1 /** @file exam_inifcns.cpp
3 * This test routine applies assorted tests on initially known higher level
7 * GiNaC Copyright (C) 1999-2015 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
25 using namespace GiNaC;
30 /* Assorted tests on other transcendental functions. */
31 static unsigned inifcns_consist_trans()
33 using GiNaC::asin; using GiNaC::acos;
34 using GiNaC::asinh; using GiNaC::acosh; using GiNaC::atanh;
40 chk = asin(1)-acos(0);
42 clog << "asin(1)-acos(0) erroneously returned " << chk
43 << " instead of 0" << endl;
47 // arbitrary check of type sin(f(x)):
48 chk = pow(sin(acos(x)),2) + pow(sin(asin(x)),2)
49 - (1+pow(x,2))*pow(sin(atan(x)),2);
50 if (chk != 1-pow(x,2)) {
51 clog << "sin(acos(x))^2 + sin(asin(x))^2 - (1+x^2)*sin(atan(x))^2 "
52 << "erroneously returned " << chk << " instead of 1-x^2" << endl;
56 // arbitrary check of type cos(f(x)):
57 chk = pow(cos(acos(x)),2) + pow(cos(asin(x)),2)
58 - (1+pow(x,2))*pow(cos(atan(x)),2);
60 clog << "cos(acos(x))^2 + cos(asin(x))^2 - (1+x^2)*cos(atan(x))^2 "
61 << "erroneously returned " << chk << " instead of 0" << endl;
65 // arbitrary check of type tan(f(x)):
66 chk = tan(acos(x))*tan(asin(x)) - tan(atan(x));
68 clog << "tan(acos(x))*tan(asin(x)) - tan(atan(x)) "
69 << "erroneously returned " << chk << " instead of -x+1" << endl;
73 // arbitrary check of type sinh(f(x)):
74 chk = -pow(sinh(acosh(x)),2).expand()*pow(sinh(atanh(x)),2)
75 - pow(sinh(asinh(x)),2);
77 clog << "expand(-(sinh(acosh(x)))^2)*(sinh(atanh(x))^2) - sinh(asinh(x))^2 "
78 << "erroneously returned " << chk << " instead of 0" << endl;
82 // arbitrary check of type cosh(f(x)):
83 chk = (pow(cosh(asinh(x)),2) - 2*pow(cosh(acosh(x)),2))
84 * pow(cosh(atanh(x)),2);
86 clog << "(cosh(asinh(x))^2 - 2*cosh(acosh(x))^2) * cosh(atanh(x))^2 "
87 << "erroneously returned " << chk << " instead of 1" << endl;
91 // arbitrary check of type tanh(f(x)):
92 chk = (pow(tanh(asinh(x)),-2) - pow(tanh(acosh(x)),2)).expand()
93 * pow(tanh(atanh(x)),2);
95 clog << "expand(tanh(acosh(x))^2 - tanh(asinh(x))^(-2)) * tanh(atanh(x))^2 "
96 << "erroneously returned " << chk << " instead of 2" << endl;
100 // check consistency of log and eta phases:
101 for (int r1=-1; r1<=1; ++r1) {
102 for (int i1=-1; i1<=1; ++i1) {
106 for (int r2=-1; r2<=1; ++r2) {
107 for (int i2=-1; i2<=1; ++i2) {
111 if (abs(evalf(eta(x1,x2)-log(x1*x2)+log(x1)+log(x2)))>.1e-12) {
112 clog << "either eta(x,y), log(x), log(y) or log(x*y) is wrong"
113 << " at x==" << x1 << ", y==" << x2 << endl;
124 /* Simple tests on the tgamma function. We stuff in arguments where the results
125 * exists in closed form and check if it's ok. */
126 static unsigned inifcns_consist_gamma()
133 for (int i=2; i<8; ++i)
135 if (e != numeric(874)) {
136 clog << "tgamma(1)+...+tgamma(7) erroneously returned "
137 << e << " instead of 874" << endl;
142 for (int i=2; i<8; ++i)
144 if (e != numeric(24883200)) {
145 clog << "tgamma(1)*...*tgamma(7) erroneously returned "
146 << e << " instead of 24883200" << endl;
150 e = tgamma(ex(numeric(5, 2)))*tgamma(ex(numeric(9, 2)))*64;
152 clog << "64*tgamma(5/2)*tgamma(9/2) erroneously returned "
153 << e << " instead of 315*Pi" << endl;
157 e = tgamma(ex(numeric(-13, 2)));
158 for (int i=-13; i<7; i=i+2)
159 e += tgamma(ex(numeric(i, 2)));
160 e = (e*tgamma(ex(numeric(15, 2)))*numeric(512));
161 if (e != numeric(633935)*Pi) {
162 clog << "512*(tgamma(-13/2)+...+tgamma(5/2))*tgamma(15/2) erroneously returned "
163 << e << " instead of 633935*Pi" << endl;
170 /* Simple tests on the Psi-function (aka polygamma-function). We stuff in
171 arguments where the result exists in closed form and check if it's ok. */
172 static unsigned inifcns_consist_psi()
181 // We check psi(1) and psi(1/2) implicitly by calculating the curious
182 // little identity tgamma(1)'/tgamma(1) - tgamma(1/2)'/tgamma(1/2) == 2*log(2).
183 e += (tgamma(x).diff(x)/tgamma(x)).subs(x==numeric(1));
184 e -= (tgamma(x).diff(x)/tgamma(x)).subs(x==numeric(1,2));
186 clog << "tgamma(1)'/tgamma(1) - tgamma(1/2)'/tgamma(1/2) erroneously returned "
187 << e << " instead of 2*log(2)" << endl;
194 /* Simple tests on the Riemann Zeta function. We stuff in arguments where the
195 * result exists in closed form and check if it's ok. Of course, this checks
196 * the Bernoulli numbers as a side effect. */
197 static unsigned inifcns_consist_zeta()
202 for (int i=0; i<13; i+=2)
203 e += zeta(i)/pow(Pi,i);
204 if (e!=numeric(-204992279,638512875)) {
205 clog << "zeta(0) + zeta(2) + ... + zeta(12) erroneously returned "
206 << e << " instead of -204992279/638512875" << endl;
211 for (int i=-1; i>-16; i--)
213 if (e!=numeric(487871,1633632)) {
214 clog << "zeta(-1) + zeta(-2) + ... + zeta(-15) erroneously returned "
215 << e << " instead of 487871/1633632" << endl;
222 static unsigned inifcns_consist_abs()
225 realsymbol a("a"), b("b"), x("x"), y("y");
229 if (!abs(exp(x+I*y)).eval().is_equal(exp(x)))
232 if (!abs(pow(p,a+I*b)).eval().is_equal(pow(p,a)))
235 if (!abs(sqrt(p)).eval().is_equal(sqrt(p)))
238 if (!abs(-sqrt(p)).eval().is_equal(sqrt(p)))
241 // also checks that abs(p)=p
242 if (!abs(pow(p,a+I*b)).eval().is_equal(pow(p,a)))
245 if (!abs(pow(x+I*y,a)).eval().is_equal(pow(abs(x+I*y),a)))
248 // it is not necessary a simplification if the following is really evaluated
249 if (!abs(pow(x+I*y,a+I*b)).eval().is_equal(abs(pow(x+I*y,a+I*b))))
252 // check expansion of abs
253 if (!abs(-7*z*a*p).expand(expand_options::expand_transcendental).is_equal(7*abs(z)*abs(a)*p))
256 if (!abs(z.conjugate()).eval().is_equal(abs(z)))
259 if (!abs(step(z)).eval().is_equal(step(z)))
262 if (!abs(p).info(info_flags::positive) || !abs(a).info(info_flags::real))
265 if (abs(a).info(info_flags::positive) || !abs(a).info(info_flags::real))
268 if (abs(z).info(info_flags::positive) || !abs(z).info(info_flags::real))
274 static unsigned inifcns_consist_exp()
277 symbol a("a"), b("b");
279 if (!exp(a+b).expand(expand_options::expand_transcendental).is_equal(exp(a)*exp(b)))
282 // shall not be expanded since the arg is not add
283 if (!exp(pow(a+b,2)).expand(expand_options::expand_transcendental).is_equal(exp(pow(a+b,2))))
287 if (!exp(pow(a+b,2)).expand(expand_options::expand_function_args | expand_options::expand_transcendental)
288 .is_equal(exp(a*a)*exp(b*b)*exp(2*a*b)))
294 static unsigned inifcns_consist_log()
297 symbol z("a"), w("b");
298 realsymbol a("a"), b("b");
299 possymbol p("p"), q("q");
302 if (!log(z*w).expand(expand_options::expand_transcendental).is_equal(log(z*w)))
306 if (!log(a*b).expand(expand_options::expand_transcendental).is_equal(log(a*b)))
310 if (!log(p*q).expand(expand_options::expand_transcendental).is_equal(log(p) + log(q)))
313 // a bit more complicated
314 ex e1 = log(-7*p*pow(q,3)*a*pow(b,2)*z*w).expand(expand_options::expand_transcendental);
315 ex e2 = log(7)+log(p)+log(pow(q,3))+log(-z*a*w*pow(b,2));
316 if (!e1.is_equal(e2))
319 // shall not do for non-real powers
320 if (ex(log(pow(p,z))).is_equal(z*log(p)))
323 // shall not do for non-positive basis
324 if (ex(log(pow(a,b))).is_equal(b*log(a)))
327 // infinite recursion log_series
329 ex ser = ex_to<pseries>(e.series(z, 1))
330 .convert_to_poly(/* no_order = */ true);
331 if (!ser.is_equal(e)) {
332 clog << "series(" << e << ", " << z << "): wrong result" << endl;
339 static unsigned inifcns_consist_various()
344 if ( binomial(n, 0) != 1 ) {
345 clog << "ERROR: binomial(n,0) != 1" << endl;
352 /* Several tests for derivatives */
353 static unsigned inifcns_consist_derivatives()
360 e=pow(x,z).conjugate().diff(x);
361 e1=pow(x,z).conjugate()*z.conjugate()/x;
362 if (! (e-e1).normal().is_zero() ) {
363 clog << "ERROR: pow(x,z).conjugate().diff(x) " << e << " != " << e1 << endl;
367 e=pow(w,z).conjugate().diff(w);
368 e1=pow(w,z).conjugate()*z.conjugate()/w;
369 if ( (e-e1).normal().is_zero() ) {
370 clog << "ERROR: pow(w,z).conjugate().diff(w) " << e << " = " << e1 << endl;
374 e=atanh(x).imag_part().diff(x);
375 if (! e.is_zero() ) {
376 clog << "ERROR: atanh(x).imag_part().diff(x) " << e << " != 0" << endl;
380 e=atanh(w).imag_part().diff(w);
382 clog << "ERROR: atanh(w).imag_part().diff(w) " << e << " = 0" << endl;
386 e=atanh(x).real_part().diff(x);
388 if (! (e-e1).normal().is_zero() ) {
389 clog << "ERROR: atanh(x).real_part().diff(x) " << e << " != " << e1 << endl;
393 e=atanh(w).real_part().diff(w);
395 if ( (e-e1).normal().is_zero() ) {
396 clog << "ERROR: atanh(w).real_part().diff(w) " << e << " = " << e1 << endl;
400 e=abs(log(z)).diff(z);
401 e1=(conjugate(log(z))/z+log(z)/conjugate(z))/abs(log(z))/2;
402 if (! (e-e1).normal().is_zero() ) {
403 clog << "ERROR: abs(log(z)).diff(z) " << e << " != " << e1 << endl;
407 e=Order(pow(x,4)).diff(x);
409 if (! (e-e1).normal().is_zero() ) {
410 clog << "ERROR: Order(pow(x,4)).diff(x) " << e << " != " << e1 << endl;
417 unsigned exam_inifcns()
421 cout << "examining consistency of symbolic functions" << flush;
423 result += inifcns_consist_trans(); cout << '.' << flush;
424 result += inifcns_consist_gamma(); cout << '.' << flush;
425 result += inifcns_consist_psi(); cout << '.' << flush;
426 result += inifcns_consist_zeta(); cout << '.' << flush;
427 result += inifcns_consist_abs(); cout << '.' << flush;
428 result += inifcns_consist_exp(); cout << '.' << flush;
429 result += inifcns_consist_log(); cout << '.' << flush;
430 result += inifcns_consist_various(); cout << '.' << flush;
431 result += inifcns_consist_derivatives(); cout << '.' << flush;
436 int main(int argc, char** argv)
438 return exam_inifcns();