+/** @file exam_inifcns.cpp
+ *
+ * This test routine applies assorted tests on initially known higher level
+ * functions. */
+
+/*
+ * GiNaC Copyright (C) 1999-2000 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;
+ }
+
+ 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 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 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;
+}