libm/e_cosh.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
  42 #ifdef __STDC__
  43 static const double one = 1.0, half=0.5, huge = 1.0e300;
  44 #else
  45 static double one = 1.0, half=0.5, huge = 1.0e300;
  46 #endif
  47
  48 #ifdef __STDC__
  49         double attribute_hidden __ieee754_cosh(double x)
  50 #else
  51         double attribute_hidden __ieee754_cosh(x)
  52         double x;
  53 #endif
  54 {
  55         double t,w;
  56         int32_t ix;
  57         u_int32_t lx;
  58
  59     /* High word of |x|. */
  60         GET_HIGH_WORD(ix,x);
  61         ix &= 0x7fffffff;
  62
  63     /* x is INF or NaN */
  64         if(ix>=0x7ff00000) return x*x;
  65
  66     /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
  67         if(ix<0x3fd62e43) {
  68             t = expm1(fabs(x));
  69             w = one+t;
  70             if (ix<0x3c800000) return w;        /* cosh(tiny) = 1 */
  71             return one+(t*t)/(w+w);
  72         }
  73
  74     /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
  75         if (ix < 0x40360000) {
  76                 t = __ieee754_exp(fabs(x));
  77                 return half*t+half/t;
  78         }
  79
  80     /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
  81         if (ix < 0x40862E42)  return half*__ieee754_exp(fabs(x));
  82
  83     /* |x| in [log(maxdouble), overflowthresold] */
  84         GET_LOW_WORD(lx,x);
  85         if (ix<0x408633CE ||
  86               ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
  87             w = __ieee754_exp(half*fabs(x));
  88             t = half*w;
  89             return t*w;
  90         }
  91
  92     /* |x| > overflowthresold, cosh(x) overflow */
  93         return huge*huge;
  94 }