1 /** @file check_inifcns.cpp
3 * This test routine applies assorted tests on initially known higher level
7 * GiNaC Copyright (C) 1999-2004 Johannes Gutenberg University Mainz, Germany
9 * This program is free software; you can redistribute it and/or modify
10 * it under the terms of the GNU General Public License as published by
11 * the Free Software Foundation; either version 2 of the License, or
12 * (at your option) any later version.
14 * This program is distributed in the hope that it will be useful,
15 * but WITHOUT ANY WARRANTY; without even the implied warranty of
16 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
17 * GNU General Public License for more details.
19 * You should have received a copy of the GNU General Public License
20 * along with this program; if not, write to the Free Software
21 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
26 /* Some tests on the sine trigonometric function. */
27 static unsigned inifcns_check_sin()
30 bool errorflag = false;
34 for (int n=-10; n<=10; ++n) {
35 if (sin(n*Pi).eval() != numeric(0) ||
36 !sin(n*Pi).eval().info(info_flags::integer))
40 // we don't count each of those errors
41 clog << "sin(n*Pi) with integer n does not always return exact 0"
46 // sin((n+1/2)*Pi) == {+|-}1?
48 for (int n=-10; n<=10; ++n) {
49 if (!sin((n+numeric(1,2))*Pi).eval().info(info_flags::integer) ||
50 !(sin((n+numeric(1,2))*Pi).eval() == numeric(1) ||
51 sin((n+numeric(1,2))*Pi).eval() == numeric(-1)))
55 clog << "sin((n+1/2)*Pi) with integer n does not always return exact {+|-}1"
60 // compare sin((q*Pi).evalf()) with sin(q*Pi).eval().evalf() at various
61 // points. E.g. if sin(Pi/10) returns something symbolic this should be
62 // equal to sqrt(5)/4-1/4. This routine will spot programming mistakes
66 numeric epsilon(double(1e-8));
67 for (int n=-340; n<=340; ++n) {
69 if (abs(sin(evalf(argument))-evalf(sin(argument)))>epsilon) {
70 clog << "sin(" << argument << ") returns "
71 << sin(argument) << endl;
81 /* Simple tests on the cosine trigonometric function. */
82 static unsigned inifcns_check_cos()
87 // cos((n+1/2)*Pi) == 0?
89 for (int n=-10; n<=10; ++n) {
90 if (cos((n+numeric(1,2))*Pi).eval() != numeric(0) ||
91 !cos((n+numeric(1,2))*Pi).eval().info(info_flags::integer))
95 clog << "cos((n+1/2)*Pi) with integer n does not always return exact 0"
102 for (int n=-10; n<=10; ++n) {
103 if (!cos(n*Pi).eval().info(info_flags::integer) ||
104 !(cos(n*Pi).eval() == numeric(1) ||
105 cos(n*Pi).eval() == numeric(-1)))
109 clog << "cos(n*Pi) with integer n does not always return exact {+|-}1"
114 // compare cos((q*Pi).evalf()) with cos(q*Pi).eval().evalf() at various
115 // points. E.g. if cos(Pi/12) returns something symbolic this should be
116 // equal to 1/4*(1+1/3*sqrt(3))*sqrt(6). This routine will spot
117 // programming mistakes of this kind:
120 numeric epsilon(double(1e-8));
121 for (int n=-340; n<=340; ++n) {
123 if (abs(cos(evalf(argument))-evalf(cos(argument)))>epsilon) {
124 clog << "cos(" << argument << ") returns "
125 << cos(argument) << endl;
135 /* Simple tests on the tangent trigonometric function. */
136 static unsigned inifcns_check_tan()
141 // compare tan((q*Pi).evalf()) with tan(q*Pi).eval().evalf() at various
142 // points. E.g. if tan(Pi/12) returns something symbolic this should be
143 // equal to 2-sqrt(3). This routine will spot programming mistakes of
147 numeric epsilon(double(1e-8));
148 for (int n=-340; n<=340; ++n) {
149 if (!(n%30) && (n%60)) // skip poles
152 if (abs(tan(evalf(argument))-evalf(tan(argument)))>epsilon) {
153 clog << "tan(" << argument << ") returns "
154 << tan(argument) << endl;
164 /* Simple tests on the dilogarithm function. */
165 static unsigned inifcns_check_Li2()
167 // NOTE: this can safely be removed once CLN supports dilogarithms and
168 // checks them itself.
172 // check the relation Li2(z^2) == 2 * (Li2(z) + Li2(-z)) numerically, which
173 // should hold in the entire complex plane:
176 numeric epsilon(double(1e-16));
177 for (int n=0; n<200; ++n) {
178 argument = numeric(20.0*rand()/(RAND_MAX+1.0)-10.0)
179 + numeric(20.0*rand()/(RAND_MAX+1.0)-10.0)*I;
180 if (abs(Li2(pow(argument,2))-2*Li2(argument)-2*Li2(-argument)) > epsilon) {
181 clog << "Li2(z) at z==" << argument
182 << " failed to satisfy Li2(z^2)==2*(Li2(z)+Li2(-z))" << endl;
193 unsigned check_inifcns()
197 cout << "checking consistency of symbolic functions" << flush;
198 clog << "---------consistency of symbolic functions:" << endl;
200 result += inifcns_check_sin(); cout << '.' << flush;
201 result += inifcns_check_cos(); cout << '.' << flush;
202 result += inifcns_check_tan(); cout << '.' << flush;
203 result += inifcns_check_Li2(); cout << '.' << flush;
206 cout << " passed " << endl;
207 clog << "(no output)" << endl;
209 cout << " failed " << endl;