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Performance

docs/reference:random:performance

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 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.

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.

	MT19937	PCG64	PCG64DXSM	Philox	SFC64	RandomState
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.

	MT19937	PCG64	PCG64DXSM	Philox	SFC64
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

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
=====================   =========  =======  ===========  ========  =======