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52 KiB
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<html>
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<head>
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<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
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<title>Performance Tuning Macros</title>
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<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
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<link rel="up" href="../perf.html" title="Chapter 16. Performance">
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<table cellpadding="2" width="100%"><tr>
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<a accesskey="p" href="multiprecision.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../perf.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="comp_compilers.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
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</div>
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<div class="section">
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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
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<a name="math_toolkit.tuning"></a><a class="link" href="tuning.html" title="Performance Tuning Macros">Performance Tuning Macros</a>
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</h2></div></div></div>
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<p>
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There are a small number of performance tuning options that are determined
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by configuration macros. These should be set in boost/math/tools/user.hpp;
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or else reported to the Boost-development mailing list so that the appropriate
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option for a given compiler and OS platform can be set automatically in our
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configuration setup.
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</p>
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<div class="informaltable"><table class="table">
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<colgroup>
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<col>
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<col>
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</colgroup>
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<thead><tr>
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<th>
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<p>
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Macro
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</p>
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</th>
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<th>
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<p>
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Meaning
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</p>
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</th>
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</tr></thead>
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<tbody>
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<tr>
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<td>
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<p>
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BOOST_MATH_POLY_METHOD
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</p>
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</td>
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<td>
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<p>
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Determines how polynomials and most rational functions are evaluated.
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Define to one of the values 0, 1, 2 or 3: see below for the meaning
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of these values.
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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BOOST_MATH_RATIONAL_METHOD
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</p>
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</td>
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<td>
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<p>
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Determines how symmetrical rational functions are evaluated: mostly
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this only effects how the Lanczos approximation is evaluated, and
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how the <code class="computeroutput"><span class="identifier">evaluate_rational</span></code>
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function behaves. Define to one of the values 0, 1, 2 or 3: see below
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for the meaning of these values.
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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BOOST_MATH_MAX_POLY_ORDER
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</p>
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</td>
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<td>
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<p>
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The maximum order of polynomial or rational function that will be
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evaluated by a method other than 0 (a simple "for" loop).
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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BOOST_MATH_INT_TABLE_TYPE(RT, IT)
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</p>
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</td>
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<td>
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<p>
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Many of the coefficients to the polynomials and rational functions
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used by this library are integers. Normally these are stored as tables
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as integers, but if mixed integer / floating point arithmetic is
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much slower than regular floating point arithmetic then they can
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be stored as tables of floating point values instead. If mixed arithmetic
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is slow then add:
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</p>
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<p>
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#define BOOST_MATH_INT_TABLE_TYPE(RT, IT) RT
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</p>
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<p>
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to boost/math/tools/user.hpp, otherwise the default of:
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</p>
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<p>
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#define BOOST_MATH_INT_TABLE_TYPE(RT, IT) IT
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</p>
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<p>
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Set in boost/math/config.hpp is fine, and may well result in smaller
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code.
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</p>
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</td>
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</tr>
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</tbody>
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</table></div>
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<p>
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The values to which <code class="computeroutput"><span class="identifier">BOOST_MATH_POLY_METHOD</span></code>
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and <code class="computeroutput"><span class="identifier">BOOST_MATH_RATIONAL_METHOD</span></code>
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may be set are as follows:
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</p>
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<div class="informaltable"><table class="table">
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<colgroup>
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<col>
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<col>
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</colgroup>
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<thead><tr>
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<th>
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<p>
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Value
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</p>
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</th>
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<th>
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<p>
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Effect
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</p>
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</th>
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</tr></thead>
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<tbody>
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<tr>
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<td>
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<p>
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0
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</p>
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</td>
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<td>
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<p>
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The polynomial or rational function is evaluated using Horner's method,
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and a simple for-loop.
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</p>
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<p>
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Note that if the order of the polynomial or rational function is
|
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a runtime parameter, or the order is greater than the value of <code class="computeroutput"><span class="identifier">BOOST_MATH_MAX_POLY_ORDER</span></code>, then
|
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this method is always used, irrespective of the value of <code class="computeroutput"><span class="identifier">BOOST_MATH_POLY_METHOD</span></code> or <code class="computeroutput"><span class="identifier">BOOST_MATH_RATIONAL_METHOD</span></code>.
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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1
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</p>
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</td>
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<td>
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<p>
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The polynomial or rational function is evaluated without the use
|
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of a loop, and using Horner's method. This only occurs if the order
|
|
of the polynomial is known at compile time and is less than or equal
|
|
to <code class="computeroutput"><span class="identifier">BOOST_MATH_MAX_POLY_ORDER</span></code>.
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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2
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</p>
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</td>
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<td>
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<p>
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The polynomial or rational function is evaluated without the use
|
|
of a loop, and using a second order Horner's method. In theory this
|
|
permits two operations to occur in parallel for polynomials, and
|
|
four in parallel for rational functions. This only occurs if the
|
|
order of the polynomial is known at compile time and is less than
|
|
or equal to <code class="computeroutput"><span class="identifier">BOOST_MATH_MAX_POLY_ORDER</span></code>.
|
|
</p>
|
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</td>
|
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</tr>
|
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<tr>
|
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<td>
|
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<p>
|
|
3
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
The polynomial or rational function is evaluated without the use
|
|
of a loop, and using a second order Horner's method. In theory this
|
|
permits two operations to occur in parallel for polynomials, and
|
|
four in parallel for rational functions. This differs from method
|
|
"2" in that the code is carefully ordered to make the parallelisation
|
|
more obvious to the compiler: rather than relying on the compiler's
|
|
optimiser to spot the parallelisation opportunities. This only occurs
|
|
if the order of the polynomial is known at compile time and is less
|
|
than or equal to <code class="computeroutput"><span class="identifier">BOOST_MATH_MAX_POLY_ORDER</span></code>.
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
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</table></div>
|
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<p>
|
|
The performance test suite generates a report for your particular compiler
|
|
showing which method is likely to work best, the following tables show the
|
|
results for MSVC-14.0 and GCC-5.1.0 (Linux). There's not much to choose between
|
|
the various methods, but generally loop-unrolled methods perform better. Interestingly,
|
|
ordering the code to try and "second guess" possible optimizations
|
|
seems not to be such a good idea (method 3 below).
|
|
</p>
|
|
<div class="table">
|
|
<a name="math_toolkit.tuning.table_Polynomial_Method_Comparison_with_Microsoft_Visual_C_version_14_0_on_Windows_x64"></a><p class="title"><b>Table 16.3. Polynomial Method Comparison with Microsoft Visual C++ version 14.0
|
|
on Windows x64</b></p>
|
|
<div class="table-contents"><table class="table" summary="Polynomial Method Comparison with Microsoft Visual C++ version 14.0
|
|
on Windows x64">
|
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<colgroup>
|
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<col>
|
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<col>
|
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<col>
|
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<col>
|
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<col>
|
|
<col>
|
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<col>
|
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<col>
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<col>
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</colgroup>
|
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<thead><tr>
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<th>
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<p>
|
|
Function
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Method 0<br> (Double Coefficients)
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Method 0<br> (Integer Coefficients)
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Method 1<br> (Double Coefficients)
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Method 1<br> (Integer Coefficients)
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Method 2<br> (Double Coefficients)
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Method 2<br> (Integer Coefficients)
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Method 3<br> (Double Coefficients)
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Method 3<br> (Integer Coefficients)
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 2
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="grey">-</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="grey">-</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (9ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (9ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (9ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (9ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
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<p>
|
|
<span class="green">1.00<br> (9ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
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<p>
|
|
<span class="green">1.00<br> (9ns)</span>
|
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</p>
|
|
</td>
|
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</tr>
|
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<tr>
|
|
<td>
|
|
<p>
|
|
Order 3
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="red">2.08<br> (25ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
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<p>
|
|
<span class="red">2.75<br> (33ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
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<p>
|
|
<span class="green">1.08<br> (13ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.08<br> (13ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.08<br> (13ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.08<br> (13ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.08<br> (13ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
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<p>
|
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<span class="green">1.00<br> (12ns)</span>
|
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</p>
|
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</td>
|
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</tr>
|
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<tr>
|
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<td>
|
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<p>
|
|
Order 4
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="red">2.06<br> (35ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="red">2.71<br> (46ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.06<br> (18ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (17ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.06<br> (18ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.06<br> (18ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (17ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
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<p>
|
|
<span class="green">1.00<br> (17ns)</span>
|
|
</p>
|
|
</td>
|
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</tr>
|
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<tr>
|
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<td>
|
|
<p>
|
|
Order 5
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.32<br> (29ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">2.00<br> (44ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (22ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (22ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.05<br> (23ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.05<br> (23ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.05<br> (23ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.05<br> (23ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 6
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.38<br> (36ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="red">2.04<br> (53ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.08<br> (28ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (26ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.08<br> (28ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.08<br> (28ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.35<br> (35ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.38<br> (36ns)</span>
|
|
</p>
|
|
</td>
|
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</tr>
|
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<tr>
|
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<td>
|
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<p>
|
|
Order 7
|
|
</p>
|
|
</td>
|
|
<td>
|
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<p>
|
|
<span class="blue">1.43<br> (43ns)</span>
|
|
</p>
|
|
</td>
|
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<td>
|
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<p>
|
|
<span class="red">2.13<br> (64ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.03<br> (31ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (30ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.10<br> (33ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.03<br> (31ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.10<br> (33ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.13<br> (34ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 8
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.65<br> (61ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="red">2.22<br> (82ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (37ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.08<br> (40ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.14<br> (42ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.05<br> (39ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.08<br> (40ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.11<br> (41ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 9
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.39<br> (57ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="red">2.05<br> (84ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.17<br> (48ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.17<br> (48ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (41ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.05<br> (43ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.15<br> (47ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.12<br> (46ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 10
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.37<br> (63ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="red">2.20<br> (101ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.22<br> (56ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.24<br> (57ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (46ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (46ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.17<br> (54ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.17<br> (54ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 11
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.59<br> (78ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="red">2.24<br> (110ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.37<br> (67ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.29<br> (63ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.22<br> (60ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (49ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.22<br> (60ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.22<br> (60ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 12
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.46<br> (83ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="red">2.16<br> (123ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.28<br> (73ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.26<br> (72ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.02<br> (58ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (57ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.07<br> (61ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.05<br> (60ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 13
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.61<br> (90ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="red">2.55<br> (143ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.32<br> (74ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.39<br> (78ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.04<br> (58ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (56ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.11<br> (62ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.07<br> (60ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 14
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.61<br> (106ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="red">2.23<br> (147ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.45<br> (96ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.45<br> (96ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.02<br> (67ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.02<br> (67ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (66ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.09<br> (72ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 15
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.49<br> (119ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="red">2.10<br> (168ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.35<br> (108ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.35<br> (108ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (80ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (80ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (80ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.02<br> (82ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 16
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.54<br> (129ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.99<br> (167ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.49<br> (125ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.45<br> (122ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.07<br> (90ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (84ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.08<br> (91ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.02<br> (86ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 17
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.51<br> (133ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="red">2.02<br> (178ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.57<br> (138ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.50<br> (132ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.02<br> (90ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (88ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.07<br> (94ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.06<br> (93ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 18
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.53<br> (148ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="red">2.16<br> (210ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.49<br> (145ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.57<br> (152ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.11<br> (108ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.09<br> (106ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (97ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.08<br> (105ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 19
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.90<br> (194ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="red">2.27<br> (232ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.62<br> (165ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.62<br> (165ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.08<br> (110ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (102ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.17<br> (119ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.19<br> (121ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 20
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.65<br> (206ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="red">2.08<br> (260ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.45<br> (181ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.44<br> (180ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (125ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (125ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.01<br> (126ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.03<br> (129ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.tuning.table_Rational_Method_Comparison_with_Microsoft_Visual_C_version_14_0_on_Windows_x64"></a><p class="title"><b>Table 16.4. Rational Method Comparison with Microsoft Visual C++ version 14.0 on
|
|
Windows x64</b></p>
|
|
<div class="table-contents"><table class="table" summary="Rational Method Comparison with Microsoft Visual C++ version 14.0 on
|
|
Windows x64">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
<p>
|
|
Function
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Method 0<br> (Double Coefficients)
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Method 0<br> (Integer Coefficients)
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Method 1<br> (Double Coefficients)
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Method 1<br> (Integer Coefficients)
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Method 2<br> (Double Coefficients)
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Method 2<br> (Integer Coefficients)
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Method 3<br> (Double Coefficients)
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Method 3<br> (Integer Coefficients)
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 2
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="grey">-</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="grey">-</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="red">2.12<br> (89ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.95<br> (82ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (42ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (42ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (42ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (42ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 3
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="red">2.10<br> (88ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="red">2.10<br> (88ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="red">2.05<br> (86ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="red">2.10<br> (88ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.05<br> (44ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (42ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (42ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (42ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 4
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="red">2.12<br> (89ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="red">2.21<br> (93ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.98<br> (83ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="red">2.10<br> (88ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.02<br> (43ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.02<br> (43ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.02<br> (43ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (42ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 5
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.07<br> (90ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.15<br> (97ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.08<br> (91ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (84ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.45<br> (122ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.46<br> (123ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.45<br> (122ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.45<br> (122ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 6
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.16<br> (102ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.58<br> (139ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (88ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.03<br> (91ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.44<br> (127ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.44<br> (127ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.41<br> (124ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.38<br> (121ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 7
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.29<br> (121ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.44<br> (135ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.01<br> (95ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (94ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.38<br> (130ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.36<br> (128ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.33<br> (125ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.36<br> (128ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 8
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.33<br> (134ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.52<br> (154ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (101ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.08<br> (109ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.38<br> (139ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.31<br> (132ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.39<br> (140ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.37<br> (138ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 9
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.18<br> (141ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.45<br> (172ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (119ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.08<br> (128ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.13<br> (135ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.26<br> (150ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.26<br> (150ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.27<br> (151ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 10
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.29<br> (180ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.28<br> (178ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.05<br> (146ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (139ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.06<br> (147ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.06<br> (147ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.18<br> (164ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.17<br> (163ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 11
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.28<br> (187ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.28<br> (187ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.06<br> (155ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.05<br> (154ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.03<br> (151ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (146ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.19<br> (174ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.47<br> (215ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 12
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.22<br> (197ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.38<br> (223ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.04<br> (168ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.04<br> (169ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (162ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.04<br> (169ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.22<br> (198ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.52<br> (246ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 13
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.23<br> (209ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.29<br> (220ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.15<br> (196ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.10<br> (187ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (170ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.15<br> (196ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.22<br> (208ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.61<br> (273ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 14
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.28<br> (242ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.39<br> (262ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.15<br> (218ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.14<br> (216ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (189ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.01<br> (191ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.49<br> (282ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.53<br> (290ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 15
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.28<br> (260ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.34<br> (273ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.12<br> (227ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.15<br> (233ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (203ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (203ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.38<br> (280ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.47<br> (298ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 16
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.35<br> (288ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.40<br> (300ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.22<br> (261ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.18<br> (252ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (214ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.23<br> (264ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.43<br> (305ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.52<br> (325ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 17
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.16<br> (259ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.47<br> (328ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.15<br> (256ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.35<br> (302ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (223ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.22<br> (273ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.50<br> (334ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.52<br> (339ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 18
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.10<br> (273ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.46<br> (363ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.10<br> (273ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.75<br> (434ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (248ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.30<br> (322ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.41<br> (349ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.46<br> (363ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 19
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.26<br> (330ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.35<br> (352ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.24<br> (324ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.33<br> (348ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (261ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.22<br> (319ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.44<br> (377ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.46<br> (381ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Order 20
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.24<br> (330ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.60<br> (427ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.22<br> (327ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.56<br> (416ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.00<br> (267ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="green">1.19<br> (317ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.57<br> (418ns)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">1.56<br> (416ns)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><p>
|
|
[table_Polynomial_Method_Comparison_with_GNU_C_version_5_1_0_on_linux]
|
|
</p>
|
|
<p>
|
|
[table_Rational_Method_Comparison_with_GNU_C_version_5_1_0_on_linux]
|
|
</p>
|
|
</div>
|
|
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
|
<td align="left"></td>
|
|
<td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal,
|
|
Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
|
|
Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani,
|
|
Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
|
|
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
|
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
|
</p>
|
|
</div></td>
|
|
</tr></table>
|
|
<hr>
|
|
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