## Generator Parameters

Each generator may contain several variants, which can be selected by setting the generator

parameterduring 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 valueSPRNG_DEFAULTis 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

initializingstreamswith the 48 bit Linear Congruential Generator with prime addend.

- SPRNG_DEFAULT

- Multiplier
a = 2875a2e7b175in base 16. This is the same as using the parameterCRAYLCG.

- CRAYLCG

- Multiplier
a = 2875a2e7b175in base 16. This multiplier is identical to that used by the FORTRAN INTRINSIC`getranf`

available on CRAY machines.

- DRAND48

- Multiplier
a = 5deece66din base 16. This multiplier is available as the default on thedrand48random number generator available on several UNIX systems. Please note that the multiplier is incorrectly documented as5deece66d16on some machines.

- FISH1

- Multiplier
a = 3eac44605265in base 16. This multiplier was analysed by Fishman.

- FISH2

- Multiplier
a = 1ee1429cc9f5in base 16. This multiplier was analysed by Fishman.

- FISH3

- Multiplier
a = 275b38eb4bbdin base 16. This multiplier was analysed by Fishman.

- FISH4

- Multiplier
a = 739a9cb08605in base 16. This multiplier was analysed by Fishman.

- FISH5

- Multiplier
a = 3228d7cc25f5in 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

initializingstreamswith the 64 bit Linear Congruential Generator with prime addend.

- SPRNG_DEFAULT

- Multiplier
a = 27bb2ee687b0b0fdin base 16. This is the same as using the parameterLECU1.

- LECU1

- Multiplier
a = 27bb2ee687b0b0fdin base 16, = 2862933555777941757, suggested by L'cuyer in his table of multipliers.

- LECU2

- Multiplier
a = 2c6fe96ee78b6955in base 16, = 3202034522624059733, suggested by L'cuyer in his table of multipliers.

- LECU3

- Multiplier
a = 369dea0f31a53f85in 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

initializingstreamswith the modified Lagged Fibonacci Generator.

- SPRNG_DEFAULT

- Lags
l = 1279, k = 861. This is the same as using the parameterLAG1279.

- 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 parameterLAG17.## 6. Prime Modulus Linear Congruential Generator

The only acceptable parameter is the value

SPRNG_DEFAULT, which corresponds to a modulus of 2^{61}-1.