tan.cpp

   1 // Tangent function of numerical and symbolic arguments
   2
   3 #include "stdafx.h"
   4 #include "defs.h"
   5
   6 void
   7 eval_tan(void)
   8 {
   9         push(cadr(p1));
  10         eval();
  11         tangent();
  12 }
  13
  14 void
  15 tangent(void)
  16 {
  17         save();
  18         yytangent();
  19         restore();
  20 }
  21
  22 void
  23 yytangent(void)
  24 {
  25         int n;
  26         double d;
  27
  28         p1 = pop();
  29
  30         if (car(p1) == symbol(ARCTAN)) {
  31                 push(cadr(p1));
  32                 return;
  33         }
  34
  35         if (isdouble(p1)) {
  36                 d = tan(p1->u.d);
  37                 if (fabs(d) < 1e-10)
  38                         d = 0.0;
  39                 push_double(d);
  40                 return;
  41         }
  42
  43         // tan function is antisymmetric, tan(-x) = -tan(x)
  44
  45         if (isnegative(p1)) {
  46                 push(p1);
  47                 negate();
  48                 tangent();
  49                 negate();
  50                 return;
  51         }
  52
  53         // multiply by 180/pi
  54
  55         push(p1);
  56         push_integer(180);
  57         multiply();
  58         push_symbol(PI);
  59         divide();
  60
  61         n = pop_integer();
  62
  63         if (n < 0) {
  64                 push(symbol(TAN));
  65                 push(p1);
  66                 list(2);
  67                 return;
  68         }
  69
  70         switch (n % 360) {
  71         case 0:
  72         case 180:
  73                 push_integer(0);
  74                 break;
  75         case 30:
  76         case 210:
  77                 push_rational(1, 3);
  78                 push_integer(3);
  79                 push_rational(1, 2);
  80                 power();
  81                 multiply();
  82                 break;
  83         case 150:
  84         case 330:
  85                 push_rational(-1, 3);
  86                 push_integer(3);
  87                 push_rational(1, 2);
  88                 power();
  89                 multiply();
  90                 break;
  91         case 45:
  92         case 225:
  93                 push_integer(1);
  94                 break;
  95         case 135:
  96         case 315:
  97                 push_integer(-1);
  98                 break;
  99         case 60:
 100         case 240:
 101                 push_integer(3);
 102                 push_rational(1, 2);
 103                 power();
 104                 break;
 105         case 120:
 106         case 300:
 107                 push_integer(3);
 108                 push_rational(1, 2);
 109                 power();
 110                 negate();
 111                 break;
 112         default:
 113                 push(symbol(TAN));
 114                 push(p1);
 115                 list(2);
 116                 break;
 117         }
 118 }
 119
 120 #if SELFTEST
 121
 122 static char *s[] = {
 123
 124         "tan(x)",
 125         "tan(x)",
 126
 127         "tan(-x)",
 128         "-tan(x)",
 129
 130         "tan(b-a)",
 131         "-tan(a-b)",
 132
 133         // check against the floating point math library
 134
 135         "f(a,x)=1+tan(float(a/360*2*pi))-float(x)+tan(a/360*2*pi)-x",
 136         "",
 137
 138         "f(0,0)",                       // 0
 139         "1",
 140
 141         "f(180,0)",                     // 180
 142         "1",
 143
 144         "f(360,0)",                     // 360
 145         "1",
 146
 147         "f(-180,0)",                    // -180
 148         "1",
 149
 150         "f(-360,0)",                    // -360
 151         "1",
 152
 153         "f(45,1)",                      // 45
 154         "1",
 155
 156         "f(135,-1)",                    // 135
 157         "1",
 158
 159         "f(225,1)",                     // 225
 160         "1",
 161
 162         "f(315,-1)",                    // 315
 163         "1",
 164
 165         "f(-45,-1)",                    // -45
 166         "1",
 167
 168         "f(-135,1)",                    // -135
 169         "1",
 170
 171         "f(-225,-1)",                   // -225
 172         "1",
 173
 174         "f(-315,1)",                    // -315
 175         "1",
 176
 177         "f(30,sqrt(3)/3)",              // 30
 178         "1",
 179
 180         "f(150,-sqrt(3)/3)",            // 150
 181         "1",
 182
 183         "f(210,sqrt(3)/3)",             // 210
 184         "1",
 185
 186         "f(330,-sqrt(3)/3)",            // 330
 187         "1",
 188
 189         "f(-30,-sqrt(3)/3)",            // -30
 190         "1",
 191
 192         "f(-150,sqrt(3)/3)",            // -150
 193         "1",
 194
 195         "f(-210,-sqrt(3)/3)",           // -210
 196         "1",
 197
 198         "f(-330,sqrt(3)/3)",            // -330
 199         "1",
 200
 201         "f(60,sqrt(3))",                // 60
 202         "1",
 203
 204         "f(120,-sqrt(3))",              // 120
 205         "1",
 206
 207         "f(240,sqrt(3))",               // 240
 208         "1",
 209
 210         "f(300,-sqrt(3))",              // 300
 211         "1",
 212
 213         "f(-60,-sqrt(3))",              // -60
 214         "1",
 215
 216         "f(-120,sqrt(3))",              // -120
 217         "1",
 218
 219         "f(-240,-sqrt(3))",             // -240
 220         "1",
 221
 222         "f(-300,sqrt(3))",              // -300
 223         "1",
 224
 225         "f=quote(f)",
 226         "",
 227
 228         "tan(arctan(x))",
 229         "x",
 230
 231         // check the default case
 232
 233         "tan(1/12*pi)",
 234         "tan(1/12*pi)",
 235 };
 236
 237 void
 238 test_tan(void)
 239 {
 240         test(__FILE__, s, sizeof s / sizeof (char *));
 241 }
 242
 243 #endif