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/*
* test2600 - 2600 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: 1995/10/13 00:13:14
* File existed as early as: 1995
*
* Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
*/
/*
* Stringent tests of some of calc's builtin functions.
* Most of the tests are concerned with the accuracy of the value
* returned for a function; usually it is expected that
* remainder (true value - calculated value) will be less in
* absolute value than "epsilon", where this is either a specified
* argument eps, or if this is omitted, the current value of epsilon().
* In some cases the remainder is to have a particular sign, or to
* have absolute value not exceeding eps/2, or in some cases 3 * eps/4.
*
* Typical of these tests is testpower("power", n, b, eps, verbose).
* Here n is the number of numbers a for which power(a, b, eps) is to
* be evaluated; the ratio c = (true value - calculated value)/eps
* is calculated and if this is not less in absolute value than
* 0.75, a "failure" is recorded and the value of a displayed.
* On completion of the tests, the minimum and maximum values of
* c are displayed.
*
* The numbers a are usually large "random" integers or sometimes
* ratios of such integers. In some cases the formulae used to
* calculate c assume eps is small compared with the value of the
* function. If eps is very small, say 1e-1000, or if the denominator
* of b in power(a, b, eps) is large, the computation required for
* a test may be very heavy.
*
* Test funcations are called as:
*
* testabc(str, ..., verbose)
*
* where str is a string that names the test. This string is printed
* without a newline (if verbose > 0), near the beginning of the function.
* The verbose parameter controls how verbose the test will be:
*
* 0 - print nothing
* 1 - print str and the error count
* 2 - print min and max errors as well
* 3 - print everything including individual loop counts
*
* All functions return the number of errors that they detected.
*/
global defaultverbose = 1; /* default verbose value */
global err;
define testismult(str, n, verbose)
{
local a, b, c, i, m;
if (isnull(verbose)) verbose = defaultverbose;
if (verbose > 0) {
print str:":",:;
}
m = 0;
for (i = 0; i < n; i++) {
if (verbose > 2) print i,:;
a = scale(rand(1,1e1000), rand(100));
b = scale(rand(1,1e1000), rand(100));
c = a * b;
if (!ismult(c,a)) {
m++;
if (verbose > 1) {
printf("*** Failure with:\na = %d\nb = %d\n",
a,b);
}
}
}
if (verbose > 0) {
if (m) {
printf("*** %d error(s)\n", m);
} else {
printf("no errors\n");
}
}
return m;
}
define testsqrt(str, n, eps, verbose)
{
local a, c, i, x, m, min, max;
if (isnull(verbose)) verbose = 2;
if (verbose > 0) {
print str:":",:;
}
m = 0;
min = 1000;
max = -1000;
if (isnull(eps))
eps = epsilon();
for (i = 1; i <= n; i++) {
if (verbose > 2) print i,:;
a = scale(rand(1,1000), rand(100));
x = sqrt(a, eps);
if (x)
c = (a/x - x)/2/eps;
else
c = a/eps; /* ??? */
if (c < min)
min = c;
if (c > max)
max = c;
if (abs(c) > 1) {
m++;
if (verbose > 1) {
printf("*** Failure with:\na = %d\neps = %d\n",
a,eps);
}
}
}
if (verbose > 0) {
if (m) {
printf("*** %d error(s)\n", m);
printf(" %s: rem/eps min=%d, max=%d\n",
str, min, max);
} else {
printf("no errors\n");
}
}
if (verbose > 1) {
printf(" %s: rem/eps min=%0.4d, max=%0.4d\n", str, min, max);
}
return m;
}
define testexp(str, n, eps, verbose)
{
local i, a, c, m, min, max;
if (isnull(verbose)) verbose = 2;
if (verbose > 0) {
print str:":",:;
}
if (isnull(eps))
eps = epsilon();
min = 1000;
max = -1000;
for (i = 1; i <= n; i++) {
if (verbose > 2) print i,:;
a = rand(1,1e20)/rand(1,1e20) + rand(50);
if (rand(1))
a = -a;
c = cexp(a, eps);
if (c < min)
min = c;
if (c > max)
max = c;
if (abs(c) > 0.02) {
m++;
if (verbose > 1) {
printf("*** Failure with:\na = %d\neps = %d\n",
a,eps);
}
}
}
if (verbose > 0) {
if (m) {
printf("*** %d error(s)\n", m);
printf(" %s: rem/eps min=%d, max=%d\n",
str, min, max);
} else {
printf("no errors\n");
}
}
if (verbose > 1) {
printf(" %s: rem/eps min=%0.4d, max=%0.4d\n", str, min, max);
}
return m;
}
define cexp(x,eps) /* Find relative rem/eps for exp(x, eps) */
{
local eps1, v, v1, c;
if (isnull(eps))
eps = epsilon();
eps1 = eps * 1e-6;
v = exp(x, eps);
v1 = exp(x, eps1);
c = round((v1 - v)/v1/eps, 6, 24);
return c;
}
define testln(str, n, eps, verbose)
{
local i, a, c, m, min, max;
if (isnull(verbose)) verbose = 2;
if (verbose > 0) {
print str:":",:;
}
if (isnull(eps))
eps = epsilon();
min = 1000;
max = -1000;
for (i = 1; i <= n; i++) {
if (verbose > 2) print i,:;
a = rand(1,1e20)/rand(1,1e20) + rand(50);
c = cln(a, eps);
if (c < min)
min = c;
if (c > max)
max = c;
if (abs(c) > 0.5) {
m++;
if (verbose > 1) {
printf("*** Failure with:\na = %d\neps = %d\n",
a,eps);
}
}
}
if (verbose > 0) {
if (m) {
printf("*** %d error(s)\n", m);
printf(" %s: rem/eps min=%d, max=%d\n",
str, min, max);
} else {
printf("no errors\n");
}
}
if (verbose > 1) {
printf(" %s: rem/eps min=%0.4d, max=%0.4d\n", str, min, max);
}
return m;
}
define cln(a, eps)
{
local eps1, v, v1, c;
if (isnull(eps))
eps = epsilon();
eps1 = eps/1e6;
v = ln(a, eps);
v1 = ln(a, eps1);
c = round((v1 - v)/eps, 6, 24);
return c;
}
define testpower(str, n, b, eps, verbose)
{
local i, a, c, m, min, max;
if (isnull(verbose)) verbose = 2;
if (verbose > 0) {
print str:":",:;
}
if (isnull(eps))
eps = epsilon();
if (!isnum(b))
quit "Second argument (exponent) to be a number";
min = 1000;
max = -1000;
for (i = 1; i <= n; i++) {
if (verbose > 2) print i,:;
a = rand(1,1e20)/rand(1,1e20);
c = cpow(a, b, eps);
if (abs(c) > .75) {
m++;
if (verbose > 1) {
printf("*** Failure for a = %d\n", a);
}
}
if (c < min)
min = c;
if (c > max)
max = c;
}
if (verbose > 0) {
if (m) {
printf("*** %d error(s)\n", m);
printf(" %s: rem/eps min=%d, max=%d\n",
str, min, max);
} else {
printf("no errors\n");
}
}
if (verbose > 1) {
printf(" %s: rem/eps min=%0.4d, max=%0.4d\n", str, min, max);
}
return m;
}
define testpower2(str, n, eps, verbose)
{
local i, a, c, m, min, max;
local b;
local num;
local c2;
local oldeps;
if (isnull(verbose)) verbose = 2;
if (verbose > 0) {
print str:":",:;
}
if (isnull(eps))
eps = epsilon();
oldeps = epsilon(eps);
epsilon(eps),;
if (!isnum(b))
quit "Second argument (exponent) to be a number";
min = 1000;
max = -1000;
for (i = 1; i <= n; i++) {
if (verbose > 2) print i,:;
/* real ^ real */
a = rand(1,1e20);
a = a / (int(a/2)+rand(1,1e20));
b = rand(1,1e20);
b = b / (int(b/2)+rand(1,1e20));
c = a ^ b;
c2 = power(a, b);
if (c != c2) {
m++;
if (verbose > 1) {
printf("*** real^real failure for a = %d\n", a);
}
}
/* complex ^ real */
a = rand(1,1e20);
a = a / (int(a/2)+rand(1,1e20));
b = rand(1,1e20);
b = b / (int(b/2)+rand(1,1e20));
c = (a*1i) ^ b;
c2 = power(a*1i, b);
if (c != c2) {
m++;
if (verbose > 1) {
printf("*** comp^real failure for a = %d\n", a);
}
}
/* real ^ complex */
a = rand(1,1e20);
a = a / (int(a/2)+rand(1,1e20));
b = rand(1,1e20);
b = b / (int(b/2)+rand(1,1e20));
c = a ^ (b*1i);
c2 = power(a, b*1i);
if (c != c2) {
m++;
if (verbose > 1) {
printf("*** real^comp failure for a = %d\n", a);
}
}
/* complex ^ complex */
a = rand(1,1e20);
a = a / (int(a/2)+rand(1,1e20));
b = rand(1,1e20);
b = b / (int(b/2)+rand(1,1e20));
c = (a*1i) ^ (b*1i);
c2 = power(a*1i, b*1i);
if (c != c2) {
m++;
if (verbose > 1) {
printf("*** comp^comp failure for a = %d\n", a);
}
}
}
epsilon(oldeps),;
if (verbose > 0) {
if (m) {
printf("*** %d error(s)\n", m);
printf(" %s: rem/eps min=%d, max=%d\n",
str, min, max);
} else {
printf("no errors\n");
}
}
if (verbose > 1) {
printf(" %s: rem/eps min=%0.4d, max=%0.4d\n", str, min, max);
}
return m;
}
define cpow(a, b, eps) /* Find rem/eps for power(a,b,eps) */
{
local v, v1, c, n, d, h;
if (isnull(eps))
eps = epsilon();
n = num(b);
d = den(b);
v = power(a, b, eps);
h = (a^n/v^d - 1) * v/d;
c = round(h/eps, 6, 24);
return c;
}
define testgcd(str, n, verbose)
{
local i, a, b, g, m;
if (isnull(verbose)) verbose = 2;
if (verbose > 0) {
print str:":",:;
}
m = 0;
for (i = 1; i <= n; i++) {
if (verbose > 2) print i,:;
a = rand(1,1e1000);
b = rand(1,1e1000);
g = gcd(a,b);
if (!ismult(a,g) || !ismult(b,g) || !g || !isrel(a/g, b/g)) {
m++;
printf("*** Failure for a = %d, b = %d\n", a, b);
}
}
if (verbose > 0) {
if (m) {
printf("*** %d error(s)\n", m);
} else {
printf("no errors\n");
}
}
return m;
}
define mkreal() = scale(rand(-1000,1001)/rand(1,1000), rand(-100, 101));
define mkcomplex() = mkreal() + 1i * mkreal();
define mkbigreal()
{
local x;
x = rand(100, 1000)/rand(1,10);
if (rand(2))
x = -x;
return x;
}
define mksmallreal() = rand(-10, 11)/rand(100,1000);
define testappr(str, n, verbose)
{
local x, y, z, m, i, p;
if (isnull(verbose))
verbose = defaultverbose;
if (verbose > 0) {
print str:":",:;
}
m = 0;
for (i = 1; i <= n; i++) {
x = rand(3) ? mkreal(): mkcomplex();
y = mkreal();
if (verbose > 2)
printf(" %d: x = %d, y = %d\n", i, x, y);
for (z = 0; z < 32; z++) {
p = checkappr(x,y,z,verbose);
if (p) {
printf("*** Failure for x=%d, y=%d, z=%d\n",
x, y, z);
m++;
}
}
}
if (verbose > 0) {
if (m) {
printf("*** %d error(s)\n", m);
} else {
printf("no errors\n");
}
}
return m;
}
define checkappr(x,y,z,verbose) /* Returns 1 if an error is detected */
{
local a;
a = appr(x,y,z);
if (verbose > 1)
printf("\ta = %d\n", a);
if (isreal(x))
return checkresult(x,y,z,a);
if (isnum(x))
return checkresult(re(x), y, z, re(a))
| checkresult(im(x), y, z, im(a));
quit "Bad first argument for checkappr()";
}
define checkresult(x,y,z,a) /* tests correctness of a = appr(x,y,z) */
{
local r, n, s, v;
if (y == 0)
return (a != x);
r = x - a;
n = a/y;
if (!isint(n))
return 1;
if (abs(r) >= abs(y))
return 1;
if (r == 0)
return 0;
if (z & 16) {
if (abs(r) > abs(y)/2)
return 1;
if (abs(r) < abs(y)/2)
return 0;
z &= 15;
}
s = sgn(r);
switch (z) {
case 0: v = (s == sgn(y)); break;
case 1: v = (s == -sgn(y)); break;
case 2: v = (s == sgn(x)); break;
case 3: v = (s == -sgn(x)); break;
case 4: v = (s > 0); break;
case 5: v = (s < 0); break;
case 6: v = (s == sgn(x/y)); break;
case 7: v = (s == -sgn(x/y)); break;
case 8: v = iseven(n); break;
case 9: v = isodd(n); break;
case 10: v = (x/y > 0) ? iseven(n) : isodd(n); break;
case 11: v = (x/y > 0) ? isodd(n) : iseven(n); break;
case 12: v = (y > 0) ? iseven(n) : isodd(n); break;
case 13: v = (y > 0) ? isodd(n) : iseven(n); break;
case 14: v = (x > 0) ? iseven(n) : isodd(n); break;
case 15: v = (x > 0) ? isodd(n) : iseven(n); break;
}
return !v;
}
/*
* test2600 - perform all of the above tests a bunch of times
*/
define test2600(verbose, tnum)
{
local n; /* test parameter */
local ep; /* test parameter */
local i;
/* set test parameters */
n = 5; /* internal test loop count */
if (isnull(verbose)) {
verbose = defaultverbose;
}
if (isnull(tnum)) {
tnum = 1; /* initial test number */
}
/*
* test a lot of stuff
*/
srand(2600e2600);
ep = 1e-250;
err += testismult(strcat(str(tnum++), ": mult"), n*20, verbose);
err += testappr(strcat(str(tnum++), ": appr"), n*40, verbose);
err += testexp(strcat(str(tnum++),": exp"), n, ep, verbose);
err += testln(strcat(str(tnum++),": ln"), n, ep, verbose);
err += testpower(strcat(str(tnum++),": power"), n,
rand(2,10), ep, verbose);
err += testgcd(strcat(str(tnum++),": gcd"), n, ep, verbose);
for (i=0; i < 32; ++i) {
config("sqrt", i);
err += testsqrt(strcat(str(tnum++),": sqrt",str(i)), n*10,
ep, verbose);
}
err += testpower2(strcat(str(tnum++),": power"), n*4, ep, verbose);
if (verbose > 1) {
if (err) {
print "***", err, "error(s) found in test2600";
} else {
print "no errors in test2600";
}
}
return tnum;
}