Identifying and understanding random number algorithms

[schniefen]

Studying different ways to generate random numbers according to a distribution and the below algorithm describes the "box method". A search on Google led to the Box-Mueller method. Are they related? Also, what would be a simple implementation of this algorithm for $f(x)=\sin{(x)}$ on $[0,\pi]$? Is it correct that $y$ should be scaled to some value in $[0,1]$?

We generate two random numbers $x$ and $y$. We scale $x$ so that it
gives a random point in the restricted range we want to generate random numbers in. Now we scale
$y$ so it matches the range from 0 to the maximum value of the function $f(x)$ we want to generate.
Now we accept $x$ if $y < f(x)$ and reject $x$ otherwise.​

Implementation example:

#include <math.h>

int main(){

double x = (double)rand();
double y = (double)rand();
 
double xs = fmod(x,pi);
double ys = fmod(y,1);

if (ys < sin(xs)) return sin(xs);
}

 

[Svein]

What is the return value if the "if" clause is not satisfied?

 

[jim mcnamara]

You do realize that rand() implements a well known pseudorandom number generator in itself. The early versions of this library call is Knuth's random number generator. The Standard Library has several other PRNG's that return double data types, all positive integers (long datatype), etc.

PS: you should read about the srand() seed other seed functions...

From man page in Linux:

double drand48(void);

double erand48(unsigned short xseed[3]);

long lrand48(void);

long nrand48(unsigned short xseed[3]);

long mrand48(void);

long jrand48(unsigned short xseed[3]);

void srand48(long seed);

unsigned short *seed48(unsigned short xseed[3]);

void lcong48(unsigned short p[7]);

DESCRIPTION
The rand48 family of functions generates pseudo-random numbers using a
linear congruential algorithm working on integers 48 bits in size. The
particular formula employed is r(n+1) = (a * r(n) + c) mod m where the
default values are for the multiplicand a = 0xfdeece66d = 25214903917
and the addend c = 0xb = 11. The modulo is always fixed at m = 2 ** 48.
r(n) is called the seed of the random number generator.