* functions. */
/*
- * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2004 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 "checks.h"
/* Some tests on the sine trigonometric function. */
-static unsigned inifcns_consist_sin(void)
+static unsigned inifcns_check_sin()
{
- unsigned result = 0;
- bool errorflag = false;
-
- // sin(n*Pi) == 0?
- errorflag = false;
- for (int n=-10; n<=10; ++n) {
- if (sin(n*Pi).eval() != numeric(0) ||
- !sin(n*Pi).eval().info(info_flags::integer))
- errorflag = true;
- }
- if (errorflag) {
- // we don't count each of those errors
- clog << "sin(n*Pi) with integer n does not always return exact 0"
- << endl;
- ++result;
- }
-
- // sin((n+1/2)*Pi) == {+|-}1?
- errorflag = false;
- for (int n=-10; n<=10; ++n) {
- if (!sin((n+numeric(1,2))*Pi).eval().info(info_flags::integer) ||
- !(sin((n+numeric(1,2))*Pi).eval() == numeric(1) ||
- sin((n+numeric(1,2))*Pi).eval() == numeric(-1)))
- errorflag = true;
- }
- if (errorflag) {
- clog << "sin((n+1/2)*Pi) with integer n does not always return exact {+|-}1"
- << endl;
- ++result;
- }
-
- // compare sin((q*Pi).evalf()) with sin(q*Pi).eval().evalf() at various
- // points. E.g. if sin(Pi/10) returns something symbolic this should be
- // equal to sqrt(5)/4-1/4. This routine will spot programming mistakes
- // of this kind:
- errorflag = false;
- ex argument;
- numeric epsilon(double(1e-8));
- for (int n=-340; n<=340; ++n) {
- argument = n*Pi/60;
- if (abs(sin(evalf(argument))-evalf(sin(argument)))>epsilon) {
- clog << "sin(" << argument << ") returns "
- << sin(argument) << endl;
- errorflag = true;
- }
- }
- if (errorflag) {
- ++result;
- }
-
- return result;
+ unsigned result = 0;
+ bool errorflag = false;
+
+ // sin(n*Pi) == 0?
+ errorflag = false;
+ for (int n=-10; n<=10; ++n) {
+ if (sin(n*Pi).eval() != numeric(0) ||
+ !sin(n*Pi).eval().info(info_flags::integer))
+ errorflag = true;
+ }
+ if (errorflag) {
+ // we don't count each of those errors
+ clog << "sin(n*Pi) with integer n does not always return exact 0"
+ << endl;
+ ++result;
+ }
+
+ // sin((n+1/2)*Pi) == {+|-}1?
+ errorflag = false;
+ for (int n=-10; n<=10; ++n) {
+ if (!sin((n+numeric(1,2))*Pi).eval().info(info_flags::integer) ||
+ !(sin((n+numeric(1,2))*Pi).eval() == numeric(1) ||
+ sin((n+numeric(1,2))*Pi).eval() == numeric(-1)))
+ errorflag = true;
+ }
+ if (errorflag) {
+ clog << "sin((n+1/2)*Pi) with integer n does not always return exact {+|-}1"
+ << endl;
+ ++result;
+ }
+
+ // compare sin((q*Pi).evalf()) with sin(q*Pi).eval().evalf() at various
+ // points. E.g. if sin(Pi/10) returns something symbolic this should be
+ // equal to sqrt(5)/4-1/4. This routine will spot programming mistakes
+ // of this kind:
+ errorflag = false;
+ ex argument;
+ numeric epsilon(double(1e-8));
+ for (int n=-340; n<=340; ++n) {
+ argument = n*Pi/60;
+ if (abs(sin(evalf(argument))-evalf(sin(argument)))>epsilon) {
+ clog << "sin(" << argument << ") returns "
+ << sin(argument) << endl;
+ errorflag = true;
+ }
+ }
+ if (errorflag)
+ ++result;
+
+ return result;
}
/* Simple tests on the cosine trigonometric function. */
-static unsigned inifcns_consist_cos(void)
+static unsigned inifcns_check_cos()
{
- unsigned result = 0;
- bool errorflag;
-
- // cos((n+1/2)*Pi) == 0?
- errorflag = false;
- for (int n=-10; n<=10; ++n) {
- if (cos((n+numeric(1,2))*Pi).eval() != numeric(0) ||
- !cos((n+numeric(1,2))*Pi).eval().info(info_flags::integer))
- errorflag = true;
- }
- if (errorflag) {
- clog << "cos((n+1/2)*Pi) with integer n does not always return exact 0"
- << endl;
- ++result;
- }
-
- // cos(n*Pi) == 0?
- errorflag = false;
- for (int n=-10; n<=10; ++n) {
- if (!cos(n*Pi).eval().info(info_flags::integer) ||
- !(cos(n*Pi).eval() == numeric(1) ||
- cos(n*Pi).eval() == numeric(-1)))
- errorflag = true;
- }
- if (errorflag) {
- clog << "cos(n*Pi) with integer n does not always return exact {+|-}1"
- << endl;
- ++result;
- }
-
- // compare cos((q*Pi).evalf()) with cos(q*Pi).eval().evalf() at various
- // points. E.g. if cos(Pi/12) returns something symbolic this should be
- // equal to 1/4*(1+1/3*sqrt(3))*sqrt(6). This routine will spot
- // programming mistakes of this kind:
- errorflag = false;
- ex argument;
- numeric epsilon(double(1e-8));
- for (int n=-340; n<=340; ++n) {
- argument = n*Pi/60;
- if (abs(cos(evalf(argument))-evalf(cos(argument)))>epsilon) {
- clog << "cos(" << argument << ") returns "
- << cos(argument) << endl;
- errorflag = true;
- }
- }
- if (errorflag) {
- ++result;
- }
-
- return result;
+ unsigned result = 0;
+ bool errorflag;
+
+ // cos((n+1/2)*Pi) == 0?
+ errorflag = false;
+ for (int n=-10; n<=10; ++n) {
+ if (cos((n+numeric(1,2))*Pi).eval() != numeric(0) ||
+ !cos((n+numeric(1,2))*Pi).eval().info(info_flags::integer))
+ errorflag = true;
+ }
+ if (errorflag) {
+ clog << "cos((n+1/2)*Pi) with integer n does not always return exact 0"
+ << endl;
+ ++result;
+ }
+
+ // cos(n*Pi) == 0?
+ errorflag = false;
+ for (int n=-10; n<=10; ++n) {
+ if (!cos(n*Pi).eval().info(info_flags::integer) ||
+ !(cos(n*Pi).eval() == numeric(1) ||
+ cos(n*Pi).eval() == numeric(-1)))
+ errorflag = true;
+ }
+ if (errorflag) {
+ clog << "cos(n*Pi) with integer n does not always return exact {+|-}1"
+ << endl;
+ ++result;
+ }
+
+ // compare cos((q*Pi).evalf()) with cos(q*Pi).eval().evalf() at various
+ // points. E.g. if cos(Pi/12) returns something symbolic this should be
+ // equal to 1/4*(1+1/3*sqrt(3))*sqrt(6). This routine will spot
+ // programming mistakes of this kind:
+ errorflag = false;
+ ex argument;
+ numeric epsilon(double(1e-8));
+ for (int n=-340; n<=340; ++n) {
+ argument = n*Pi/60;
+ if (abs(cos(evalf(argument))-evalf(cos(argument)))>epsilon) {
+ clog << "cos(" << argument << ") returns "
+ << cos(argument) << endl;
+ errorflag = true;
+ }
+ }
+ if (errorflag)
+ ++result;
+
+ return result;
}
/* Simple tests on the tangent trigonometric function. */
-static unsigned inifcns_consist_tan(void)
+static unsigned inifcns_check_tan()
{
- unsigned result = 0;
- bool errorflag;
-
- // compare tan((q*Pi).evalf()) with tan(q*Pi).eval().evalf() at various
- // points. E.g. if tan(Pi/12) returns something symbolic this should be
- // equal to 2-sqrt(3). This routine will spot programming mistakes of
- // this kind:
- errorflag = false;
- ex argument;
- numeric epsilon(double(1e-8));
- for (int n=-340; n<=340; ++n) {
- if (!(n%30) && (n%60)) // skip poles
- ++n;
- argument = n*Pi/60;
- if (abs(tan(evalf(argument))-evalf(tan(argument)))>epsilon) {
- clog << "tan(" << argument << ") returns "
- << tan(argument) << endl;
- errorflag = true;
- }
- }
- if (errorflag) {
- ++result;
- }
-
- return result;
+ unsigned result = 0;
+ bool errorflag;
+
+ // compare tan((q*Pi).evalf()) with tan(q*Pi).eval().evalf() at various
+ // points. E.g. if tan(Pi/12) returns something symbolic this should be
+ // equal to 2-sqrt(3). This routine will spot programming mistakes of
+ // this kind:
+ errorflag = false;
+ ex argument;
+ numeric epsilon(double(1e-8));
+ for (int n=-340; n<=340; ++n) {
+ if (!(n%30) && (n%60)) // skip poles
+ ++n;
+ argument = n*Pi/60;
+ if (abs(tan(evalf(argument))-evalf(tan(argument)))>epsilon) {
+ clog << "tan(" << argument << ") returns "
+ << tan(argument) << endl;
+ errorflag = true;
+ }
+ }
+ if (errorflag)
+ ++result;
+
+ return result;
}
-/* Assorted tests on other transcendental functions. */
-static unsigned inifcns_consist_trans(void)
+/* Simple tests on the dilogarithm function. */
+static unsigned inifcns_check_Li2()
{
- 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;
+ // NOTE: this can safely be removed once CLN supports dilogarithms and
+ // checks them itself.
+ unsigned result = 0;
+ bool errorflag;
+
+ // check the relation Li2(z^2) == 2 * (Li2(z) + Li2(-z)) numerically, which
+ // should hold in the entire complex plane:
+ errorflag = false;
+ ex argument;
+ numeric epsilon(double(1e-16));
+ for (int n=0; n<200; ++n) {
+ argument = numeric(20.0*rand()/(RAND_MAX+1.0)-10.0)
+ + numeric(20.0*rand()/(RAND_MAX+1.0)-10.0)*I;
+ if (abs(Li2(pow(argument,2))-2*Li2(argument)-2*Li2(-argument)) > epsilon) {
+ clog << "Li2(z) at z==" << argument
+ << " failed to satisfy Li2(z^2)==2*(Li2(z)+Li2(-z))" << endl;
+ errorflag = true;
+ }
+ }
+
+ if (errorflag)
+ ++result;
+
+ return result;
}
-/* Simple tests on the Gamma 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 check_inifcns()
{
- unsigned result = 0;
- ex e;
-
- e = gamma(ex(1));
- for (int i=2; i<8; ++i)
- e += gamma(ex(i));
- if (e != numeric(874)) {
- clog << "gamma(1)+...+gamma(7) erroneously returned "
- << e << " instead of 874" << endl;
- ++result;
- }
-
- e = gamma(ex(1));
- for (int i=2; i<8; ++i)
- e *= gamma(ex(i));
- if (e != numeric(24883200)) {
- clog << "gamma(1)*...*gamma(7) erroneously returned "
- << e << " instead of 24883200" << endl;
- ++result;
- }
-
- e = gamma(ex(numeric(5, 2)))*gamma(ex(numeric(9, 2)))*64;
- if (e != 315*Pi) {
- clog << "64*gamma(5/2)*gamma(9/2) erroneously returned "
- << e << " instead of 315*Pi" << endl;
- ++result;
- }
-
- e = gamma(ex(numeric(-13, 2)));
- for (int i=-13; i<7; i=i+2)
- e += gamma(ex(numeric(i, 2)));
- e = (e*gamma(ex(numeric(15, 2)))*numeric(512));
- if (e != numeric(633935)*Pi) {
- clog << "512*(gamma(-13/2)+...+gamma(5/2))*gamma(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 gamma(1)'/gamma(1) - gamma(1/2)'/gamma(1/2) == 2*log(2).
- e += (gamma(x).diff(x)/gamma(x)).subs(x==numeric(1));
- e -= (gamma(x).diff(x)/gamma(x)).subs(x==numeric(1,2));
- if (e!=2*log(2)) {
- clog << "gamma(1)'/gamma(1) - gamma(1/2)'/gamma(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 check_inifcns(void)
-{
- unsigned result = 0;
-
- cout << "checking consistency of symbolic functions" << flush;
- clog << "---------consistency of symbolic functions:" << endl;
-
- result += inifcns_consist_sin(); cout << '.' << flush;
- result += inifcns_consist_cos(); cout << '.' << flush;
- result += inifcns_consist_tan(); cout << '.' << flush;
- result += inifcns_consist_trans(); cout << '.' << flush;
- result += inifcns_consist_gamma(); cout << '.' << flush;
- result += inifcns_consist_psi(); cout << '.' << flush;
- result += inifcns_consist_zeta(); cout << '.' << flush;
+ unsigned result = 0;
- if (!result) {
- cout << " passed " << endl;
- clog << "(no output)" << endl;
- } else {
- cout << " failed " << endl;
- }
-
- return result;
+ cout << "checking consistency of symbolic functions" << flush;
+ clog << "---------consistency of symbolic functions:" << endl;
+
+ result += inifcns_check_sin(); cout << '.' << flush;
+ result += inifcns_check_cos(); cout << '.' << flush;
+ result += inifcns_check_tan(); cout << '.' << flush;
+ result += inifcns_check_Li2(); cout << '.' << flush;
+
+ if (!result) {
+ cout << " passed " << endl;
+ clog << "(no output)" << endl;
+ } else {
+ cout << " failed " << endl;
+ }
+
+ return result;
}
git://www.ginac.de / ginac.git / blobdiff