src/math/sin.c

   1 /* origin: FreeBSD /usr/src/lib/msun/src/s_sin.c */
   2 /*
   3  * ====================================================
   4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   5  *
   6  * Developed at SunPro, a Sun Microsystems, Inc. business.
   7  * Permission to use, copy, modify, and distribute this
   8  * software is freely granted, provided that this notice
   9  * is preserved.
  10  * ====================================================
  11  */
  12 /* sin(x)
  13  * Return sine function of x.
  14  *
  15  * kernel function:
  16  *      __sin            ... sine function on [-pi/4,pi/4]
  17  *      __cos            ... cose function on [-pi/4,pi/4]
  18  *      __rem_pio2       ... argument reduction routine
  19  *
  20  * Method.
  21  *      Let S,C and T denote the sin, cos and tan respectively on
  22  *      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
  23  *      in [-pi/4 , +pi/4], and let n = k mod 4.
  24  *      We have
  25  *
  26  *          n        sin(x)      cos(x)        tan(x)
  27  *     ----------------------------------------------------------
  28  *          0          S           C             T
  29  *          1          C          -S            -1/T
  30  *          2         -S          -C             T
  31  *          3         -C           S            -1/T
  32  *     ----------------------------------------------------------
  33  *
  34  * Special cases:
  35  *      Let trig be any of sin, cos, or tan.
  36  *      trig(+-INF)  is NaN, with signals;
  37  *      trig(NaN)    is that NaN;
  38  *
  39  * Accuracy:
  40  *      TRIG(x) returns trig(x) nearly rounded
  41  */
  42
  43 #include "libm.h"
  44
  45 double sin(double x)
  46 {
  47         double y[2];
  48         uint32_t ix;
  49         unsigned n;
  50
  51         /* High word of x. */
  52         GET_HIGH_WORD(ix, x);
  53         ix &= 0x7fffffff;
  54
  55         /* |x| ~< pi/4 */
  56         if (ix <= 0x3fe921fb) {
  57                 if (ix < 0x3e500000) {  /* |x| < 2**-26 */
  58                         /* raise inexact if x != 0 and underflow if subnormal*/
  59                         FORCE_EVAL(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f);
  60                         return x;
  61                 }
  62                 return __sin(x, 0.0, 0);
  63         }
  64
  65         /* sin(Inf or NaN) is NaN */
  66         if (ix >= 0x7ff00000)
  67                 return x - x;
  68
  69         /* argument reduction needed */
  70         n = __rem_pio2(x, y);
  71         switch (n&3) {
  72         case 0: return  __sin(y[0], y[1], 1);
  73         case 1: return  __cos(y[0], y[1]);
  74         case 2: return -__sin(y[0], y[1], 1);
  75         default:
  76                 return -__cos(y[0], y[1]);
  77         }
  78 }