--- /dev/null
+// check/inifcns_consist.cpp
+
+/* This test routine applies assorted tests on initially known higher level
+ * functions. */
+
+#include "ginac.h"
+
+/* Simple tests on the sine trigonometric function. */
+static unsigned inifcns_consist_sin(void)
+{
+ unsigned result = 0;
+ bool errorflag;
+
+ // 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 ) {
+ 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;
+ }
+
+ return result;
+}
+
+/* Simple tests on the cosine trigonometric function. */
+static unsigned inifcns_consist_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;
+ }
+
+ return result;
+}
+
+/* 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;
+ }
+
+ return result;
+}
+
+/* Simple tests on the Gamma combinatorial function. We stuff in arguments
+ * where the result exists in closed form and check if it's ok. */
+static unsigned inifcns_consist_gamma(void)
+{
+ 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;
+}
+
+unsigned inifcns_consist(void)
+{
+ unsigned result = 0;
+
+ cout << "checking consistency of symbolic functions..." << flush;
+ clog << "---------consistency of symbolic functions:" << endl;
+
+ result += inifcns_consist_sin();
+ result += inifcns_consist_cos();
+ result += inifcns_consist_trans();
+ result += inifcns_consist_gamma();
+
+ if ( !result ) {
+ cout << " passed ";
+ clog << "(no output)" << endl;
+ } else {
+ cout << " failed ";
+ }
+
+ return result;
+}
git://www.ginac.de / ginac.git / blobdiff