/** @file exam_numeric.cpp
*
* These exams creates some numbers and check the result of several boolean
* tests on these numbers like is_integer() etc... */
/*
* GiNaC Copyright (C) 1999-2008 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
#include
#include "ginac.h"
using namespace std;
using namespace GiNaC;
/* Simple and maybe somewhat pointless consistency tests of assorted tests and
* conversions. */
static unsigned exam_numeric1()
{
unsigned result = 0;
numeric test_int1(42);
numeric test_int2(5);
numeric test_rat1 = test_int1; test_rat1 /= test_int2;
test_rat1 = -test_rat1; // -42/5
numeric test_crat = test_rat1+I*test_int2; // 5*I-42/5
symbol a("a");
ex e1, e2;
if (!test_int1.is_integer()) {
clog << test_int1
<< " erroneously not recognized as integer" << endl;
++result;
}
if (!test_int1.is_rational()) {
clog << test_int1
<< " erroneously not recognized as rational" << endl;
++result;
}
if (!test_rat1.is_rational()) {
clog << test_rat1
<< " erroneously not recognized as rational" << endl;
++result;
}
if (test_rat1.is_integer()) {
clog << test_rat1
<< " erroneously recognized as integer" << endl;
++result;
}
if (!test_crat.is_crational()) {
clog << test_crat
<< " erroneously not recognized as complex rational" << endl;
++result;
}
int i = numeric(1984).to_int();
if (i-1984) {
clog << "conversion of " << i
<< " from numeric to int failed" << endl;
++result;
}
e1 = test_int1;
if (!e1.info(info_flags::posint)) {
clog << "expression " << e1
<< " erroneously not recognized as positive integer" << endl;
++result;
}
e2 = test_int1 + a;
if (e2.info(info_flags::integer)) {
clog << "expression " << e2
<< " erroneously recognized as integer" << endl;
++result;
}
// The next two were two actual bugs in CLN till June, 12, 1999:
test_rat1 = numeric(3)/numeric(2);
test_rat1 += test_rat1;
if (!test_rat1.is_integer()) {
clog << "3/2 + 3/2 erroneously not integer 3 but instead "
<< test_rat1 << endl;
++result;
}
test_rat1 = numeric(3)/numeric(2);
numeric test_rat2 = test_rat1 + numeric(1); // 5/2
test_rat2 -= test_rat1; // 1
if (!test_rat2.is_integer()) {
clog << "5/2 - 3/2 erroneously not integer 1 but instead "
<< test_rat2 << endl;
++result;
}
return result;
}
/* We had some fun with a bug in CLN that caused it to loop forever when
* calculating expt(a,b) if b is a rational and a a nonnegative integer.
* Implementing a workaround sadly introduced another bug on May 28th 1999
* that was fixed on May 31st. The workaround turned out to be stupid and
* the original bug in CLN was finally killed on September 2nd. */
static unsigned exam_numeric2()
{
unsigned result = 0;
ex zero = numeric(0);
ex two = numeric(2);
ex three = numeric(3);
// The hang in this code was the reason for the original workaround
if (pow(two,two/three)==42) {
clog << "pow(2,2/3) erroneously returned 42" << endl;
++result; // cannot happen
}
// Actually, this used to raise a FPE after introducing the workaround
if (two*zero!=zero) {
clog << "2*0 erroneously returned " << two*zero << endl;
++result;
}
// And this returned a cl_F due to the implicit call of numeric::power()
ex six = two*three;
if (!six.info(info_flags::integer)) {
clog << "2*3 erroneously returned the non-integer " << six << endl;
++result;
}
// The fix in the workaround left a whole which was fixed hours later...
ex another_zero = pow(zero,numeric(1)/numeric(2));
if (!another_zero.is_zero()) {
clog << "pow(0,1/2) erroneously returned" << another_zero << endl;
++result;
}
return result;
}
/* Assorted tests to ensure some crucial functions behave exactly as specified
* in the documentation. */
static unsigned exam_numeric3()
{
unsigned result = 0;
numeric calc_rem, calc_quo;
numeric a, b;
// check if irem(a, b) and irem(a, b, q) really behave like Maple's
// irem(a, b) and irem(a, b, 'q') as advertised in our documentation.
// These overloaded routines indeed need to be checked separately since
// internally they might be doing something completely different:
a = 23; b = 4; calc_rem = irem(a, b);
if (calc_rem != 3) {
clog << "irem(" << a << "," << b << ") erroneously returned "
<< calc_rem << endl;
++result;
}
a = 23; b = -4; calc_rem = irem(a, b);
if (calc_rem != 3) {
clog << "irem(" << a << "," << b << ") erroneously returned "
<< calc_rem << endl;
++result;
}
a = -23; b = 4; calc_rem = irem(a, b);
if (calc_rem != -3) {
clog << "irem(" << a << "," << b << ") erroneously returned "
<< calc_rem << endl;
++result;
}
a = -23; b = -4; calc_rem = irem(a, b);
if (calc_rem != -3) {
clog << "irem(" << a << "," << b << ") erroneously returned "
<< calc_rem << endl;
++result;
}
// and now the overloaded irem(a,b,q):
a = 23; b = 4; calc_rem = irem(a, b, calc_quo);
if (calc_rem != 3 || calc_quo != 5) {
clog << "irem(" << a << "," << b << ",q) erroneously returned "
<< calc_rem << " with q=" << calc_quo << endl;
++result;
}
a = 23; b = -4; calc_rem = irem(a, b, calc_quo);
if (calc_rem != 3 || calc_quo != -5) {
clog << "irem(" << a << "," << b << ",q) erroneously returned "
<< calc_rem << " with q=" << calc_quo << endl;
++result;
}
a = -23; b = 4; calc_rem = irem(a, b, calc_quo);
if (calc_rem != -3 || calc_quo != -5) {
clog << "irem(" << a << "," << b << ",q) erroneously returned "
<< calc_rem << " with q=" << calc_quo << endl;
++result;
}
a = -23; b = -4; calc_rem = irem(a, b, calc_quo);
if (calc_rem != -3 || calc_quo != 5) {
clog << "irem(" << a << "," << b << ",q) erroneously returned "
<< calc_rem << " with q=" << calc_quo << endl;
++result;
}
// check if iquo(a, b) and iquo(a, b, r) really behave like Maple's
// iquo(a, b) and iquo(a, b, 'r') as advertised in our documentation.
// These overloaded routines indeed need to be checked separately since
// internally they might be doing something completely different:
a = 23; b = 4; calc_quo = iquo(a, b);
if (calc_quo != 5) {
clog << "iquo(" << a << "," << b << ") erroneously returned "
<< calc_quo << endl;
++result;
}
a = 23; b = -4; calc_quo = iquo(a, b);
if (calc_quo != -5) {
clog << "iquo(" << a << "," << b << ") erroneously returned "
<< calc_quo << endl;
++result;
}
a = -23; b = 4; calc_quo = iquo(a, b);
if (calc_quo != -5) {
clog << "iquo(" << a << "," << b << ") erroneously returned "
<< calc_quo << endl;
++result;
}
a = -23; b = -4; calc_quo = iquo(a, b);
if (calc_quo != 5) {
clog << "iquo(" << a << "," << b << ") erroneously returned "
<< calc_quo << endl;
++result;
}
// and now the overloaded iquo(a,b,r):
a = 23; b = 4; calc_quo = iquo(a, b, calc_rem);
if (calc_quo != 5 || calc_rem != 3) {
clog << "iquo(" << a << "," << b << ",r) erroneously returned "
<< calc_quo << " with r=" << calc_rem << endl;
++result;
}
a = 23; b = -4; calc_quo = iquo(a, b, calc_rem);
if (calc_quo != -5 || calc_rem != 3) {
clog << "iquo(" << a << "," << b << ",r) erroneously returned "
<< calc_quo << " with r=" << calc_rem << endl;
++result;
}
a = -23; b = 4; calc_quo = iquo(a, b, calc_rem);
if (calc_quo != -5 || calc_rem != -3) {
clog << "iquo(" << a << "," << b << ",r) erroneously returned "
<< calc_quo << " with r=" << calc_rem << endl;
++result;
}
a = -23; b = -4; calc_quo = iquo(a, b, calc_rem);
if (calc_quo != 5 || calc_rem != -3) {
clog << "iquo(" << a << "," << b << ",r) erroneously returned "
<< calc_quo << " with r=" << calc_rem << endl;
++result;
}
return result;
}
/* Now we perform some less trivial checks about several functions which should
* return exact numbers if possible. */
static unsigned exam_numeric4()
{
unsigned result = 0;
bool passed;
// square roots of squares of integers:
passed = true;
for (int i=0; i<42; ++i)
if (!sqrt(numeric(i*i)).is_integer())
passed = false;
if (!passed) {
clog << "One or more square roots of squares of integers did not return exact integers" << endl;
++result;
}
// square roots of squares of rationals:
passed = true;
for (int num=0; num<41; ++num)
for (int den=1; den<42; ++den)
if (!sqrt(numeric(num*num)/numeric(den*den)).is_rational())
passed = false;
if (!passed) {
clog << "One or more square roots of squares of rationals did not return exact integers" << endl;
++result;
}
return result;
}
/* This test examines that simplifications of the form 5^(3/2) -> 5*5^(1/2)
* are carried out properly. */
static unsigned exam_numeric5()
{
unsigned result = 0;
// A variation of one of Ramanujan's wonderful identities must be
// verifiable with very primitive means:
ex e1 = pow(1 + pow(3,numeric(1,5)) - pow(3,numeric(2,5)),3);
ex e2 = expand(e1 - 10 + 5*pow(3,numeric(3,5)));
if (!e2.is_zero()) {
clog << "expand((1+3^(1/5)-3^(2/5))^3-10+5*3^(3/5)) returned "
<< e2 << " instead of 0." << endl;
++result;
}
return result;
}
/* This test checks whether the numeric output/parsing routines are
consistent. */
static unsigned exam_numeric6()
{
unsigned result = 0;
symbol sym("sym");
vector test_numbers;
test_numbers.push_back(numeric(0)); // zero
test_numbers.push_back(numeric(1)); // one
test_numbers.push_back(numeric(-1)); // minus one
test_numbers.push_back(numeric(42)); // positive integer
test_numbers.push_back(numeric(-42)); // negative integer
test_numbers.push_back(numeric(14,3)); // positive rational
test_numbers.push_back(numeric(-14,3)); // negative rational
test_numbers.push_back(numeric(3.141)); // positive decimal
test_numbers.push_back(numeric(-3.141)); // negative decimal
test_numbers.push_back(numeric(0.1974)); // positive decimal, leading zero
test_numbers.push_back(numeric(-0.1974)); // negative decimal, leading zero
test_numbers.push_back(sym); // symbol
for (vector::const_iterator br=test_numbers.begin(); br::const_iterator bi=test_numbers.begin(); bi::const_iterator er=test_numbers.begin(); er::const_iterator ei=test_numbers.begin(); ei