libquadmath/math/sinq.c

   1 /* sinq.c -- __float128 version of s_sin.c.
   2  * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
   3  */
   4
   5 /*
   6  * ====================================================
   7  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   8  *
   9  * Developed at SunPro, a Sun Microsystems, Inc. business.
  10  * Permission to use, copy, modify, and distribute this
  11  * software is freely granted, provided that this notice
  12  * is preserved.
  13  * ====================================================
  14  */
  15
  16 /* sinq(x)
  17  * Return sine function of x.
  18  *
  19  * kernel function:
  20  *      __quadmath_kernel_sinq  ... sine function on [-pi/4,pi/4]
  21  *      __quadmath_kernel_cosq  ... cose function on [-pi/4,pi/4]
  22  *      __quadmath_rem_pio2q    ... argument reduction routine
  23  *
  24  * Method.
  25  *      Let S,C and T denote the sin, cos and tan respectively on
  26  *      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
  27  *      in [-pi/4 , +pi/4], and let n = k mod 4.
  28  *      We have
  29  *
  30  *          n        sin(x)      cos(x)        tan(x)
  31  *     ----------------------------------------------------------
  32  *          0          S           C             T
  33  *          1          C          -S            -1/T
  34  *          2         -S          -C             T
  35  *          3         -C           S            -1/T
  36  *     ----------------------------------------------------------
  37  *
  38  * Special cases:
  39  *      Let trig be any of sin, cos, or tan.
  40  *      trig(+-INF)  is NaN, with signals;
  41  *      trig(NaN)    is that NaN;
  42  *
  43  * Accuracy:
  44  *      TRIG(x) returns trig(x) nearly rounded
  45  */
  46
  47 #include "quadmath-imp.h"
  48
  49 __float128
  50 sinq (__float128 x)
  51 {
  52         __float128 y[2],z=0.0Q;
  53         int64_t n, ix;
  54
  55     /* High word of x. */
  56         GET_FLT128_MSW64(ix,x);
  57
  58     /* |x| ~< pi/4 */
  59         ix &= 0x7fffffffffffffffLL;
  60         if(ix <= 0x3ffe921fb54442d1LL)
  61           return __quadmath_kernel_sinq(x,z,0);
  62
  63     /* sin(Inf or NaN) is NaN */
  64         else if (ix>=0x7fff000000000000LL) {
  65             if (ix == 0x7fff000000000000LL) {
  66                 GET_FLT128_LSW64(n,x);
  67             }
  68             return x-x;
  69         }
  70
  71     /* argument reduction needed */
  72         else {
  73             n = __quadmath_rem_pio2q(x,y);
  74             switch(n&3) {
  75                 case 0: return  __quadmath_kernel_sinq(y[0],y[1],1);
  76                 case 1: return  __quadmath_kernel_cosq(y[0],y[1]);
  77                 case 2: return -__quadmath_kernel_sinq(y[0],y[1],1);
  78                 default:
  79                         return -__quadmath_kernel_cosq(y[0],y[1]);
  80             }
  81         }
  82 }