Next-gen RandomState supporting multiple PRNGs

## Future development in randomgen

This library was designed to bring alternative generators to the NumPy infrastructure. It as been successful in advancing the conversation for a future implementation of a new random number API in NumPy which will allow new algorithms and/or generators. The next step in this process is to separate the basic (or core RNG) from the functions that transform random bits into useful random numbers. This has been implemented in a successor project randomgen available on GitHub or PyPi.

randomgen has a slightly different API, so please see the randomgen documentation.

### Introduction

This is a library and generic interface for alternative random generators in Python and NumPy.

### Features

• Immediate drop in replacement for NumPy’s RandomState

# import numpy.random as rnd
import randomstate as rnd
x = rnd.standard_normal(100)
y = rnd.random_sample(100)
z = rnd.randn(10,10)
• Default random generator is identical to NumPy’s RandomState (i.e., same seed, same random numbers).

• Support for random number generators that support independent streams and jumping ahead so that sub-streams can be generated

• Faster random number generation, especially for normal, standard exponential and standard gamma using the Ziggurat method

import randomstate as rnd
w = rnd.standard_normal(10000, method='zig')
x = rnd.standard_exponential(10000, method='zig')
y = rnd.standard_gamma(5.5, 10000, method='zig')
• Support for 32-bit floating randoms for core generators. Currently supported:

• Uniforms (random_sample)

• Exponentials (standard_exponential, both Inverse CDF and Ziggurat)

• Normals (standard_normal, both Box-Muller and Ziggurat)

• Standard Gammas (via standard_gamma, both Inverse CDF and Ziggurat)

WARNING: The 32-bit generators are experimental and subject to change.

Note: There are no plans to extend the alternative precision generation to all random number types.

• Support for filling existing arrays using out keyword argument. Currently supported in (both 32- and 64-bit outputs)

• Uniforms (random_sample)

• Exponentials (standard_exponential)

• Normals (standard_normal)

• Standard Gammas (via standard_gamma)

### Included Pseudo Random Number Generators

This modules includes a number of alternative random number generators in addition to the MT19937 that is included in NumPy. The RNGs include:

• MT19937, the NumPy rng

• dSFMT a SSE2-aware version of the MT19937 generator that is especially fast at generating doubles

• SFMT a SSE2-aware version of the MT19937 generator that is optimized for integer values

• PCG32 and PCG64

• MRG32K3A

• A multiplicative lagged fibonacci generator (LFG(63, 1279, 861, *))

### Differences from numpy.random.RandomState

#### New Features

• standard_normal, normal, randn and multivariate_normal all support an additional method keyword argument which can be bm or zig where bm corresponds to the current method using the Box-Muller transformation and zig uses the much faster (100%+) Ziggurat method.

• standard_exponential and standard_gamma both support an additional method keyword argument which can be inv or zig where inv corresponds to the current method using the inverse CDF and zig uses the much faster (100%+) Ziggurat method.

• Core random number generators can produce either single precision (np.float32) or double precision (np.float64, the default) using an the optional keyword argument dtype

• Core random number generators can fill existing arrays using the out keyword argument

#### New Functions

• random_entropy - Read from the system entropy provider, which is commonly used in cryptographic applications

• random_raw - Direct access to the values produced by the underlying PRNG. The range of the values returned depends on the specifics of the PRNG implementation.

• random_uintegers - unsigned integers, either 32- ([0, 2**32-1]) or 64-bit ([0, 2**64-1])

• jump - Jumps RNGs that support it. jump moves the state a great distance. Only available if supported by the RNG.

• advance - Advanced the core RNG ‘as-if’ a number of draws were made, without actually drawing the numbers. Only available if supported by the RNG.

### Status

• Complete drop-in replacement for numpy.random.RandomState. The mt19937 generator is identical to numpy.random.RandomState, and will produce an identical sequence of random numbers for a given seed.

• Builds and passes all tests on:

• Linux 32/64 bit, Python 2.7, 3.4, 3.5, 3.6 (probably works on 2.6 and 3.3)

• PC-BSD (FreeBSD) 64-bit, Python 2.7

• OSX 64-bit, Python 2.7

• Windows 32/64 bit (only tested on Python 2.7, 3.5 and 3.6, but should work on 3.3/3.4)

### Version

The version matched the latest version of NumPy where randomstate.prng.mt19937 passes all NumPy test.

### Documentation

An occasionally updated build of the documentation is available on my github pages.

### Plans

This module is essentially complete. There are a few rough edges that need to be smoothed.

• Stream support for MLFG

• Creation of additional streams from a RandomState where supported (i.e. a next_stream() method)

### Requirements

Building requires:

• Python (2.7, 3.4, 3.5, 3.6)

• NumPy (1.9, 1.10, 1.11, 1.12)

• Cython (0.22, not 0.23, 0.24, 0.25)

• tempita (0.5+), if not provided by Cython

Testing requires pytest (3.0+).

Note: it might work with other versions but only tested with these versions.

### Development and Testing

All development has been on 64-bit Linux, and it is regularly tested on Travis-CI. The library is occasionally tested on Linux 32-bit,
OSX 10.10, PC-BSD 10.2 (should also work on Free BSD) and Windows (Python 2.7/3.5, both 32 and 64-bit).

Basic tests are in place for all RNGs. The MT19937 is tested against NumPy’s implementation for identical results. It also passes NumPy’s test suite.

### Installing

python setup.py install

#### SSE2

dSFTM makes use of SSE2 by default. If you have a very old computer or are building on non-x86, you can install using:

python setup.py install --no-sse2

#### Windows

Either use a binary installer, or if building from scratch, use Python 3.5 with Visual Studio 2015 Community Edition. It can also be build using Microsoft Visual C++ Compiler for Python 2.7 and Python 2.7, although some modifications may be needed to distutils to find the compiler.

### Using

The separate generators are importable from randomstate.prng.

import randomstate
rs = randomstate.prng.xorshift128.RandomState()
rs.random_sample(100)

rs = randomstate.prng.pcg64.RandomState()
rs.random_sample(100)

# Identical to NumPy
rs = randomstate.prng.mt19937.RandomState()
rs.random_sample(100)

Like NumPy, randomstate also exposes a single instance of the mt19937 generator directly at the module level so that commands like

import randomstate
randomstate.standard_normal()
randomstate.exponential(1.0, 1.0, size=10)

will work.

Standard NCSA, plus sub licenses for components.

### Performance

Performance is promising, and even the mt19937 seems to be faster than NumPy’s mt19937.

Speed-up relative to NumPy (Uniform Doubles)
************************************************************
randomstate.prng-dsfmt-random_sample               313.5%
randomstate.prng-mlfg_1279_861-random_sample       459.4%
randomstate.prng-mrg32k3a-random_sample            -57.6%
randomstate.prng-mt19937-random_sample              72.5%
randomstate.prng-pcg32-random_sample               232.8%
randomstate.prng-pcg64-random_sample               330.6%
randomstate.prng-xoroshiro128plus-random_sample    609.9%
randomstate.prng-xorshift1024-random_sample        348.8%
randomstate.prng-xorshift128-random_sample         489.7%

Speed-up relative to NumPy (Normals using Box-Muller)
************************************************************
randomstate.prng-dsfmt-standard_normal                26.8%
randomstate.prng-mlfg_1279_861-standard_normal        30.9%
randomstate.prng-mrg32k3a-standard_normal            -14.8%
randomstate.prng-mt19937-standard_normal              17.7%
randomstate.prng-pcg32-standard_normal                24.5%
randomstate.prng-pcg64-standard_normal                26.2%
randomstate.prng-xoroshiro128plus-standard_normal     31.4%
randomstate.prng-xorshift1024-standard_normal         27.4%
randomstate.prng-xorshift128-standard_normal          30.3%

Speed-up relative to NumPy (Normals using Ziggurat)
************************************************************
randomstate.prng-dsfmt-standard_normal               491.7%
randomstate.prng-mlfg_1279_861-standard_normal       439.6%
randomstate.prng-mrg32k3a-standard_normal            101.2%
randomstate.prng-mt19937-standard_normal             354.4%
randomstate.prng-pcg32-standard_normal               531.0%
randomstate.prng-pcg64-standard_normal               517.9%
randomstate.prng-xoroshiro128plus-standard_normal    674.0%
randomstate.prng-xorshift1024-standard_normal        486.7%
randomstate.prng-xorshift128-standard_normal         617.0%

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