GNU Scientific Library – Reference Manual: Unix random number generators

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### 18.10 Unix random number generators

The standard Unix random number generators `rand`, `random` and `rand48` are provided as part of GSL. Although these generators are widely available individually often they aren’t all available on the same platform. This makes it difficult to write portable code using them and so we have included the complete set of Unix generators in GSL for convenience. Note that these generators don’t produce high-quality randomness and aren’t suitable for work requiring accurate statistics. However, if you won’t be measuring statistical quantities and just want to introduce some variation into your program then these generators are quite acceptable.

Generator: gsl_rng_rand

  This is the BSD `rand` generator. Its sequence is with a = 1103515245, c = 12345 and m = 2^31. The seed specifies the initial value, x_1. The period of this generator is 2^31, and it uses 1 word of storage per generator.

Generator: gsl_rng_random_bsd
Generator: gsl_rng_random_libc5
Generator: gsl_rng_random_glibc2

  These generators implement the `random` family of functions, a set of linear feedback shift register generators originally used in BSD Unix. There are several versions of `random` in use today: the original BSD version (e.g. on SunOS4), a libc5 version (found on older GNU/Linux systems) and a glibc2 version. Each version uses a different seeding procedure, and thus produces different sequences.

  The original BSD routines accepted a variable length buffer for the generator state, with longer buffers providing higher-quality randomness. The `random` function implemented algorithms for buffer lengths of 8, 32, 64, 128 and 256 bytes, and the algorithm with the largest length that would fit into the user-supplied buffer was used. To support these algorithms additional generators are available with the following names,

      gsl_rng_random8_bsd
      gsl_rng_random32_bsd
      gsl_rng_random64_bsd
      gsl_rng_random128_bsd
      gsl_rng_random256_bsd

  where the numeric suffix indicates the buffer length. The original BSD `random` function used a 128-byte default buffer and so `gsl_rng_random_bsd` has been made equivalent to `gsl_rng_random128_bsd`. Corresponding versions of the `libc5` and `glibc2` generators are also available, with the names `gsl_rng_random8_libc5`, `gsl_rng_random8_glibc2`, etc.

Generator: gsl_rng_rand48

  This is the Unix `rand48` generator. Its sequence is defined on 48-bit unsigned integers with a = 25214903917, c = 11 and m = 2^48. The seed specifies the upper 32 bits of the initial value, x_1, with the lower 16 bits set to `0x330E`. The function `gsl_rng_get` returns the upper 32 bits from each term of the sequence. This does not have a direct parallel in the original `rand48` functions, but forcing the result to type `long int` reproduces the output of `mrand48`. The function `gsl_rng_uniform` uses the full 48 bits of internal state to return the double precision number x_n/m, which is equivalent to the function `drand48`. Note that some versions of the GNU C Library contained a bug in `mrand48` function which caused it to produce different results (only the lower 16-bits of the return value were set).

Next: Other random number generators, Previous: Random number generator algorithms, Up: Random Number Generation [Index]