X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=check%2Fexam_inifcns.cpp;h=96ea9cc7cd4a3feb8e3750d45eba145b062ea6a5;hp=d91c02c0178346ccaed73f77d8976b3d2f5bce4b;hb=3ab7092e925aba28498d7508f50da9f913dcffd2;hpb=27d8eeed808afec4b319cea040d62365b65d49bc diff --git a/check/exam_inifcns.cpp b/check/exam_inifcns.cpp index d91c02c0..96ea9cc7 100644 --- a/check/exam_inifcns.cpp +++ b/check/exam_inifcns.cpp @@ -4,7 +4,7 @@ * functions. */ /* - * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2001 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 @@ -26,137 +26,158 @@ /* 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; + 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; + } + + // check consistency of log and eta phases: + for (int r1=-1; r1<=1; ++r1) { + for (int i1=-1; i1<=1; ++i1) { + ex x1 = r1+I*i1; + if (x1.is_zero()) + continue; + for (int r2=-1; r2<=1; ++r2) { + for (int i2=-1; i2<=1; ++i2) { + ex x2 = r2+I*i2; + if (x2.is_zero()) + continue; + if (abs(evalf(eta(x1,x2)-log(x1*x2)+log(x1)+log(x2)))>.1e-12) { + clog << "either eta(x,y), log(x), log(y) or log(x*y) is wrong" + << " at x==" << x1 << ", y==" << x2 << endl; + ++result; + } + } + } + } + } + + return result; } -/* Simple tests on the Gamma function. We stuff in arguments where the results +/* Simple tests on the tgamma 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; + unsigned result = 0; + ex e; + + e = tgamma(1); + for (int i=2; i<8; ++i) + e += tgamma(ex(i)); + if (e != numeric(874)) { + clog << "tgamma(1)+...+tgamma(7) erroneously returned " + << e << " instead of 874" << endl; + ++result; + } + + e = tgamma(1); + for (int i=2; i<8; ++i) + e *= tgamma(ex(i)); + if (e != numeric(24883200)) { + clog << "tgamma(1)*...*tgamma(7) erroneously returned " + << e << " instead of 24883200" << endl; + ++result; + } + + e = tgamma(ex(numeric(5, 2)))*tgamma(ex(numeric(9, 2)))*64; + if (e != 315*Pi) { + clog << "64*tgamma(5/2)*tgamma(9/2) erroneously returned " + << e << " instead of 315*Pi" << endl; + ++result; + } + + e = tgamma(ex(numeric(-13, 2))); + for (int i=-13; i<7; i=i+2) + e += tgamma(ex(numeric(i, 2))); + e = (e*tgamma(ex(numeric(15, 2)))*numeric(512)); + if (e != numeric(633935)*Pi) { + clog << "512*(tgamma(-13/2)+...+tgamma(5/2))*tgamma(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; + unsigned result = 0; + symbol x; + ex e, f; + + // We check psi(1) and psi(1/2) implicitly by calculating the curious + // little identity tgamma(1)'/tgamma(1) - tgamma(1/2)'/tgamma(1/2) == 2*log(2). + e += (tgamma(x).diff(x)/tgamma(x)).subs(x==numeric(1)); + e -= (tgamma(x).diff(x)/tgamma(x)).subs(x==numeric(1,2)); + if (e!=2*log(2)) { + clog << "tgamma(1)'/tgamma(1) - tgamma(1/2)'/tgamma(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 @@ -164,47 +185,47 @@ static unsigned inifcns_consist_psi(void) * 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 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; + 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; }