StdLib/LibC/Math/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 #include  <LibConfig.h>
  13 #include  <sys/EfiCdefs.h>
  14 #if defined(LIBM_SCCS) && !defined(lint)
  15 __RCSID("$NetBSD: e_cosh.c,v 1.11 2002/05/26 22:01:49 wiz Exp $");
  16 #endif
  17
  18 #if defined(_MSC_VER)           /* Handle Microsoft VC++ compiler specifics. */
  19   // C4756: overflow in constant arithmetic
  20   #pragma warning ( disable : 4756 )
  21 #endif
  22
  23 /* __ieee754_cosh(x)
  24  * Method :
  25  * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
  26  *  1. Replace x by |x| (cosh(x) = cosh(-x)).
  27  *  2.
  28  *                                            [ exp(x) - 1 ]^2
  29  *      0        <= x <= ln2/2  :  cosh(x) := 1 + -------------------
  30  *                             2*exp(x)
  31  *
  32  *                                      exp(x) +  1/exp(x)
  33  *      ln2/2    <= x <= 22     :  cosh(x) := -------------------
  34  *                            2
  35  *      22       <= x <= lnovft :  cosh(x) := exp(x)/2
  36  *      lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)
  37  *      ln2ovft  <  x     :  cosh(x) := huge*huge (overflow)
  38  *
  39  * Special cases:
  40  *  cosh(x) is |x| if x is +INF, -INF, or NaN.
  41  *  only cosh(0)=1 is exact for finite x.
  42  */
  43
  44 #include "math.h"
  45 #include "math_private.h"
  46
  47 static const double one = 1.0, half=0.5, huge = 1.0e300;
  48
  49 double
  50 __ieee754_cosh(double x)
  51 {
  52   double t,w;
  53   int32_t ix;
  54   u_int32_t lx;
  55
  56     /* High word of |x|. */
  57   GET_HIGH_WORD(ix,x);
  58   ix &= 0x7fffffff;
  59
  60     /* x is INF or NaN */
  61   if(ix>=0x7ff00000) return x*x;
  62
  63     /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
  64   if(ix<0x3fd62e43) {
  65       t = expm1(fabs(x));
  66       w = one+t;
  67       if (ix<0x3c800000) return w;  /* cosh(tiny) = 1 */
  68       return one+(t*t)/(w+w);
  69   }
  70
  71     /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
  72   if (ix < 0x40360000) {
  73     t = __ieee754_exp(fabs(x));
  74     return half*t+half/t;
  75   }
  76
  77     /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
  78   if (ix < 0x40862E42)  return half*__ieee754_exp(fabs(x));
  79
  80     /* |x| in [log(maxdouble), overflowthresold] */
  81   GET_LOW_WORD(lx,x);
  82   if (ix<0x408633CE ||
  83         ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
  84       w = __ieee754_exp(half*fabs(x));
  85       t = half*w;
  86       return t*w;
  87   }
  88
  89     /* |x| > overflowthresold, cosh(x) overflow */
  90   return huge*huge;
  91 }