random.c File Reference

pseudo-random number generators More...

#include "random.h"
#include "normal.h"
#include "stdfix-full-iso.h"
#include "stdfix-exp.h"

Macros
#define	R   32
	Size of the global WELL1024a state vector.

Functions
void	init_WELL1024a_simp (void)
	The initialiser function that MUST BE CALLED ONCE before WELLRNG1024a_simp() is used. Global WELL1024a seed is randomised each time it is called.
uint32_t	WELL1024a_simp (void)
	The WELL generator itself.
void	validate_WELL1024a_seed (WELL1024a_seed_t seed)
	MUST USE THIS before passing the seed to WELL1024a_seed() the first time.
uint32_t	WELL1024a_seed (WELL1024a_seed_t STATE)
	The WELL 1024a RNG with custom seed.
uint32_t	mars_kiss32 (void)
	Marsaglia 32-bit KISS generator using no multiplication instructions.
uint32_t	mars_kiss64_simp (void)
	Implementation of Marsaglia JKISS RNG uses 64-bit value and 2x multiplies.
uint32_t	mars_kiss64_seed (mars_kiss64_seed_t seed)
	The Marsaglia KISS 64 RNG with custom seed.
void	validate_mars_kiss64_seed (mars_kiss64_seed_t seed)
	Validate seed for Marsaglia KISS 64.
s1615	exponential_dist_variate (uniform_rng uni_rng, uint32_t *seed_arg)
	Von Neuman's exponential distribution generator.
s1615	gaussian_dist_variate (uniform_rng uni_rng, uint32_t *seed_arg)
	Returns standard Gaussian deviate.
uint32_t	poisson_dist_variate (uniform_rng uni_rng, uint32_t *seed_arg, s1615 lambda)
	A poisson distributed random variable, given \( \exp(-\lambda) \).
uint32_t	poisson_dist_variate_exp_minus_lambda (uniform_rng uni_rng, uint32_t *seed_arg, u032 exp_minus_lambda)
	Use this version for Poisson with pre-calculated exp(-λ) for speed gain.

Variables
static uint32_t	STATE [R]
	The global state vector for WELL1024a_simp()

Detailed Description

pseudo-random number generators

Author

Michael Hopkins

Date

February 2014

For all of these, to get a high resolution fixed-point number in (0,1) that uses the entire generator space use ulrbits() around return value to give a 32-bit unsigned long fract

Also other options to get a 16-bit unsigned fract by taking 16 MSBs of result and urbits()

If floating point is available then multiply by 2.32830643653869628906e-10

spin1_rand() takes 134.9 nanosecs (i.e. 27 ticks) per call

WELL 1024a long cycle generator (2^1024 - 1) from L'Ecuyer & Panneton

Better equi-distribution and warm-up performance than Mersenne Twister, and faster

294.9 nanosecs (i.e. 59 ticks) per call

Function Documentation

WELL1024a_simp()

uint32_t WELL1024a_simp

(

void

)

The WELL generator itself.

Returns

A uniformly randomly distributed 32-bit value.

validate_WELL1024a_seed()

void validate_WELL1024a_seed

(

WELL1024a_seed_t

seed

)

MUST USE THIS before passing the seed to WELL1024a_seed() the first time.

Parameters

[in]

seed

The seed to validate

WELL1024a_seed()

uint32_t WELL1024a_seed

(

WELL1024a_seed_t

seed

)

The WELL 1024a RNG with custom seed.

Parameters

[in]

seed

The RNG state, including seed value.

Returns

A uniformly randomly distributed 32-bit value.

mars_kiss32()

uint32_t mars_kiss32

(

void

)

Marsaglia 32-bit KISS generator using no multiplication instructions.

Only available in simple form. Very good for single stream of PRNs.

Returns

A pseudo-random unsigned 32-bit integer.

mars_kiss64_simp()

uint32_t mars_kiss64_simp

(

void

)

Implementation of Marsaglia JKISS RNG uses 64-bit value and 2x multiplies.

The best general purpose trade-off between speed, equidistribution and cycle length.

Returns

A normally distributed 32-bit unsigned integer.

mars_kiss64_seed()

uint32_t mars_kiss64_seed

(

mars_kiss64_seed_t

seed

)

The Marsaglia KISS 64 RNG with custom seed.

Parameters

[in]

seed

The RNG state, including seed value.

Returns

A uniformly randomly distributed 32-bit value.

validate_mars_kiss64_seed()

void validate_mars_kiss64_seed

(

mars_kiss64_seed_t

seed

)

Validate seed for Marsaglia KISS 64.

Note

MUST USE THIS before passing the seed to mars_kiss64_seed() the first time.

Parameters

[in]

seed

The seed to validate

exponential_dist_variate()

s1615 exponential_dist_variate	(	uniform_rng	uni_rng,
		uint32_t *	seed_arg
	)

Von Neuman's exponential distribution generator.

from Ripley p.230 and adapted for our types

Mean number of U(0,1) per call = 5.2

Parameters

[in]	uni_rng	The uniform random number generator
[in]	seed_arg	The seed argument to the uniform RNG.

Returns

Exponentially distributed random number.

gaussian_dist_variate()

s1615 gaussian_dist_variate	(	uniform_rng	uni_rng,
		uint32_t *	seed_arg
	)

Returns standard Gaussian deviate.

translation of NR in C version of Box-Muller

Parameters

[in]	uni_rng	The uniform random number generator
[in]	seed_arg	The seed argument to the uniform RNG.

Returns

Gaussian-distributed random number.

poisson_dist_variate()

uint32_t poisson_dist_variate	(	uniform_rng	uni_rng,
		uint32_t *	seed_arg,
		s1615	lambda
	)

A poisson distributed random variable, given \( \exp(-\lambda) \).

This is Knuth's method, and is \( O(n) \), so don't use for large \( \lambda \)

Parameters

[in]	uni_rng	The uniform random number generator
[in]	seed_arg	The seed argument to the uniform RNG.
[in]	lambda	The shape parameter of the distribution, \( \lambda \)

Returns

Poisson-distributed random number.

Remarks

DRL thinks the cast (from s16.15 to u0.32) might be wasteful.

poisson_dist_variate_exp_minus_lambda()

uint32_t poisson_dist_variate_exp_minus_lambda	(	uniform_rng	uni_rng,
		uint32_t *	seed_arg,
		u032	exp_minus_lambda
	)

Use this version for Poisson with pre-calculated exp(-λ) for speed gain.

Parameters

[in]	uni_rng	The uniform random number generator
[in]	seed_arg	The seed argument to the uniform RNG.
[in]	exp_minus_lambda	The shape parameter of the distribution, \( \exp(-\lambda) \).

Returns

Poisson-distributed random number.

Remarks

DRL thinks this can be simplified to the following code:

while (p > exp_minus_lambda) {
    p *= ulrbits(uni_rng(seed_arg));
    k++;
}

return k;