* these oopses for good, so we run those stupid tests... */
/*
- * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2004 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 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(void)
+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;
+ 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(void)
+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;
+ 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(void)
+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;
+ 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(void)
+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;
+ 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(void)
+static unsigned exam_paranoia5()
{
- unsigned result = 0;
- symbol x("x"), y("y");
+ 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;
+ 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;
- }
+ 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;
+ return result;
}
// This one was discovered on Jun 1st 1999 and fixed the same day:
-static unsigned exam_paranoia6(void)
+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;
+ 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(void)
+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;
+ 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(void)
+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;
+ 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
// 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(void)
+static unsigned exam_paranoia9()
{
- unsigned result = 0;
- symbol x("x");
+ 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();
+ 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;
+ 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(void)
+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;
+ 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(void)
+static unsigned exam_paranoia11()
{
- unsigned result = 0;
+ unsigned result = 0;
symbol x("x");
ex e = ((-5-2*x)-((2-5*x)/(-2+x))*(3+2*x))/(5-4*x);
clog << "normal(" << e << ") returns " << f << " instead of " << d << endl;
++result;
}
- return 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(void)
+static unsigned exam_paranoia12()
{
- unsigned result = 0;
+ 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;
+ << " 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(void)
+static unsigned exam_paranoia13()
{
- unsigned result = 0;
+ unsigned result = 0;
symbol a("a"), b("b"), c("c");
-
+
ex e = (b*a-c*a)/(4-a);
- ex f = e.normal();
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;
+}
- if (!(f - d).expand().is_zero()) {
- clog << "normal(" << e << ") returns " << f << " instead of " << d << endl;
+// 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(void)
+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;
-
- if (!result) {
- cout << " passed " << endl;
- clog << "(no output)" << endl;
- } else {
- cout << " failed " << endl;
- }
-
- return result;
+ 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;
}
git://www.ginac.de / ginac.git / blobdiff