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 #if defined(LIBM_SCCS) && !defined(lint)
  14 static char rcsid[] = "$NetBSD: e_cosh.c,v 1.7 1995/05/10 20:44:58 jtc Exp $";
  15 #endif
  16
  17 /* __ieee754_cosh(x)
  18  * Method :
  19  * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
  20  *      1. Replace x by |x| (cosh(x) = cosh(-x)).
  21  *      2.
  22  *                                                      [ exp(x) - 1 ]^2
  23  *          0        <= x <= ln2/2  :  cosh(x) := 1 + -------------------
  24  *                                                         2*exp(x)
  25  *
  26  *                                                exp(x) +  1/exp(x)
  27  *          ln2/2    <= x <= 22     :  cosh(x) := -------------------
  28  *                                                        2
  29  *          22       <= x <= lnovft :  cosh(x) := exp(x)/2
  30  *          lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)
  31  *          ln2ovft  <  x           :  cosh(x) := huge*huge (overflow)
  32  *
  33  * Special cases:
  34  *      cosh(x) is |x| if x is +INF, -INF, or NaN.
  35  *      only cosh(0)=1 is exact for finite x.
  36  */
  37
  38 #include "math.h"
  39 #include "math_private.h"
  40
  41 #ifdef __STDC__
  42 static const long double one = 1.0L, half=0.5L, huge = 1.0e300L;
  43 #else
  44 static long double one = 1.0L, half=0.5L, huge = 1.0e300L;
  45 #endif
  46
  47 #ifdef __STDC__
  48         long double __ieee754_coshl(long double x)
  49 #else
  50         long double __ieee754_coshl(x)
  51         long double x;
  52 #endif
  53 {
  54         long double t,w;
  55         int64_t ix;
  56
  57     /* High word of |x|. */
  58         GET_LDOUBLE_MSW64(ix,x);
  59         ix &= 0x7fffffffffffffffLL;
  60
  61     /* x is INF or NaN */
  62         if(ix>=0x7ff0000000000000LL) return x*x;
  63
  64     /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
  65         if(ix<0x3fd62e42fefa39efLL) {
  66             t = __expm1l(fabsl(x));
  67             w = one+t;
  68             if (ix<0x3c80000000000000LL) return w;      /* cosh(tiny) = 1 */
  69             return one+(t*t)/(w+w);
  70         }
  71
  72     /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
  73         if (ix < 0x4036000000000000LL) {
  74                 t = __ieee754_expl(fabsl(x));
  75                 return half*t+half/t;
  76         }
  77
  78     /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
  79         if (ix < 0x40862e42fefa39efLL)  return half*__ieee754_expl(fabsl(x));
  80
  81     /* |x| in [log(maxdouble), overflowthresold] */
  82         if (ix < 0x408633ce8fb9f87dLL) {
  83             w = __ieee754_expl(half*fabsl(x));
  84             t = half*w;
  85             return t*w;
  86         }
  87
  88     /* |x| > overflowthresold, cosh(x) overflow */
  89         return huge*huge;
  90 }