cos.cpp

   1 // Cosine function of numerical and symbolic arguments
   2
   3 #include "stdafx.h"
   4 #include "defs.h"
   5
   6 void
   7 eval_cos(void)
   8 {
   9         push(cadr(p1));
  10         eval();
  11         cosine();
  12 }
  13
  14 void
  15 cosine(void)
  16 {
  17         save();
  18         p1 = pop();
  19         if (car(p1) == symbol(ADD))
  20                 cosine_of_angle_sum();
  21         else
  22                 cosine_of_angle();
  23         restore();
  24 }
  25
  26 // Use angle sum formula for special angles.
  27
  28 #define A p3
  29 #define B p4
  30
  31 void
  32 cosine_of_angle_sum(void)
  33 {
  34         p2 = cdr(p1);
  35         while (iscons(p2)) {
  36                 B = car(p2);
  37                 if (isnpi(B)) {
  38                         push(p1);
  39                         push(B);
  40                         subtract();
  41                         A = pop();
  42                         push(A);
  43                         cosine();
  44                         push(B);
  45                         cosine();
  46                         multiply();
  47                         push(A);
  48                         sine();
  49                         push(B);
  50                         sine();
  51                         multiply();
  52                         subtract();
  53                         return;
  54                 }
  55                 p2 = cdr(p2);
  56         }
  57         cosine_of_angle();
  58 }
  59
  60 void
  61 cosine_of_angle(void)
  62 {
  63         int n;
  64         double d;
  65
  66         if (car(p1) == symbol(ARCCOS)) {
  67                 push(cadr(p1));
  68                 return;
  69         }
  70
  71         if (isdouble(p1)) {
  72                 d = cos(p1->u.d);
  73                 if (fabs(d) < 1e-10)
  74                         d = 0.0;
  75                 push_double(d);
  76                 return;
  77         }
  78
  79         // cosine function is symmetric, cos(-x) = cos(x)
  80
  81         if (isnegative(p1)) {
  82                 push(p1);
  83                 negate();
  84                 p1 = pop();
  85         }
  86
  87         // cos(arctan(x)) = 1 / sqrt(1 + x^2)
  88
  89         // see p. 173 of the CRC Handbook of Mathematical Sciences
  90
  91         if (car(p1) == symbol(ARCTAN)) {
  92                 push_integer(1);
  93                 push(cadr(p1));
  94                 push_integer(2);
  95                 power();
  96                 add();
  97                 push_rational(-1, 2);
  98                 power();
  99                 return;
 100         }
 101
 102         // multiply by 180/pi
 103
 104         push(p1);
 105         push_integer(180);
 106         multiply();
 107         push_symbol(PI);
 108         divide();
 109
 110         n = pop_integer();
 111
 112         if (n < 0) {
 113                 push(symbol(COS));
 114                 push(p1);
 115                 list(2);
 116                 return;
 117         }
 118
 119         switch (n % 360) {
 120         case 90:
 121         case 270:
 122                 push_integer(0);
 123                 break;
 124         case 60:
 125         case 300:
 126                 push_rational(1, 2);
 127                 break;
 128         case 120:
 129         case 240:
 130                 push_rational(-1, 2);
 131                 break;
 132         case 45:
 133         case 315:
 134                 push_rational(1, 2);
 135                 push_integer(2);
 136                 push_rational(1, 2);
 137                 power();
 138                 multiply();
 139                 break;
 140         case 135:
 141         case 225:
 142                 push_rational(-1, 2);
 143                 push_integer(2);
 144                 push_rational(1, 2);
 145                 power();
 146                 multiply();
 147                 break;
 148         case 30:
 149         case 330:
 150                 push_rational(1, 2);
 151                 push_integer(3);
 152                 push_rational(1, 2);
 153                 power();
 154                 multiply();
 155                 break;
 156         case 150:
 157         case 210:
 158                 push_rational(-1, 2);
 159                 push_integer(3);
 160                 push_rational(1, 2);
 161                 power();
 162                 multiply();
 163                 break;
 164         case 0:
 165                 push_integer(1);
 166                 break;
 167         case 180:
 168                 push_integer(-1);
 169                 break;
 170         default:
 171                 push(symbol(COS));
 172                 push(p1);
 173                 list(2);
 174                 break;
 175         }
 176 }