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 static const long double one = 1.0, half=0.5, huge = 1.0e4900L;
  41
  42 long double
  43 __ieee754_coshl (long double x)
  44 {
  45         long double t,w;
  46         int32_t ex;
  47         u_int32_t mx,lx;
  48
  49     /* High word of |x|. */
  50         GET_LDOUBLE_WORDS(ex,mx,lx,x);
  51         ex &= 0x7fff;
  52
  53     /* |x| in [0,22] */
  54         if (ex < 0x4003 || (ex == 0x4003 && mx < 0xb0000000u)) {
  55             /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */
  56                 if(ex < 0x3ffd || (ex == 0x3ffd && mx < 0xb17217f7u)) {
  57                     if (ex<0x3fbc) return one;  /* cosh(tiny) = 1 */
  58                     t = __expm1l(fabsl(x));
  59                     w = one+t;
  60                     return one+(t*t)/(w+w);
  61                 }
  62
  63             /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
  64                 t = __ieee754_expl(fabsl(x));
  65                 return half*t+half/t;
  66         }
  67
  68     /* |x| in [22, ln(maxdouble)] return half*exp(|x|) */
  69         if (ex < 0x400c || (ex == 0x400c && mx < 0xb1700000u))
  70                 return half*__ieee754_expl(fabsl(x));
  71
  72     /* |x| in [log(maxdouble), log(2*maxdouble)) */
  73         if (ex == 0x400c && (mx < 0xb174ddc0u
  74                              || (mx == 0xb174ddc0u && lx < 0x31aec0ebu)))
  75         {
  76             w = __ieee754_expl(half*fabsl(x));
  77             t = half*w;
  78             return t*w;
  79         }
  80
  81     /* x is INF or NaN */
  82         if(ex==0x7fff) return x*x;
  83
  84     /* |x| >= log(2*maxdouble), cosh(x) overflow */
  85         return huge*huge;
  86 }
  87 strong_alias (__ieee754_coshl, __coshl_finite)