User's Guide:Details: Generators:Parameters

Generator Parameters

Each generator may contain several variants, which can be selected by setting the generator parameter during initialization. For example, the multiplier is a parameter for the 48 bit linear congruential generator. Choosing different multipliers will give diferent sets of streams. The value SPRNG_DEFAULT is always an acceptable parameter. Tests to verify the quality of each generator are based on the default parameter.

1. Combined Multiple Recursive Generator

The acceptable parameter values are identical to those for the 64 Bit Linear Congruential Generator.

2. 48 Bit Linear Congruential Generator with Prime Addend

We give below the different choices of parameters available to the user while initializing streams with the 48 bit Linear Congruential Generator with prime addend.

SPRNG_DEFAULT

Multiplier a = 2875a2e7b175 in base 16. This is the same as using the parameter CRAYLCG.

CRAYLCG

Multiplier a = 2875a2e7b175 in base 16. This multiplier is identical to that used by the FORTRAN INTRINSIC getranf available on CRAY machines.

DRAND48

Multiplier a = 5deece66d in base 16. This multiplier is available as the default on the drand48 random number generator available on several UNIX systems. Please note that the multiplier is incorrectly documented as 5deece66d16 on some machines.

FISH1

Multiplier a = 3eac44605265 in base 16. This multiplier was analysed by Fishman.

FISH2

Multiplier a = 1ee1429cc9f5 in base 16. This multiplier was analysed by Fishman.

FISH3

Multiplier a = 275b38eb4bbd in base 16. This multiplier was analysed by Fishman.

FISH4

Multiplier a = 739a9cb08605 in base 16. This multiplier was analysed by Fishman.

FISH5

Multiplier a = 3228d7cc25f5 in base 16. This multiplier was analysed by Fishman.

3. 64 Bit Linear Congruential Generator with Prime Addend

We give below the different choices of parameters available to the user while initializing streams with the 64 bit Linear Congruential Generator with prime addend.

SPRNG_DEFAULT

Multiplier a = 27bb2ee687b0b0fd in base 16. This is the same as using the parameter LECU1.

LECU1

Multiplier a = 27bb2ee687b0b0fd in base 16, = 2862933555777941757, suggested by L'cuyer in his table of multipliers.

LECU2

Multiplier a = 2c6fe96ee78b6955 in base 16, = 3202034522624059733, suggested by L'cuyer in his table of multipliers.

LECU3

Multiplier a = 369dea0f31a53f85 in base 16, = 3935559000370003845, suggested by L'cuyer in his table of multipliers.

4. Modified Lagged Fibonacci Generator

We give below the different choices of parameters available to the user while initializing streams with the modified Lagged Fibonacci Generator.

SPRNG_DEFAULT

Lags l = 1279, k = 861. This is the same as using the parameter LAG1279.

LAG1279

Lags l = 1279, k = 861.

LAG17

Lags l = 17, k = 5.

LAG31

Lags l = 31, k = 6.

LAG55

Lags l = 55, k = 24.

LAG63

Lags l = 63, k = 31.

LAG127

Lags l = 127, k = 97.

LAG521

Lags l = 521, k = 353.

LAG521B

Lags l = 521, k = 168.

LAG607

Lags l = 607, k = 334.

LAG607B

Lags l = 607, k = 273.

LAG1279B

Lags l = 1279, k = 418.

5. Multiplicative Lagged Fibonacci Generator

The lags are identical to that of the Modified Lagged Fibonacci Generator, except the following:

SPRNG_DEFAULT

Lags l = 17, k = 5. This is the same as using the parameter LAG17.

6. Prime Modulus Linear Congruential Generator

The only acceptable parameter is the value SPRNG_DEFAULT, which corresponds to a modulus of 2⁶¹-1.

Example