* functions. */
/*
- * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2019 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
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
-#include "exams.h"
+#include "ginac.h"
+using namespace GiNaC;
+
+#include <iostream>
+using namespace std;
/* Assorted tests on other transcendental functions. */
-static unsigned inifcns_consist_trans(void)
+static unsigned inifcns_consist_trans()
{
- 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;
+ using GiNaC::asin; using GiNaC::acos;
+ using GiNaC::asinh; using GiNaC::acosh; using GiNaC::atanh;
+
+ 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 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)
+static unsigned inifcns_consist_gamma()
{
- unsigned result = 0;
- ex e;
-
- e = tgamma(ex(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(ex(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;
+ using GiNaC::tgamma;
+ 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)
+static unsigned inifcns_consist_psi()
{
- 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;
+ using GiNaC::log;
+ using GiNaC::tgamma;
+
+ 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
* 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)
+static unsigned inifcns_consist_zeta()
+{
+ 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;
+}
+
+static unsigned inifcns_consist_abs()
+{
+ unsigned result = 0;
+ realsymbol a("a"), b("b"), x("x"), y("y");
+ possymbol p("p");
+ symbol z("z");
+
+ if (!abs(exp(x+I*y)).eval().is_equal(exp(x)))
+ ++result;
+
+ if (!abs(pow(p,a+I*b)).eval().is_equal(pow(p,a)))
+ ++result;
+
+ if (!abs(sqrt(p)).eval().is_equal(sqrt(p)))
+ ++result;
+
+ if (!abs(-sqrt(p)).eval().is_equal(sqrt(p)))
+ ++result;
+
+ // also checks that abs(p)=p
+ if (!abs(pow(p,a+I*b)).eval().is_equal(pow(p,a)))
+ ++result;
+
+ if (!abs(pow(x+I*y,a)).eval().is_equal(pow(abs(x+I*y),a)))
+ ++result;
+
+ // it is not necessary a simplification if the following is really evaluated
+ if (!abs(pow(x+I*y,a+I*b)).eval().is_equal(abs(pow(x+I*y,a+I*b))))
+ ++result;
+
+ // check expansion of abs
+ if (!abs(-7*z*a*p).expand(expand_options::expand_transcendental).is_equal(7*abs(z)*abs(a)*p))
+ ++result;
+
+ if (!abs(z.conjugate()).eval().is_equal(abs(z)))
+ ++result;
+
+ if (!abs(step(z)).eval().is_equal(step(z)))
+ ++result;
+
+ if (!abs(p).info(info_flags::positive) || !abs(a).info(info_flags::real))
+ ++result;
+
+ if (abs(a).info(info_flags::positive) || !abs(a).info(info_flags::real))
+ ++result;
+
+ if (abs(z).info(info_flags::positive) || !abs(z).info(info_flags::real))
+ ++result;
+
+ return result;
+}
+
+static unsigned inifcns_consist_exp()
+{
+ unsigned result = 0;
+ symbol a("a"), b("b");
+
+ if (!exp(a+b).expand(expand_options::expand_transcendental).is_equal(exp(a)*exp(b)))
+ ++result;
+
+ // shall not be expanded since the arg is not add
+ if (!exp(pow(a+b,2)).expand(expand_options::expand_transcendental).is_equal(exp(pow(a+b,2))))
+ ++result;
+
+ // expand now
+ if (!exp(pow(a+b,2)).expand(expand_options::expand_function_args | expand_options::expand_transcendental)
+ .is_equal(exp(a*a)*exp(b*b)*exp(2*a*b)))
+ ++result;
+
+ return result;
+}
+
+static unsigned inifcns_consist_log()
+{
+ using GiNaC::log;
+ unsigned result = 0;
+ symbol z("a"), w("b");
+ realsymbol a("a"), b("b");
+ possymbol p("p"), q("q");
+
+ // do not expand
+ if (!log(z*w).expand(expand_options::expand_transcendental).is_equal(log(z*w)))
+ ++result;
+
+ // do not expand
+ if (!log(a*b).expand(expand_options::expand_transcendental).is_equal(log(a*b)))
+ ++result;
+
+ // shall expand
+ if (!log(p*q).expand(expand_options::expand_transcendental).is_equal(log(p) + log(q)))
+ ++result;
+
+ // a bit more complicated
+ ex e1 = log(-7*p*pow(q,3)*a*pow(b,2)*z*w).expand(expand_options::expand_transcendental);
+ ex e2 = log(7)+log(p)+log(pow(q,3))+log(-z*a*w*pow(b,2));
+ if (!e1.is_equal(e2))
+ ++result;
+
+ // shall not do for non-real powers
+ if (ex(log(pow(p,z))).is_equal(z*log(p)))
+ ++result;
+
+ // shall not do for non-positive basis
+ if (ex(log(pow(a,b))).is_equal(b*log(a)))
+ ++result;
+
+ // infinite recursion log_series
+ ex e(log(-p));
+ ex ser = ex_to<pseries>(e.series(z, 1))
+ .convert_to_poly(/* no_order = */ true);
+ if (!ser.is_equal(e)) {
+ clog << "series(" << e << ", " << z << "): wrong result" << endl;
+ ++result;
+ }
+
+ return result;
+}
+
+static unsigned inifcns_consist_various()
+{
+ unsigned result = 0;
+ symbol n;
+
+ if ( binomial(n, 0) != 1 ) {
+ clog << "ERROR: binomial(n,0) != 1" << endl;
+ ++result;
+ }
+
+ return result;
+}
+
+/* Several tests for derivatives */
+static unsigned inifcns_consist_derivatives()
+{
+ unsigned result = 0;
+ symbol z, w;
+ realsymbol x;
+ ex e, e1;
+
+ e=pow(x,z).conjugate().diff(x);
+ e1=pow(x,z).conjugate()*z.conjugate()/x;
+ if (! (e-e1).normal().is_zero() ) {
+ clog << "ERROR: pow(x,z).conjugate().diff(x) " << e << " != " << e1 << endl;
+ ++result;
+ }
+
+ e=pow(w,z).conjugate().diff(w);
+ e1=pow(w,z).conjugate()*z.conjugate()/w;
+ if ( (e-e1).normal().is_zero() ) {
+ clog << "ERROR: pow(w,z).conjugate().diff(w) " << e << " = " << e1 << endl;
+ ++result;
+ }
+
+ e=atanh(x).imag_part().diff(x);
+ if (! e.is_zero() ) {
+ clog << "ERROR: atanh(x).imag_part().diff(x) " << e << " != 0" << endl;
+ ++result;
+ }
+
+ e=atanh(w).imag_part().diff(w);
+ if ( e.is_zero() ) {
+ clog << "ERROR: atanh(w).imag_part().diff(w) " << e << " = 0" << endl;
+ ++result;
+ }
+
+ e=atanh(x).real_part().diff(x);
+ e1=pow(1-x*x,-1);
+ if (! (e-e1).normal().is_zero() ) {
+ clog << "ERROR: atanh(x).real_part().diff(x) " << e << " != " << e1 << endl;
+ ++result;
+ }
+
+ e=atanh(w).real_part().diff(w);
+ e1=pow(1-w*w,-1);
+ if ( (e-e1).normal().is_zero() ) {
+ clog << "ERROR: atanh(w).real_part().diff(w) " << e << " = " << e1 << endl;
+ ++result;
+ }
+
+ e=abs(log(z)).diff(z);
+ e1=(conjugate(log(z))/z+log(z)/conjugate(z))/abs(log(z))/2;
+ if (! (e-e1).normal().is_zero() ) {
+ clog << "ERROR: abs(log(z)).diff(z) " << e << " != " << e1 << endl;
+ ++result;
+ }
+
+ e=Order(pow(x,4)).diff(x);
+ e1=Order(pow(x,3));
+ if (! (e-e1).normal().is_zero() ) {
+ clog << "ERROR: Order(pow(x,4)).diff(x) " << e << " != " << e1 << endl;
+ ++result;
+ }
+
+ return result;
+}
+
+unsigned exam_inifcns()
{
- 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;
+
+ cout << "examining consistency of symbolic functions" << 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;
+ result += inifcns_consist_abs(); cout << '.' << flush;
+ result += inifcns_consist_exp(); cout << '.' << flush;
+ result += inifcns_consist_log(); cout << '.' << flush;
+ result += inifcns_consist_various(); cout << '.' << flush;
+ result += inifcns_consist_derivatives(); cout << '.' << flush;
+
+ return result;
}
-unsigned exam_inifcns(void)
+int main(int argc, char** argv)
{
- 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;
+ return exam_inifcns();
}
git://www.ginac.de / ginac.git / blobdiff