1 /** @file exam_paranoia.cpp
3 * This set of tests checks for some of GiNaC's oopses which showed up during
4 * development. Things were evaluated wrongly and so. Such a sick behaviour
5 * shouldn't occur any more. But we are paranoic and we want to exclude these
6 * these oopses for good, so we run those stupid tests... */
9 * GiNaC Copyright (C) 1999-2010 Johannes Gutenberg University Mainz, Germany
11 * This program is free software; you can redistribute it and/or modify
12 * it under the terms of the GNU General Public License as published by
13 * the Free Software Foundation; either version 2 of the License, or
14 * (at your option) any later version.
16 * This program is distributed in the hope that it will be useful,
17 * but WITHOUT ANY WARRANTY; without even the implied warranty of
18 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
19 * GNU General Public License for more details.
21 * You should have received a copy of the GNU General Public License
22 * along with this program; if not, write to the Free Software
23 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
27 using namespace GiNaC;
32 // The very first pair of historic problems had its roots in power.cpp and was
33 // finally resolved on April 27th 1999. (Fixing the first on April 23rd
34 // actually introduced the second.)
35 static unsigned exam_paranoia1()
38 symbol x("x"), y("y"), z("z");
45 // In the first one expand did not do any job at all:
46 if (!g.expand().is_equal(x)) {
47 clog << "e = x*y*z; f = y*z; expand(e/f) erroneously returned "
48 << g.expand() << endl;
52 // This one somehow used to return 0:
54 if (!e.expand().is_equal(e)) {
55 clog << "expand(pow(x + 1, -1)) erroneously returned "
56 << e.expand() << endl;
63 // And here the second oops which showed up until May 17th 1999. It had to do
64 // with lexicographic canonicalization and thus showed up only if the variables
65 // had the names as given here:
66 static unsigned exam_paranoia2()
69 symbol x("x"), y("y"), z("z");
76 // After .expand(), g should be zero:
77 if (!g.expand().is_zero()) {
78 clog << "e = (x + z*x); f = e*y; expand(f - e*y) erroneously returned "
79 << g.expand() << endl;
82 // After .eval(), g should be zero:
83 if (!g.eval().is_zero()) {
84 clog << "e = (x + z*x); f = e*y; eval(f - e*y) erroneously returned "
88 // This actually worked already back in April 1999.
89 // But we are *very* paranoic!
90 if (!g.expand().eval().is_zero()) {
91 clog << "e = (x + z*x); f = e*y; eval(expand(f - e*y)) erroneously returned "
92 << g.expand().eval() << endl;
99 // The third bug was introduced on May 18th 1999, discovered on May 19 and
100 // fixed that same day. It worked when x was substituted by 1 but not with
102 static unsigned exam_paranoia3()
105 symbol x("x"), y("y");
111 if (!f.is_equal(y)) {
112 clog << "e = x*y - y; f = e.subs(x == 2) erroneously returned "
116 if (!f.eval().is_equal(y)) {
117 clog << "e = x*y - y; eval(e.subs(x == 2)) erroneously returned "
121 if (!f.expand().is_equal(y)) {
122 clog << "e = x*y - y; expand(e.subs(x == 2)) erroneously returned "
123 << f.expand() << endl;
130 // The fourth bug was also discovered on May 19th 1999 and fixed immediately:
131 static unsigned exam_paranoia4()
137 e = pow(x, 2) + x + 1;
138 f = pow(x, 2) + x + 1;
142 clog << "e = pow(x,2) + x + 1; f = pow(x,2) + x + 1; g = e-f; g erroneously returned "
147 clog << "e = pow(x,2) + x + 1; f = pow(x,2) + x + 1; g = e-f; g.eval() erroneously returned "
155 // The fifth oops was discovered on May 20th 1999 and fixed a day later:
156 static unsigned exam_paranoia5()
159 symbol x("x"), y("y");
163 f = pow(x, 2) * pow(y, 2) + 2*x*y + 1;
165 if (!(e-f).expand().is_zero()) {
166 clog << "e = pow(x*y+1,2); f = pow(x,2)*pow(y,2) + 2*x*y + 1; (e-f).expand() erroneously returned "
167 << (e-f).expand() << endl;
174 // This one was discovered on Jun 1st 1999 and fixed the same day:
175 static unsigned exam_paranoia6()
184 if (!f.is_equal(pow(x, 5))) {
185 clog << "e = pow(x, -5); f = e.denom(); f was " << f << " (should be x^5)" << endl;
191 // This one was introduced on June 1st 1999 by some aggressive manual
192 // optimization. Discovered and fixed on June 2nd.
193 static unsigned exam_paranoia7()
196 symbol x("x"), y("y");
199 ex f = expand(pow(e, 2) - (e*y*(x + 1)));
202 clog << "e=y+y*x+2; f=expand(pow(e,2)-(e*y*(x+1))) has "
203 << f.nops() << " arguments instead of 3 ( f=="
204 << f << " )" << endl;
210 // This one was a result of the rewrite of mul::max_coefficient when we
211 // introduced the overall_coefficient field in expairseq objects on Oct 1st
212 // 1999. Fixed on Oct 4th.
213 static unsigned exam_paranoia8()
223 if (!f.is_equal(e)) {
224 clog << "normal(-x/(x+1)) returns " << f << " instead of -x/(x+1)\n";
227 } catch (const exception &err) {
228 clog << "normal(-x/(x+1) throws " << err.what() << endl;
234 // This one was a result of a modification to frac_cancel() & Co. to avoid
235 // expanding the numerator and denominator when bringing them from Q[X] to
236 // Z[X]. multiply_lcm() forgot to multiply the x-linear term with the LCM of
237 // the coefficient's denominators (2 in this case). Introduced on Jan 25th
238 // 2000 and fixed on Jan 31th.
239 static unsigned exam_paranoia9()
244 ex e = (exp(-x)-2*x*exp(-x)+pow(x,2)/2*exp(-x))/exp(-x);
247 if (!f.is_equal(1-2*x+pow(x,2)/2)) {
248 clog << "normal(" << e << ") returns " << f << " instead of 1-2*x+1/2*x^2\n";
254 // I have no idea when this broke. It has been working long ago, before 0.4.0
255 // and on Feb 13th 2000 I found out that things like 2^(3/2) throw an exception
256 // "power::eval(): pow(0,0) is undefined" instead of simplifying to 2*2^(1/2).
257 // It was fixed that same day.
258 static unsigned exam_paranoia10()
268 if (!(r-2*sqrt(ex(2))).is_zero()) {
269 clog << "2^(3/2) erroneously returned " << r << " instead of 2*sqrt(2)" << endl;
272 } catch (const exception &err) {
273 clog << "2^(3/2) throws " << err.what() << endl;
279 // After the rewriting of basic::normal() & Co. to return {num, den} lists,
280 // add::normal() forgot to multiply the denominator of the overall_coeff of
281 // its expanded and normalized children with the denominator of the expanded
282 // child (did you get this? Well, never mind...). Fixed on Feb 21th 2000.
283 static unsigned exam_paranoia11()
288 ex e = ((-5-2*x)-((2-5*x)/(-2+x))*(3+2*x))/(5-4*x);
290 ex d = normal((4+10*x+8*pow(x,2))/(x-2)/(5-4*x));
292 if (!(f - d).expand().is_zero()) {
293 clog << "normal(" << e << ") returns " << f << " instead of " << d << endl;
299 // This one returned 0 because add::normal() incorrectly assumed that if the
300 // common denominator is 1, all the denominators would be 1 (they can in fact
301 // be +/-1). Fixed on Aug 2nd 2000.
302 static unsigned exam_paranoia12()
307 ex e = 2-2*(1+x)/(-1-x);
311 if (!(f - d).expand().is_zero()) {
312 clog << "normal(" << e << ") returns " << f
313 << " instead of " << d << endl;
319 // This one caused a division by 0 because heur_gcd() didn't check its
320 // input polynomials against 0. Fixed on Aug 4th 2000.
321 static unsigned exam_paranoia13()
324 symbol a("a"), b("b"), c("c");
326 ex e = (b*a-c*a)/(4-a);
327 ex d = (c*a-b*a)/(a-4);
331 if (!(f - d).expand().is_zero()) {
332 clog << "normal(" << e << ") returns " << f
333 << " instead of " << d << endl;
336 } catch (const exception &err) {
337 clog << "normal(" << e << ") throws " << err.what() << endl;
343 // A bug introduced on July 19, 2001. quo() and rem() would sometimes call
344 // vector::reserve() with a negative argument. Fixed on Dec 20, 2001.
345 static unsigned exam_paranoia14()
350 ex q = quo(1, pow(x, 3), x);
352 clog << "quo(1,x^3,x) erroneously returned " << q << " instead of 0\n";
359 // Under certain conditions, power::expand_add_2() could produce non-canonical
360 // numeric expairs. Fixed on Oct 24, 2002.
361 static unsigned exam_paranoia15()
365 ex q = (pow(pow(2, numeric(1, 2))*2+1, 2)).expand();
366 // this used to produce "1+4*sqrt(2)+4*2" which would never evaluate
369 if (!(q-9-4*pow(2, numeric(1, 2))).is_zero()) {
370 clog << "expand((sqrt(2)*2+1)^2) erroneously returned " << q << " instead of 9-4*sqrt(2)\n";
377 // Expanding products containing powers of sums could return results that
378 // were not fully expanded. Fixed on Dec 10, 2003.
379 static unsigned exam_paranoia16()
382 symbol a("a"), b("b"), c("c"), d("d"), e("e");
385 e1 = pow(1+a*sqrt(b+c), 2);
388 if (e2.has(pow(a, 2)*(b+c))) {
389 clog << "expand(" << e1 << ") didn't fully expand\n";
393 e1 = (d*sqrt(a+b)+a*sqrt(c+d))*(b*sqrt(a+b)+a*sqrt(c+d));
396 if (e2.has(pow(a, 2)*(c+d))) {
397 clog << "expand(" << e1 << ") didn't fully expand\n";
401 e1 = (a+sqrt(b+c))*sqrt(b+c)*(d+sqrt(b+c));
404 if (e2.has(a*(b+c))) {
405 clog << "expand(" << e1 << ") didn't fully expand\n";
409 e1 = pow(sqrt(a+b)+sqrt(c+d), 3);
412 if (e2.has(3*(a+b)*sqrt(c+d)) || e2.has(3*(c+d)*sqrt(a+b))) {
413 clog << "expand(" << e1 << ") didn't fully expand\n";
420 if (e2.has(c*(d+e))) {
421 clog << "expand(" << e1 << ") didn't fully expand\n";
425 e1 = 2*pow(1+a, 2)/a;
428 if (e2.has(pow(a, 2))) {
429 clog << "expand(" << e1 << ") didn't fully expand\n";
434 e2 = pow(pow(e1, -1), -1);
437 clog << "double reciprocal expanded where it should not\n";
444 // Bug in reposition_dummy_indices() could result in correct expression
445 // turned into one with inconsistent indices. Fixed on Aug 29, 2006
446 static unsigned exam_paranoia17()
448 varidx mu1(symbol("mu1"), 4);
449 varidx mu2(symbol("mu2"), 4);
450 varidx mu3(symbol("mu3"), 4);
451 varidx mu4(symbol("mu4"), 4);
452 varidx mu5(symbol("mu5"), 4);
453 varidx mu6(symbol("mu6"), 4);
456 ev2.push_back(mu3.toggle_variance());
458 ev2.push_back(mu5.toggle_variance());
459 ev2.push_back(mu6.toggle_variance());
462 // notice: all indices are contracted ...
464 ex test_cycl = indexed(symbol("A"), sy_cycl(), ev2);
465 test_cycl = test_cycl.simplify_indexed();
466 // ... so there should be zero free indices in the end.
467 return test_cycl.get_free_indices().size();
471 unsigned exam_paranoia()
475 cout << "examining several historic failures just out of paranoia" << flush;
477 result += exam_paranoia1(); cout << '.' << flush;
478 result += exam_paranoia2(); cout << '.' << flush;
479 result += exam_paranoia3(); cout << '.' << flush;
480 result += exam_paranoia4(); cout << '.' << flush;
481 result += exam_paranoia5(); cout << '.' << flush;
482 result += exam_paranoia6(); cout << '.' << flush;
483 result += exam_paranoia7(); cout << '.' << flush;
484 result += exam_paranoia8(); cout << '.' << flush;
485 result += exam_paranoia9(); cout << '.' << flush;
486 result += exam_paranoia10(); cout << '.' << flush;
487 result += exam_paranoia11(); cout << '.' << flush;
488 result += exam_paranoia12(); cout << '.' << flush;
489 result += exam_paranoia13(); cout << '.' << flush;
490 result += exam_paranoia14(); cout << '.' << flush;
491 result += exam_paranoia15(); cout << '.' << flush;
492 result += exam_paranoia16(); cout << '.' << flush;
493 result += exam_paranoia17(); cout << '.' << flush;
498 int main(int argc, char** argv)
500 return exam_paranoia();