sysdeps/ieee754/ldbl-128ibm/s_cosl.c

   1 /* s_cosl.c -- long double version of s_cos.c.
   2  */
   3
   4 /*
   5  * ====================================================
   6  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   7  *
   8  * Developed at SunPro, a Sun Microsystems, Inc. business.
   9  * Permission to use, copy, modify, and distribute this
  10  * software is freely granted, provided that this notice
  11  * is preserved.
  12  * ====================================================
  13  */
  14
  15 /* cosl(x)
  16  * Return cosine function of x.
  17  *
  18  * kernel function:
  19  *      __kernel_sinl           ... sine function on [-pi/4,pi/4]
  20  *      __kernel_cosl           ... cosine function on [-pi/4,pi/4]
  21  *      __ieee754_rem_pio2l     ... argument reduction routine
  22  *
  23  * Method.
  24  *      Let S,C and T denote the sin, cos and tan respectively on
  25  *      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
  26  *      in [-pi/4 , +pi/4], and let n = k mod 4.
  27  *      We have
  28  *
  29  *          n        sin(x)      cos(x)        tan(x)
  30  *     ----------------------------------------------------------
  31  *          0          S           C             T
  32  *          1          C          -S            -1/T
  33  *          2         -S          -C             T
  34  *          3         -C           S            -1/T
  35  *     ----------------------------------------------------------
  36  *
  37  * Special cases:
  38  *      Let trig be any of sin, cos, or tan.
  39  *      trig(+-INF)  is NaN, with signals;
  40  *      trig(NaN)    is that NaN;
  41  *
  42  * Accuracy:
  43  *      TRIG(x) returns trig(x) nearly rounded
  44  */
  45
  46 #include <errno.h>
  47 #include <math.h>
  48 #include <math_private.h>
  49 #include <math_ldbl_opt.h>
  50
  51 long double __cosl(long double x)
  52 {
  53         long double y[2],z=0.0L;
  54         int64_t n, ix;
  55         double xhi;
  56
  57     /* High word of x. */
  58         xhi = ldbl_high (x);
  59         EXTRACT_WORDS64 (ix, xhi);
  60
  61     /* |x| ~< pi/4 */
  62         ix &= 0x7fffffffffffffffLL;
  63         if(ix <= 0x3fe921fb54442d18LL)
  64           return __kernel_cosl(x,z);
  65
  66     /* cos(Inf or NaN) is NaN */
  67         else if (ix>=0x7ff0000000000000LL) {
  68             if (ix == 0x7ff0000000000000LL)
  69                 __set_errno (EDOM);
  70             return x-x;
  71         }
  72     /* argument reduction needed */
  73         else {
  74             n = __ieee754_rem_pio2l(x,y);
  75             switch(n&3) {
  76                 case 0:
  77                     return  __kernel_cosl(y[0],y[1]);
  78                 case 1:
  79                     return -__kernel_sinl(y[0],y[1],1);
  80                 case 2:
  81                     return -__kernel_cosl(y[0],y[1]);
  82                 default:
  83                     return  __kernel_sinl(y[0],y[1],1);
  84             }
  85         }
  86 }
  87 long_double_symbol (libm, __cosl, cosl);