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