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a31078bbec
Some folks might think: “you still use RCS”?!? And we will say, hey, at least we switched from SCCS to RCS back in … I think it was around 1994 ... at least we are keeping up! :-) :-) :-) Logs say that SCCS version 18 became RCS version 19 on 1994 March 18. RCS served us well. But now it is time to move on. And so we are switching to git. Calc releases produce a lot of file changes. In the 125 releases of calc since 1996, when I started managing calc releases, there have been 15473 file mods!
319 lines
6.8 KiB
Plaintext
319 lines
6.8 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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* 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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