Performance =========== .. currentmodule:: numpy.random Recommendation -------------- The recommended generator for general use is `PCG64` or its upgraded variant `PCG64DXSM` 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 :ref:`upgrading-pcg64` for details on when heavy parallelism would indicate using `PCG64DXSM`. `Philox` 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 `Philox` is your choice. `SFC64` 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. `MT19937` `fails some statistical tests`_ 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 `~.RandomState` for reproducing old results. That said, it has a very long history as a default in many systems. .. _`fails some statistical tests`: https://www.iro.umontreal.ca/~lecuyer/myftp/papers/testu01.pdf Timings ------- The timings below are the time in ns to produce 1 random value from a specific distribution. The original `MT19937` generator is much slower since it requires 2 32-bit values to equal the output of the faster generators. Integer performance has a similar ordering. The pattern is similar for other, more complex generators. The normal performance of the legacy `RandomState` 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 `RandomState` but produces random variates using `Generator`. .. csv-table:: :header: ,MT19937,PCG64,PCG64DXSM,Philox,SFC64,RandomState :widths: 14,14,14,14,14,14,14 32-bit Unsigned Ints,3.3,1.9,2.0,3.3,1.8,3.1 64-bit Unsigned Ints,5.6,3.2,2.9,4.9,2.5,5.5 Uniforms,5.9,3.1,2.9,5.0,2.6,6.0 Normals,13.9,10.8,10.5,12.0,8.3,56.8 Exponentials,9.1,6.0,5.8,8.1,5.4,63.9 Gammas,37.2,30.8,28.9,34.0,27.5,77.0 Binomials,21.3,17.4,17.6,19.3,15.6,21.4 Laplaces,73.2,72.3,76.1,73.0,72.3,82.5 Poissons,111.7,103.4,100.5,109.4,90.7,115.2 The next table presents the performance in percentage relative to values generated by the legacy generator, ``RandomState(MT19937())``. The overall performance was computed using a geometric mean. .. csv-table:: :header: ,MT19937,PCG64,PCG64DXSM,Philox,SFC64 :widths: 14,14,14,14,14,14 32-bit Unsigned Ints,96,162,160,96,175 64-bit Unsigned Ints,97,171,188,113,218 Uniforms,102,192,206,121,233 Normals,409,526,541,471,684 Exponentials,701,1071,1101,784,1179 Gammas,207,250,266,227,281 Binomials,100,123,122,111,138 Laplaces,113,114,108,113,114 Poissons,103,111,115,105,127 Overall,159,219,225,174,251 .. note:: All timings were taken using Linux on an AMD Ryzen 9 3900X processor. Performance on different Operating Systems ------------------------------------------ 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. 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. 64-bit Linux ~~~~~~~~~~~~ ===================== ========= ======= =========== ======== ======= Distribution MT19937 PCG64 PCG64DXSM Philox SFC64 ===================== ========= ======= =========== ======== ======= 32-bit Unsigned Ints 100 168 166 100 182 64-bit Unsigned Ints 100 176 193 116 224 Uniforms 100 188 202 118 228 Normals 100 128 132 115 167 Exponentials 100 152 157 111 168 Overall 100 161 168 112 192 ===================== ========= ======= =========== ======== ======= 64-bit Windows ~~~~~~~~~~~~~~ The relative performance on 64-bit Linux and 64-bit Windows is broadly similar with the notable exception of the Philox generator. ===================== ========= ======= =========== ======== ======= Distribution MT19937 PCG64 PCG64DXSM Philox SFC64 ===================== ========= ======= =========== ======== ======= 32-bit Unsigned Ints 100 155 131 29 150 64-bit Unsigned Ints 100 157 143 25 154 Uniforms 100 151 144 24 155 Normals 100 129 128 37 150 Exponentials 100 150 145 28 159 **Overall** 100 148 138 28 154 ===================== ========= ======= =========== ======== ======= 32-bit Windows ~~~~~~~~~~~~~~ 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. ===================== ========= ======= =========== ======== ======= Distribution MT19937 PCG64 PCG64DXSM Philox SFC64 ===================== ========= ======= =========== ======== ======= 32-bit Unsigned Ints 100 24 34 14 57 64-bit Unsigned Ints 100 21 32 14 74 Uniforms 100 21 34 16 73 Normals 100 36 57 28 101 Exponentials 100 28 44 20 88 **Overall** 100 25 39 18 77 ===================== ========= ======= =========== ======== ======= .. note:: 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.