/** @file exam_inifcns.cpp
 *
 *  This test routine applies assorted tests on initially known higher level
 *  functions. */

/*
 *  GiNaC Copyright (C) 1999-2020 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
 *  the Free Software Foundation; either version 2 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  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., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 */

#include "ginac.h"
using namespace GiNaC;

#include <iostream>
using namespace std;

/* Assorted tests on other transcendental functions. */
static unsigned inifcns_consist_trans()
{
	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()
{
	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()
{
	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()
{
	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;
	
	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;
}

int main(int argc, char** argv)
{
	return exam_inifcns();
}