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<title>Issue 512: Seeding subtract_with_carry_01 from a single unsigned long</title>
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<p><em>This page is a snapshot from the LWG issues list, see the <a href="lwg-active.html">Library Active Issues List</a> for more information and the meaning of <a href="lwg-active.html#NAD_Editorial">NAD Editorial</a> status.</em></p>
<h3 id="512"><a href="lwg-closed.html#512">512</a>. Seeding <code>subtract_with_carry_01</code> from a single unsigned long</h3>
<p><b>Section:</b> 29.5.4 <a href="https://wg21.link/rand.eng">[rand.eng]</a>, 99 [tr.rand.eng.sub1] <b>Status:</b> <a href="lwg-active.html#NAD_Editorial">NAD Editorial</a>
 <b>Submitter:</b> Walter Brown <b>Opened:</b> 2005-07-03 <b>Last modified:</b> 2016-01-28</p>
<p><b>Priority: </b>Not Prioritized
</p>
<p><b>View all other</b> <a href="lwg-index.html#rand.eng">issues</a> in [rand.eng].</p>
<p><b>View all issues with</b> <a href="lwg-status.html#NAD Editorial">NAD Editorial</a> status.</p>
<p><b>Discussion:</b></p>
<p>
Paragraph 8 specifies the algorithm by which a <code>subtract_with_carry_01</code> engine
is to be seeded given a single unsigned long.  This algorithm is seriously
flawed in the case where the engine parameter w (also known as word_size)
exceeds 31 [bits].  The key part of the paragraph reads:
</p>
<blockquote><p>
sets x(-r) ... x(-1) to (lcg(1)*2**(-w)) mod 1
</p></blockquote>
<p>
and so forth. 
</p>
<p>
Since the specified linear congruential engine, lcg, delivers numbers with
a maximum of 2147483563 (just a shade under 31 bits), then when w is, for
example, 48, each of the x(i) will be less than 2**-17.  The consequence
is that roughly the first 400 numbers delivered will be conspicuously
close to either zero or one.
</p>
<p>
Unfortunately, this is not an innocuous flaw:  One of the predefined engines
in [tr.rand.predef], namely <code>ranlux64_base_01</code>, has w = 48 and would exhibit
this poor behavior, while the original N1378 proposal states that these
pre-defined engines are intended to be of "known good properties."
</p>


<p id="res-512"><b>Proposed resolution:</b></p>
<p>
In 5.1.4.4 [tr.rand.eng.sub1], replace the "effects" clause for
void seed(unsigned long value = 19780503) by
</p>

<blockquote><p>
<i>Effects:</i> If <code>value == 0</code>, sets value to <code>19780503</code>. In any
case, <del>with a linear congruential generator <code>lcg</code>(i) having parameters
<code><i>m<sub>lcg</sub></i> = 2147483563</code>, <code><i>a<sub>lcg</sub></i> = 40014</code>,
<code><i>c<sub>lcg</sub></i> = 0</code>, and <code><i>lcg</i>(0) = value</code>,</del>
sets <ins>carry<code>(-1)</code> and</ins> <code>x(-r) &hellip; x(-1)</code>
<ins>as if executing</ins></p>

<blockquote><pre><ins>
linear_congruential&lt;unsigned long, 40014, 0, 2147483563&gt; lcg(value);
seed(lcg);
</ins></pre></blockquote>

<p>
<del>to <code>(<i>lcg</i>(1) &middot; 2<sup>-<i>w</i></sup>) mod 1
&hellip; (<i>lcg</i>(<i>r</i>) &middot; 2<sup>-<i>w</i></sup>) mod 1</code>,
respectively. If <code><i>x</i>(-1) == 0</code>, sets carry<code>(-1) = 2<sup>-<i>w</i></sup></code>,
else sets carry<code>(-1) = 0</code>.</del></p>
</blockquote>

<p><i>[
Jens provided revised wording post Mont Tremblant.
]</i></p>


<p><i>[
Berlin: N1932 adopts the originally-proposed resolution of the issue.
Jens's supplied wording is a clearer description of what is
intended.  Moved to Ready.
]</i></p>




<p><b>Rationale:</b></p>
<p>
Jens: I'm using an explicit type here, because fixing the
prose would probably not qualify for the (with issue <a href="lwg-closed.html#504" title="Integer types in pseudo-random number engine requirements (Status: NAD Editorial)">504</a><sup><a href="https://cplusplus.github.io/LWG/issue504" title="Latest snapshot">(i)</a></sup> even
stricter) requirements we have for seed(Gen&amp;).
</p>

<p><i>[
Portland: Subsumed by N2111.
]</i></p>






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