/** @file exam_paranoia.cpp
*
* This set of tests checks for some of GiNaC's oopses which showed up during
* development. Things were evaluated wrongly and so. Such a sick behaviour
* shouldn't occur any more. But we are paranoic and we want to exclude these
* these oopses for good, so we run those stupid tests... */
/*
* GiNaC Copyright (C) 1999-2005 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., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
#include "exams.h"
// The very first pair of historic problems had its roots in power.cpp and was
// finally resolved on April 27th 1999. (Fixing the first on April 23rd
// actually introduced the second.)
static unsigned exam_paranoia1()
{
unsigned result = 0;
symbol x("x"), y("y"), z("z");
ex e, f, g;
e = x * y * z;
f = y * z;
g = e / f;
// In the first one expand did not do any job at all:
if (!g.expand().is_equal(x)) {
clog << "e = x*y*z; f = y*z; expand(e/f) erroneously returned "
<< g.expand() << endl;
++result;
}
// This one somehow used to return 0:
e = pow(x + 1, -1);
if (!e.expand().is_equal(e)) {
clog << "expand(pow(x + 1, -1)) erroneously returned "
<< e.expand() << endl;
++result;
}
return result;
}
// And here the second oops which showed up until May 17th 1999. It had to do
// with lexicographic canonicalization and thus showed up only if the variables
// had the names as given here:
static unsigned exam_paranoia2()
{
unsigned result = 0;
symbol x("x"), y("y"), z("z");
ex e, f, g;
e = x + z*x;
f = e*y;
g = f - e*y;
// After .expand(), g should be zero:
if (!g.expand().is_zero()) {
clog << "e = (x + z*x); f = e*y; expand(f - e*y) erroneously returned "
<< g.expand() << endl;
++result;
}
// After .eval(), g should be zero:
if (!g.eval().is_zero()) {
clog << "e = (x + z*x); f = e*y; eval(f - e*y) erroneously returned "
<< g.eval() << endl;
++result;
}
// This actually worked already back in April 1999.
// But we are *very* paranoic!
if (!g.expand().eval().is_zero()) {
clog << "e = (x + z*x); f = e*y; eval(expand(f - e*y)) erroneously returned "
<< g.expand().eval() << endl;
++result;
}
return result;
}
// The third bug was introduced on May 18th 1999, discovered on May 19 and
// fixed that same day. It worked when x was substituted by 1 but not with
// other numbers:
static unsigned exam_paranoia3()
{
unsigned result = 0;
symbol x("x"), y("y");
ex e, f;
e = x*y - y;
f = e.subs(x == 2);
if (!f.is_equal(y)) {
clog << "e = x*y - y; f = e.subs(x == 2) erroneously returned "
<< f << endl;
++result;
}
if (!f.eval().is_equal(y)) {
clog << "e = x*y - y; eval(e.subs(x == 2)) erroneously returned "
<< f.eval() << endl;
++result;
}
if (!f.expand().is_equal(y)) {
clog << "e = x*y - y; expand(e.subs(x == 2)) erroneously returned "
<< f.expand() << endl;
++result;
}
return result;
}
// The fourth bug was also discovered on May 19th 1999 and fixed immediately:
static unsigned exam_paranoia4()
{
unsigned result = 0;
symbol x("x");
ex e, f, g;
e = pow(x, 2) + x + 1;
f = pow(x, 2) + x + 1;
g = e - f;
if (!g.is_zero()) {
clog << "e = pow(x,2) + x + 1; f = pow(x,2) + x + 1; g = e-f; g erroneously returned "
<< g << endl;
++result;
}
if (!g.is_zero()) {
clog << "e = pow(x,2) + x + 1; f = pow(x,2) + x + 1; g = e-f; g.eval() erroneously returned "
<< g.eval() << endl;
++result;
}
return result;
}
// The fifth oops was discovered on May 20th 1999 and fixed a day later:
static unsigned exam_paranoia5()
{
unsigned result = 0;
symbol x("x"), y("y");
ex e, f;
e = pow(x*y + 1, 2);
f = pow(x, 2) * pow(y, 2) + 2*x*y + 1;
if (!(e-f).expand().is_zero()) {
clog << "e = pow(x*y+1,2); f = pow(x,2)*pow(y,2) + 2*x*y + 1; (e-f).expand() erroneously returned "
<< (e-f).expand() << endl;
++result;
}
return result;
}
// This one was discovered on Jun 1st 1999 and fixed the same day:
static unsigned exam_paranoia6()
{
unsigned result = 0;
symbol x("x");
ex e, f;
e = pow(x, -5);
f = e.denom();
if (!f.is_equal(pow(x, 5))) {
clog << "e = pow(x, -5); f = e.denom(); f was " << f << " (should be x^5)" << endl;
++result;
}
return result;
}
// This one was introduced on June 1st 1999 by some aggressive manual
// optimization. Discovered and fixed on June 2nd.
static unsigned exam_paranoia7()
{
unsigned result = 0;
symbol x("x"), y("y");
ex e = y + y*x + 2;
ex f = expand(pow(e, 2) - (e*y*(x + 1)));
if (f.nops() > 3) {
clog << "e=y+y*x+2; f=expand(pow(e,2)-(e*y*(x+1))) has "
<< f.nops() << " arguments instead of 3 ( f=="
<< f << " )" << endl;
++result;
}
return result;
}
// This one was a result of the rewrite of mul::max_coefficient when we
// introduced the overall_coefficient field in expairseq objects on Oct 1st
// 1999. Fixed on Oct 4th.
static unsigned exam_paranoia8()
{
unsigned result = 0;
symbol x("x");
ex e = -x / (x+1);
ex f;
try {
f = e.normal();
if (!f.is_equal(e)) {
clog << "normal(-x/(x+1)) returns " << f << " instead of -x/(x+1)\n";
++result;
}
} catch (const exception &err) {
clog << "normal(-x/(x+1) throws " << err.what() << endl;
++result;
}
return result;
}
// This one was a result of a modification to frac_cancel() & Co. to avoid
// expanding the numerator and denominator when bringing them from Q[X] to
// Z[X]. multiply_lcm() forgot to multiply the x-linear term with the LCM of
// the coefficient's denominators (2 in this case). Introduced on Jan 25th
// 2000 and fixed on Jan 31th.
static unsigned exam_paranoia9()
{
unsigned result = 0;
symbol x("x");
ex e = (exp(-x)-2*x*exp(-x)+pow(x,2)/2*exp(-x))/exp(-x);
ex f = e.normal();
if (!f.is_equal(1-2*x+pow(x,2)/2)) {
clog << "normal(" << e << ") returns " << f << " instead of 1-2*x+1/2*x^2\n";
++result;
}
return result;
}
// I have no idea when this broke. It has been working long ago, before 0.4.0
// and on Feb 13th 2000 I found out that things like 2^(3/2) throw an exception
// "power::eval(): pow(0,0) is undefined" instead of simplifying to 2*2^(1/2).
// It was fixed that same day.
static unsigned exam_paranoia10()
{
unsigned result = 0;
ex b = numeric(2);
ex e = numeric(3,2);
ex r;
try {
r = pow(b,e).eval();
if (!(r-2*sqrt(ex(2))).is_zero()) {
clog << "2^(3/2) erroneously returned " << r << " instead of 2*sqrt(2)" << endl;
++result;
}
} catch (const exception &err) {
clog << "2^(3/2) throws " << err.what() << endl;
++result;
}
return result;
}
// After the rewriting of basic::normal() & Co. to return {num, den} lists,
// add::normal() forgot to multiply the denominator of the overall_coeff of
// its expanded and normalized children with the denominator of the expanded
// child (did you get this? Well, never mind...). Fixed on Feb 21th 2000.
static unsigned exam_paranoia11()
{
unsigned result = 0;
symbol x("x");
ex e = ((-5-2*x)-((2-5*x)/(-2+x))*(3+2*x))/(5-4*x);
ex f = e.normal();
ex d = (4+10*x+8*pow(x,2))/(x-2)/(5-4*x);
if (!(f - d).expand().is_zero()) {
clog << "normal(" << e << ") returns " << f << " instead of " << d << endl;
++result;
}
return result;
}
// This one returned 0 because add::normal() incorrectly assumed that if the
// common denominator is 1, all the denominators would be 1 (they can in fact
// be +/-1). Fixed on Aug 2nd 2000.
static unsigned exam_paranoia12()
{
unsigned result = 0;
symbol x("x");
ex e = 2-2*(1+x)/(-1-x);
ex f = e.normal();
ex d = 4;
if (!(f - d).expand().is_zero()) {
clog << "normal(" << e << ") returns " << f
<< " instead of " << d << endl;
++result;
}
return result;
}
// This one caused a division by 0 because heur_gcd() didn't check its
// input polynomials against 0. Fixed on Aug 4th 2000.
static unsigned exam_paranoia13()
{
unsigned result = 0;
symbol a("a"), b("b"), c("c");
ex e = (b*a-c*a)/(4-a);
ex d = (c*a-b*a)/(a-4);
try {
ex f = e.normal();
if (!(f - d).expand().is_zero()) {
clog << "normal(" << e << ") returns " << f
<< " instead of " << d << endl;
++result;
}
} catch (const exception &err) {
clog << "normal(" << e << ") throws " << err.what() << endl;
++result;
}
return result;
}
// A bug introduced on July 19, 2001. quo() and rem() would sometimes call
// vector::reserve() with a negative argument. Fixed on Dec 20, 2001.
static unsigned exam_paranoia14()
{
unsigned result = 0;
symbol x("x");
ex q = quo(1, pow(x, 3), x);
if (!q.is_zero()) {
clog << "quo(1,x^3,x) erroneously returned " << q << " instead of 0\n";
++result;
}
return result;
}
// Under certain conditions, power::expand_add_2() could produce non-canonical
// numeric expairs. Fixed on Oct 24, 2002.
static unsigned exam_paranoia15()
{
unsigned result = 0;
ex q = (pow(pow(2, numeric(1, 2))*2+1, 2)).expand();
// this used to produce "1+4*sqrt(2)+4*2" which would never evaluate
// to "9+4*sqrt(2)"
if (!(q-9-4*pow(2, numeric(1, 2))).is_zero()) {
clog << "expand((sqrt(2)*2+1)^2) erroneously returned " << q << " instead of 9-4*sqrt(2)\n";
++result;
}
return result;
}
// Expanding products containing powers of sums could return results that
// were not fully expanded. Fixed on Dec 10, 2003.
static unsigned exam_paranoia16()
{
unsigned result = 0;
symbol a("a"), b("b"), c("c"), d("d"), e("e");
ex e1, e2, e3;
e1 = pow(1+a*sqrt(b+c), 2);
e2 = e1.expand();
if (e2.has(pow(a, 2)*(b+c))) {
clog << "expand(" << e1 << ") didn't fully expand\n";
++result;
}
e1 = (d*sqrt(a+b)+a*sqrt(c+d))*(b*sqrt(a+b)+a*sqrt(c+d));
e2 = e1.expand();
if (e2.has(pow(a, 2)*(c+d))) {
clog << "expand(" << e1 << ") didn't fully expand\n";
++result;
}
e1 = (a+sqrt(b+c))*sqrt(b+c)*(d+sqrt(b+c));
e2 = e1.expand();
if (e2.has(a*(b+c))) {
clog << "expand(" << e1 << ") didn't fully expand\n";
++result;
}
e1 = pow(sqrt(a+b)+sqrt(c+d), 3);
e2 = e1.expand();
if (e2.has(3*(a+b)*sqrt(c+d)) || e2.has(3*(c+d)*sqrt(a+b))) {
clog << "expand(" << e1 << ") didn't fully expand\n";
++result;
}
e1 = a*(b+c*(d+e));
e2 = e1.expand();
if (e2.has(c*(d+e))) {
clog << "expand(" << e1 << ") didn't fully expand\n";
++result;
}
e1 = 2*pow(1+a, 2)/a;
e2 = e1.expand();
if (e2.has(pow(a, 2))) {
clog << "expand(" << e1 << ") didn't fully expand\n";
++result;
}
e1 = a*(a+b);
e2 = pow(pow(e1, -1), -1);
if (e2.has(a*b)) {
clog << "double reciprocal expanded where it should not\n";
++result;
}
return result;
}
unsigned exam_paranoia()
{
unsigned result = 0;
cout << "examining several historic failures just out of paranoia" << flush;
clog << "----------several historic failures:" << endl;
result += exam_paranoia1(); cout << '.' << flush;
result += exam_paranoia2(); cout << '.' << flush;
result += exam_paranoia3(); cout << '.' << flush;
result += exam_paranoia4(); cout << '.' << flush;
result += exam_paranoia5(); cout << '.' << flush;
result += exam_paranoia6(); cout << '.' << flush;
result += exam_paranoia7(); cout << '.' << flush;
result += exam_paranoia8(); cout << '.' << flush;
result += exam_paranoia9(); cout << '.' << flush;
result += exam_paranoia10(); cout << '.' << flush;
result += exam_paranoia11(); cout << '.' << flush;
result += exam_paranoia12(); cout << '.' << flush;
result += exam_paranoia13(); cout << '.' << flush;
result += exam_paranoia14(); cout << '.' << flush;
result += exam_paranoia15(); cout << '.' << flush;
result += exam_paranoia16(); cout << '.' << flush;
if (!result) {
cout << " passed " << endl;
clog << "(no output)" << endl;
} else {
cout << " failed " << endl;
}
return result;
}