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17.4 Sampling from a random number generator

The following functions return uniformly distributed random numbers, either as integers or double precision floating point numbers. To obtain non-uniform distributions see 19.

Function: unsigned long int gsl_rng_get (const gsl_rng * r)

This function returns a random integer from the generator r. The minimum and maximum values depend on the algorithm used, but all integers in the range [min,max] are equally likely. The values of min and max can determined using the auxiliary functions gsl_rng_max (r) and gsl_rng_min (r).

Function: double gsl_rng_uniform (const gsl_rng * r)

This function returns a double precision floating point number uniformly distributed in the range [0,1). The range includes 0.0 but excludes 1.0. The value is typically obtained by dividing the result of gsl_rng_get(r) by gsl_rng_max(r) + 1.0 in double precision. Some generators compute this ratio internally so that they can provide floating point numbers with more than 32 bits of randomness (the maximum number of bits that can be portably represented in a single unsigned long int).

Function: double gsl_rng_uniform_pos (const gsl_rng * r)

This function returns a positive double precision floating point number uniformly distributed in the range (0,1), excluding both 0.0 and 1.0. The number is obtained by sampling the generator with the algorithm of gsl_rng_uniform until a non-zero value is obtained. You can use this function if you need to avoid a singularity at 0.0.

Function: unsigned long int gsl_rng_uniform_int (const gsl_rng * r, unsigned long int n)

This function returns a random integer from 0 to n-1 inclusive by scaling down and/or discarding samples from the generator r. All integers in the range [0,n-1] are produced with equal probability. For generators with a non-zero minimum value an offset is applied so that zero is returned with the correct probability.

Note that this function is designed for sampling from ranges smaller than the range of the underlying generator. The parameter n must be less than or equal to the range of the generator r. If n is larger than the range of the generator then the function calls the error handler with an error code of GSL_EINVAL and returns zero.

In particular, this function is not intended for generating the full range of unsigned integer values [0,2^32-1]. Instead choose a generator with the maximal integer range and zero mimimum value, such as gsl_rng_ranlxd1, gsl_rng_mt19937 or gsl_rng_taus, and sample it directly using gsl_rng_get. The range of each generator can be found using the auxiliary functions described in the next section.