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<div class="section" lang="en">
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.perf.comparisons"></a><a class="link" href="comparisons.html" title="Comparisons to Other Open Source Libraries"> Comparisons to Other
Open Source Libraries</a>
</h3></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>
<a name="math_toolkit.perf.comparisons.comparison_to_gsl_1_13_and_cephes"></a><h5>
<a name="id1280172"></a>
<a class="link" href="comparisons.html#math_toolkit.perf.comparisons.comparison_to_gsl_1_13_and_cephes">Comparison
to GSL-1.13 and Cephes</a>
</h5>
<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="../special/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="../special/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="../special/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="../special/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="../special/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="../special/sf_erf/error_function.html" title="Error Functions">erf</a>
and <a class="link" href="../special/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="../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_p</a>
and <a class="link" href="../special/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="../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inv</a>
and <a class="link" href="../special/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 <sup>[<a name="id1281521" href="#ftn.id1281521" class="footnote">1</a>]</sup>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>
and <a class="link" href="../special/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="../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inv</a>
and <a class="link" href="../special/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="../special/bessel/bessel.html" title="Bessel Functions of the First and Second Kinds">cyl_bessel_j</a>
</p>
</td>
<td>
<p>
</p>
<p>17.89<sup>[<a name="id1281678" href="#ftn.id1281678" class="footnote">2</a>]</sup></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="../special/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="../special/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="../special/bessel/bessel.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 class="footnote"><p><sup>[<a name="ftn.id1281521" href="#id1281521" class="para">1</a>] </sup>
Cephes gets stuck in an infinite loop while trying to execute
our test cases.
</p></div>
<div class="footnote"><p><sup>[<a name="ftn.id1281678" href="#id1281678" class="para">2</a>] </sup>
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>
<a name="math_toolkit.perf.comparisons.comparison_to_the_r_and_dcdflib_statistical_libraries_on_windows"></a><h5>
<a name="id1281922"></a>
<a class="link" href="comparisons.html#math_toolkit.perf.comparisons.comparison_to_the_r_and_dcdflib_statistical_libraries_on_windows">Comparison
to the R and DCDFLIB Statistical Libraries on Windows</a>
</h5>
<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="id1281935"></a><p class="title"><b>Table 51. 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/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/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<sup>[<a name="id1282085" href="#ftn.id1282085" class="footnote">1</a>]</sup></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/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/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/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/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/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/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/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/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/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/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/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/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/dist_ref/dists/hypergeometric_dist.html" title="Hypergeometric Distribution">Hypergeometric
Distribution</a> CDF
</p>
</td>
<td>
<p>
</p>
<p>3.60<sup>[<a name="id1282843" href="#ftn.id1282843" class="footnote">2</a>]</sup></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/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/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/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/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/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/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/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<sup>[<a name="id1283264" href="#ftn.id1283264" class="footnote">3</a>]</sup></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/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/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<sup>[<a name="id1283390" href="#ftn.id1283390" class="footnote">4</a>]</sup></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/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/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/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/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><sup>[<a name="id1283641" href="#ftn.id1283641" class="footnote">5</a>]</sup></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/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/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/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/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/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/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/dist_ref/dists/weibull.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/dist_ref/dists/weibull.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 class="footnote"><p><sup>[<a name="ftn.id1282085" href="#id1282085" class="para">1</a>] </sup>
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 class="footnote"><p><sup>[<a name="ftn.id1282843" href="#id1282843" class="para">2</a>] </sup>
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 class="footnote"><p><sup>[<a name="ftn.id1283264" href="#id1283264" class="para">3</a>] </sup>
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 class="footnote"><p><sup>[<a name="ftn.id1283390" href="#id1283390" class="para">4</a>] </sup>
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 class="footnote"><p><sup>[<a name="ftn.id1283641" href="#id1283641" class="para">5</a>] </sup>
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"><a name="math_toolkit.perf.comparisons.comparison_to_the_r_statistical_library_on_linux"></a><h5>
<a name="id1284145"></a>
<a class="link" href="comparisons.html#math_toolkit.perf.comparisons.comparison_to_the_r_statistical_library_on_linux">Comparison
to the R Statistical Library on Linux</a>
</h5>
<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="id1284159"></a><p class="title"><b>Table 52. 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/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/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<sup>[<a name="id1284309" href="#ftn.id1284309" class="footnote">1</a>]</sup></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/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/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/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/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/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/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>
<p>
</p>
<p>1.34</p>
<p> </p>
<p>(5.700e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>3.47</p>
<p> </p>
<p>(1.477e-005s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../dist/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>(1.342e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.25</p>
<p> </p>
<p>(1.677e-007s)</p>
<p>
</p>
</td>
<td>
<p>
NA
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential
Distribution</a> Quantile
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(8.827e-008s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.07</p>
<p> </p>
<p>(9.470e-008s)</p>
<p>
</p>
</td>
<td>
<p>
NA
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../dist/dist_ref/dists/f_dist.html" title="F Distribution">Fisher
F Distribution</a> CDF
</p>
</td>
<td>
<p>
</p>
<p>1.62</p>
<p> </p>
<p>(2.324e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.19</p>
<p> </p>
<p>(1.711e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.437e-006s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../dist/dist_ref/dists/f_dist.html" title="F Distribution">Fisher
F Distribution</a> Quantile
</p>
</td>
<td>
<p>
</p>
<p>1.53</p>
<p> </p>
<p>(1.577e-005s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.033e-005s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>2.63</p>
<p> </p>
<p>(2.719e-005s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma
Distribution</a> CDF
</p>
</td>
<td>
<p>
</p>
<p>3.18</p>
<p> </p>
<p>(1.582e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>2.63</p>
<p> </p>
<p>(1.309e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(4.980e-007s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma
Distribution</a> Quantile
</p>
</td>
<td>
<p>
</p>
<p>2.19</p>
<p> </p>
<p>(4.770e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>6.94</p>
<p> </p>
<p>(1.513e-005s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(2.179e-006s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../dist/dist_ref/dists/hypergeometric_dist.html" title="Hypergeometric Distribution">Hypergeometric
Distribution</a> CDF
</p>
</td>
<td>
<p>
</p>
<p>2.20<sup>[<a name="id1285065" href="#ftn.id1285065" class="footnote">2</a>]</sup></p>
<p> </p>
<p>(3.522e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.601e-007s)</p>
<p>
</p>
</td>
<td>
<p>
NA
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../dist/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>(8.279e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>2.57</p>
<p> </p>
<p>(2.125e-006s)</p>
<p>
</p>
</td>
<td>
<p>
NA
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../dist/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>(9.398e-008s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>2.75</p>
<p> </p>
<p>(2.588e-007s)</p>
<p>
</p>
</td>
<td>
<p>
NA
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic
Distribution</a> Quantile
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(9.893e-008s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.30</p>
<p> </p>
<p>(1.285e-007s)</p>
<p>
</p>
</td>
<td>
<p>
NA
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../dist/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>(1.831e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.39</p>
<p> </p>
<p>(2.539e-007s)</p>
<p>
</p>
</td>
<td>
<p>
NA
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log-normal
Distribution</a> Quantile
</p>
</td>
<td>
<p>
</p>
<p>1.10</p>
<p> </p>
<p>(5.551e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(5.037e-007s)</p>
<p>
</p>
</td>
<td>
<p>
NA
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative
Binomial Distribution</a> CDF
</p>
</td>
<td>
<p>
</p>
<p>1.08</p>
<p> </p>
<p>(1.563e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.444e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.444e-006s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../dist/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>(1.700e-005s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>25.92<sup>[<a name="id1285480" href="#ftn.id1285480" class="footnote">3</a>]</sup></p>
<p> </p>
<p>(4.407e-004s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.93</p>
<p> </p>
<p>(3.274e-005s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../dist/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>5.06</p>
<p> </p>
<p>(2.841e-005s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>25.01</p>
<p> </p>
<p>(1.405e-004s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(5.617e-006s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../dist/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>8.47</p>
<p> </p>
<p>(1.879e-003s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>144.91<sup>[<a name="id1285606" href="#ftn.id1285606" class="footnote">4</a>]</sup></p>
<p> </p>
<p>(3.214e-002s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(2.218e-004s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral
F Distribution</a> CDF
</p>
</td>
<td>
<p>
</p>
<p>10.33</p>
<p> </p>
<p>(5.868e-005s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.42</p>
<p> </p>
<p>(8.058e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(5.682e-006s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral
F Distribution</a> Quantile
</p>
</td>
<td>
<p>
</p>
<p>5.64</p>
<p> </p>
<p>(7.869e-004s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>6.63</p>
<p> </p>
<p>(9.256e-004s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.396e-004s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">noncentral
T distribution</a> CDF
</p>
</td>
<td>
<p>
</p>
<p>4.91</p>
<p> </p>
<p>(3.357e-005s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(6.844e-006s)</p>
<p>
</p>
</td>
<td>
<p>
NA
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">noncentral
T distribution</a> Quantile
</p>
</td>
<td>
<p>
</p>
<p>1.57</p>
<p> </p>
<p>(9.265e-004s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span><sup>[<a name="id1285852" href="#ftn.id1285852" class="footnote">5</a>]</sup></p>
<p> </p>
<p>(5.916e-004s)</p>
<p>
</p>
</td>
<td>
<p>
NA
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../dist/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>(1.074e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.16</p>
<p> </p>
<p>(1.245e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>5.36</p>
<p> </p>
<p>(5.762e-007s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal
Distribution</a> Quantile
</p>
</td>
<td>
<p>
</p>
<p>1.28</p>
<p> </p>
<p>(1.902e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(1.490e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>10.35</p>
<p> </p>
<p>(1.542e-006s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson
Distribution</a> CDF
</p>
</td>
<td>
<p>
</p>
<p>2.43</p>
<p> </p>
<p>(1.198e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>2.25</p>
<p> </p>
<p>(1.110e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(4.937e-007s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson
Distribution</a>
</p>
</td>
<td>
<p>
</p>
<p>1.11</p>
<p> </p>
<p>(3.032e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(2.724e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>4.07</p>
<p> </p>
<p>(1.110e-005s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students
t Distribution</a> CDF
</p>
</td>
<td>
<p>
</p>
<p>2.17</p>
<p> </p>
<p>(2.020e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(9.321e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.10</p>
<p> </p>
<p>(1.021e-006s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students
t Distribution</a> Quantile
</p>
</td>
<td>
<p>
</p>
<p>1.18</p>
<p> </p>
<p>(3.972e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span></p>
<p> </p>
<p>(3.364e-006s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>3.89</p>
<p> </p>
<p>(1.308e-005s)</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../dist/dist_ref/dists/weibull.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>(3.662e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.04</p>
<p> </p>
<p>(3.808e-007s)</p>
<p>
</p>
</td>
<td>
<p>
NA
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../dist/dist_ref/dists/weibull.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>(4.112e-007s)</p>
<p>
</p>
</td>
<td>
<p>
</p>
<p>1.05</p>
<p> </p>
<p>(4.317e-007s)</p>
<p>
</p>
</td>
<td>
<p>
NA
</p>
</td>
</tr>
</tbody>
<tbody class="footnotes"><tr><td colspan="4">
<div class="footnote"><p><sup>[<a name="ftn.id1284309" href="#id1284309" class="para">1</a>] </sup>
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 class="footnote"><p><sup>[<a name="ftn.id1285065" href="#id1285065" class="para">2</a>] </sup>
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 class="footnote"><p><sup>[<a name="ftn.id1285480" href="#id1285480" class="para">3</a>] </sup>
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 class="footnote"><p><sup>[<a name="ftn.id1285606" href="#id1285606" class="para">4</a>] </sup>
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 class="footnote"><p><sup>[<a name="ftn.id1285852" href="#id1285852" class="para">5</a>] </sup>
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">
</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 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<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>
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