* functions. */
/*
- * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2003 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
#include "exams.h"
/* Assorted tests on other transcendental functions. */
-static unsigned inifcns_consist_trans(void)
+static unsigned inifcns_consist_trans()
{
- 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;
- }
-
- return result;
+ using GiNaC::asin; using GiNaC::acos;
+
+ 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)
+static unsigned inifcns_consist_gamma()
{
- unsigned result = 0;
- ex e;
-
- e = tgamma(ex(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(ex(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;
+ 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)
+static unsigned inifcns_consist_psi()
{
- 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;
+ using GiNaC::log;
+
+ 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)
+static unsigned inifcns_consist_zeta()
{
- 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 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 exam_inifcns()
{
- 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;
+ 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;
}
git://www.ginac.de / ginac.git / blobdiff