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<body>
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<div id="org-div-home-and-up">
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<a accesskey="h" href=""> UP </a>
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<a accesskey="H" href="index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Numerical precision</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#orgef9c58d">1. Control of the numerical precision</a></li>
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<li><a href="#orgdf8549f">2. Precision</a></li>
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<li><a href="#org5b054a7">3. Range</a></li>
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<li><a href="#orgaa262b1">4. Helper functions</a></li>
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</ul>
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</div>
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</div>
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<div id="outline-container-orgef9c58d" class="outline-2">
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<h2 id="orgef9c58d"><span class="section-number-2">1</span> Control of the numerical precision</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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Controlling numerical precision enables optimizations. Here, the
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default parameters determining the target numerical precision and
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range are defined. Following the IEEE Standard for Floating-Point
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Arithmetic (IEEE 754),
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<i>precision</i> refers to the number of significand bits and <i>range</i>
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refers to the number of exponent bits.
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</p>
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<table id="org1a75a7a" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<col class="org-right" />
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<tbody>
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<tr>
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<td class="org-left"><code>QMCKL_DEFAULT_PRECISION</code></td>
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<td class="org-right">53</td>
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</tr>
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<tr>
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<td class="org-left"><code>QMCKL_DEFAULT_RANGE</code></td>
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<td class="org-right">11</td>
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</tr>
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</tbody>
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</table>
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<div class="org-src-container">
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<pre class="src src-c"><span style="color: #a020f0;">typedef</span> <span style="color: #a020f0;">struct</span> <span style="color: #228b22;">qmckl_numprec_struct</span> {
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<span style="color: #228b22;">uint32_t</span> <span style="color: #a0522d;">precision</span>;
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<span style="color: #228b22;">uint32_t</span> <span style="color: #a0522d;">range</span>;
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} <span style="color: #228b22;">qmckl_numprec_struct</span>;
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</pre>
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</div>
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<p>
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The following functions set and get the required precision and
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range. <code>precision</code> is an integer between 2 and 53, and <code>range</code> is an
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integer between 2 and 11.
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</p>
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<p>
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The setter functions functions return a new context as a 64-bit
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integer. The getter functions return the value, as a 32-bit
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integer. The update functions return <code>QMCKL_SUCCESS</code> or
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<code>QMCKL_FAILURE</code>.
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</p>
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</div>
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</div>
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<div id="outline-container-orgdf8549f" class="outline-2">
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<h2 id="orgdf8549f"><span class="section-number-2">2</span> Precision</h2>
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<div class="outline-text-2" id="text-2">
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<p>
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<code>qmckl_context_set_numprec_precision</code> modifies the parameter for the
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numerical precision in the context.
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</p>
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<div class="org-src-container">
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<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_set_numprec_precision</span>(<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">precision</span>) {
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|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT)
|
|
<span style="color: #a020f0;">return</span> QMCKL_INVALID_CONTEXT;
|
|
|
|
<span style="color: #a020f0;">if</span> (precision < 2) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_INVALID_ARG_2,
|
|
<span style="color: #8b2252;">"qmckl_update_numprec_precision"</span>,
|
|
<span style="color: #8b2252;">"precision < 2"</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">if</span> (precision > 53) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_INVALID_ARG_2,
|
|
<span style="color: #8b2252;">"qmckl_update_numprec_precision"</span>,
|
|
<span style="color: #8b2252;">"precision > 53"</span>);
|
|
}
|
|
|
|
<span style="color: #228b22;">qmckl_context_struct</span>* <span style="color: #a020f0;">const</span> <span style="color: #a0522d;">ctx</span> = (<span style="color: #228b22;">qmckl_context_struct</span>*) context;
|
|
|
|
/* <span style="color: #b22222;">This should be always true because the context is valid</span> */
|
|
assert (ctx != <span style="color: #008b8b;">NULL</span>);
|
|
|
|
qmckl_lock(context);
|
|
{
|
|
ctx->numprec.precision = (<span style="color: #228b22;">uint32_t</span>) precision;
|
|
}
|
|
qmckl_unlock(context);
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90"><span style="color: #a020f0;">interface</span>
|
|
<span style="color: #228b22;">integer</span> (qmckl_exit_code) <span style="color: #a020f0;">function</span> <span style="color: #0000ff;">qmckl_set_numprec_precision</span>(context, precision) <span style="color: #a020f0;">bind</span>(C)
|
|
<span style="color: #a020f0;">use</span>, <span style="color: #a020f0;">intrinsic</span> :: <span style="color: #0000ff;">iso_c_binding</span>
|
|
<span style="color: #a020f0;">import</span>
|
|
<span style="color: #228b22;">integer</span> (qmckl_context), <span style="color: #a020f0;">intent</span>(in), <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> context</span>
|
|
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int32_t</span>), <span style="color: #a020f0;">intent</span>(in), <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> precision</span>
|
|
<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">qmckl_set_numprec_precision</span>
|
|
<span style="color: #a020f0;">end interface</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
<code>qmckl_get_numprec_precision</code> returns the value of the numerical precision in the context.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">int</span> <span style="color: #0000ff;">qmckl_get_numprec_precision</span>(<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>) {
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_INVALID_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_get_numprec_precision"</span>,
|
|
<span style="color: #8b2252;">""</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context_struct</span>* <span style="color: #a020f0;">const</span> <span style="color: #a0522d;">ctx</span> = (<span style="color: #228b22;">qmckl_context_struct</span>*) context;
|
|
<span style="color: #a020f0;">return</span> ctx->numprec.precision;
|
|
}
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90"><span style="color: #a020f0;">interface</span>
|
|
<span style="color: #228b22;">integer</span> (qmckl_exit_code) <span style="color: #a020f0;">function</span> <span style="color: #0000ff;">qmckl_get_numprec_precision</span>(context) <span style="color: #a020f0;">bind</span>(C)
|
|
<span style="color: #a020f0;">use</span>, <span style="color: #a020f0;">intrinsic</span> :: <span style="color: #0000ff;">iso_c_binding</span>
|
|
<span style="color: #a020f0;">import</span>
|
|
<span style="color: #228b22;">integer</span> (qmckl_context), <span style="color: #a020f0;">intent</span>(in), <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> context</span>
|
|
<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">qmckl_get_numprec_precision</span>
|
|
<span style="color: #a020f0;">end interface</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org5b054a7" class="outline-2">
|
|
<h2 id="org5b054a7"><span class="section-number-2">3</span> Range</h2>
|
|
<div class="outline-text-2" id="text-3">
|
|
<p>
|
|
<code>qmckl_set_numprec_range</code> modifies the parameter for the numerical
|
|
range in a given context.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_set_numprec_range</span>(<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">range</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT)
|
|
<span style="color: #a020f0;">return</span> QMCKL_INVALID_CONTEXT;
|
|
|
|
<span style="color: #a020f0;">if</span> (range < 2) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_INVALID_ARG_2,
|
|
<span style="color: #8b2252;">"qmckl_set_numprec_range"</span>,
|
|
<span style="color: #8b2252;">"range < 2"</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">if</span> (range > 11) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_INVALID_ARG_2,
|
|
<span style="color: #8b2252;">"qmckl_set_numprec_range"</span>,
|
|
<span style="color: #8b2252;">"range > 11"</span>);
|
|
}
|
|
|
|
<span style="color: #228b22;">qmckl_context_struct</span>* <span style="color: #a020f0;">const</span> <span style="color: #a0522d;">ctx</span> = (<span style="color: #228b22;">qmckl_context_struct</span>*) context;
|
|
|
|
/* <span style="color: #b22222;">This should be always true because the context is valid</span> */
|
|
assert (ctx != <span style="color: #008b8b;">NULL</span>);
|
|
|
|
qmckl_lock(context);
|
|
{
|
|
ctx->numprec.range = (<span style="color: #228b22;">uint32_t</span>) range;
|
|
}
|
|
qmckl_unlock(context);
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90"><span style="color: #a020f0;">interface</span>
|
|
<span style="color: #228b22;">integer</span> (qmckl_exit_code) <span style="color: #a020f0;">function</span> <span style="color: #0000ff;">qmckl_set_numprec_range</span>(context, range) <span style="color: #a020f0;">bind</span>(C)
|
|
<span style="color: #a020f0;">use</span>, <span style="color: #a020f0;">intrinsic</span> :: <span style="color: #0000ff;">iso_c_binding</span>
|
|
<span style="color: #a020f0;">import</span>
|
|
<span style="color: #228b22;">integer</span> (qmckl_context), <span style="color: #a020f0;">intent</span>(in), <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> context</span>
|
|
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int32_t</span>), <span style="color: #a020f0;">intent</span>(in), <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> range</span>
|
|
<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">qmckl_set_numprec_range</span>
|
|
<span style="color: #a020f0;">end interface</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
<code>qmckl_get_numprec_range</code> returns the value of the numerical range in the context.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">int</span> <span style="color: #0000ff;">qmckl_get_numprec_range</span>(<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>) {
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_INVALID_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_get_numprec_range"</span>,
|
|
<span style="color: #8b2252;">""</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context_struct</span>* <span style="color: #a020f0;">const</span> <span style="color: #a0522d;">ctx</span> = (<span style="color: #228b22;">qmckl_context_struct</span>*) context;
|
|
<span style="color: #a020f0;">return</span> ctx->numprec.range;
|
|
}
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="outline-container-orgaa262b1" class="outline-2">
|
|
<h2 id="orgaa262b1"><span class="section-number-2">4</span> Helper functions</h2>
|
|
<div class="outline-text-2" id="text-4">
|
|
<p>
|
|
<code>qmckl_get_numprec_epsilon</code> returns \(\epsilon = 2^{1-n}\) where <code>n</code> is the precision.
|
|
We need to remove the sign bit from the precision.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">double</span> <span style="color: #0000ff;">qmckl_get_numprec_epsilon</span>(<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>) {
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">precision</span> = qmckl_get_numprec_precision(context);
|
|
<span style="color: #a020f0;">return</span> 1. / (<span style="color: #228b22;">double</span>) (1L << (precision-2));
|
|
}
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="postamble" class="status">
|
|
<p class="author">Author: TREX CoE</p>
|
|
<p class="date">Created: 2023-08-24 Thu 08:01</p>
|
|
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
|
</div>
|
|
</body>
|
|
</html>
|