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/* sum/test.c
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*
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* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Gerard Jungman, Brian Gough
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3 of the License, or (at
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* your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*/
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/* Author: G. Jungman */
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#include <config.h>
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#include <stdlib.h>
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#include <stdio.h>
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#include <gsl/gsl_math.h>
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#include <gsl/gsl_test.h>
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#include <gsl/gsl_sum.h>
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#include <gsl/gsl_ieee_utils.h>
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#define N 50
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void check_trunc (double * t, double expected, const char * desc);
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void check_full (double * t, double expected, const char * desc);
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int
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main (void)
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{
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gsl_ieee_env_setup ();
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{
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double t[N];
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int n;
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const double zeta_2 = M_PI * M_PI / 6.0;
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/* terms for zeta(2) */
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for (n = 0; n < N; n++)
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{
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double np1 = n + 1.0;
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t[n] = 1.0 / (np1 * np1);
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}
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check_trunc (t, zeta_2, "zeta(2)");
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check_full (t, zeta_2, "zeta(2)");
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}
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{
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double t[N];
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double x, y;
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int n;
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/* terms for exp(10.0) */
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x = 10.0;
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y = exp(x);
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t[0] = 1.0;
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for (n = 1; n < N; n++)
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{
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t[n] = t[n - 1] * (x / n);
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}
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check_trunc (t, y, "exp(10)");
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check_full (t, y, "exp(10)");
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}
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{
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double t[N];
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double x, y;
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int n;
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/* terms for exp(-10.0) */
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x = -10.0;
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y = exp(x);
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t[0] = 1.0;
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for (n = 1; n < N; n++)
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{
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t[n] = t[n - 1] * (x / n);
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}
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check_trunc (t, y, "exp(-10)");
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check_full (t, y, "exp(-10)");
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}
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{
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double t[N];
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double x, y;
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int n;
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/* terms for -log(1-x) */
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x = 0.5;
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y = -log(1-x);
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t[0] = x;
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for (n = 1; n < N; n++)
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{
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t[n] = t[n - 1] * (x * n) / (n + 1.0);
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}
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check_trunc (t, y, "-log(1/2)");
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check_full (t, y, "-log(1/2)");
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}
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{
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double t[N];
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double x, y;
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int n;
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/* terms for -log(1-x) */
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x = -1.0;
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y = -log(1-x);
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t[0] = x;
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for (n = 1; n < N; n++)
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{
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t[n] = t[n - 1] * (x * n) / (n + 1.0);
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}
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check_trunc (t, y, "-log(2)");
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check_full (t, y, "-log(2)");
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}
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{
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double t[N];
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int n;
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double result = 0.192594048773;
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/* terms for an alternating asymptotic series */
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t[0] = 3.0 / (M_PI * M_PI);
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for (n = 1; n < N; n++)
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{
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t[n] = -t[n - 1] * (4.0 * (n + 1.0) - 1.0) / (M_PI * M_PI);
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}
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check_trunc (t, result, "asymptotic series");
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check_full (t, result, "asymptotic series");
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}
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{
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double t[N];
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int n;
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/* Euler's gamma from GNU Calc (precision = 32) */
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double result = 0.5772156649015328606065120900824;
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/* terms for Euler's gamma */
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t[0] = 1.0;
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for (n = 1; n < N; n++)
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{
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t[n] = 1/(n+1.0) + log(n/(n+1.0));
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}
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check_trunc (t, result, "Euler's constant");
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check_full (t, result, "Euler's constant");
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}
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{
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double t[N];
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int n;
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/* eta(1/2) = sum_{k=1}^{\infty} (-1)^(k+1) / sqrt(k)
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From Levin, Intern. J. Computer Math. B3:371--388, 1973.
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I=(1-sqrt(2))zeta(1/2)
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=(2/sqrt(pi))*integ(1/(exp(x^2)+1),x,0,inf) */
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double result = 0.6048986434216305; /* approx */
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/* terms for eta(1/2) */
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for (n = 0; n < N; n++)
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{
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t[n] = (n%2 ? -1 : 1) * 1.0 /sqrt(n + 1.0);
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}
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check_trunc (t, result, "eta(1/2)");
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check_full (t, result, "eta(1/2)");
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}
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{
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double t[N];
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int n;
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double result = 1.23;
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for (n = 0; n < N; n++)
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{
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t[n] = (n == 0) ? 1.23 : 0.0;
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}
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check_trunc (t, result, "1.23 + 0 + 0 + 0...");
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check_full (t, result, "1.23 + 0 + 0 + 0...");
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}
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exit (gsl_test_summary ());
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}
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void
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check_trunc (double * t, double expected, const char * desc)
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{
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double sum_accel, prec;
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gsl_sum_levin_utrunc_workspace * w = gsl_sum_levin_utrunc_alloc (N);
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gsl_sum_levin_utrunc_accel (t, N, w, &sum_accel, &prec);
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gsl_test_rel (sum_accel, expected, 1e-8, "trunc result, %s", desc);
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/* No need to check precision for truncated result since this is not
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a meaningful number */
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gsl_sum_levin_utrunc_free (w);
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}
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void
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check_full (double * t, double expected, const char * desc)
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{
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double sum_accel, err_est, sd_actual, sd_est;
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gsl_sum_levin_u_workspace * w = gsl_sum_levin_u_alloc (N);
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gsl_sum_levin_u_accel (t, N, w, &sum_accel, &err_est);
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gsl_test_rel (sum_accel, expected, 1e-8, "full result, %s", desc);
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sd_est = -log10 (err_est/fabs(sum_accel) + GSL_DBL_EPSILON);
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sd_actual = -log10 (DBL_EPSILON + fabs ((sum_accel - expected)/expected));
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/* Allow one digit of slop */
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gsl_test (sd_est > sd_actual + 1.0, "full significant digits, %s (%g vs %g)", desc, sd_est, sd_actual);
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gsl_sum_levin_u_free (w);
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}
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