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<article class="bd-article">
<section id="performance">
<h1>Performance<a class="headerlink" href="#performance" title="Link to this heading">#</a></h1>
<section id="recommendation">
<h2>Recommendation<a class="headerlink" href="#recommendation" title="Link to this heading">#</a></h2>
<p>The recommended generator for general use is <a class="reference internal" href="bit_generators/pcg64.html#numpy.random.PCG64" title="numpy.random.PCG64"><code class="xref py py-obj docutils literal notranslate"><span class="pre">PCG64</span></code></a> or its upgraded variant
<a class="reference internal" href="bit_generators/pcg64dxsm.html#numpy.random.PCG64DXSM" title="numpy.random.PCG64DXSM"><code class="xref py py-obj docutils literal notranslate"><span class="pre">PCG64DXSM</span></code></a> for heavily-parallel use cases. They are statistically high quality,
full-featured, and fast on most platforms, but somewhat slow when compiled for
32-bit processes. See <a class="reference internal" href="upgrading-pcg64.html#upgrading-pcg64"><span class="std std-ref">Upgrading PCG64 with PCG64DXSM</span></a> for details on when heavy
parallelism would indicate using <a class="reference internal" href="bit_generators/pcg64dxsm.html#numpy.random.PCG64DXSM" title="numpy.random.PCG64DXSM"><code class="xref py py-obj docutils literal notranslate"><span class="pre">PCG64DXSM</span></code></a>.</p>
<p><a class="reference internal" href="bit_generators/philox.html#numpy.random.Philox" title="numpy.random.Philox"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Philox</span></code></a> is fairly slow, but its statistical properties have
very high quality, and it is easy to get an assuredly-independent stream by using
unique keys. If that is the style you wish to use for parallel streams, or you
are porting from another system that uses that style, then
<a class="reference internal" href="bit_generators/philox.html#numpy.random.Philox" title="numpy.random.Philox"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Philox</span></code></a> is your choice.</p>
<p><a class="reference internal" href="bit_generators/sfc64.html#numpy.random.SFC64" title="numpy.random.SFC64"><code class="xref py py-obj docutils literal notranslate"><span class="pre">SFC64</span></code></a> is statistically high quality and very fast. However, it
lacks jumpability. If you are not using that capability and want lots of speed,
even on 32-bit processes, this is your choice.</p>
<p><a class="reference internal" href="bit_generators/mt19937.html#numpy.random.MT19937" title="numpy.random.MT19937"><code class="xref py py-obj docutils literal notranslate"><span class="pre">MT19937</span></code></a> <a class="reference external" href="https://www.iro.umontreal.ca/~lecuyer/myftp/papers/testu01.pdf">fails some statistical tests</a> and is not especially
fast compared to modern PRNGs. For these reasons, we mostly do not recommend
using it on its own, only through the legacy <a class="reference internal" href="legacy.html#numpy.random.RandomState" title="numpy.random.RandomState"><code class="xref py py-obj docutils literal notranslate"><span class="pre">RandomState</span></code></a> for
reproducing old results. That said, it has a very long history as a default in
many systems.</p>
</section>
<section id="timings">
<h2>Timings<a class="headerlink" href="#timings" title="Link to this heading">#</a></h2>
<p>The timings below are the time in ns to produce 1 random value from a
specific distribution. The original <a class="reference internal" href="bit_generators/mt19937.html#numpy.random.MT19937" title="numpy.random.MT19937"><code class="xref py py-obj docutils literal notranslate"><span class="pre">MT19937</span></code></a> generator is
much slower since it requires 2 32-bit values to equal the output of the
faster generators.</p>
<p>Integer performance has a similar ordering.</p>
<p>The pattern is similar for other, more complex generators. The normal
performance of the legacy <a class="reference internal" href="legacy.html#numpy.random.RandomState" title="numpy.random.RandomState"><code class="xref py py-obj docutils literal notranslate"><span class="pre">RandomState</span></code></a> generator is much
lower than the other since it uses the Box-Muller transform rather
than the Ziggurat method. The performance gap for Exponentials is also
large due to the cost of computing the log function to invert the CDF.
The column labeled MT19973 uses the same 32-bit generator as
<a class="reference internal" href="legacy.html#numpy.random.RandomState" title="numpy.random.RandomState"><code class="xref py py-obj docutils literal notranslate"><span class="pre">RandomState</span></code></a> but produces random variates using <a class="reference internal" href="generator.html#numpy.random.Generator" title="numpy.random.Generator"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Generator</span></code></a>.</p>
<div class="pst-scrollable-table-container"><table class="table">
<colgroup>
<col style="width: 14.3%" />
<col style="width: 14.3%" />
<col style="width: 14.3%" />
<col style="width: 14.3%" />
<col style="width: 14.3%" />
<col style="width: 14.3%" />
<col style="width: 14.3%" />
</colgroup>
<thead>
<tr class="row-odd"><th class="head"></th>
<th class="head"><p>MT19937</p></th>
<th class="head"><p>PCG64</p></th>
<th class="head"><p>PCG64DXSM</p></th>
<th class="head"><p>Philox</p></th>
<th class="head"><p>SFC64</p></th>
<th class="head"><p>RandomState</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>32-bit Unsigned Ints</p></td>
<td><p>3.3</p></td>
<td><p>1.9</p></td>
<td><p>2.0</p></td>
<td><p>3.3</p></td>
<td><p>1.8</p></td>
<td><p>3.1</p></td>
</tr>
<tr class="row-odd"><td><p>64-bit Unsigned Ints</p></td>
<td><p>5.6</p></td>
<td><p>3.2</p></td>
<td><p>2.9</p></td>
<td><p>4.9</p></td>
<td><p>2.5</p></td>
<td><p>5.5</p></td>
</tr>
<tr class="row-even"><td><p>Uniforms</p></td>
<td><p>5.9</p></td>
<td><p>3.1</p></td>
<td><p>2.9</p></td>
<td><p>5.0</p></td>
<td><p>2.6</p></td>
<td><p>6.0</p></td>
</tr>
<tr class="row-odd"><td><p>Normals</p></td>
<td><p>13.9</p></td>
<td><p>10.8</p></td>
<td><p>10.5</p></td>
<td><p>12.0</p></td>
<td><p>8.3</p></td>
<td><p>56.8</p></td>
</tr>
<tr class="row-even"><td><p>Exponentials</p></td>
<td><p>9.1</p></td>
<td><p>6.0</p></td>
<td><p>5.8</p></td>
<td><p>8.1</p></td>
<td><p>5.4</p></td>
<td><p>63.9</p></td>
</tr>
<tr class="row-odd"><td><p>Gammas</p></td>
<td><p>37.2</p></td>
<td><p>30.8</p></td>
<td><p>28.9</p></td>
<td><p>34.0</p></td>
<td><p>27.5</p></td>
<td><p>77.0</p></td>
</tr>
<tr class="row-even"><td><p>Binomials</p></td>
<td><p>21.3</p></td>
<td><p>17.4</p></td>
<td><p>17.6</p></td>
<td><p>19.3</p></td>
<td><p>15.6</p></td>
<td><p>21.4</p></td>
</tr>
<tr class="row-odd"><td><p>Laplaces</p></td>
<td><p>73.2</p></td>
<td><p>72.3</p></td>
<td><p>76.1</p></td>
<td><p>73.0</p></td>
<td><p>72.3</p></td>
<td><p>82.5</p></td>
</tr>
<tr class="row-even"><td><p>Poissons</p></td>
<td><p>111.7</p></td>
<td><p>103.4</p></td>
<td><p>100.5</p></td>
<td><p>109.4</p></td>
<td><p>90.7</p></td>
<td><p>115.2</p></td>
</tr>
</tbody>
</table>
</div>
<p>The next table presents the performance in percentage relative to values
generated by the legacy generator, <code class="docutils literal notranslate"><span class="pre">RandomState(MT19937())</span></code>. The overall
performance was computed using a geometric mean.</p>
<div class="pst-scrollable-table-container"><table class="table">
<colgroup>
<col style="width: 16.7%" />
<col style="width: 16.7%" />
<col style="width: 16.7%" />
<col style="width: 16.7%" />
<col style="width: 16.7%" />
<col style="width: 16.7%" />
</colgroup>
<thead>
<tr class="row-odd"><th class="head"></th>
<th class="head"><p>MT19937</p></th>
<th class="head"><p>PCG64</p></th>
<th class="head"><p>PCG64DXSM</p></th>
<th class="head"><p>Philox</p></th>
<th class="head"><p>SFC64</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>32-bit Unsigned Ints</p></td>
<td><p>96</p></td>
<td><p>162</p></td>
<td><p>160</p></td>
<td><p>96</p></td>
<td><p>175</p></td>
</tr>
<tr class="row-odd"><td><p>64-bit Unsigned Ints</p></td>
<td><p>97</p></td>
<td><p>171</p></td>
<td><p>188</p></td>
<td><p>113</p></td>
<td><p>218</p></td>
</tr>
<tr class="row-even"><td><p>Uniforms</p></td>
<td><p>102</p></td>
<td><p>192</p></td>
<td><p>206</p></td>
<td><p>121</p></td>
<td><p>233</p></td>
</tr>
<tr class="row-odd"><td><p>Normals</p></td>
<td><p>409</p></td>
<td><p>526</p></td>
<td><p>541</p></td>
<td><p>471</p></td>
<td><p>684</p></td>
</tr>
<tr class="row-even"><td><p>Exponentials</p></td>
<td><p>701</p></td>
<td><p>1071</p></td>
<td><p>1101</p></td>
<td><p>784</p></td>
<td><p>1179</p></td>
</tr>
<tr class="row-odd"><td><p>Gammas</p></td>
<td><p>207</p></td>
<td><p>250</p></td>
<td><p>266</p></td>
<td><p>227</p></td>
<td><p>281</p></td>
</tr>
<tr class="row-even"><td><p>Binomials</p></td>
<td><p>100</p></td>
<td><p>123</p></td>
<td><p>122</p></td>
<td><p>111</p></td>
<td><p>138</p></td>
</tr>
<tr class="row-odd"><td><p>Laplaces</p></td>
<td><p>113</p></td>
<td><p>114</p></td>
<td><p>108</p></td>
<td><p>113</p></td>
<td><p>114</p></td>
</tr>
<tr class="row-even"><td><p>Poissons</p></td>
<td><p>103</p></td>
<td><p>111</p></td>
<td><p>115</p></td>
<td><p>105</p></td>
<td><p>127</p></td>
</tr>
<tr class="row-odd"><td><p>Overall</p></td>
<td><p>159</p></td>
<td><p>219</p></td>
<td><p>225</p></td>
<td><p>174</p></td>
<td><p>251</p></td>
</tr>
</tbody>
</table>
</div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>All timings were taken using Linux on an AMD Ryzen 9 3900X processor.</p>
</div>
</section>
<section id="performance-on-different-operating-systems">
<h2>Performance on different operating systems<a class="headerlink" href="#performance-on-different-operating-systems" title="Link to this heading">#</a></h2>
<p>Performance differs across platforms due to compiler and hardware availability
(e.g., register width) differences. The default bit generator has been chosen
to perform well on 64-bit platforms. Performance on 32-bit operating systems
is very different.</p>
<p>The values reported are normalized relative to the speed of MT19937 in
each table. A value of 100 indicates that the performance matches the MT19937.
Higher values indicate improved performance. These values cannot be compared
across tables.</p>
<section id="bit-linux">
<h3>64-bit Linux<a class="headerlink" href="#bit-linux" title="Link to this heading">#</a></h3>
<div class="pst-scrollable-table-container"><table class="table">
<thead>
<tr class="row-odd"><th class="head"><p>Distribution</p></th>
<th class="head"><p>MT19937</p></th>
<th class="head"><p>PCG64</p></th>
<th class="head"><p>PCG64DXSM</p></th>
<th class="head"><p>Philox</p></th>
<th class="head"><p>SFC64</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>32-bit Unsigned Ints</p></td>
<td><p>100</p></td>
<td><p>168</p></td>
<td><p>166</p></td>
<td><p>100</p></td>
<td><p>182</p></td>
</tr>
<tr class="row-odd"><td><p>64-bit Unsigned Ints</p></td>
<td><p>100</p></td>
<td><p>176</p></td>
<td><p>193</p></td>
<td><p>116</p></td>
<td><p>224</p></td>
</tr>
<tr class="row-even"><td><p>Uniforms</p></td>
<td><p>100</p></td>
<td><p>188</p></td>
<td><p>202</p></td>
<td><p>118</p></td>
<td><p>228</p></td>
</tr>
<tr class="row-odd"><td><p>Normals</p></td>
<td><p>100</p></td>
<td><p>128</p></td>
<td><p>132</p></td>
<td><p>115</p></td>
<td><p>167</p></td>
</tr>
<tr class="row-even"><td><p>Exponentials</p></td>
<td><p>100</p></td>
<td><p>152</p></td>
<td><p>157</p></td>
<td><p>111</p></td>
<td><p>168</p></td>
</tr>
<tr class="row-odd"><td><p>Overall</p></td>
<td><p>100</p></td>
<td><p>161</p></td>
<td><p>168</p></td>
<td><p>112</p></td>
<td><p>192</p></td>
</tr>
</tbody>
</table>
</div>
</section>
<section id="bit-windows">
<h3>64-bit Windows<a class="headerlink" href="#bit-windows" title="Link to this heading">#</a></h3>
<p>The relative performance on 64-bit Linux and 64-bit Windows is broadly similar
with the notable exception of the Philox generator.</p>
<div class="pst-scrollable-table-container"><table class="table">
<thead>
<tr class="row-odd"><th class="head"><p>Distribution</p></th>
<th class="head"><p>MT19937</p></th>
<th class="head"><p>PCG64</p></th>
<th class="head"><p>PCG64DXSM</p></th>
<th class="head"><p>Philox</p></th>
<th class="head"><p>SFC64</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>32-bit Unsigned Ints</p></td>
<td><p>100</p></td>
<td><p>155</p></td>
<td><p>131</p></td>
<td><p>29</p></td>
<td><p>150</p></td>
</tr>
<tr class="row-odd"><td><p>64-bit Unsigned Ints</p></td>
<td><p>100</p></td>
<td><p>157</p></td>
<td><p>143</p></td>
<td><p>25</p></td>
<td><p>154</p></td>
</tr>
<tr class="row-even"><td><p>Uniforms</p></td>
<td><p>100</p></td>
<td><p>151</p></td>
<td><p>144</p></td>
<td><p>24</p></td>
<td><p>155</p></td>
</tr>
<tr class="row-odd"><td><p>Normals</p></td>
<td><p>100</p></td>
<td><p>129</p></td>
<td><p>128</p></td>
<td><p>37</p></td>
<td><p>150</p></td>
</tr>
<tr class="row-even"><td><p>Exponentials</p></td>
<td><p>100</p></td>
<td><p>150</p></td>
<td><p>145</p></td>
<td><p>28</p></td>
<td><p>159</p></td>
</tr>
<tr class="row-odd"><td><p><strong>Overall</strong></p></td>
<td><p>100</p></td>
<td><p>148</p></td>
<td><p>138</p></td>
<td><p>28</p></td>
<td><p>154</p></td>
</tr>
</tbody>
</table>
</div>
</section>
<section id="id1">
<h3>32-bit Windows<a class="headerlink" href="#id1" title="Link to this heading">#</a></h3>
<p>The performance of 64-bit generators on 32-bit Windows is much lower than on 64-bit
operating systems due to register width. MT19937, the generator that has been
in NumPy since 2005, operates on 32-bit integers.</p>
<div class="pst-scrollable-table-container"><table class="table">
<thead>
<tr class="row-odd"><th class="head"><p>Distribution</p></th>
<th class="head"><p>MT19937</p></th>
<th class="head"><p>PCG64</p></th>
<th class="head"><p>PCG64DXSM</p></th>
<th class="head"><p>Philox</p></th>
<th class="head"><p>SFC64</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>32-bit Unsigned Ints</p></td>
<td><p>100</p></td>
<td><p>24</p></td>
<td><p>34</p></td>
<td><p>14</p></td>
<td><p>57</p></td>
</tr>
<tr class="row-odd"><td><p>64-bit Unsigned Ints</p></td>
<td><p>100</p></td>
<td><p>21</p></td>
<td><p>32</p></td>
<td><p>14</p></td>
<td><p>74</p></td>
</tr>
<tr class="row-even"><td><p>Uniforms</p></td>
<td><p>100</p></td>
<td><p>21</p></td>
<td><p>34</p></td>
<td><p>16</p></td>
<td><p>73</p></td>
</tr>
<tr class="row-odd"><td><p>Normals</p></td>
<td><p>100</p></td>
<td><p>36</p></td>
<td><p>57</p></td>
<td><p>28</p></td>
<td><p>101</p></td>
</tr>
<tr class="row-even"><td><p>Exponentials</p></td>
<td><p>100</p></td>
<td><p>28</p></td>
<td><p>44</p></td>
<td><p>20</p></td>
<td><p>88</p></td>
</tr>
<tr class="row-odd"><td><p><strong>Overall</strong></p></td>
<td><p>100</p></td>
<td><p>25</p></td>
<td><p>39</p></td>
<td><p>18</p></td>
<td><p>77</p></td>
</tr>
</tbody>
</table>
</div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>Linux timings used Ubuntu 20.04 and GCC 9.3.0. Windows timings were made on
Windows 10 using Microsoft C/C++ Optimizing Compiler Version 19 (Visual
Studio 2019). All timings were produced on an AMD Ryzen 9 3900X processor.</p>
</div>
</section>
</section>
</section>
</article>
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