SciPy

Performance

Recommendation

The recommended generator for general use is PCG64. It is statistically high quality, full-featured, and fast on most platforms, but somewhat slow when compiled for 32-bit processes.

Philox is fairly slow, but its statistical properties have very high quality, and it is easy to get 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.

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 transformation rather than the Ziggurat generator. 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 is used the same 32-bit generator as RandomState but produces random values using Generator.

  MT19937 PCG64 Philox SFC64 RandomState
32-bit Unsigned Ints 3.2 2.7 4.9 2.7 3.2
64-bit Unsigned Ints 5.6 3.7 6.3 2.9 5.7
Uniforms 7.3 4.1 8.1 3.1 7.3
Normals 13.1 10.2 13.5 7.8 34.6
Exponentials 7.9 5.4 8.5 4.1 40.3
Gammas 34.8 28.0 34.7 25.1 58.1
Binomials 25.0 21.4 26.1 19.5 25.2
Laplaces 45.1 40.7 45.5 38.1 45.6
Poissons 67.6 52.4 69.2 46.4 78.1

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.

  MT19937 PCG64 Philox SFC64
32-bit Unsigned Ints 101 121 67 121
64-bit Unsigned Ints 102 156 91 199
Uniforms 100 179 90 235
Normals 263 338 257 443
Exponentials 507 752 474 985
Gammas 167 207 167 231
Binomials 101 118 96 129
Laplaces 101 112 100 120
Poissons 116 149 113 168
Overall 144 192 132 225

Note

All timings were taken using Linux on a i5-3570 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 Philox SFC64
32-bit Unsigned Int 100 119.8 67.7 120.2
64-bit Unsigned Int 100 152.9 90.8 213.3
Uniforms 100 179.0 87.0 232.0
Normals 100 128.5 99.2 167.8
Exponentials 100 148.3 93.0 189.3
Overall 100 144.3 86.8 180.0

64-bit Windows

The relative performance on 64-bit Linux and 64-bit Windows is broadly similar.

Distribution MT19937 PCG64 Philox SFC64
32-bit Unsigned Int 100 129.1 35.0 135.0
64-bit Unsigned Int 100 146.9 35.7 176.5
Uniforms 100 165.0 37.0 192.0
Normals 100 128.5 48.5 158.0
Exponentials 100 151.6 39.0 172.8
Overall 100 143.6 38.7 165.7

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 Philox SFC64
32-bit Unsigned Int 100 30.5 21.1 77.9
64-bit Unsigned Int 100 26.3 19.2 97.0
Uniforms 100 28.0 23.0 106.0
Normals 100 40.1 31.3 112.6
Exponentials 100 33.7 26.3 109.8
Overall 100 31.4 23.8 99.8

Note

Linux timings used Ubuntu 18.04 and GCC 7.4. Windows timings were made on Windows 10 using Microsoft C/C++ Optimizing Compiler Version 19 (Visual Studio 2015). All timings were produced on a i5-3570 processor.