check/genex.cpp

   1 /** @file genex.cpp
   2  *
   3  *  Provides some routines for generating expressions that are later used as
   4  *  input in the consistency checks. */
   5
   6 /*
   7  *  GiNaC Copyright (C) 1999-2001 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., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  22  */
  23
  24 // For rand() and friends:
  25 #include <stdlib.h>
  26
  27 #include "ginac.h"
  28
  29 #ifndef NO_NAMESPACE_GINAC
  30 using namespace GiNaC;
  31 #endif // ndef NO_NAMESPACE_GINAC
  32
  33 /* Create a dense univariate random polynomial in x.
  34  * (of the form 9 - 22*a - 17*a^2 + 14*a^3 + 7*a^4 + 7a^5 if degree==5) */
  35 const ex
  36 dense_univariate_poly(const symbol & x, unsigned degree)
  37 {
  38         ex unipoly;
  39
  40         for (unsigned i=0; i<=degree; ++i)
  41                 unipoly += numeric((rand()-RAND_MAX/2))*pow(x,i);
  42
  43         return unipoly;
  44 }
  45
  46 /* Create a dense bivariate random polynomial in x1 and x2.
  47  * (of the form 9 + 52*x1 - 27*x1^2 + 84*x2 + 7*x2^2 - 12*x1*x2 if degree==2)
  48  */
  49 const ex
  50 dense_bivariate_poly(const symbol & x1, const symbol & x2, unsigned degree)
  51 {
  52         ex bipoly;
  53
  54         for (unsigned i1=0; i1<=degree; ++i1)
  55                 for (unsigned i2=0; i2<=degree-i1; ++i2)
  56                         bipoly += numeric((rand()-RAND_MAX/2))*pow(x1,i1)*pow(x2,i2);
  57
  58         return bipoly;
  59 }
  60
  61 /* Chose a randum symbol or number from the argument list. */
  62 const ex
  63 random_symbol(const symbol & x,
  64                           const symbol & y,
  65                           const symbol & z,
  66                           bool rational = true,
  67                           bool complex = false)
  68 {
  69         ex e;
  70         switch (abs(rand()) % 4) {
  71                 case 0:
  72                         e = x;
  73                         break;
  74                 case 1:
  75                         e = y;
  76                         break;
  77                 case 2:
  78                         e = z;
  79                         break;
  80                 case 3: {
  81                         int c1;
  82                         do { c1 = rand()%20 - 10; } while (!c1);
  83                         int c2;
  84                         do { c2 = rand()%20 - 10; } while (!c2);
  85                         if (!rational)
  86                                 c2 = 1;
  87                         e = numeric(c1, c2);
  88                         if (complex && !(rand()%5))
  89                                 e = e*I;
  90                         break;
  91                 }
  92         }
  93         return e;
  94 }
  95
  96 /* Create a sparse random tree in three symbols. */
  97 const ex
  98 sparse_tree(const symbol & x,
  99                         const symbol & y,
 100                         const symbol & z,
 101                         int level,
 102                         bool trig = false,      // true includes trigonomatric functions
 103                         bool rational = true, // false excludes coefficients in Q
 104                         bool complex = false) // true includes complex numbers
 105 {
 106         if (level == 0)
 107                 return random_symbol(x,y,z,rational,complex);
 108         switch (abs(rand()) % 10) {
 109                 case 0:
 110                 case 1:
 111                 case 2:
 112                 case 3:
 113                         return add(sparse_tree(x,y,z,level-1, trig, rational),
 114                                            sparse_tree(x,y,z,level-1, trig, rational));
 115                 case 4:
 116                 case 5:
 117                 case 6:
 118                         return mul(sparse_tree(x,y,z,level-1, trig, rational),
 119                                            sparse_tree(x,y,z,level-1, trig, rational));
 120                 case 7:
 121                 case 8: {
 122                         ex powbase;
 123                         do {
 124                                 powbase = sparse_tree(x,y,z,level-1, trig, rational);
 125                         } while (powbase.is_zero());
 126                         return pow(powbase, abs(rand() % 4));
 127                         break;
 128                 }
 129                 case 9:
 130                         if (trig) {
 131                                 switch (abs(rand()) % 4) {
 132                                         case 0:
 133                                                 return sin(sparse_tree(x,y,z,level-1, trig, rational));
 134                                         case 1:
 135                                                 return cos(sparse_tree(x,y,z,level-1, trig, rational));
 136                                         case 2:
 137                                                 return exp(sparse_tree(x,y,z,level-1, trig, rational));
 138                                         case 3: {
 139                                                 ex logex;
 140                                                 do {
 141                                                         ex logarg;
 142                                                         do {
 143                                                                 logarg = sparse_tree(x,y,z,level-1, trig, rational);
 144                                                         } while (logarg.is_zero());
 145                                                         // Keep the evaluator from accidentally plugging an
 146                                                         // unwanted I in the tree:
 147                                                         if (!complex && logarg.info(info_flags::negative))
 148                                                                 logarg = -logarg;
 149                                                         logex = log(logarg);
 150                                                 } while (logex.is_zero());
 151                                                 return logex;
 152                                                 break;
 153                                         }
 154                                 }
 155                         } else
 156                                 return random_symbol(x,y,z,rational,complex);
 157         }
 158 }