Q: I need a random number generator.
A: The Standard C library has one: rand. The implementation on your system may not be perfect, but writing a better one isn't necessarily easy, either.
If you do find yourself needing to implement your own random number generator, there is plenty of literature out there; see the References below or the sci.math.num-analysis FAQ list. There are also any number of packages on the net: old standbys are r250, RANLIB, and FSULTRA (see question 18.16), and there is much recent work by Marsaglia, and Matumoto and Nishimura (the ``Mersenne Twister''), and some code collected by Don Knuth on his web pages.
Here is a portable C implementation of the ``minimal standard'' generator proposed by Park and Miller:
#define a 16807
#define m 2147483647
#define q (m / a)
#define r (m % a)
static long int seed = 1;
long int PMrand()
{
long int hi = seed / q;
long int lo = seed % q;
long int test = a * lo - r * hi;
if(test > 0)
seed = test;
else seed = test + m;
return seed;
}
(The ``minimal standard'' is adequately good;
it is something ``against which all others should be judged'';
it is recommended for use
``unless one has access to a random number generator
known to be better.'')
This code implements the generator
X <- (aX + c) mod mfor a = 16807, m = 2147483647 (which is 2**31-1), and c = 0.[footnote] The multiplication is carried out using a technique described by Schrage, ensuring that the intermediate result aX does not overflow. The implementation above returns long int values in the range [1, 2147483646]; that is, it corresponds to C's rand with a RAND_MAX of 2147483646, except that it never returns 0. To alter it to return floating-point numbers in the range (0, 1) (as in the Park and Miller paper), change the declaration to
double PMrand()and the last line to
return (double)seed / m;For slightly better statistical properties, Park and Miller now recommend using a = 48271.
References:
K&R2 Sec. 2.7 p. 46, Sec. 7.8.7 p. 168
ISO Sec. 7.10.2.1
H&S Sec. 17.7 p. 393
PCS Sec. 11 p. 172
Knuth Vol. 2 Chap. 3 pp. 1-177
Park and Miller, ``Random Number Generators: Good Ones are Hard to Find''
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