libm/s_sin.c

   1 /*
   2  * ====================================================
   3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   4  *
   5  * Developed at SunPro, a Sun Microsystems, Inc. business.
   6  * Permission to use, copy, modify, and distribute this
   7  * software is freely granted, provided that this notice
   8  * is preserved.
   9  * ====================================================
  10  */
  11
  12 /* sin(x)
  13  * Return sine function of x.
  14  *
  15  * kernel function:
  16  *      __kernel_sin            ... sine function on [-pi/4,pi/4]
  17  *      __kernel_cos            ... cose function on [-pi/4,pi/4]
  18  *      __ieee754_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 "math.h"
  44 #include "math_private.h"
  45
  46 double sin(double x)
  47 {
  48         double y[2],z=0.0;
  49         int32_t n, ix;
  50
  51     /* High word of x. */
  52         GET_HIGH_WORD(ix,x);
  53
  54     /* |x| ~< pi/4 */
  55         ix &= 0x7fffffff;
  56         if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0);
  57
  58     /* sin(Inf or NaN) is NaN */
  59         else if (ix>=0x7ff00000) return x-x;
  60
  61     /* argument reduction needed */
  62         else {
  63             n = __ieee754_rem_pio2(x,y);
  64             switch(n&3) {
  65                 case 0: return  __kernel_sin(y[0],y[1],1);
  66                 case 1: return  __kernel_cos(y[0],y[1]);
  67                 case 2: return -__kernel_sin(y[0],y[1],1);
  68                 default:
  69                         return -__kernel_cos(y[0],y[1]);
  70             }
  71         }
  72 }
  73 libm_hidden_def(sin)