arctan.cpp

   1 #include "stdafx.h"
   2 #include "defs.h"
   3
   4 void
   5 eval_arctan(void)
   6 {
   7         push(cadr(p1));
   8         eval();
   9         arctan();
  10 }
  11
  12 void
  13 arctan(void)
  14 {
  15         double d;
  16
  17         save();
  18
  19         p1 = pop();
  20
  21         if (car(p1) == symbol(TAN)) {
  22                 push(cadr(p1));
  23                 restore();
  24                 return;
  25         }
  26
  27         if (isdouble(p1)) {
  28                 errno = 0;
  29                 d = atan(p1->u.d);
  30                 if (errno)
  31                         stop("arctan function error");
  32                 push_double(d);
  33                 restore();
  34                 return;
  35         }
  36
  37         if (iszero(p1)) {
  38                 push(zero);
  39                 restore();
  40                 return;
  41         }
  42
  43         if (isnegative(p1)) {
  44                 push(p1);
  45                 negate();
  46                 arctan();
  47                 negate();
  48                 restore();
  49                 return;
  50         }
  51
  52         // arctan(sin(a) / cos(a)) ?
  53
  54         if (find(p1, symbol(SIN)) && find(p1, symbol(COS))) {
  55                 push(p1);
  56                 numerator();
  57                 p2 = pop();
  58                 push(p1);
  59                 denominator();
  60                 p3 = pop();
  61                 if (car(p2) == symbol(SIN) && car(p3) == symbol(COS) && equal(cadr(p2), cadr(p3))) {
  62                         push(cadr(p2));
  63                         restore();
  64                         return;
  65                 }
  66         }
  67
  68         // arctan(1/sqrt(3)) -> pi/6
  69
  70         if (car(p1) == symbol(POWER) && equaln(cadr(p1), 3) && equalq(caddr(p1), -1, 2)) {
  71                 push_rational(1, 6);
  72                 push(symbol(PI));
  73                 multiply();
  74                 restore();
  75                 return;
  76         }
  77
  78         // arctan(1) -> pi/4
  79
  80         if (equaln(p1, 1)) {
  81                 push_rational(1, 4);
  82                 push(symbol(PI));
  83                 multiply();
  84                 restore();
  85                 return;
  86         }
  87
  88         // arctan(sqrt(3)) -> pi/3
  89
  90         if (car(p1) == symbol(POWER) && equaln(cadr(p1), 3) && equalq(caddr(p1), 1, 2)) {
  91                 push_rational(1, 3);
  92                 push(symbol(PI));
  93                 multiply();
  94                 restore();
  95                 return;
  96         }
  97
  98         push_symbol(ARCTAN);
  99         push(p1);
 100         list(2);
 101
 102         restore();
 103 }