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323 lines
6.9 KiB
Plaintext
323 lines
6.9 KiB
Plaintext
/*
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* test3400 - 3400 series of the regress.cal test suite
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*
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* Copyright (C) 1999 Ernest Bowen and Landon Curt Noll
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*
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* Primary author: Ernest Bowen
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*
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* Calc is open software; you can redistribute it and/or modify it under
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* the terms of the version 2.1 of the GNU Lesser General Public License
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* as published by the Free Software Foundation.
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*
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* Calc is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
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* Public License for more details.
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*
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* A copy of version 2.1 of the GNU Lesser General Public License is
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* distributed with calc under the filename COPYING-LGPL. You should have
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* received a copy with calc; if not, write to Free Software Foundation, Inc.
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* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*
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* @(#) $Revision: 30.1 $
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* @(#) $Id: test3400.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
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* @(#) $Source: /usr/local/src/bin/calc/cal/RCS/test3400.cal,v $
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*
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* Under source code control: 1995/12/02 05:20:11
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* File existed as early as: 1995
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*
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* Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
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*/
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/*
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* tests of performance of some trigonometric functions
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*
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* test3401 tests abs(acot(cot(x)) - x) <= eps for x = k * eps < pi
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* test3402 tests abs(tan(x/2) - csc(x) + cot(x)) <= eps
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* test3403 tests abs(tan(x) - cot(x) + 2 * cot(2 * x)) <= eps
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* test3404 tests abs(cot(x/2) - csc(x) - cot(x)) <= eps
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* test3405 tests atan(tan(x)) == x for x = k * eps, abs(x) <= pi/2
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* test3406 tests abs(sec(x) - sec(x + 2 * N * pi)) <= eps
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*
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* To run say, test1 n times give instruction test1(n, eps); eps
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* defaults to epsilon().
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*
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* Here pi1k is pi to 1000 decimal places; x is a random real number
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* except when x is described as k * eps, in which case k is a random
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* integer such that x is in the specified range.
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*
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* In the last test N is a large random integer, but it is assumed
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* that eps is large compared with N * 1e-1000.
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*
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* I am surprised that test3406 seems to give no errors - I had expected
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* that the two sides might differ by eps. [[test changed to test eps error]]
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*/
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defaultverbose = 1; /* default verbose value */
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global pi1k = pi(1e-1000);
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define test3401(str, n, eps, verbose)
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{
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local i, m, x, y, N;
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if (isnull(verbose)) verbose = defaultverbose;
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if (verbose > 0) {
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print str:":",:;
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}
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if (isnull(n)) n = 250;
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if (isnull(eps)) eps = epsilon();
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m = 0;
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N = pi(eps)/eps;
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for (i = 0; i < n; i++) {
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x = rand(1, N) * eps;
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y = cot(x, eps);
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if (verbose > 1)
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printf("%r\n", x);
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if (abs(acot(y, eps) - x) > eps) {
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if (verbose > 1) {
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printf("*** Failure for x = %r\n", x);
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}
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m++;
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}
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}
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if (verbose > 0) {
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if (m) {
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printf("*** %d error(s)\n", m);
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} else {
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printf("no errors\n");
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}
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}
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return m;
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}
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define test3402(str, n, eps, verbose)
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{
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local i, m, x, y, N;
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if (isnull(verbose)) verbose = defaultverbose;
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if (verbose > 0) {
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print str:":",:;
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}
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if (isnull(n)) n = 250;
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if (isnull(eps)) eps = epsilon();
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eps = abs(eps);
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m = 0;
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N = 1e10;
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for (i = 0; i < n; i++) {
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x = rand(-N, N)/rand(1, N);
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y = tan(x/2, eps) - csc(x,eps) + cot(x,eps);
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if (verbose > 1)
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printf("%r\n", x);
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if (abs(y) > eps) {
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if (verbose > 1) {
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printf("*** Failure for x = %r\n", x);
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}
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m++;
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}
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}
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if (verbose > 0) {
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if (m) {
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printf("*** %d error(s)\n", m);
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} else {
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printf("no errors\n");
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}
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}
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return m;
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}
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define test3403(str, n, eps, verbose)
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{
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local i, m, x, y, N;
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if (isnull(verbose)) verbose = defaultverbose;
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if (verbose > 0) {
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print str:":",:;
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}
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if (isnull(n)) n = 250;
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if (isnull(eps)) eps = epsilon();
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eps = abs(eps);
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m = 0;
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N = 1e10;
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for (i = 0; i < n; i++) {
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x = rand(-N, N)/rand(1, N);
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y = tan(x, eps) - cot(x,eps) + 2 * cot(2 * x,eps);
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if (verbose > 1)
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printf("%r\n", x);
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if (abs(y) > eps) {
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m++;
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if (verbose > 1) {
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printf("*** Failure for x = %r\n", x);
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}
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}
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}
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if (verbose > 0) {
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if (m) {
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printf("*** %d error(s)\n", m);
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} else {
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printf("no errors\n");
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}
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}
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return m;
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}
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define test3404(str, n, eps, verbose)
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{
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local i, m, x, y, N;
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if (isnull(verbose)) verbose = defaultverbose;
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if (verbose > 0) {
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print str:":",:;
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}
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if (isnull(n)) n = 250;
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if (isnull(eps)) eps = epsilon();
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eps = abs(eps);
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m = 0;
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N = 1e10;
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for (i = 0; i < n; i++) {
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x = rand(-N, N)/rand(1, N);
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y = cot(x/2, eps) - csc(x,eps) - cot(x,eps);
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if (verbose > 1)
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printf("%r\n", x);
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if (abs(y) > eps) {
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m++;
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if (verbose > 1) {
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printf("*** Failure for x = %r\n", x);
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}
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}
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}
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if (verbose > 0) {
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if (m) {
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printf("*** %d error(s)\n", m);
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} else {
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printf("no errors\n");
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}
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}
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return m;
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}
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define test3405(str, n, eps, verbose)
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{
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local i, m, x, y, N;
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if (isnull(verbose)) verbose = defaultverbose;
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if (verbose > 0) {
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print str:":",:;
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}
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if (isnull(n)) n = 250;
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if (isnull(eps)) eps = epsilon();
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m = 0;
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N = pi(eps)/eps;
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N = quo(N, 2, 0);
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for (i = 0; i < n; i++) {
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x = rand(-N, N) * eps;
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y = tan(x, eps);
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if (verbose > 1)
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printf("%r\n", x);
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if (atan(y, eps) != x) {
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m++;
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if (verbose > 1) {
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printf("*** Failure for x = %r\n", x);
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}
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}
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}
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if (verbose > 0) {
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if (m) {
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printf("*** %d error(s)\n", m);
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} else {
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printf("no errors\n");
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}
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}
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return m;
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}
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define test3406(str, n, eps, verbose)
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{
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local i, m, x, y, z, N;
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if (isnull(verbose)) verbose = defaultverbose;
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if (verbose > 0) {
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print str:":",:;
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}
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if (isnull(n)) n = 250;
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if (isnull(eps)) eps = epsilon();
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m = 0;
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for (i = 0; i < n; i++) {
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x = rand(-1e10, 1e10)/rand(1, 1e10);
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N = rand(-1e10, 1e10);
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y = sec(x, eps);
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z = sec(x + 2 * N * pi1k, eps);
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if (verbose > 1)
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printf("%r, %d\n", x, N);
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if (abs(y-z) > eps) {
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m++;
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if (verbose > 1) {
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printf("*** Failure for x = %r\n", x);
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}
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}
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}
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if (verbose > 0) {
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if (m) {
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printf("*** %d error(s)\n", m);
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} else {
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printf("no errors\n");
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}
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}
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return m;
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}
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/*
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* test3400 - perform all of the above tests
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*/
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define test3400(verbose, tnum)
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{
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local n; /* test parameter */
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local eps; /* test parameter */
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local i;
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/*
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* set test parameters
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*/
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if (isnull(verbose)) {
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verbose = defaultverbose;
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}
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n = 250;
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eps = epsilon();
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srand(3400e3400);
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/*
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* test a lot of stuff
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*/
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err += test3401(strcat(str(tnum++), \
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": acot(cot(x))"), n, eps, verbose);
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err += test3402(strcat(str(tnum++), \
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": tan(x/2)-csc(x)+cot(x)"), n, eps, verbose);
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err += test3403(strcat(str(tnum++), \
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": tan(x)-cot(x)+2*cot(2*x)"), n, eps, verbose);
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err += test3404(strcat(str(tnum++), \
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": cot(x/2)-csc(x)-cot(x)"), n, eps, verbose);
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err += test3405(strcat(str(tnum++), \
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": atan(tan(x))"), n, eps, verbose);
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err += test3406(strcat(str(tnum++), \
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": sec(x)-sec(x+2*N*pi)"), n, eps, verbose);
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/*
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* test results
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*/
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if (verbose > 1) {
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if (err) {
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print "***", err, "error(s) found in test3400";
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} else {
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print "no errors in test3400";
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}
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}
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return tnum;
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}
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