# 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 with PCG64DXSM 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

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.

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