Thread-safe random number generation for Monte-Carlo integration - multithreading

Question

Im trying to write something which very quickly calculates random numbers and can be applied on multiple threads. My current code is:
/* Approximating PI using a Monte-Carlo method. */
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>
#include <omp.h>
#define N 1000000000 /* As lareg as possible for increased accuracy */
double random_function(void);
int main(void)
{
int i = 0;
double X, Y;
double count_inside_temp = 0.0, count_inside = 0.0;
unsigned int th_id = omp_get_thread_num();
#pragma omp parallel private(i, X, Y) firstprivate(count_inside_temp)
{
srand(th_id);
#pragma omp for schedule(static)
for (i = 0; i <= N; i++) {
X = 2.0 * random_function() - 1.0;
Y = 2.0 * random_function() - 1.0;
if ((X * X) + (Y * Y) < 1.0) {
count_inside_temp += 1.0;
}
}
#pragma omp atomic
count_inside += count_inside_temp;
}
printf("Approximation to PI is = %.10lf\n", (count_inside * 4.0)/ N);
return 0;
}
double random_function(void)
{
return ((double) rand() / (double) RAND_MAX);
}
This works but from observing a resource manager I know its not using all the threads. Does rand() work for multithreaded code? And if not is there a good alternative? Many Thanks. Jack

Answer 1

Is rand() thread safe? Maybe, maybe not:
The rand() function need not be reentrant. A function that is not required to be reentrant is not required to be thread-safe."
One test and good learning exercise would be to replace the call to rand() with, say, a fixed integer and see what happens.
The way I think of pseudo-random number generators is as a black box which take an integer as input and return an integer as output. For any given input the output is always the same, but there is no pattern in the sequence of numbers and the sequence is uniformly distributed over the range of possible outputs. (This model isn't entirely accurate, but it'll do.) The way you use this black box is to choose a staring number (the seed) use the output value in your application and as the input for the next call to the random number generator. There are two common approaches to designing an API:
Two functions, one to set the initial seed (e.g. srand(seed)) and one to retrieve the next value from the sequence (e.g. rand()). The state of the PRNG is stored internally in sort of global variable. Generating a new random number either will not be thread safe (hard to tell, but the output stream won't be reproducible) or will be slow in multithreded code (you end up with some serialization around the state value).
A interface where the PRNG state is exposed to the application programmer. Here you typically have three functions: init_prng(seed), which returns some opaque representation of the PRNG state, get_prng(state), which returns a random number and changes the state variable, and destroy_peng(state), which just cleans up allocated memory and so on. PRNGs with this type of API should all be thread safe and run in parallel with no locking (because you are in charge of managing the (now thread local) state variable.
I generally write in Fortran and use Ladd's implementation of the Mersenne Twister PRNG (that link is worth reading). There are lots of suitable PRNG's in C which expose the state to your control. PRNG looks good and using this (with initialization and destroy calls inside the parallel region and private state variables) should give you a decent speedup.
Finally, it's often the case that PRNGs can be made to perform better if you ask for a whole sequence of random numbers in one go (e.g. the compiler can vectorize the PRNG internals). Because of this libraries often have something like get_prng_array(state) functions which give you back an array full of random numbers as if you put get_prng in a loop filling the array elements - they just do it more quickly. This would be a second optimization (and would need an added for loop inside the parallel for loop. Obviously, you don't want to run out of per-thread stack space doing this!