* functions. */
/*
- * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2001 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
/* Some tests on the sine trigonometric function. */
static unsigned inifcns_check_sin(void)
{
- 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_check_cos(void)
{
- 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_check_tan(void)
{
- 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;
+}
+
+/* Simple tests on the dilogarithm function. */
+static unsigned inifcns_check_Li2(void)
+{
+ // 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;
}
unsigned check_inifcns(void)
{
- unsigned result = 0;
+ unsigned result = 0;
- 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;
-
- 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;
}