sysdeps/ieee754/ldbl-96/e_coshl.c

   1 /*
   2  * ====================================================
   3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   4  *
   5  * Developed at SunPro, a Sun Microsystems, Inc. business.
   6  * Permission to use, copy, modify, and distribute this
   7  * software is freely granted, provided that this notice
   8  * is preserved.
   9  * ====================================================
  10  */
  11
  12 #if defined(LIBM_SCCS) && !defined(lint)
  13 static char rcsid[] = "$NetBSD: e_cosh.c,v 1.7 1995/05/10 20:44:58 jtc Exp $";
  14 #endif
  15
  16 /* __ieee754_coshl(x)
  17  * Method :
  18  * mathematically coshl(x) if defined to be (exp(x)+exp(-x))/2
  19  *      1. Replace x by |x| (coshl(x) = coshl(-x)).
  20  *      2.
  21  *                                                      [ exp(x) - 1 ]^2
  22  *          0        <= x <= ln2/2  :  coshl(x) := 1 + -------------------
  23  *                                                         2*exp(x)
  24  *
  25  *                                                 exp(x) +  1/exp(x)
  26  *          ln2/2    <= x <= 22     :  coshl(x) := -------------------
  27  *                                                         2
  28  *          22       <= x <= lnovft :  coshl(x) := expl(x)/2
  29  *          lnovft   <= x <= ln2ovft:  coshl(x) := expl(x/2)/2 * expl(x/2)
  30  *          ln2ovft  <  x           :  coshl(x) := huge*huge (overflow)
  31  *
  32  * Special cases:
  33  *      coshl(x) is |x| if x is +INF, -INF, or NaN.
  34  *      only coshl(0)=1 is exact for finite x.
  35  */
  36
  37 #include "math.h"
  38 #include "math_private.h"
  39
  40 #ifdef __STDC__
  41 static const long double one = 1.0, half=0.5, huge = 1.0e4900L;
  42 #else
  43 static long double one = 1.0, half=0.5, huge = 1.0e4900L;
  44 #endif
  45
  46 #ifdef __STDC__
  47         long double __ieee754_coshl(long double x)
  48 #else
  49         long double __ieee754_coshl(x)
  50         long double x;
  51 #endif
  52 {
  53         long double t,w;
  54         int32_t ex;
  55         u_int32_t mx,lx;
  56
  57     /* High word of |x|. */
  58         GET_LDOUBLE_WORDS(ex,mx,lx,x);
  59         ex &= 0x7fff;
  60
  61     /* x is INF or NaN */
  62         if(ex==0x7fff) return x*x;
  63
  64     /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */
  65         if(ex < 0x3ffd || (ex == 0x3ffd && mx < 0xb17217f7u)) {
  66             t = __expm1l(fabsl(x));
  67             w = one+t;
  68             if (ex<0x3fbc) 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 (ex < 0x4003 || (ex == 0x4003 && mx < 0xb0000000u)) {
  74                 t = __ieee754_expl(fabsl(x));
  75                 return half*t+half/t;
  76         }
  77
  78     /* |x| in [22, ln(maxdouble)] return half*exp(|x|) */
  79         if (ex < 0x400c || (ex == 0x400c && mx < 0xb1700000u))
  80                 return half*__ieee754_expl(fabsl(x));
  81
  82     /* |x| in [log(maxdouble), log(2*maxdouble)) */
  83         if (ex == 0x400c && (mx < 0xb174ddc0u
  84                              || (mx == 0xb174ddc0u && lx < 0x31aec0ebu)))
  85         {
  86             w = __ieee754_expl(half*fabsl(x));
  87             t = half*w;
  88             return t*w;
  89         }
  90
  91     /* |x| >= log(2*maxdouble), cosh(x) overflow */
  92         return huge*huge;
  93 }