sphvol.c

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/*
 *                   SPHERE VOLUME
 *                   by Melinda Green
 *                   [e-mail]
 *
 * Calculates and prints the volumes of the unit hyperspheres for
 * dimensions zero through the given value, or 9 by default.
 * Prints in the form of a C array of double called sphere_volumes.
 *
 * From formule in "Regular Polytopes" by H.S.M Coxeter, the volume
 * of a hypersphere of dimension d is:
 *        Pi^(d/2) / gamma(d/2 + 1)
 * 
 * This implementation works by first computing the log of the above
 * function and then returning the exp of that value in order to avoid
 * instabilities due to the huge values that the real gamma function
 * would return.
 *
 * Multiply the output volumes by R^n to get the volume of an n
 * dimensional sphere of radius R.
 */

#include <stdio.h>
#include <math.h>

#ifndef M_PI
#	define M_PI 3.1415926535
#endif

static void print_volume(int dimension, double volume)
{
	printf("\t%.6f,  /* dimension %3d */\n", volume, dimension);
}

static double sphere_volume(double dimension)
{
	const double log_pi = log(M_PI);
	double log_gamma, log_volume;
	log_gamma = gamma(dimension/2.0 + 1);
	log_volume = dimension/2.0 * log_pi - log_gamma;
	return exp(log_volume);
}

extern int main(int argc, char *argv[])
{
	int dim, max_dims=9;

	if(2 == argc)
		max_dims = atoi(argv[1]);

	printf("static const double sphere_volumes[] = {\n");
	for(dim=0; dim<max_dims+1; dim++)
		print_volume(dim, sphere_volume(dim));
	printf("};\n");
	return 0;
}