Random Number Generators

This document indexes the various pseudo-random number generators available on NERSC computers. The systems are covered individually and in combinations. Further information about the software listed here may be available as man pages on the target systems.

Some of the available generators can be used in parallel programs, but special considerations apply to such use, see A Brief on Parallel Random Number Generators.

Except where specifically indicated, the routines named have not been tested. Similar names on different platforms do not guarantee similar generators or output sequences. Repeatable behavior between runs or in parallel usage, may or may not be possible. Even in the case of identical generators, differences between platforms may arise, due to differences in arithmetic, operand lengths, and compiler options.

pranf

The PRANF genarator suite provides the generator of SGI/Cray's RANF function, along with a set of seed generation routines, in Fortran, using radix-4096 (12-bit) integer calculations. This offers portability and deterministic parallelism at the expense of performance. PRANF is intended for use on shared memory systems. It has not yet been tested on the SP system by NERSC staff. For more information, see The PRANF Portable Parallel Random Number Generator.

rand, srand (libc.a), RAND (xlf intrinsic)

libc.a: The rand subroutine generates a pseudo-random number using a multiplicative congruential algorithm. The random-number generator has a period of 2**32, and it returns successive pseudo-random numbers in the range from 0 through (2**15)-1. The srand subroutine resets the rand generator to a new starting point. It uses the Seed parameter as a seed for a new sequence of pseudo-random numbers to be returned by subsequent calls to the rand subroutine. This version of these two routines is from the standard C library, libc.a.

xlf: Another pair of routines named rand and srand exist as disparaged intrinsics in the Fortran compiler. Their functionality is approximately the same, but the numbers generated are uniformly distributed greater than or equal to zero and less then one. Use of these two routines is not recommended. The more modern Fortran 90 intrinsics, RANDOM_NUMBER and RANDOM_SEED are recommended instead.

rand_r

Multithread-safe version of rand, discussed above.

random, srandom, initstate, setstate

Generates pseudo-random numbers more efficiently. The random subroutine uses a non-linear additive feedback random-number generator to return successive pseudo-random numbers in the range from 0 to 2**31-1. The random and srandom subroutines have almost the same calling sequence and initialization properties as the rand and srand subroutines. The difference is that the rand subroutine produces a much less random sequence; the low dozen bits generated by the rand subroutine go through a cyclic pattern, while all the bits generated by the random subroutine are usable. The initstate subroutine allows a state array, passed in as an argument, to be initialized for future use. The setstate subroutine allows rapid switching between states.

srandom_r, initstate_r, or setstate_r

Multithread-safe version of random, srandom, initstate, setstate, discussed above.

drand48, erand48, jrand48, lcong48, lrand48, mrand48, nrand48, seed48, srand48

Generate uniformly distributed pseudo-random number sequences. This family of subroutines generates pseudo-random numbers using the linear congruential algorithm and 48-bit integer arithmetic. The drand48 and erand48 subroutines return positive double-precision floating-point values uniformly distributed over the interval [0.0, 1.0). The lrand48 and nrand48 subroutines return positive long integers uniformly distributed over the interval [0,2**31). The mrand48 and jrand48 subroutines return signed long integers uniformly distributed over the interval [-2**31, 2**31). The srand48, seed48, and lcong48 subroutines initialize the random-number generator. Programs must call one of them before calling the drand48, lrand48 or mrand48 subroutines.

erand48_r, lrand48_r, nrand48_r, mrand48_r, jrand48_r, srand48_r

Multithread-safe versions of erand48, lrand48, nrand48, mrand48, jrand48, srand48, discussed above.

RANDOM_NUMBER, RANDOM_SEED

The RANDOM_NUMBER Fortran 90 intrinsic subroutine returns one pseudorandom number or an array of pseudorandom numbers from the uniform distribution over the range 0 <= x < 1. The RANDOM_SEED Fortran 90 intrinsic subroutine restarts or queries the pseudorandom number generator used by RANDOM_NUMBER.

SURAND, DURAND, SNRAND, DNRAND, SURXOR, DURXOR

Subroutines SURAND and DURAND generate vectors of uniformly distributed random numbers, in short and long precision, respectively. Subroutines SNRAND and DNRAND generate vectors of normally distributed random numbers, in short and long precision, respectively. Subroutines SURXOR and DURXOR generate vectors of long period uniformly distributed random numbers, in short and long precision, respectively. These routines are all part of the ESSL library. For more information, the Random Numer Generation section of the ESSL Guide and Reference.

URNG, PDURNG

Subroutine URNG generates a vector of uniform pseudo-random numbers in the ranges (0,1) or (-1,1), depending on an argument. The random numbers are generated using the multiplicative congruential method with a user-specified seed. Subroutine PDURNG generates a global vector of uniform pseudo-random numbers in the ranges (0,1) or (-1,1), depending on an argument. The random numbers are generated using the multiplicative congruential method with a user-specified seed. These routines are all part of the PESSL library. For more information, see the Random Numer Generation section of the PESSL Guide and Reference.

sprng

The Scalable Parallel Random Number Generators (SPRNG) library provides a variety of generators and a "spawn" facility to generate new streams. The user must select among the various generators, which include

1. lcg - a 48-Bit Linear Congruential Generator with Prime Addend
2. lcg64 - a 64-Bit Linear Congruential Generator with Prime Addend
3. lfg - a Modified Lagged Fibonacci Generator
4. mlcg - a Multiplicative Lagged Fibonacci Generator
5. cmrg - a Combined Multiple Recursive Generator

It is available in its own module; type "module load sprng" to make it available. For more information, and to see the test code source with sample parallel usage, see Using SPRNG at NERSC.

Common Libraries

NAG

Chapter G05 of the NAG web documentation contains over 40 routines for generating and manipulating random numbers of many kinds and from many distributions. The IBM SP has double precision version.