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<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.comparisons"></a><a class="link" href="comparisons.html" title="Comparisons to Other Open Source Libraries">Comparisons to Other Open Source
Libraries</a>
</h2></div></div></div>
<p>
We've run our performance tests both for our own code, and against other open
source implementations of the same functions. The results are presented below
to give you a rough idea of how they all compare.
</p>
<div class="caution"><table border="0" summary="Caution">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../doc/src/images/caution.png"></td>
<th align="left">Caution</th>
</tr>
<tr><td align="left" valign="top"><p>
You should exercise extreme caution when interpreting these results, relative
performance may vary by platform, the tests use data that gives good code
coverage of <span class="emphasis"><em>our</em></span> code, but which may skew the results
towards the corner cases. Finally, remember that different libraries make
different choices with regard to performance verses numerical stability.
</p></td></tr>
</table></div>
<h4>
<a name="math_toolkit.comparisons.h0"></a>
<span class="phrase"><a name="math_toolkit.comparisons.comparison_to_gsl_1_13_and_cephe"></a></span><a class="link" href="comparisons.html#math_toolkit.comparisons.comparison_to_gsl_1_13_and_cephe">Comparison
to GSL-1.13 and Cephes</a>
</h4>
<p>
All the results were measured on a 2.0GHz Intel T5800 Core 2 Duo, 4Gb RAM,
Windows Vista machine, with the test program compiled with Microsoft Visual
C++ 2009 using the /Ox option.
</p>
<div class="informaltable"><table class="table">
<colgroup>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
Function
</p>
</th>
<th>
<p>
Boost
</p>
</th>
<th>
<p>
GSL-1.9
</p>
</th>
<th>
<p>
Cephes
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
<a class="link" href="powers/cbrt.html" title="cbrt">cbrt</a>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(4.873e-007s)</p>
<p>
</p>
</td>
<td>
<p>
N/A
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(6.699e-007s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="powers/log1p.html" title="log1p">log1p</a>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.664e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(2.677e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.189e-007s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="powers/expm1.html" title="expm1">expm1</a>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(8.760e-008s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.248e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(8.169e-008s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="sf_gamma/tgamma.html" title="Gamma">tgamma</a>
</p>
</td>
<td>
<p>
</p>
<p>1.80</p>
<p> </p>
<p>(2.997e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.54</p>
<p> </p>
<p>(2.569e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.666e-007s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="sf_gamma/lgamma.html" title="Log Gamma">lgamma</a>
</p>
</td>
<td>
<p>
</p>
<p>2.20</p>
<p> </p>
<p>(3.045e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>4.14</p>
<p> </p>
<p>(5.713e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.381e-007s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="sf_erf/error_function.html" title="Error Functions">erf</a> and
<a class="link" href="sf_erf/error_function.html" title="Error Functions">erfc</a>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.483e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(7.052e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.722e-007s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_p</a> and
<a class="link" href="sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_q</a>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(6.182e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>3.57</p>
<p> </p>
<p>(2.209e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>4.29</p>
<p> </p>
<p>(2.651e-006s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inv</a>
and <a class="link" href="sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inv</a>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.943e-006s)</p>
<p>
</p>
</td>
<td>
<p>
N/A
</p>
</td>
<td>
<p>
+INF <a href="#ftn.math_toolkit.comparisons.f0" class="footnote" name="math_toolkit.comparisons.f0"><sup class="footnote">[1]</sup></a>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>
and <a class="link" href="sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibetac</a>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.670e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.16</p>
<p> </p>
<p>(1.935e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.16</p>
<p> </p>
<p>(1.935e-006s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inv</a>
and <a class="link" href="sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_inv</a>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(6.075e-006s)</p>
<p>
</p>
</td>
<td>
<p>
N/A
</p>
</td>
<td>
<p>
</p>
<p>2.45</p>
<p> </p>
<p>(1.489e-005s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="bessel/bessel_first.html" title="Bessel Functions of the First and Second Kinds">cyl_bessel_j</a>
</p>
</td>
<td>
<p>
</p>
<p>17.89<a href="#ftn.math_toolkit.comparisons.f1" class="footnote" name="math_toolkit.comparisons.f1"><sup class="footnote">[2]</sup></a></p>
<p> </p>
<p>(4.248e-005s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(5.214e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(2.374e-006s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">cyl_bessel_i</a>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(5.924e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(4.487e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(4.823e-006s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">cyl_bessel_k</a>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(2.783e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(3.927e-006s)</p>
<p>
</p>
</td>
<td>
<p>
N/A
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="bessel/bessel_first.html" title="Bessel Functions of the First and Second Kinds">cyl_neumann</a>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(4.465e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.230e-005s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(4.977e-006s)</p>
<p>
</p>
</td>
</tr>
</tbody>
<tbody class="footnotes"><tr><td colspan="4">
<div id="ftn.math_toolkit.comparisons.f0" class="footnote"><p><a href="#math_toolkit.comparisons.f0" class="para"><sup class="para">[1] </sup></a>
Cephes gets stuck in an infinite loop while trying to execute our
test cases.
</p></div>
<div id="ftn.math_toolkit.comparisons.f1" class="footnote"><p><a href="#math_toolkit.comparisons.f1" class="para"><sup class="para">[2] </sup></a>
The performance here is dominated by a few cases where the parameters
grow very large: faster asymptotic expansions are available, but
are of limited (or even frankly terrible) precision. The same issue
effects all of our Bessel function implementations, but doesn't
necessarily show in the current performance data. More investigation
is needed here.
</p></div>
</td></tr></tbody>
</table></div>
<h4>
<a name="math_toolkit.comparisons.h1"></a>
<span class="phrase"><a name="math_toolkit.comparisons.comparison_to_the_r_and_dcdflib_"></a></span><a class="link" href="comparisons.html#math_toolkit.comparisons.comparison_to_the_r_and_dcdflib_">Comparison
to the R and DCDFLIB Statistical Libraries on Windows</a>
</h4>
<p>
All the results were measured on a 2.0GHz Intel T5800 Core 2 Duo, 4Gb RAM,
Windows Vista machine, with the test program compiled with Microsoft Visual
C++ 2009, and R-2.9.2 compiled in "standalone mode" with MinGW-4.3
(R-2.9.2 appears not to be buildable with Visual C++).
</p>
<div class="table">
<a name="math_toolkit.comparisons.a_comparison_to_the_r_statistica"></a><p class="title"><b>Table 15.5. A Comparison to the R Statistical Library on Windows XP</b></p>
<div class="table-contents"><table class="table" summary="A Comparison to the R Statistical Library on Windows XP">
<colgroup>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
Statistical Function
</p>
</th>
<th>
<p>
Boost
</p>
</th>
<th>
<p>
R
</p>
</th>
<th>
<p>
DCDFLIB
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a>
CDF
</p>
</td>
<td>
<p>
</p>
<p>1.08</p>
<p> </p>
<p>(1.385e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.278e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.06</p>
<p> </p>
<p>(1.349e-006s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a>
Quantile
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(4.975e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>67.66<a href="#ftn.math_toolkit.comparisons.f2" class="footnote" name="math_toolkit.comparisons.f2"><sup class="footnote">[1]</sup></a></p>
<p> </p>
<p>(3.366e-004s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>4.23</p>
<p> </p>
<p>(2.103e-005s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial
Distribution</a> CDF
</p>
</td>
<td>
<p>
</p>
<p>1.06</p>
<p> </p>
<p>(4.503e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.81</p>
<p> </p>
<p>(7.680e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(4.239e-007s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial
Distribution</a> Quantile
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(3.254e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.15</p>
<p> </p>
<p>(3.746e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>7.25</p>
<p> </p>
<p>(2.358e-005s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy Distribution</a>
CDF
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.134e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.08</p>
<p> </p>
<p>(1.227e-007s)</p>
<p>
</p>
</td>
<td>
<p>
NA
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy Distribution</a>
Quantile
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.203e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.203e-007s)</p>
<p>
</p>
</td>
<td>
<p>
NA
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi
Squared Distribution</a> CDF
</p>
</td>
<td>
<p>
</p>
<p>1.21</p>
<p> </p>
<p>(5.021e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>2.83</p>
<p> </p>
<p>(1.176e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(4.155e-007s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi
Squared Distribution</a> Quantile
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.930e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>2.72</p>
<p> </p>
<p>(5.243e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>5.73</p>
<p> </p>
<p>(1.106e-005s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential
Distribution</a> CDF
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(3.798e-008s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>5.89</p>
<p> </p>
<p>(2.236e-007s)</p>
<p>
</p>
</td>
<td>
<p>
NA
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential
Distribution</a> Quantile
</p>
</td>
<td>
<p>
</p>
<p>1.41</p>
<p> </p>
<p>(9.006e-008s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(6.380e-008s)</p>
<p>
</p>
</td>
<td>
<p>
NA
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/f_dist.html" title="F Distribution">Fisher F Distribution</a>
CDF
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(9.556e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.34</p>
<p> </p>
<p>(1.283e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.24</p>
<p> </p>
<p>(1.183e-006s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/f_dist.html" title="F Distribution">Fisher F Distribution</a>
Quantile
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(6.987e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.33</p>
<p> </p>
<p>(9.325e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>3.16</p>
<p> </p>
<p>(2.205e-005s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma Distribution</a>
CDF
</p>
</td>
<td>
<p>
</p>
<p>1.52</p>
<p> </p>
<p>(6.240e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>3.11</p>
<p> </p>
<p>(1.279e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(4.111e-007s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma Distribution</a>
Quantile
</p>
</td>
<td>
<p>
</p>
<p>1.24</p>
<p> </p>
<p>(2.179e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>6.25</p>
<p> </p>
<p>(1.102e-005s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.764e-006s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/hypergeometric_dist.html" title="Hypergeometric Distribution">hypergeometric
Distribution</a> CDF
</p>
</td>
<td>
<p>
</p>
<p>3.60<a href="#ftn.math_toolkit.comparisons.f3" class="footnote" name="math_toolkit.comparisons.f3"><sup class="footnote">[2]</sup></a></p>
<p> </p>
<p>(5.987e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.665e-007s)</p>
<p>
</p>
</td>
<td>
<p>
NA
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/hypergeometric_dist.html" title="Hypergeometric Distribution">hypergeometric
Distribution</a> Quantile
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(5.684e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>3.53</p>
<p> </p>
<p>(2.004e-006s)</p>
<p>
</p>
</td>
<td>
<p>
NA
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic
Distribution</a> CDF
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.714e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>5.24</p>
<p> </p>
<p>(8.984e-007s)</p>
<p>
</p>
</td>
<td>
<p>
NA
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic
Distribution</a> Quantile
</p>
</td>
<td>
<p>
</p>
<p>1.02</p>
<p> </p>
<p>(2.084e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(2.043e-007s)</p>
<p>
</p>
</td>
<td>
<p>
NA
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log-normal
Distribution</a> CDF
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(3.579e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.49</p>
<p> </p>
<p>(5.332e-007s)</p>
<p>
</p>
</td>
<td>
<p>
NA
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log-normal
Distribution</a> Quantile
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(9.622e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.57</p>
<p> </p>
<p>(1.507e-006s)</p>
<p>
</p>
</td>
<td>
<p>
NA
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative
Binomial Distribution</a> CDF
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(6.227e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>2.25</p>
<p> </p>
<p>(1.403e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>2.21</p>
<p> </p>
<p>(1.378e-006s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative
Binomial Distribution</a> Quantile
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(8.594e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>43.43<a href="#ftn.math_toolkit.comparisons.f4" class="footnote" name="math_toolkit.comparisons.f4"><sup class="footnote">[3]</sup></a></p>
<p> </p>
<p>(3.732e-004s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>3.48</p>
<p> </p>
<p>(2.994e-005s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral
Chi Squared Distribution</a> CDF
</p>
</td>
<td>
<p>
</p>
<p>2.16</p>
<p> </p>
<p>(3.926e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>79.93</p>
<p> </p>
<p>(1.450e-004s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.814e-006s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral
Chi Squared Distribution</a> Quantile
</p>
</td>
<td>
<p>
</p>
<p>5.00</p>
<p> </p>
<p>(3.393e-004s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>393.90<a href="#ftn.math_toolkit.comparisons.f5" class="footnote" name="math_toolkit.comparisons.f5"><sup class="footnote">[4]</sup></a></p>
<p> </p>
<p>(2.673e-002s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(6.786e-005s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral
F Distribution</a> CDF
</p>
</td>
<td>
<p>
</p>
<p>1.59</p>
<p> </p>
<p>(1.128e-005s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(7.087e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(4.274e-006s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral
F Distribution</a> Quantile
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(4.750e-004s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.62</p>
<p> </p>
<p>(7.681e-004s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(4.274e-006s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">noncentral
T distribution</a> CDF
</p>
</td>
<td>
<p>
</p>
<p>3.41</p>
<p> </p>
<p>(1.852e-005s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(5.436e-006s)</p>
<p>
</p>
</td>
<td>
<p>
NA
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">noncentral
T distribution</a> Quantile
</p>
</td>
<td>
<p>
</p>
<p>1.31</p>
<p> </p>
<p>(5.768e-004s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span><a href="#ftn.math_toolkit.comparisons.f6" class="footnote" name="math_toolkit.comparisons.f6"><sup class="footnote">[5]</sup></a></p>
<p> </p>
<p>(4.411e-004s)</p>
<p>
</p>
</td>
<td>
<p>
NA
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal Distribution</a>
CDF
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(8.373e-008s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.68</p>
<p> </p>
<p>(1.409e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>6.01</p>
<p> </p>
<p>(5.029e-007s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal Distribution</a>
Quantile
</p>
</td>
<td>
<p>
</p>
<p>1.29</p>
<p> </p>
<p>(1.521e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.182e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>10.85</p>
<p> </p>
<p>(1.283e-006s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson
Distribution</a> CDF
</p>
</td>
<td>
<p>
</p>
<p>1.18</p>
<p> </p>
<p>(5.193e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>2.98</p>
<p> </p>
<p>(1.314e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(4.410e-007s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson
Distribution</a>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.203e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>2.20</p>
<p> </p>
<p>(2.642e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>7.86</p>
<p> </p>
<p>(9.457e-006s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students
t Distribution</a> CDF
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(8.655e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.06</p>
<p> </p>
<p>(9.166e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.04</p>
<p> </p>
<p>(8.999e-007s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students
t Distribution</a> Quantile
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(2.294e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.36</p>
<p> </p>
<p>(3.131e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>4.82</p>
<p> </p>
<p>(1.106e-005s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/weibull_dist.html" title="Weibull Distribution">Weibull
Distribution</a> CDF
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.865e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>2.33</p>
<p> </p>
<p>(4.341e-007s)</p>
<p>
</p>
</td>
<td>
<p>
NA
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/weibull_dist.html" title="Weibull Distribution">Weibull
Distribution</a> Quantile
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(3.608e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.22</p>
<p> </p>
<p>(4.410e-007s)</p>
<p>
</p>
</td>
<td>
<p>
NA
</p>
</td>
</tr>
</tbody>
<tbody class="footnotes"><tr><td colspan="4">
<div id="ftn.math_toolkit.comparisons.f2" class="footnote"><p><a href="#math_toolkit.comparisons.f2" class="para"><sup class="para">[1] </sup></a>
There are a small number of our test cases where the R library
fails to converge on a result: these tend to dominate the performance
result.
</p></div>
<div id="ftn.math_toolkit.comparisons.f3" class="footnote"><p><a href="#math_toolkit.comparisons.f3" class="para"><sup class="para">[2] </sup></a>
This result is somewhat misleading: for small values of the parameters
there is virtually no difference between the two libraries, but
for large values the Boost implementation is <span class="emphasis"><em>much</em></span>
slower, albeit with much improved precision.
</p></div>
<div id="ftn.math_toolkit.comparisons.f4" class="footnote"><p><a href="#math_toolkit.comparisons.f4" class="para"><sup class="para">[3] </sup></a>
The R library appears to use a linear-search strategy, that can
perform very badly in a small number of pathological cases, but
may or may not be more efficient in "typical" cases
</p></div>
<div id="ftn.math_toolkit.comparisons.f5" class="footnote"><p><a href="#math_toolkit.comparisons.f5" class="para"><sup class="para">[4] </sup></a>
There are a small number of our test cases where the R library
fails to converge on a result: these tend to dominate the performance
result.
</p></div>
<div id="ftn.math_toolkit.comparisons.f6" class="footnote"><p><a href="#math_toolkit.comparisons.f6" class="para"><sup class="para">[5] </sup></a>
There are a small number of our test cases where the R library
fails to converge on a result: these tend to dominate the performance
result.
</p></div>
</td></tr></tbody>
</table></div>
</div>
<br class="table-break"><h4>
<a name="math_toolkit.comparisons.h2"></a>
<span class="phrase"><a name="math_toolkit.comparisons.comparison_to_the_r_statistical_"></a></span><a class="link" href="comparisons.html#math_toolkit.comparisons.comparison_to_the_r_statistical_">Comparison
to the R Statistical Library on Linux</a>
</h4>
<p>
All the results were measured on a 2.0GHz Intel T5800 Core 2 Duo, 4Gb RAM,
Ubuntu Linux 9 machine, with the test program and R-2.9.2 compiled with GNU
G++ 4.3.3 using -O3 -DNDEBUG=1.
</p>
<div class="table">
<a name="math_toolkit.comparisons.a_comparison_to_the_r_statistic0"></a><p class="title"><b>Table 15.6. A Comparison to the R Statistical Library on Linux</b></p>
<div class="table-contents"><table class="table" summary="A Comparison to the R Statistical Library on Linux">
<colgroup>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
Statistical Function
</p>
</th>
<th>
<p>
Boost
</p>
</th>
<th>
<p>
R
</p>
</th>
<th>
<p>
DCDFLIB
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a>
CDF
</p>
</td>
<td>
<p>
</p>
<p>2.09</p>
<p> </p>
<p>(3.189e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.526e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.19</p>
<p> </p>
<p>(1.822e-006s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a>
Quantile
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.185e-005s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>30.51<a href="#ftn.math_toolkit.comparisons.f7" class="footnote" name="math_toolkit.comparisons.f7"><sup class="footnote">[1]</sup></a></p>
<p> </p>
<p>(3.616e-004s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>2.52</p>
<p> </p>
<p>(2.989e-005s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial
Distribution</a> CDF
</p>
</td>
<td>
<p>
</p>
<p>4.41</p>
<p> </p>
<p>(9.175e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>3.59</p>
<p> </p>
<p>(7.476e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(2.081e-007s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial
Distribution</a> Quantile
</p>
</td>
<td>
<p>
</p>
<p>1.57</p>
<p> </p>
<p>(6.925e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(4.407e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>7.43</p>
<p> </p>
<p>(3.274e-005s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy Distribution</a>
CDF
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.594e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.04</p>
<p> </p>
<p>(1.654e-007s)</p>
<p>
</p>
</td>
<td>
<p>
NA
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy Distribution</a>
Quantile
</p>
</td>
<td>
<p>
</p>
<p>1.21</p>
<p> </p>
<p>(1.752e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.448e-007s)</p>
<p>
</p>
</td>
<td>
<p>
NA
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi
Squared Distribution</a> CDF
</p>
</td>
<td>
<p>
</p>
<p>2.61</p>
<p> </p>
<p>(1.376e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>2.36</p>
<p> </p>
<p>(1.243e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(5.270e-007s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi
Squared Distribution</a> Quantile
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(4.252e-006s)</p>
<p>
</p>
</td>
<td>