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

   1 /* @(#)e_cosh.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 /* __ieee754_cosh(x)
  14  * Method :
  15  * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
  16  *      1. Replace x by |x| (cosh(x) = cosh(-x)).
  17  *      2.
  18  *                                                      [ exp(x) - 1 ]^2
  19  *          0        <= x <= ln2/2  :  cosh(x) := 1 + -------------------
  20  *                                                         2*exp(x)
  21  *
  22  *                                                exp(x) +  1/exp(x)
  23  *          ln2/2    <= x <= 40     :  cosh(x) := -------------------
  24  *                                                        2
  25  *          40       <= x <= lnovft :  cosh(x) := exp(x)/2
  26  *          lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)
  27  *          ln2ovft  <  x           :  cosh(x) := huge*huge (overflow)
  28  *
  29  * Special cases:
  30  *      cosh(x) is |x| if x is +INF, -INF, or NaN.
  31  *      only cosh(0)=1 is exact for finite x.
  32  */
  33
  34 #include <math.h>
  35 #include <math_private.h>
  36
  37 static const long double one = 1.0L, half=0.5L, huge = 1.0e300L;
  38
  39 long double
  40 __ieee754_coshl (long double x)
  41 {
  42         long double t,w;
  43         int64_t ix;
  44         double xhi;
  45
  46     /* High word of |x|. */
  47         xhi = ldbl_high (x);
  48         EXTRACT_WORDS64 (ix, xhi);
  49         ix &= 0x7fffffffffffffffLL;
  50
  51     /* x is INF or NaN */
  52         if(ix>=0x7ff0000000000000LL) return x*x;
  53
  54     /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
  55         if(ix<0x3fd62e42fefa39efLL) {
  56             if (ix<0x3c80000000000000LL) return one;    /* cosh(tiny) = 1 */
  57             t = __expm1l(fabsl(x));
  58             w = one+t;
  59             return one+(t*t)/(w+w);
  60         }
  61
  62     /* |x| in [0.5*ln2,40], return (exp(|x|)+1/exp(|x|)/2; */
  63         if (ix < 0x4044000000000000LL) {
  64                 t = __ieee754_expl(fabsl(x));
  65                 return half*t+half/t;
  66         }
  67
  68     /* |x| in [40, log(maxdouble)] return half*exp(|x|) */
  69         if (ix < 0x40862e42fefa39efLL)  return half*__ieee754_expl(fabsl(x));
  70
  71     /* |x| in [log(maxdouble), overflowthresold] */
  72         if (ix < 0x408633ce8fb9f87fLL) {
  73             w = __ieee754_expl(half*fabsl(x));
  74             t = half*w;
  75             return t*w;
  76         }
  77
  78     /* |x| > overflowthresold, cosh(x) overflow */
  79         return huge*huge;
  80 }
  81 strong_alias (__ieee754_coshl, __coshl_finite)