalizedparent"><a class="marginalized">a</a></span>
<em>Mandates:</em> <code class="sourceCode default">T</code> is a
complete type, and <code class="sourceCode default">is_trivially_relocatable_v&lt;T&gt; &amp;&amp; !is_const_v&lt;T&gt;</code>
is <code class="sourceCode default">true</code>.</p>
<p><span class="marginalizedparent"><a class="marginalized">b</a></span>
<em>Preconditions:</em></p>
<p><span class="marginalizedparent"><a class="marginalized">(b.1)</a></span> —
<span class="math inline">\([\)</span><code class="sourceCode default">first</code>,
<code class="sourceCode default">last</code><span class="math inline">\()\)</span> is a valid range.</p>
<p><span class="marginalizedparent"><a class="marginalized">(b.2)</a></span> —
<span class="math inline">\([\)</span><code class="sourceCode default">result</code>,
<code class="sourceCode default">result + (last - first)</code><span class="math inline">\()\)</span> denotes a region of storage that is a
subset of the region of storage reachable through (<span>6.8.4
<a href="https://wg21.link/N4993#basic.compound">[basic.compound]</a></span>)
<code class="sourceCode default">result</code> and suitably aligned for
the type <code class="sourceCode default">T</code>.</p>
<p><span class="marginalizedparent"><a class="marginalized">(b.3)</a></span> —
<code class="sourceCode default">(last - first) != 1</code>, or
<code class="sourceCode default">*first</code> points to a complete
object (<span>6.7.2
<a href="https://wg21.link/N4993#intro.object">[intro.object]</a></span>).</p>
<p><span class="marginalizedparent"><a class="marginalized">c</a></span>
<em>Postconditions:</em></p>
<p>No effect if
<code class="sourceCode default">result == first</code>.</p>
<p>Otherwise, the range denoted by <span class="math inline">\([\)</span><code class="sourceCode default">result</code>,
<code class="sourceCode default">result + (last - first)</code><span class="math inline">\()\)</span> contains objects (including subobjects)
whose lifetime has begun and whose object representations are the
original object representations of the corresponding objects in the
source range <span class="math inline">\([\)</span><code class="sourceCode default">first</code>,
<code class="sourceCode default">last</code><span class="math inline">\()\)</span>. If any of the aforementioned objects
is a union, its active member is the same as that of the corresponding
union in the source range. If any of the aforementioned objects has a
non-static data member of reference type, that reference refers to the
same entity as does the corresponding reference in the source range. The
lifetime of the original objects in the source range has ended.</p>
<p><span class="marginalizedparent"><a class="marginalized">d</a></span>
<em>Returns:</em>
<code class="sourceCode default">result + (last - first)</code>.</p>
<p><span class="marginalizedparent"><a class="marginalized">e</a></span>
<em>Throws:</em> Nothing.</p>
<p><span class="marginalizedparent"><a class="marginalized">f</a></span>
<em>Complexity:</em> Linear in the length of the source range.</p>
<p><span class="marginalizedparent"><a class="marginalized">g</a></span>
<em>Remarks:</em> No constructors or destructors are invoked.</p>
<!-- jmb and cj believe this note is not helpful. -->
<!--
[i]{.pnum}
\[_Note:_ A likely implementation will use compiler-specific functionality
that simply calls `memmove` and updates its notion of the object lifetime.
---_end note_\]
 -->
<div class="sourceCode" id="cb34"><pre class="sourceCode default default"><code class="sourceCode default"><span id="cb34-1"><a href="#cb34-1" aria-hidden="true" tabindex="-1"></a>template &lt;class T&gt;</span>
<span id="cb34-2"><a href="#cb34-2" aria-hidden="true" tabindex="-1"></a>  constexpr T* relocate(T* first, T* last, T* result);</span></code></pre></div>
<p><span class="marginalizedparent"><a class="marginalized">u</a></span>
<em>Mandates</em>: <code class="sourceCode default">is_nothrow_relocatable_v&lt;T&gt; &amp;&amp; !is_const_v&lt;T&gt;</code>
is <code class="sourceCode default">true</code>.</p>
<p><span class="marginalizedparent"><a class="marginalized">v</a></span>
<em>Preconditions</em>:
<code class="sourceCode default">(last - first) != 1</code>, or
<code class="sourceCode default">*first</code> points to a complete
object (<span>6.7.2
<a href="https://wg21.link/N4993#intro.object">[intro.object]</a></span>).</p>
<p><span class="marginalizedparent"><a class="marginalized">w</a></span>
<em>Effects</em>: No effect if
<code class="sourceCode default">result == first</code>; otherwise, if
not called during constant evaluation and
<code class="sourceCode default">T</code> is trivially relocatable, then
has effects equivalent to <code class="sourceCode default">trivially_relocate(first, last, result)</code>;
otherwise, for each element in <span class="math inline">\([\)</span><code class="sourceCode default">first</code>,
<code class="sourceCode default">last</code><span class="math inline">\()\)</span>, move constructs that element to the
corresponding location in <span class="math inline">\([\)</span><code class="sourceCode default">result</code>,
<code class="sourceCode default">result + (last - first)</code><span class="math inline">\()\)</span> and then invokes that element’s
destructor.</p>
<p><span class="marginalizedparent"><a class="marginalized">x</a></span>
<em>Remarks:</em> Overlapping ranges are supported.</p>
<p><span class="marginalizedparent"><a class="marginalized">y</a></span>
<em>Returns:</em>
<code class="sourceCode default">result + (last-first)</code>.</p>
<p><span class="marginalizedparent"><a class="marginalized">z</a></span>
<em>Throws</em>: Nothing.</p>
</div>
<h3 data-number="17.9.1" id="feature-test-macro"><span class="header-section-number">17.9.1</span> Feature-test macro<a href="#feature-test-macro" class="self-link"></a></h3>
<p>Add a new
<code class="sourceCode cpp">__cpp_lib_trivially_relocatable</code>
feature-test macro in [version.syn]:</p>
<div class="sourceCode" id="cb35"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb35-1"><a href="#cb35-1" aria-hidden="true" tabindex="-1"></a><span class="pp">#define __cpp_lib_trivially_relocatable </span><span class="dv">20</span><span class="er">XXXXL</span><span class="pp"> </span><span class="co">// also in &lt;memory&gt;, &lt;type_traits&gt;</span></span></code></pre></div>
<h1 data-number="18" id="acknowledgements"><span class="header-section-number">18</span> Acknowledgements<a href="#acknowledgements" class="self-link"></a></h1>
<p>This document is written in Markdown and depends on the extensions in
<a href="https://pandoc.org/MANUAL.html#pandocs-markdown"><code class="sourceCode cpp">pandoc</code></a>
and <a href="https://github.com/mpark/wg21"><code class="sourceCode cpp">mpark<span class="op">/</span>wg21</code></a>,
and we would like to thank the authors of those extensions and
associated libraries.</p>
<p>The authors would also like to thank Brian Bi for his assistance in
proofreading this paper, especially the proposed Core wording.
Additional thanks to Jens Maurer who helped to greatly refine the
wording in advance of its first Core review.</p>
<p>Additional thanks are due to Giuseppe D’Angelo for clearly
articulating weaknesses in our earlier proposals and working with us to
improve the specification and to Louis Dionne for authoring <span class="citation" data-cites="P3516R0">[<a href="https://isocpp.org/files/papers/P3516R0.html" role="doc-biblioref">P3516R0</a>]</span>, which allows for a complete
consideration of the consumer interface for relocation.</p>
<p>Also, this paper has been greatly improved by feedback from Arthur
O’Dwyer, author of <span class="citation" data-cites="P1144">[<a href="https://wg21.link/p1144" role="doc-biblioref">P1144</a>]</span>,
who corrected many bad assumptions we made about his paper and helped
bring the technical differences into focus. We also benefited from
several examples he shared to help illustrate those differences and
misunderstandings.</p>
<!--
I believe we understand what we want the implementation of swap_value_representations to do:
* Swap the range of bytes that are not padding bytes
* leave lifetimes of objects that have corresponding objects alone
* start/end lifetimes of objects that do not have corresponding objects, or where the corresponding object is not replaceable
* active union members are properly still active
* references now reference what the corresponding source reference referenced
* objects created withiin storage that is being swapped are also transferred along (if they are trivially copyable or trivially relocatable)

We expect an implementation to just do the first thing --- shift around a bunch of bytes --- and then make sure that the right object lifetimes are maintained (or no assumption is made that those object lifetimes are *not* maintained).
Our implementation of swap_value_representations currently just does that --- although it probably also stamps on nested padding bits, that's commonly assumed to not matter.

Regarding object lifetimes,
* The top-level objects and their base classes, including their types, should be left alone.  We just need to talk about the value representation of the object (if it has one) or what happens to subobjects (otherwise).
* We should maintain object lifetime of an object nested within the operands if:
  * The object's type is trivially relocatable
  * The object's type if replaceable (need this, otherwise we end up changing the referents of references within their lifetimes)
  * There is a corresponding object of the same type being swapped with.
* If any of the above are *not* true, we instead want to start the lifetimes of new objects/end the lifetimes of old object, just as a call to trivially_relocate would do.   The only difference from trivially_relocate is that we want to be more careful to not step on padding bits (we are not writing into uninitialized storage, we are aiming to just write over the things with values.

So here is the current wording we have for swap_value_representations:
_Postconditions:_
`a` has the value representation that `b` had prior to this function call; `b`
has the value representation that `a` had prior to this function call; both
objects and all their base class subobjects retain their original dynamic types.
* For every non-base object `c` within `a` with a corresponding object `d`
  within `b`, `c` has the value representation that `d` had prior to this
  function call and `d` has the value representation that `c` had prior to this
  function call.  If `c` and `d` are unions, the active member of each is the
  member that was the active member of the other one prior to this function call.
* For every trivially relocatable object `x` within `a` or `b`, create a new
  object `y` at the same relative location within the other enclosing object
  having the value `x` had prior to this function call and end the lifetime of
  `x`.  If `y` is a union, its active member is the same member that `x` had
  prior to this function call.
* End the lifetime of all other non-base objects within `a` and `b`.

And here is my updated version that tries to cover the the above concerns --- note that It's basically just saying "swap the bits of anything with a value representation, start and end lifetimes correctly".
_Postconditions_:
For every object within its lifetime `u` of type `U` nested within `a` or `b` that is a not a base-class subobject of `a` or `b`,  where `v` is the corresponding object nested within the other operand (`b` or `a`):
* If `U` is trivially copyable, and `v` is an object within its lifetime, then `v` has the value representation that `u` had prior to this function call;
* If `U` is a union type, then the active member of `v` is the active member `u` had prior to this function call;
* If `U` has reference type, the `v` is bound to the same object that `u` was bound to prior to this function call;
* If `U` is not replaceable, or `v` is not within its lifetime, then end the lifetime of `u` and start the lifetime of `v`.
[Note: The lifetimes of `a`, `b`, their bases, and any replaceable objects whose corresponding object is also within its lifetime are all left unchanged by this function. ]
[Note: The above applies to all objects within the footprints of `a` and `b`, and is equivalent to swapping all no-padding bits of `a` and `b` that do not encode the dynamic type of `a` or `b`.]

I'm not 100% sure about the formulation of the notes, but I think we want something to unwrap the scary wording and explain that the actual effect is really really simple.     I would put something on both points in the notes either way, even if they get stripped out during wording review.

Thoughts?

-->
<h1 data-number="19" id="bibliography"><span class="header-section-number">19</span> References<a href="#bibliography" class="self-link"></a></h1>
<div id="refs" class="references csl-bib-body hanging-indent" data-entry-spacing="1" role="doc-bibliography">
<div id="ref-CWG1734" class="csl-entry" role="doc-biblioentry">
[CWG1734] James Widman. 2013-08-09. Nontrivial deleted copy functions.
<a href="https://wg21.link/cwg1734"><div class="csl-block">https://wg21.link/cwg1734</div></a>
</div>
<div id="ref-N4993" class="csl-entry" role="doc-biblioentry">
[N4993] Thomas Köppe. 2024-10-16. Working Draft, Programming Languages —
C++. <a href="https://wg21.link/n4993"><div class="csl-block">https://wg21.link/n4993</div></a>
</div>
<div id="ref-P1144" class="csl-entry" role="doc-biblioentry">
[P1144] Arthur O’Dwyer. std::is_trivially_relocatable. <a href="https://wg21.link/p1144"><div class="csl-block">https://wg21.link/p1144</div></a>
</div>
<div id="ref-P2786R10" class="csl-entry" role="doc-biblioentry">
[P2786R10] Pablo Halpern, Alisdair Meredith, Joshua Berne, Corentin
Jabot, Pablo Halpern, Lori Hughes. 2024-11-21. Trivial Relocatability
For C++26. <a href="https://wg21.link/p2786r10"><div class="csl-block">https://wg21.link/p2786r10</div></a>
</div>
<div id="ref-P2786R11" class="csl-entry" role="doc-biblioentry">
[P2786R11] Pablo Halpern, Joshua Berne, Corentin Jabot, Pablo Halpern,
Lori Hughes. 2024-12-17. Trivial Relocatability For C++26. <a href="https://wg21.link/p2786r11"><div class="csl-block">https://wg21.link/p2786r11</div></a>
</div>
<div id="ref-P2786R6" class="csl-entry" role="doc-biblioentry">
[P2786R6] Mungo Gill, Alisdair Meredith. 2024-05-21. Trivial
Relocatability For C++26. <a href="https://wg21.link/p2786r6"><div class="csl-block">https://wg21.link/p2786r6</div></a>
</div>
<div id="ref-P2786R9" class="csl-entry" role="doc-biblioentry">
[P2786R9] Pablo Halpern, Alisdair Meredith, Joshua Berne, Corentin
Jabot, Pablo Halpern, Lori Hughes. 2024-11-16. Trivial Relocatability
For C++26. <a href="https://wg21.link/p2786r9"><div class="csl-block">https://wg21.link/p2786r9</div></a>
</div>
<div id="ref-P2839R0" class="csl-entry" role="doc-biblioentry">
[P2839R0] Brian Bi, Joshua Berne. 2023-05-15. Nontrivial relocation via
a new <span>“owning reference”</span> type. <a href="https://wg21.link/p2839r0"><div class="csl-block">https://wg21.link/p2839r0</div></a>
</div>
<div id="ref-P2959R0" class="csl-entry" role="doc-biblioentry">
[P2959R0] Alisdair Meredith. 2023-10-15. Container Relocation. <a href="https://wg21.link/p2959r0"><div class="csl-block">https://wg21.link/p2959r0</div></a>
</div>
<div id="ref-P3239R0" class="csl-entry" role="doc-biblioentry">
[P3239R0] Alisdair Meredith. 2024-05-22. A Relocating Swap. <a href="https://wg21.link/p3239r0"><div class="csl-block">https://wg21.link/p3239r0</div></a>
</div>
<div id="ref-P3516R0" class="csl-entry" role="doc-biblioentry">
[P3516R0] Louis Dionne and Giuseppe D’Angelo. Uninitialized algorithms
for relocation. <a href="https://isocpp.org/files/papers/P3516R0.html"><div class="csl-block">https://isocpp.org/files/papers/P3516R0.html</div></a>
</div>
</div>
<section class="footnotes footnotes-end-of-document" role="doc-endnotes">
<hr />
<ol>
<li id="fn1" role="doc-endnote"><p>All citations to the Standard are to
working draft N4993 unless otherwise specified.<a href="#fnref1" class="footnote-back" role="doc-backlink">↩︎</a></p></li>
<li id="fn2" role="doc-endnote"><p>Much rationale related to
<strong>trivial relocation</strong> can be found in <span class="citation" data-cites="P2786R6">[<a href="https://wg21.link/p2786r6" role="doc-biblioref">P2786R6</a>]</span>.<a href="#fnref2" class="footnote-back" role="doc-backlink">↩︎</a></p></li>
<li id="fn3" role="doc-endnote"><p>This implementation can be seen
compiling on Compiler Explorer here: <a href="https://compiler-explorer.com/z/q7GY3q6cn">compiler-explorer</a>.<a href="#fnref3" class="footnote-back" role="doc-backlink">↩︎</a></p></li>
<li id="fn4" role="doc-endnote"><p>This implementation can be seen
compiling on Compiler Explorer here: <a href="https://compiler-explorer.com/z/z3M8KdqW8">compiler-explorer</a>.<a href="#fnref4" class="footnote-back" role="doc-backlink">↩︎</a></p></li>
</ol>
</section>
</div>
</div>
</body>
</html>
