X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=check%2Fcheck_inifcns.cpp;h=b63839dd683a3be69a8dd349a088382112f25eff;hp=fb7d99933be268a47535dd7f3942f2582ad40f3c;hb=6d225ee55693c0617d254e6fa283c00c71bd2919;hpb=f4ea690a3f118bf364190f0ef3c3f6d2ccdf6206 diff --git a/check/check_inifcns.cpp b/check/check_inifcns.cpp index fb7d9993..b63839dd 100644 --- a/check/check_inifcns.cpp +++ b/check/check_inifcns.cpp @@ -4,7 +4,7 @@ * functions. */ /* - * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2004 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 @@ -24,331 +24,190 @@ #include "checks.h" /* Some tests on the sine trigonometric function. */ -static unsigned inifcns_consist_sin(void) +static unsigned inifcns_check_sin() { - unsigned result = 0; - bool errorflag = false; - - // sin(n*Pi) == 0? - errorflag = false; - for (int n=-10; n<=10; ++n) { - if (sin(n*Pi).eval() != numeric(0) || - !sin(n*Pi).eval().info(info_flags::integer)) - errorflag = true; - } - if (errorflag) { - // we don't count each of those errors - clog << "sin(n*Pi) with integer n does not always return exact 0" - << endl; - ++result; - } - - // sin((n+1/2)*Pi) == {+|-}1? - errorflag = false; - for (int n=-10; n<=10; ++n) { - if (!sin((n+numeric(1,2))*Pi).eval().info(info_flags::integer) || - !(sin((n+numeric(1,2))*Pi).eval() == numeric(1) || - sin((n+numeric(1,2))*Pi).eval() == numeric(-1))) - errorflag = true; - } - if (errorflag) { - clog << "sin((n+1/2)*Pi) with integer n does not always return exact {+|-}1" - << endl; - ++result; - } - - // compare sin((q*Pi).evalf()) with sin(q*Pi).eval().evalf() at various - // points. E.g. if sin(Pi/10) returns something symbolic this should be - // equal to sqrt(5)/4-1/4. This routine will spot programming mistakes - // of this kind: - errorflag = false; - ex argument; - numeric epsilon(double(1e-8)); - for (int n=-340; n<=340; ++n) { - argument = n*Pi/60; - if (abs(sin(evalf(argument))-evalf(sin(argument)))>epsilon) { - clog << "sin(" << argument << ") returns " - << sin(argument) << endl; - errorflag = true; - } - } - if (errorflag) { - ++result; - } - - return result; + unsigned result = 0; + bool errorflag = false; + + // sin(n*Pi) == 0? + errorflag = false; + for (int n=-10; n<=10; ++n) { + if (sin(n*Pi).eval() != numeric(0) || + !sin(n*Pi).eval().info(info_flags::integer)) + errorflag = true; + } + if (errorflag) { + // we don't count each of those errors + clog << "sin(n*Pi) with integer n does not always return exact 0" + << endl; + ++result; + } + + // sin((n+1/2)*Pi) == {+|-}1? + errorflag = false; + for (int n=-10; n<=10; ++n) { + if (!sin((n+numeric(1,2))*Pi).eval().info(info_flags::integer) || + !(sin((n+numeric(1,2))*Pi).eval() == numeric(1) || + sin((n+numeric(1,2))*Pi).eval() == numeric(-1))) + errorflag = true; + } + if (errorflag) { + clog << "sin((n+1/2)*Pi) with integer n does not always return exact {+|-}1" + << endl; + ++result; + } + + // compare sin((q*Pi).evalf()) with sin(q*Pi).eval().evalf() at various + // points. E.g. if sin(Pi/10) returns something symbolic this should be + // equal to sqrt(5)/4-1/4. This routine will spot programming mistakes + // of this kind: + errorflag = false; + ex argument; + numeric epsilon(double(1e-8)); + for (int n=-340; n<=340; ++n) { + argument = n*Pi/60; + if (abs(sin(evalf(argument))-evalf(sin(argument)))>epsilon) { + clog << "sin(" << argument << ") returns " + << sin(argument) << endl; + errorflag = true; + } + } + if (errorflag) + ++result; + + return result; } /* Simple tests on the cosine trigonometric function. */ -static unsigned inifcns_consist_cos(void) +static unsigned inifcns_check_cos() { - unsigned result = 0; - bool errorflag; - - // cos((n+1/2)*Pi) == 0? - errorflag = false; - for (int n=-10; n<=10; ++n) { - if (cos((n+numeric(1,2))*Pi).eval() != numeric(0) || - !cos((n+numeric(1,2))*Pi).eval().info(info_flags::integer)) - errorflag = true; - } - if (errorflag) { - clog << "cos((n+1/2)*Pi) with integer n does not always return exact 0" - << endl; - ++result; - } - - // cos(n*Pi) == 0? - errorflag = false; - for (int n=-10; n<=10; ++n) { - if (!cos(n*Pi).eval().info(info_flags::integer) || - !(cos(n*Pi).eval() == numeric(1) || - cos(n*Pi).eval() == numeric(-1))) - errorflag = true; - } - if (errorflag) { - clog << "cos(n*Pi) with integer n does not always return exact {+|-}1" - << endl; - ++result; - } - - // compare cos((q*Pi).evalf()) with cos(q*Pi).eval().evalf() at various - // points. E.g. if cos(Pi/12) returns something symbolic this should be - // equal to 1/4*(1+1/3*sqrt(3))*sqrt(6). This routine will spot - // programming mistakes of this kind: - errorflag = false; - ex argument; - numeric epsilon(double(1e-8)); - for (int n=-340; n<=340; ++n) { - argument = n*Pi/60; - if (abs(cos(evalf(argument))-evalf(cos(argument)))>epsilon) { - clog << "cos(" << argument << ") returns " - << cos(argument) << endl; - errorflag = true; - } - } - if (errorflag) { - ++result; - } - - return result; + unsigned result = 0; + bool errorflag; + + // cos((n+1/2)*Pi) == 0? + errorflag = false; + for (int n=-10; n<=10; ++n) { + if (cos((n+numeric(1,2))*Pi).eval() != numeric(0) || + !cos((n+numeric(1,2))*Pi).eval().info(info_flags::integer)) + errorflag = true; + } + if (errorflag) { + clog << "cos((n+1/2)*Pi) with integer n does not always return exact 0" + << endl; + ++result; + } + + // cos(n*Pi) == 0? + errorflag = false; + for (int n=-10; n<=10; ++n) { + if (!cos(n*Pi).eval().info(info_flags::integer) || + !(cos(n*Pi).eval() == numeric(1) || + cos(n*Pi).eval() == numeric(-1))) + errorflag = true; + } + if (errorflag) { + clog << "cos(n*Pi) with integer n does not always return exact {+|-}1" + << endl; + ++result; + } + + // compare cos((q*Pi).evalf()) with cos(q*Pi).eval().evalf() at various + // points. E.g. if cos(Pi/12) returns something symbolic this should be + // equal to 1/4*(1+1/3*sqrt(3))*sqrt(6). This routine will spot + // programming mistakes of this kind: + errorflag = false; + ex argument; + numeric epsilon(double(1e-8)); + for (int n=-340; n<=340; ++n) { + argument = n*Pi/60; + if (abs(cos(evalf(argument))-evalf(cos(argument)))>epsilon) { + clog << "cos(" << argument << ") returns " + << cos(argument) << endl; + errorflag = true; + } + } + if (errorflag) + ++result; + + return result; } /* Simple tests on the tangent trigonometric function. */ -static unsigned inifcns_consist_tan(void) +static unsigned inifcns_check_tan() { - unsigned result = 0; - bool errorflag; - - // compare tan((q*Pi).evalf()) with tan(q*Pi).eval().evalf() at various - // points. E.g. if tan(Pi/12) returns something symbolic this should be - // equal to 2-sqrt(3). This routine will spot programming mistakes of - // this kind: - errorflag = false; - ex argument; - numeric epsilon(double(1e-8)); - for (int n=-340; n<=340; ++n) { - if (!(n%30) && (n%60)) // skip poles - ++n; - argument = n*Pi/60; - if (abs(tan(evalf(argument))-evalf(tan(argument)))>epsilon) { - clog << "tan(" << argument << ") returns " - << tan(argument) << endl; - errorflag = true; - } - } - if (errorflag) { - ++result; - } - - return result; + unsigned result = 0; + bool errorflag; + + // compare tan((q*Pi).evalf()) with tan(q*Pi).eval().evalf() at various + // points. E.g. if tan(Pi/12) returns something symbolic this should be + // equal to 2-sqrt(3). This routine will spot programming mistakes of + // this kind: + errorflag = false; + ex argument; + numeric epsilon(double(1e-8)); + for (int n=-340; n<=340; ++n) { + if (!(n%30) && (n%60)) // skip poles + ++n; + argument = n*Pi/60; + if (abs(tan(evalf(argument))-evalf(tan(argument)))>epsilon) { + clog << "tan(" << argument << ") returns " + << tan(argument) << endl; + errorflag = true; + } + } + if (errorflag) + ++result; + + return result; } -/* Assorted tests on other transcendental functions. */ -static unsigned inifcns_consist_trans(void) +/* Simple tests on the dilogarithm function. */ +static unsigned inifcns_check_Li2() { - 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; + // NOTE: this can safely be removed once CLN supports dilogarithms and + // checks them itself. + unsigned result = 0; + bool errorflag; + + // check the relation Li2(z^2) == 2 * (Li2(z) + Li2(-z)) numerically, which + // should hold in the entire complex plane: + errorflag = false; + ex argument; + numeric epsilon(double(1e-16)); + for (int n=0; n<200; ++n) { + argument = numeric(20.0*rand()/(RAND_MAX+1.0)-10.0) + + numeric(20.0*rand()/(RAND_MAX+1.0)-10.0)*I; + if (abs(Li2(pow(argument,2))-2*Li2(argument)-2*Li2(-argument)) > epsilon) { + clog << "Li2(z) at z==" << argument + << " failed to satisfy Li2(z^2)==2*(Li2(z)+Li2(-z))" << endl; + errorflag = true; + } + } + + if (errorflag) + ++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 check_inifcns() { - 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 check_inifcns(void) -{ - unsigned result = 0; - - cout << "checking consistency of symbolic functions" << flush; - clog << "---------consistency of symbolic functions:" << endl; - - result += inifcns_consist_sin(); cout << '.' << flush; - result += inifcns_consist_cos(); cout << '.' << flush; - result += inifcns_consist_tan(); cout << '.' << flush; - result += inifcns_consist_trans(); cout << '.' << flush; - result += inifcns_consist_gamma(); cout << '.' << flush; - result += inifcns_consist_psi(); cout << '.' << flush; - result += inifcns_consist_zeta(); cout << '.' << flush; + unsigned result = 0; - if (!result) { - cout << " passed " << endl; - clog << "(no output)" << endl; - } else { - cout << " failed " << endl; - } - - return result; + cout << "checking consistency of symbolic functions" << flush; + clog << "---------consistency of symbolic functions:" << endl; + + result += inifcns_check_sin(); cout << '.' << flush; + result += inifcns_check_cos(); cout << '.' << flush; + result += inifcns_check_tan(); cout << '.' << flush; + result += inifcns_check_Li2(); cout << '.' << flush; + + if (!result) { + cout << " passed " << endl; + clog << "(no output)" << endl; + } else { + cout << " failed " << endl; + } + + return result; }