lib/libm/src/s_sin.c

   1 /* @(#)s_sin.c 5.1 93/09/24 */
   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
  13 /* sin(x)
  14  * Return sine function of x.
  15  *
  16  * kernel function:
  17  *      __kernel_sin            ... sine function on [-pi/4,pi/4]
  18  *      __kernel_cos            ... cose function on [-pi/4,pi/4]
  19  *      __ieee754_rem_pio2      ... argument reduction routine
  20  *
  21  * Method.
  22  *      Let S,C and T denote the sin, cos and tan respectively on
  23  *      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
  24  *      in [-pi/4 , +pi/4], and let n = k mod 4.
  25  *      We have
  26  *
  27  *          n        sin(x)      cos(x)        tan(x)
  28  *     ----------------------------------------------------------
  29  *          0          S           C             T
  30  *          1          C          -S            -1/T
  31  *          2         -S          -C             T
  32  *          3         -C           S            -1/T
  33  *     ----------------------------------------------------------
  34  *
  35  * Special cases:
  36  *      Let trig be any of sin, cos, or tan.
  37  *      trig(+-INF)  is NaN, with signals;
  38  *      trig(NaN)    is that NaN;
  39  *
  40  * Accuracy:
  41  *      TRIG(x) returns trig(x) nearly rounded
  42  */
  43
  44 #include <float.h>
  45 #include <math.h>
  46
  47 #include "math_private.h"
  48
  49 double
  50 sin(double x)
  51 {
  52         double y[2],z=0.0;
  53         int32_t n, ix;
  54
  55     /* High word of x. */
  56         GET_HIGH_WORD(ix,x);
  57
  58     /* |x| ~< pi/4 */
  59         ix &= 0x7fffffff;
  60         if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0);
  61
  62     /* sin(Inf or NaN) is NaN */
  63         else if (ix>=0x7ff00000) return x-x;
  64
  65     /* argument reduction needed */
  66         else {
  67             n = __ieee754_rem_pio2(x,y);
  68             switch(n&3) {
  69                 case 0: return  __kernel_sin(y[0],y[1],1);
  70                 case 1: return  __kernel_cos(y[0],y[1]);
  71                 case 2: return -__kernel_sin(y[0],y[1],1);
  72                 default:
  73                         return -__kernel_cos(y[0],y[1]);
  74             }
  75         }
  76 }
  77
  78 #if     LDBL_MANT_DIG == 53
  79 __strong_alias(sinl, sin);
  80 #endif  /* LDBL_MANT_DIG == 53 */