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) 1999-2003 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., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
28 // The very first pair of historic problems had its roots in power.cpp and was
29 // finally resolved on April 27th 1999. (Fixing the first on April 23rd
30 // actually introduced the second.)
31 static unsigned exam_paranoia1()
34 symbol x("x"), y("y"), z("z");
41 // In the first one expand did not do any job at all:
42 if (!g.expand().is_equal(x)) {
43 clog << "e = x*y*z; f = y*z; expand(e/f) erroneously returned "
44 << g.expand() << endl;
48 // This one somehow used to return 0:
50 if (!e.expand().is_equal(e)) {
51 clog << "expand(pow(x + 1, -1)) erroneously returned "
52 << e.expand() << endl;
59 // And here the second oops which showed up until May 17th 1999. It had to do
60 // with lexicographic canonicalization and thus showed up only if the variables
61 // had the names as given here:
62 static unsigned exam_paranoia2()
65 symbol x("x"), y("y"), z("z");
72 // After .expand(), g should be zero:
73 if (!g.expand().is_zero()) {
74 clog << "e = (x + z*x); f = e*y; expand(f - e*y) erroneously returned "
75 << g.expand() << endl;
78 // After .eval(), g should be zero:
79 if (!g.eval().is_zero()) {
80 clog << "e = (x + z*x); f = e*y; eval(f - e*y) erroneously returned "
84 // This actually worked already back in April 1999.
85 // But we are *very* paranoic!
86 if (!g.expand().eval().is_zero()) {
87 clog << "e = (x + z*x); f = e*y; eval(expand(f - e*y)) erroneously returned "
88 << g.expand().eval() << endl;
95 // The third bug was introduced on May 18th 1999, discovered on May 19 and
96 // fixed that same day. It worked when x was substituted by 1 but not with
98 static unsigned exam_paranoia3()
101 symbol x("x"), y("y");
107 if (!f.is_equal(y)) {
108 clog << "e = x*y - y; f = e.subs(x == 2) erroneously returned "
112 if (!f.eval().is_equal(y)) {
113 clog << "e = x*y - y; eval(e.subs(x == 2)) erroneously returned "
117 if (!f.expand().is_equal(y)) {
118 clog << "e = x*y - y; expand(e.subs(x == 2)) erroneously returned "
119 << f.expand() << endl;
126 // The fourth bug was also discovered on May 19th 1999 and fixed immediately:
127 static unsigned exam_paranoia4()
133 e = pow(x, 2) + x + 1;
134 f = pow(x, 2) + x + 1;
138 clog << "e = pow(x,2) + x + 1; f = pow(x,2) + x + 1; g = e-f; g erroneously returned "
143 clog << "e = pow(x,2) + x + 1; f = pow(x,2) + x + 1; g = e-f; g.eval() erroneously returned "
151 // The fifth oops was discovered on May 20th 1999 and fixed a day later:
152 static unsigned exam_paranoia5()
155 symbol x("x"), y("y");
159 f = pow(x, 2) * pow(y, 2) + 2*x*y + 1;
161 if (!(e-f).expand().is_zero()) {
162 clog << "e = pow(x*y+1,2); f = pow(x,2)*pow(y,2) + 2*x*y + 1; (e-f).expand() erroneously returned "
163 << (e-f).expand() << endl;
170 // This one was discovered on Jun 1st 1999 and fixed the same day:
171 static unsigned exam_paranoia6()
180 if (!f.is_equal(pow(x, 5))) {
181 clog << "e = pow(x, -5); f = e.denom(); f was " << f << " (should be x^5)" << endl;
187 // This one was introduced on June 1st 1999 by some aggressive manual
188 // optimization. Discovered and fixed on June 2nd.
189 static unsigned exam_paranoia7()
192 symbol x("x"), y("y");
195 ex f = expand(pow(e, 2) - (e*y*(x + 1)));
198 clog << "e=y+y*x+2; f=expand(pow(e,2)-(e*y*(x+1))) has "
199 << f.nops() << " arguments instead of 3 ( f=="
200 << f << " )" << endl;
206 // This one was a result of the rewrite of mul::max_coefficient when we
207 // introduced the overall_coefficient field in expairseq objects on Oct 1st
208 // 1999. Fixed on Oct 4th.
209 static unsigned exam_paranoia8()
219 if (!f.is_equal(e)) {
220 clog << "normal(-x/(x+1)) returns " << f << " instead of -x/(x+1)\n";
223 } catch (const exception &err) {
224 clog << "normal(-x/(x+1) throws " << err.what() << endl;
230 // This one was a result of a modification to frac_cancel() & Co. to avoid
231 // expanding the numerator and denominator when bringing them from Q[X] to
232 // Z[X]. multiply_lcm() forgot to multiply the x-linear term with the LCM of
233 // the coefficient's denominators (2 in this case). Introduced on Jan 25th
234 // 2000 and fixed on Jan 31th.
235 static unsigned exam_paranoia9()
240 ex e = (exp(-x)-2*x*exp(-x)+pow(x,2)/2*exp(-x))/exp(-x);
243 if (!f.is_equal(1-2*x+pow(x,2)/2)) {
244 clog << "normal(" << e << ") returns " << f << " instead of 1-2*x+1/2*x^2\n";
250 // I have no idea when this broke. It has been working long ago, before 0.4.0
251 // and on Feb 13th 2000 I found out that things like 2^(3/2) throw an exception
252 // "power::eval(): pow(0,0) is undefined" instead of simplifying to 2*2^(1/2).
253 // It was fixed that same day.
254 static unsigned exam_paranoia10()
264 if (!(r-2*sqrt(ex(2))).is_zero()) {
265 clog << "2^(3/2) erroneously returned " << r << " instead of 2*sqrt(2)" << endl;
268 } catch (const exception &err) {
269 clog << "2^(3/2) throws " << err.what() << endl;
275 // After the rewriting of basic::normal() & Co. to return {num, den} lists,
276 // add::normal() forgot to multiply the denominator of the overall_coeff of
277 // its expanded and normalized children with the denominator of the expanded
278 // child (did you get this? Well, never mind...). Fixed on Feb 21th 2000.
279 static unsigned exam_paranoia11()
284 ex e = ((-5-2*x)-((2-5*x)/(-2+x))*(3+2*x))/(5-4*x);
286 ex d = (4+10*x+8*pow(x,2))/(x-2)/(5-4*x);
288 if (!(f - d).expand().is_zero()) {
289 clog << "normal(" << e << ") returns " << f << " instead of " << d << endl;
295 // This one returned 0 because add::normal() incorrectly assumed that if the
296 // common denominator is 1, all the denominators would be 1 (they can in fact
297 // be +/-1). Fixed on Aug 2nd 2000.
298 static unsigned exam_paranoia12()
303 ex e = 2-2*(1+x)/(-1-x);
307 if (!(f - d).expand().is_zero()) {
308 clog << "normal(" << e << ") returns " << f
309 << " instead of " << d << endl;
315 // This one caused a division by 0 because heur_gcd() didn't check its
316 // input polynomials against 0. Fixed on Aug 4th 2000.
317 static unsigned exam_paranoia13()
320 symbol a("a"), b("b"), c("c");
322 ex e = (b*a-c*a)/(4-a);
323 ex d = (c*a-b*a)/(a-4);
327 if (!(f - d).expand().is_zero()) {
328 clog << "normal(" << e << ") returns " << f
329 << " instead of " << d << endl;
332 } catch (const exception &err) {
333 clog << "normal(" << e << ") throws " << err.what() << endl;
339 // A bug introduced on July 19, 2001. quo() and rem() would sometimes call
340 // vector::reserve() with a negative argument. Fixed on Dec 20, 2001.
341 static unsigned exam_paranoia14()
346 ex q = quo(1, pow(x, 3), x);
348 clog << "quo(1,x^3,x) erroneously returned " << q << " instead of 0\n";
355 // Under certain conditions, power::expand_add_2() could produce non-canonical
356 // numeric expairs. Fixed on Oct 24, 2002.
357 static unsigned exam_paranoia15()
361 ex q = (pow(pow(2, numeric(1, 2))*2+1, 2)).expand();
362 // this used to produce "1+4*sqrt(2)+4*2" which would never evaluate
365 if (!(q-9-4*pow(2, numeric(1, 2))).is_zero()) {
366 clog << "expand((sqrt(2)*2+1)^2) erroneously returned " << q << " instead of 9-4*sqrt(2)\n";
373 // Expanding products containing powers of sums could return results that
374 // were not fully expanded. Fixed on Dec 10, 2003.
375 static unsigned exam_paranoia16()
378 symbol a("a"), b("b"), c("c"), d("d");
381 e1 = pow(1+a*sqrt(b+c), 2);
384 if (e2.has(pow(a, 2)*(b+c))) {
385 clog << "expand(" << e1 << ") didn't fully expand\n";
389 e1 = (d*sqrt(a+b)+a*sqrt(c+d))*(b*sqrt(a+b)+a*sqrt(c+d));
392 if (e2.has(pow(a, 2)*(c+d))) {
393 clog << "expand(" << e1 << ") didn't fully expand\n";
397 e1 = (a+sqrt(b+c))*sqrt(b+c)*(d+sqrt(b+c));
400 if (e2.has(a*(b+c))) {
401 clog << "expand(" << e1 << ") didn't fully expand\n";
408 unsigned exam_paranoia()
412 cout << "examining several historic failures just out of paranoia" << flush;
413 clog << "----------several historic failures:" << endl;
415 result += exam_paranoia1(); cout << '.' << flush;
416 result += exam_paranoia2(); cout << '.' << flush;
417 result += exam_paranoia3(); cout << '.' << flush;
418 result += exam_paranoia4(); cout << '.' << flush;
419 result += exam_paranoia5(); cout << '.' << flush;
420 result += exam_paranoia6(); cout << '.' << flush;
421 result += exam_paranoia7(); cout << '.' << flush;
422 result += exam_paranoia8(); cout << '.' << flush;
423 result += exam_paranoia9(); cout << '.' << flush;
424 result += exam_paranoia10(); cout << '.' << flush;
425 result += exam_paranoia11(); cout << '.' << flush;
426 result += exam_paranoia12(); cout << '.' << flush;
427 result += exam_paranoia13(); cout << '.' << flush;
428 result += exam_paranoia14(); cout << '.' << flush;
429 result += exam_paranoia15(); cout << '.' << flush;
430 result += exam_paranoia16(); cout << '.' << flush;
433 cout << " passed " << endl;
434 clog << "(no output)" << endl;
436 cout << " failed " << endl;