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.