gammavol.c

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/****************************************************************************
 * MODULE:       R-Tree library
 *
 * AUTHOR(S):    Antonin Guttman - original code
 *               Daniel Green (green@superliminal.com) - major clean-up
 *                               and implementation of bounding spheres
 *               Markus Metz - file-based and memory-based R*-tree
 *
 * PURPOSE:      Multidimensional index
 *
 * SPDX-FileCopyrightText: 2010 GRASS Development Team
 * SPDX-License-Identifier: GPL-2.0-or-later
 *****************************************************************************/
 
#include <stdio.h>
#include <math.h>
 
#ifndef ABS
#define ABS(a) ((a) > 0 ? (a) : -(a))
#endif
 
#define EP .0000000001
 
double sphere_volume(double dimension)
{
    double log_gamma, log_volume;
 
    log_gamma = lgamma(dimension / 2.0 + 1);
    log_volume = dimension / 2.0 * log(M_PI) - log_gamma;
    return exp(log_volume);
}
 
int main(void)
{
    double dim = 0, delta = 1;
 
    while (ABS(delta) > EP)
        if (sphere_volume(dim + delta) > sphere_volume(dim))
            dim += delta;
        else
            delta /= -2;
    fprintf(stdout, "max volume = %.10f at dimension %.10f\n",
            sphere_volume(dim), dim);
    return 0;
}