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/** @file exam_inifcns.cpp
*
* This test routine applies assorted tests on initially known higher level
* functions. */
/*
* GiNaC Copyright (C) 1999-2002 Johannes Gutenberg University Mainz, Germany
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program 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 General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
#include "exams.h"
/* Assorted tests on other transcendental functions. */
static unsigned inifcns_consist_trans(void)
{
unsigned result = 0;
symbol x("x");
ex chk;
chk = asin(1)-acos(0);
if (!chk.is_zero()) {
clog << "asin(1)-acos(0) erroneously returned " << chk
<< " instead of 0" << endl;
++result;
}
// arbitrary check of type sin(f(x)):
chk = pow(sin(acos(x)),2) + pow(sin(asin(x)),2)
- (1+pow(x,2))*pow(sin(atan(x)),2);
if (chk != 1-pow(x,2)) {
clog << "sin(acos(x))^2 + sin(asin(x))^2 - (1+x^2)*sin(atan(x))^2 "
<< "erroneously returned " << chk << " instead of 1-x^2" << endl;
++result;
}
// arbitrary check of type cos(f(x)):
chk = pow(cos(acos(x)),2) + pow(cos(asin(x)),2)
- (1+pow(x,2))*pow(cos(atan(x)),2);
if (!chk.is_zero()) {
clog << "cos(acos(x))^2 + cos(asin(x))^2 - (1+x^2)*cos(atan(x))^2 "
<< "erroneously returned " << chk << " instead of 0" << endl;
++result;
}
// arbitrary check of type tan(f(x)):
chk = tan(acos(x))*tan(asin(x)) - tan(atan(x));
if (chk != 1-x) {
clog << "tan(acos(x))*tan(asin(x)) - tan(atan(x)) "
<< "erroneously returned " << chk << " instead of -x+1" << endl;
++result;
}
// arbitrary check of type sinh(f(x)):
chk = -pow(sinh(acosh(x)),2).expand()*pow(sinh(atanh(x)),2)
- pow(sinh(asinh(x)),2);
if (!chk.is_zero()) {
clog << "expand(-(sinh(acosh(x)))^2)*(sinh(atanh(x))^2) - sinh(asinh(x))^2 "
<< "erroneously returned " << chk << " instead of 0" << endl;
++result;
}
// arbitrary check of type cosh(f(x)):
chk = (pow(cosh(asinh(x)),2) - 2*pow(cosh(acosh(x)),2))
* pow(cosh(atanh(x)),2);
if (chk != 1) {
clog << "(cosh(asinh(x))^2 - 2*cosh(acosh(x))^2) * cosh(atanh(x))^2 "
<< "erroneously returned " << chk << " instead of 1" << endl;
++result;
}
// arbitrary check of type tanh(f(x)):
chk = (pow(tanh(asinh(x)),-2) - pow(tanh(acosh(x)),2)).expand()
* pow(tanh(atanh(x)),2);
if (chk != 2) {
clog << "expand(tanh(acosh(x))^2 - tanh(asinh(x))^(-2)) * tanh(atanh(x))^2 "
<< "erroneously returned " << chk << " instead of 2" << endl;
++result;
}
// check consistency of log and eta phases:
for (int r1=-1; r1<=1; ++r1) {
for (int i1=-1; i1<=1; ++i1) {
ex x1 = r1+I*i1;
if (x1.is_zero())
continue;
for (int r2=-1; r2<=1; ++r2) {
for (int i2=-1; i2<=1; ++i2) {
ex x2 = r2+I*i2;
if (x2.is_zero())
continue;
if (abs(evalf(eta(x1,x2)-log(x1*x2)+log(x1)+log(x2)))>.1e-12) {
clog << "either eta(x,y), log(x), log(y) or log(x*y) is wrong"
<< " at x==" << x1 << ", y==" << x2 << endl;
++result;
}
}
}
}
}
return result;
}
/* Simple tests on the tgamma function. We stuff in arguments where the results
* exists in closed form and check if it's ok. */
static unsigned inifcns_consist_gamma(void)
{
unsigned result = 0;
ex e;
e = tgamma(1);
for (int i=2; i<8; ++i)
e += tgamma(ex(i));
if (e != numeric(874)) {
clog << "tgamma(1)+...+tgamma(7) erroneously returned "
<< e << " instead of 874" << endl;
++result;
}
e = tgamma(1);
for (int i=2; i<8; ++i)
e *= tgamma(ex(i));
if (e != numeric(24883200)) {
clog << "tgamma(1)*...*tgamma(7) erroneously returned "
<< e << " instead of 24883200" << endl;
++result;
}
e = tgamma(ex(numeric(5, 2)))*tgamma(ex(numeric(9, 2)))*64;
if (e != 315*Pi) {
clog << "64*tgamma(5/2)*tgamma(9/2) erroneously returned "
<< e << " instead of 315*Pi" << endl;
++result;
}
e = tgamma(ex(numeric(-13, 2)));
for (int i=-13; i<7; i=i+2)
e += tgamma(ex(numeric(i, 2)));
e = (e*tgamma(ex(numeric(15, 2)))*numeric(512));
if (e != numeric(633935)*Pi) {
clog << "512*(tgamma(-13/2)+...+tgamma(5/2))*tgamma(15/2) erroneously returned "
<< e << " instead of 633935*Pi" << endl;
++result;
}
return result;
}
/* Simple tests on the Psi-function (aka polygamma-function). We stuff in
arguments where the result exists in closed form and check if it's ok. */
static unsigned inifcns_consist_psi(void)
{
unsigned result = 0;
symbol x;
ex e, f;
// We check psi(1) and psi(1/2) implicitly by calculating the curious
// little identity tgamma(1)'/tgamma(1) - tgamma(1/2)'/tgamma(1/2) == 2*log(2).
e += (tgamma(x).diff(x)/tgamma(x)).subs(x==numeric(1));
e -= (tgamma(x).diff(x)/tgamma(x)).subs(x==numeric(1,2));
if (e!=2*log(2)) {
clog << "tgamma(1)'/tgamma(1) - tgamma(1/2)'/tgamma(1/2) erroneously returned "
<< e << " instead of 2*log(2)" << endl;
++result;
}
return result;
}
/* Simple tests on the Riemann Zeta function. We stuff in arguments where the
* result exists in closed form and check if it's ok. Of course, this checks
* the Bernoulli numbers as a side effect. */
static unsigned inifcns_consist_zeta(void)
{
unsigned result = 0;
ex e;
for (int i=0; i<13; i+=2)
e += zeta(i)/pow(Pi,i);
if (e!=numeric(-204992279,638512875)) {
clog << "zeta(0) + zeta(2) + ... + zeta(12) erroneously returned "
<< e << " instead of -204992279/638512875" << endl;
++result;
}
e = 0;
for (int i=-1; i>-16; i--)
e += zeta(i);
if (e!=numeric(487871,1633632)) {
clog << "zeta(-1) + zeta(-2) + ... + zeta(-15) erroneously returned "
<< e << " instead of 487871/1633632" << endl;
++result;
}
return result;
}
unsigned exam_inifcns(void)
{
unsigned result = 0;
cout << "examining consistency of symbolic functions" << flush;
clog << "----------consistency of symbolic functions:" << endl;
result += inifcns_consist_trans(); cout << '.' << flush;
result += inifcns_consist_gamma(); cout << '.' << flush;
result += inifcns_consist_psi(); cout << '.' << flush;
result += inifcns_consist_zeta(); cout << '.' << flush;
if (!result) {
cout << " passed " << endl;
clog << "(no output)" << endl;
} else {
cout << " failed " << endl;
}
return result;
}
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