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

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