The recommended generator for single use is xoroshiro128+
(xoroshiro128plus). The recommended generator
for use in large-scale parallel applications is
xorshift1024* (xorshift1024)
where the jump method is used to advance the state.
The timings below are ns/random value. The fastest generator is the raw generator (random_raw) which does not make any transformation to the underlying random value. xoroshiro128+ is the fastest, followed by xorshift1024* and the two SIMD aware MT generators. 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 although dSFMT is slower since it generates 53-bit floating point values rather than integer values. On the other hand, it is very fast for uniforms, although slower than xoroshiro128+.
The patterm is similar for other, more complex generators. The normal performance of NumPy’s MT19937 is much lower than the other since it uses the Box-Muller transformation rather than the Ziggurat generator.
| NumPy MT19937 | MT19937 | SFMT | dSFMT | xoroshiro128+ | xorshift1024 | PCG64 | |
|---|---|---|---|---|---|---|---|
| Raw | 4.21 | 1.81 | 1.7 | 1.06 | 1.5 | 2.67 | |
| Random Integers | 4.56 | 3.11 | 2.09 | 2.96 | 1.93 | 2.34 | 2.22 |
| Uniforms | 9.77 | 6.13 | 2.41 | 2.22 | 1.46 | 2.37 | 2.56 |
| Normal | 62.47 | 13.77 | 9.11 | 10.89 | 7.8 | 10.48 | 10.67 |
| Exponential | 98.35 | 9.85 | 5.72 | 7.22 | 5.56 | 6.32 | 10.88 |
| Complex Normal | 37.07 | 24.41 | 27.88 | 23.31 | 27.78 | 28.34 | |
| Gamma | 97.99 | 44.94 | 38.27 | 33.41 | 31.2 | 34.18 | 34.09 |
| Binomial | 87.99 | 79.95 | 78.85 | 77.12 | 76.88 | 76.09 | 76.99 |
| Laplace | 101.73 | 103.95 | 91.57 | 89.02 | 91.94 | 93.61 | 92.13 |
| Poisson | 131.93 | 119.95 | 99.42 | 94.84 | 92.71 | 100.28 | 101.17 |
| Neg. Binomial | 433.77 | 416.69 | 410.2 | 397.71 | 389.21 | 396.14 | 394.78 |
| Multinomial | 1072.82 | 1043.98 | 1021.58 | 1019.22 | 1016.7 | 1013.15 | 1018.41 |
The next table presents the performance relative to xoroshiro128+. The overall performance was computed using a geometric mean.
| NumPy MT19937 | MT19937 | SFMT | dSFMT | xoroshiro128+ | xorshift1024 | PCG64 | |
|---|---|---|---|---|---|---|---|
| Raw | 3.97 | 1.71 | 1.6 | 1.0 | 1.42 | 2.52 | |
| Random Integers | 2.36 | 1.61 | 1.08 | 1.53 | 1.0 | 1.21 | 1.15 |
| Uniforms | 6.69 | 4.2 | 1.65 | 1.52 | 1.0 | 1.62 | 1.75 |
| Normal | 8.01 | 1.77 | 1.17 | 1.4 | 1.0 | 1.34 | 1.37 |
| Exponential | 17.69 | 1.77 | 1.03 | 1.3 | 1.0 | 1.14 | 1.96 |
| Complex Normal | 1.59 | 1.05 | 1.2 | 1.0 | 1.19 | 1.22 | |
| Gamma | 3.14 | 1.44 | 1.23 | 1.07 | 1.0 | 1.1 | 1.09 |
| Binomial | 1.14 | 1.04 | 1.03 | 1.0 | 1.0 | 0.99 | 1.0 |
| Laplace | 1.11 | 1.13 | 1.0 | 0.97 | 1.0 | 1.02 | 1.0 |
| Poisson | 1.42 | 1.29 | 1.07 | 1.02 | 1.0 | 1.08 | 1.09 |
| Neg. Binomial | 1.11 | 1.07 | 1.05 | 1.02 | 1.0 | 1.02 | 1.01 |
| Multinomial | 1.06 | 1.03 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 |
| Overall | 2.61 | 1.62 | 1.15 | 1.2 | 1.0 | 1.16 | 1.28 |
Note
All timings were taken using Linux and gcc 5.4 on a i5-3570 processor.