X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=check%2Fexam_inifcns.cpp;h=667d08426aa2288648bf016ce0449159cf03a3ce;hp=16788c54d2c658f675d7172739b27e3952a6047e;hb=8cffcdf13d817a47f217f1a1043317d95969e070;hpb=61434b009f39c40ea85ae7bb4ec14d8d203e2a85

diff --git a/check/exam_inifcns.cpp b/check/exam_inifcns.cpp
index 16788c54..667d0842 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) 1999-2019 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
@@ -18,193 +18,423 @@
  *
  *  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 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)
+static unsigned inifcns_consist_gamma()
 {
-    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;
+	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 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;
+	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();
 }