prepared for 1.0.13 release
[ginac.git] / check / exam_inifcns.cpp
1 /** @file exam_inifcns.cpp
2  *
3  *  This test routine applies assorted tests on initially known higher level
4  *  functions. */
5
6 /*
7  *  GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
8  *
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.
13  *
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.
18  *
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
22  */
23
24 #include "exams.h"
25
26 /* Assorted tests on other transcendental functions. */
27 static unsigned inifcns_consist_trans(void)
28 {
29         unsigned result = 0;
30         symbol x("x");
31         ex chk;
32         
33         chk = asin(1)-acos(0);
34         if (!chk.is_zero()) {
35                 clog << "asin(1)-acos(0) erroneously returned " << chk
36                      << " instead of 0" << endl;
37                 ++result;
38         }
39         
40         // arbitrary check of type sin(f(x)):
41         chk = pow(sin(acos(x)),2) + pow(sin(asin(x)),2)
42                 - (1+pow(x,2))*pow(sin(atan(x)),2);
43         if (chk != 1-pow(x,2)) {
44                 clog << "sin(acos(x))^2 + sin(asin(x))^2 - (1+x^2)*sin(atan(x))^2 "
45                      << "erroneously returned " << chk << " instead of 1-x^2" << endl;
46                 ++result;
47         }
48         
49         // arbitrary check of type cos(f(x)):
50         chk = pow(cos(acos(x)),2) + pow(cos(asin(x)),2)
51                 - (1+pow(x,2))*pow(cos(atan(x)),2);
52         if (!chk.is_zero()) {
53                 clog << "cos(acos(x))^2 + cos(asin(x))^2 - (1+x^2)*cos(atan(x))^2 "
54                      << "erroneously returned " << chk << " instead of 0" << endl;
55                 ++result;
56         }
57         
58         // arbitrary check of type tan(f(x)):
59         chk = tan(acos(x))*tan(asin(x)) - tan(atan(x));
60         if (chk != 1-x) {
61                 clog << "tan(acos(x))*tan(asin(x)) - tan(atan(x)) "
62                      << "erroneously returned " << chk << " instead of -x+1" << endl;
63                 ++result;
64         }
65         
66         // arbitrary check of type sinh(f(x)):
67         chk = -pow(sinh(acosh(x)),2).expand()*pow(sinh(atanh(x)),2)
68                 - pow(sinh(asinh(x)),2);
69         if (!chk.is_zero()) {
70                 clog << "expand(-(sinh(acosh(x)))^2)*(sinh(atanh(x))^2) - sinh(asinh(x))^2 "
71                      << "erroneously returned " << chk << " instead of 0" << endl;
72                 ++result;
73         }
74         
75         // arbitrary check of type cosh(f(x)):
76         chk = (pow(cosh(asinh(x)),2) - 2*pow(cosh(acosh(x)),2))
77                 * pow(cosh(atanh(x)),2);
78         if (chk != 1) {
79                 clog << "(cosh(asinh(x))^2 - 2*cosh(acosh(x))^2) * cosh(atanh(x))^2 "
80                      << "erroneously returned " << chk << " instead of 1" << endl;
81                 ++result;
82         }
83         
84         // arbitrary check of type tanh(f(x)):
85         chk = (pow(tanh(asinh(x)),-2) - pow(tanh(acosh(x)),2)).expand()
86                 * pow(tanh(atanh(x)),2);
87         if (chk != 2) {
88                 clog << "expand(tanh(acosh(x))^2 - tanh(asinh(x))^(-2)) * tanh(atanh(x))^2 "
89                      << "erroneously returned " << chk << " instead of 2" << endl;
90                 ++result;
91         }
92         
93         // check consistency of log and eta phases:
94         for (int r1=-1; r1<=1; ++r1) {
95                 for (int i1=-1; i1<=1; ++i1) {
96                         ex x1 = r1+I*i1;
97                         if (x1.is_zero())
98                                 continue;
99                         for (int r2=-1; r2<=1; ++r2) {
100                                 for (int i2=-1; i2<=1; ++i2) {
101                                         ex x2 = r2+I*i2;
102                                         if (x2.is_zero())
103                                                 continue;
104                                         if (abs(evalf(eta(x1,x2)-log(x1*x2)+log(x1)+log(x2)))>.1e-12) {
105                                                 clog << "either eta(x,y), log(x), log(y) or log(x*y) is wrong"
106                                                      << " at x==" << x1 << ", y==" << x2 << endl;
107                                                 ++result;
108                                         }
109                                 }
110                         }
111                 }
112         }
113                 
114         return result;
115 }
116
117 /* Simple tests on the tgamma function.  We stuff in arguments where the results
118  * exists in closed form and check if it's ok. */
119 static unsigned inifcns_consist_gamma(void)
120 {
121         unsigned result = 0;
122         ex e;
123         
124         e = tgamma(1);
125         for (int i=2; i<8; ++i)
126                 e += tgamma(ex(i));
127         if (e != numeric(874)) {
128                 clog << "tgamma(1)+...+tgamma(7) erroneously returned "
129                      << e << " instead of 874" << endl;
130                 ++result;
131         }
132         
133         e = tgamma(1);
134         for (int i=2; i<8; ++i)
135                 e *= tgamma(ex(i));     
136         if (e != numeric(24883200)) {
137                 clog << "tgamma(1)*...*tgamma(7) erroneously returned "
138                      << e << " instead of 24883200" << endl;
139                 ++result;
140         }
141         
142         e = tgamma(ex(numeric(5, 2)))*tgamma(ex(numeric(9, 2)))*64;
143         if (e != 315*Pi) {
144                 clog << "64*tgamma(5/2)*tgamma(9/2) erroneously returned "
145                      << e << " instead of 315*Pi" << endl;
146                 ++result;
147         }
148         
149         e = tgamma(ex(numeric(-13, 2)));
150         for (int i=-13; i<7; i=i+2)
151                 e += tgamma(ex(numeric(i, 2)));
152         e = (e*tgamma(ex(numeric(15, 2)))*numeric(512));
153         if (e != numeric(633935)*Pi) {
154                 clog << "512*(tgamma(-13/2)+...+tgamma(5/2))*tgamma(15/2) erroneously returned "
155                      << e << " instead of 633935*Pi" << endl;
156                 ++result;
157         }
158         
159         return result;
160 }
161
162 /* Simple tests on the Psi-function (aka polygamma-function).  We stuff in
163    arguments where the result exists in closed form and check if it's ok. */
164 static unsigned inifcns_consist_psi(void)
165 {
166         unsigned result = 0;
167         symbol x;
168         ex e, f;
169         
170         // We check psi(1) and psi(1/2) implicitly by calculating the curious
171         // little identity tgamma(1)'/tgamma(1) - tgamma(1/2)'/tgamma(1/2) == 2*log(2).
172         e += (tgamma(x).diff(x)/tgamma(x)).subs(x==numeric(1));
173         e -= (tgamma(x).diff(x)/tgamma(x)).subs(x==numeric(1,2));
174         if (e!=2*log(2)) {
175                 clog << "tgamma(1)'/tgamma(1) - tgamma(1/2)'/tgamma(1/2) erroneously returned "
176                      << e << " instead of 2*log(2)" << endl;
177                 ++result;
178         }
179         
180         return result;
181 }
182
183 /* Simple tests on the Riemann Zeta function.  We stuff in arguments where the
184  * result exists in closed form and check if it's ok.  Of course, this checks
185  * the Bernoulli numbers as a side effect. */
186 static unsigned inifcns_consist_zeta(void)
187 {
188         unsigned result = 0;
189         ex e;
190         
191         for (int i=0; i<13; i+=2)
192                 e += zeta(i)/pow(Pi,i);
193         if (e!=numeric(-204992279,638512875)) {
194                 clog << "zeta(0) + zeta(2) + ... + zeta(12) erroneously returned "
195                      << e << " instead of -204992279/638512875" << endl;
196                 ++result;
197         }
198         
199         e = 0;
200         for (int i=-1; i>-16; i--)
201                 e += zeta(i);
202         if (e!=numeric(487871,1633632)) {
203                 clog << "zeta(-1) + zeta(-2) + ... + zeta(-15) erroneously returned "
204                      << e << " instead of 487871/1633632" << endl;
205                 ++result;
206         }
207         
208         return result;
209 }
210
211 unsigned exam_inifcns(void)
212 {
213         unsigned result = 0;
214         
215         cout << "examining consistency of symbolic functions" << flush;
216         clog << "----------consistency of symbolic functions:" << endl;
217         
218         result += inifcns_consist_trans();  cout << '.' << flush;
219         result += inifcns_consist_gamma();  cout << '.' << flush;
220         result += inifcns_consist_psi();  cout << '.' << flush;
221         result += inifcns_consist_zeta();  cout << '.' << flush;
222         
223         if (!result) {
224                 cout << " passed " << endl;
225                 clog << "(no output)" << endl;
226         } else {
227                 cout << " failed " << endl;
228         }
229         
230         return result;
231 }