check/exam_numeric.cpp

   1 /** @file exam_numeric.cpp
   2  *
   3  *  These exams creates some numbers and check the result of several boolean
   4  *  tests on these numbers like is_integer() etc... */
   5
   6 /*
   7  *  GiNaC Copyright (C) 1999-2008 Johannes Gutenberg University Mainz, Germany
   8  *
   9  *  This program is free software; you can redistribute it and/or modify
  10  *  it under the terms of the GNU General Public License as published by
  11  *  the Free Software Foundation; either version 2 of the License, or
  12  *  (at your option) any later version.
  13  *
  14  *  This program is distributed in the hope that it will be useful,
  15  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
  16  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  17  *  GNU General Public License for more details.
  18  *
  19  *  You should have received a copy of the GNU General Public License
  20  *  along with this program; if not, write to the Free Software
  21  *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
  22  */
  23
  24 #include <iostream>
  25 #include <sstream>
  26 #include "ginac.h"
  27 using namespace std;
  28 using namespace GiNaC;
  29
  30
  31 /* Simple and maybe somewhat pointless consistency tests of assorted tests and
  32  * conversions. */
  33 static unsigned exam_numeric1()
  34 {
  35         unsigned result = 0;
  36         numeric test_int1(42);
  37         numeric test_int2(5);
  38         numeric test_rat1 = test_int1; test_rat1 /= test_int2;
  39         test_rat1 = -test_rat1;          // -42/5
  40         numeric test_crat = test_rat1+I*test_int2;  // 5*I-42/5
  41         symbol a("a");
  42         ex e1, e2;
  43
  44         if (!test_int1.is_integer()) {
  45                 clog << test_int1
  46                      << " erroneously not recognized as integer" << endl;
  47                 ++result;
  48         }
  49         if (!test_int1.is_rational()) {
  50                 clog << test_int1
  51                      << " erroneously not recognized as rational" << endl;
  52                 ++result;
  53         }
  54
  55         if (!test_rat1.is_rational()) {
  56                 clog << test_rat1
  57                      << " erroneously not recognized as rational" << endl;
  58                 ++result;
  59         }
  60         if (test_rat1.is_integer()) {
  61                 clog << test_rat1
  62                          << " erroneously recognized as integer" << endl;
  63                 ++result;
  64         }
  65
  66         if (!test_crat.is_crational()) {
  67                 clog << test_crat
  68                      << " erroneously not recognized as complex rational" << endl;
  69                 ++result;
  70         }
  71
  72         int i = numeric(1984).to_int();
  73         if (i-1984) {
  74                 clog << "conversion of " << i
  75                      << " from numeric to int failed" << endl;
  76                 ++result;
  77         }
  78
  79         e1 = test_int1;
  80         if (!e1.info(info_flags::posint)) {
  81                 clog << "expression " << e1
  82                      << " erroneously not recognized as positive integer" << endl;
  83                 ++result;
  84         }
  85
  86         e2 = test_int1 + a;
  87         if (e2.info(info_flags::integer)) {
  88                 clog << "expression " << e2
  89                      << " erroneously recognized as integer" << endl;
  90                 ++result;
  91         }
  92
  93         // The next two were two actual bugs in CLN till June, 12, 1999:
  94         test_rat1 = numeric(3)/numeric(2);
  95         test_rat1 += test_rat1;
  96         if (!test_rat1.is_integer()) {
  97                 clog << "3/2 + 3/2 erroneously not integer 3 but instead "
  98                      << test_rat1 << endl;
  99                 ++result;
 100         }
 101         test_rat1 = numeric(3)/numeric(2);
 102         numeric test_rat2 = test_rat1 + numeric(1);  // 5/2
 103         test_rat2 -= test_rat1;  // 1
 104         if (!test_rat2.is_integer()) {
 105                 clog << "5/2 - 3/2 erroneously not integer 1 but instead "
 106                      << test_rat2 << endl;
 107                 ++result;
 108         }
 109
 110         return result;
 111 }
 112
 113 /* We had some fun with a bug in CLN that caused it to loop forever when
 114  * calculating expt(a,b) if b is a rational and a a nonnegative integer.
 115  * Implementing a workaround sadly introduced another bug on May 28th 1999
 116  * that was fixed on May 31st.  The workaround turned out to be stupid and
 117  * the original bug in CLN was finally killed on September 2nd. */
 118 static unsigned exam_numeric2()
 119 {
 120         unsigned result = 0;
 121
 122         ex zero = numeric(0);
 123         ex two = numeric(2);
 124         ex three = numeric(3);
 125
 126         // The hang in this code was the reason for the original workaround
 127         if (pow(two,two/three)==42) {
 128                 clog << "pow(2,2/3) erroneously returned 42" << endl;
 129                 ++result;  // cannot happen
 130         }
 131
 132         // Actually, this used to raise a FPE after introducing the workaround
 133         if (two*zero!=zero) {
 134                 clog << "2*0 erroneously returned " << two*zero << endl;
 135                 ++result;
 136         }
 137
 138         // And this returned a cl_F due to the implicit call of numeric::power()
 139         ex six = two*three;
 140         if (!six.info(info_flags::integer)) {
 141                 clog << "2*3 erroneously returned the non-integer " << six << endl;
 142                 ++result;
 143         }
 144
 145         // The fix in the workaround left a whole which was fixed hours later...
 146         ex another_zero = pow(zero,numeric(1)/numeric(2));
 147         if (!another_zero.is_zero()) {
 148                 clog << "pow(0,1/2) erroneously returned" << another_zero << endl;
 149                 ++result;
 150         }
 151
 152         return result;
 153 }
 154
 155 /* Assorted tests to ensure some crucial functions behave exactly as specified
 156  * in the documentation. */
 157 static unsigned exam_numeric3()
 158 {
 159         unsigned result = 0;
 160         numeric calc_rem, calc_quo;
 161         numeric a, b;
 162
 163         // check if irem(a, b) and irem(a, b, q) really behave like Maple's
 164         // irem(a, b) and irem(a, b, 'q') as advertised in our documentation.
 165         // These overloaded routines indeed need to be checked separately since
 166         // internally they might be doing something completely different:
 167         a = 23; b = 4; calc_rem = irem(a, b);
 168         if (calc_rem != 3) {
 169                 clog << "irem(" << a << "," << b << ") erroneously returned "
 170                      << calc_rem << endl;
 171                 ++result;
 172         }
 173         a = 23; b = -4; calc_rem = irem(a, b);
 174         if (calc_rem != 3) {
 175                 clog << "irem(" << a << "," << b << ") erroneously returned "
 176                          << calc_rem << endl;
 177                 ++result;
 178         }
 179         a = -23; b = 4; calc_rem = irem(a, b);
 180         if (calc_rem != -3) {
 181                 clog << "irem(" << a << "," << b << ") erroneously returned "
 182                      << calc_rem << endl;
 183                 ++result;
 184         }
 185         a = -23; b = -4; calc_rem = irem(a, b);
 186         if (calc_rem != -3) {
 187                 clog << "irem(" << a << "," << b << ") erroneously returned "
 188                      << calc_rem << endl;
 189                 ++result;
 190         }
 191         // and now the overloaded irem(a,b,q):
 192         a = 23; b = 4; calc_rem = irem(a, b, calc_quo);
 193         if (calc_rem != 3 || calc_quo != 5) {
 194                 clog << "irem(" << a << "," << b << ",q) erroneously returned "
 195                      << calc_rem << " with q=" << calc_quo << endl;
 196                 ++result;
 197         }
 198         a = 23; b = -4; calc_rem = irem(a, b, calc_quo);
 199         if (calc_rem != 3 || calc_quo != -5) {
 200                 clog << "irem(" << a << "," << b << ",q) erroneously returned "
 201                      << calc_rem << " with q=" << calc_quo << endl;
 202                 ++result;
 203         }
 204         a = -23; b = 4; calc_rem = irem(a, b, calc_quo);
 205         if (calc_rem != -3 || calc_quo != -5) {
 206                 clog << "irem(" << a << "," << b << ",q) erroneously returned "
 207                      << calc_rem << " with q=" << calc_quo << endl;
 208                 ++result;
 209         }
 210         a = -23; b = -4; calc_rem = irem(a, b, calc_quo);
 211         if (calc_rem != -3 || calc_quo != 5) {
 212                 clog << "irem(" << a << "," << b << ",q) erroneously returned "
 213                      << calc_rem << " with q=" << calc_quo << endl;
 214                 ++result;
 215         }
 216         // check if iquo(a, b) and iquo(a, b, r) really behave like Maple's
 217         // iquo(a, b) and iquo(a, b, 'r') as advertised in our documentation.
 218         // These overloaded routines indeed need to be checked separately since
 219         // internally they might be doing something completely different:
 220         a = 23; b = 4; calc_quo = iquo(a, b);
 221         if (calc_quo != 5) {
 222                 clog << "iquo(" << a << "," << b << ") erroneously returned "
 223                      << calc_quo << endl;
 224                 ++result;
 225         }
 226         a = 23; b = -4; calc_quo = iquo(a, b);
 227         if (calc_quo != -5) {
 228                 clog << "iquo(" << a << "," << b << ") erroneously returned "
 229                      << calc_quo << endl;
 230                 ++result;
 231         }
 232         a = -23; b = 4; calc_quo = iquo(a, b);
 233         if (calc_quo != -5) {
 234                 clog << "iquo(" << a << "," << b << ") erroneously returned "
 235                      << calc_quo << endl;
 236                 ++result;
 237         }
 238         a = -23; b = -4; calc_quo = iquo(a, b);
 239         if (calc_quo != 5) {
 240                 clog << "iquo(" << a << "," << b << ") erroneously returned "
 241                      << calc_quo << endl;
 242                 ++result;
 243         }
 244         // and now the overloaded iquo(a,b,r):
 245         a = 23; b = 4; calc_quo = iquo(a, b, calc_rem);
 246         if (calc_quo != 5 || calc_rem != 3) {
 247                 clog << "iquo(" << a << "," << b << ",r) erroneously returned "
 248                      << calc_quo << " with r=" << calc_rem << endl;
 249                 ++result;
 250         }
 251         a = 23; b = -4; calc_quo = iquo(a, b, calc_rem);
 252         if (calc_quo != -5 || calc_rem != 3) {
 253                 clog << "iquo(" << a << "," << b << ",r) erroneously returned "
 254                      << calc_quo << " with r=" << calc_rem << endl;
 255                 ++result;
 256         }
 257         a = -23; b = 4; calc_quo = iquo(a, b, calc_rem);
 258         if (calc_quo != -5 || calc_rem != -3) {
 259                 clog << "iquo(" << a << "," << b << ",r) erroneously returned "
 260                      << calc_quo << " with r=" << calc_rem << endl;
 261                 ++result;
 262         }
 263         a = -23; b = -4; calc_quo = iquo(a, b, calc_rem);
 264         if (calc_quo != 5 || calc_rem != -3) {
 265                 clog << "iquo(" << a << "," << b << ",r) erroneously returned "
 266                      << calc_quo << " with r=" << calc_rem << endl;
 267                 ++result;
 268         }
 269
 270         return result;
 271 }
 272
 273 /* Now we perform some less trivial checks about several functions which should
 274  * return exact numbers if possible. */
 275 static unsigned exam_numeric4()
 276 {
 277         unsigned result = 0;
 278         bool passed;
 279
 280         // square roots of squares of integers:
 281         passed = true;
 282         for (int i=0; i<42; ++i)
 283                 if (!sqrt(numeric(i*i)).is_integer())
 284                         passed = false;
 285         if (!passed) {
 286                 clog << "One or more square roots of squares of integers did not return exact integers" << endl;
 287                 ++result;
 288         }
 289
 290         // square roots of squares of rationals:
 291         passed = true;
 292         for (int num=0; num<41; ++num)
 293                 for (int den=1; den<42; ++den)
 294                         if (!sqrt(numeric(num*num)/numeric(den*den)).is_rational())
 295                                 passed = false;
 296         if (!passed) {
 297                 clog << "One or more square roots of squares of rationals did not return exact integers" << endl;
 298                 ++result;
 299         }
 300
 301         return result;
 302 }
 303
 304 /* This test examines that simplifications of the form 5^(3/2) -> 5*5^(1/2)
 305  * are carried out properly. */
 306 static unsigned exam_numeric5()
 307 {
 308         unsigned result = 0;
 309
 310         // A variation of one of Ramanujan's wonderful identities must be
 311         // verifiable with very primitive means:
 312         ex e1 = pow(1 + pow(3,numeric(1,5)) - pow(3,numeric(2,5)),3);
 313         ex e2 = expand(e1 - 10 + 5*pow(3,numeric(3,5)));
 314         if (!e2.is_zero()) {
 315                 clog << "expand((1+3^(1/5)-3^(2/5))^3-10+5*3^(3/5)) returned "
 316                      << e2 << " instead of 0." << endl;
 317                 ++result;
 318         }
 319
 320         return result;
 321 }
 322
 323 /* This test checks whether the numeric output/parsing routines are
 324    consistent. */
 325 static unsigned exam_numeric6()
 326 {
 327         unsigned result = 0;
 328
 329         symbol sym("sym");
 330         vector<ex> test_numbers;
 331         test_numbers.push_back(numeric(0));                     // zero
 332         test_numbers.push_back(numeric(1));                     // one
 333         test_numbers.push_back(numeric(-1));            // minus one
 334         test_numbers.push_back(numeric(42));            // positive integer
 335         test_numbers.push_back(numeric(-42));           // negative integer
 336         test_numbers.push_back(numeric(14,3));          // positive rational
 337         test_numbers.push_back(numeric(-14,3));         // negative rational
 338         test_numbers.push_back(numeric(3.141));         // positive decimal
 339         test_numbers.push_back(numeric(-3.141));        // negative decimal
 340         test_numbers.push_back(numeric(0.1974));        // positive decimal, leading zero
 341         test_numbers.push_back(numeric(-0.1974));       // negative decimal, leading zero
 342         test_numbers.push_back(sym);                            // symbol
 343
 344         for (vector<ex>::const_iterator br=test_numbers.begin(); br<test_numbers.end(); ++br) {
 345                 for (vector<ex>::const_iterator bi=test_numbers.begin(); bi<test_numbers.end(); ++bi) {
 346
 347                         for (vector<ex>::const_iterator er=test_numbers.begin(); er<test_numbers.end(); ++er) {
 348                                 for (vector<ex>::const_iterator ei=test_numbers.begin(); ei<test_numbers.end(); ++ei) {
 349
 350                                         // Construct expression, don't test invalid ones
 351                                         ex base = (*br) + (*bi)*I, exponent = (*er) + (*ei)*I, x;
 352                                         try {
 353                                                 x = pow(base, exponent);
 354                                         } catch (...) {
 355                                                 continue;
 356                                         }
 357
 358                                         // Print to string
 359                                         std::ostringstream s;
 360                                         s << x;
 361
 362                                         // Read back expression from string
 363                                         string x_as_string = s.str();
 364                                         ex x_again(x_as_string, lst(sym));
 365
 366                                         // They should be equal
 367                                         if (!x_again.is_equal(x)) {
 368                                                 clog << x << " was read back as " << x_again << endl;
 369                                                 ++result;
 370                                         }
 371                                 }
 372                         }
 373                 }
 374         }
 375
 376         return result;
 377 }
 378
 379 unsigned exam_numeric()
 380 {
 381         unsigned result = 0;
 382
 383         cout << "examining consistency of numeric types" << flush;
 384
 385         result += exam_numeric1();  cout << '.' << flush;
 386         result += exam_numeric2();  cout << '.' << flush;
 387         result += exam_numeric3();  cout << '.' << flush;
 388         result += exam_numeric4();  cout << '.' << flush;
 389         result += exam_numeric5();  cout << '.' << flush;
 390         result += exam_numeric6();  cout << '.' << flush;
 391
 392         return result;
 393 }
 394
 395 int main(int argc, char** argv)
 396 {
 397         return exam_numeric();
 398 }