toolchain/gcc/newlib/libm/math/s_sin.c

   1
   2 /* @(#)s_sin.c 5.1 93/09/24 */
   3 /*
   4  * ====================================================
   5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   6  *
   7  * Developed at SunPro, a Sun Microsystems, Inc. business.
   8  * Permission to use, copy, modify, and distribute this
   9  * software is freely granted, provided that this notice
  10  * is preserved.
  11  * ====================================================
  12  */
  13
  14 /*
  15 FUNCTION
  16         <<sin>>, <<sinf>>, <<cos>>, <<cosf>>---sine or cosine
  17 INDEX
  18 sin
  19 INDEX
  20 sinf
  21 INDEX
  22 cos
  23 INDEX
  24 cosf
  25 ANSI_SYNOPSIS
  26         #include <math.h>
  27         double sin(double <[x]>);
  28         float  sinf(float <[x]>);
  29         double cos(double <[x]>);
  30         float cosf(float <[x]>);
  31
  32 TRAD_SYNOPSIS
  33         #include <math.h>
  34         double sin(<[x]>)
  35         double <[x]>;
  36         float  sinf(<[x]>)
  37         float <[x]>;
  38
  39         double cos(<[x]>)
  40         double <[x]>;
  41         float cosf(<[x]>)
  42         float <[x]>;
  43
  44 DESCRIPTION
  45         <<sin>> and <<cos>> compute (respectively) the sine and cosine
  46         of the argument <[x]>.  Angles are specified in radians.
  47
  48         <<sinf>> and <<cosf>> are identical, save that they take and
  49         return <<float>> values.
  50
  51
  52 RETURNS
  53         The sine or cosine of <[x]> is returned.
  54
  55 PORTABILITY
  56         <<sin>> and <<cos>> are ANSI C.
  57         <<sinf>> and <<cosf>> are extensions.
  58
  59 QUICKREF
  60         sin ansi pure
  61         sinf - pure
  62 */
  63
  64 /* sin(x)
  65  * Return sine function of x.
  66  *
  67  * kernel function:
  68  *      __kernel_sin            ... sine function on [-pi/4,pi/4]
  69  *      __kernel_cos            ... cose function on [-pi/4,pi/4]
  70  *      __ieee754_rem_pio2      ... argument reduction routine
  71  *
  72  * Method.
  73  *      Let S,C and T denote the sin, cos and tan respectively on
  74  *      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
  75  *      in [-pi/4 , +pi/4], and let n = k mod 4.
  76  *      We have
  77  *
  78  *          n        sin(x)      cos(x)        tan(x)
  79  *     ----------------------------------------------------------
  80  *          0          S           C             T
  81  *          1          C          -S            -1/T
  82  *          2         -S          -C             T
  83  *          3         -C           S            -1/T
  84  *     ----------------------------------------------------------
  85  *
  86  * Special cases:
  87  *      Let trig be any of sin, cos, or tan.
  88  *      trig(+-INF)  is NaN, with signals;
  89  *      trig(NaN)    is that NaN;
  90  *
  91  * Accuracy:
  92  *      TRIG(x) returns trig(x) nearly rounded
  93  */
  94
  95 #include "fdlibm.h"
  96
  97 #ifndef _DOUBLE_IS_32BITS
  98
  99 #ifdef __STDC__
 100         double sin(double x)
 101 #else
 102         double sin(x)
 103         double x;
 104 #endif
 105 {
 106         double y[2],z=0.0;
 107         __int32_t n,ix;
 108
 109     /* High word of x. */
 110         GET_HIGH_WORD(ix,x);
 111
 112     /* |x| ~< pi/4 */
 113         ix &= 0x7fffffff;
 114         if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0);
 115
 116     /* sin(Inf or NaN) is NaN */
 117         else if (ix>=0x7ff00000) return x-x;
 118
 119     /* argument reduction needed */
 120         else {
 121             n = __ieee754_rem_pio2(x,y);
 122             switch(n&3) {
 123                 case 0: return  __kernel_sin(y[0],y[1],1);
 124                 case 1: return  __kernel_cos(y[0],y[1]);
 125                 case 2: return -__kernel_sin(y[0],y[1],1);
 126                 default:
 127                         return -__kernel_cos(y[0],y[1]);
 128             }
 129         }
 130 }
 131
 132 #endif /* _DOUBLE_IS_32BITS */