StdLib/LibC/Math/e_cosh.c

/* @(#)e_cosh.c 5.1 93/09/24 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */
#include  <LibConfig.h>
#include  <sys/EfiCdefs.h>
#if defined(LIBM_SCCS) && !defined(lint)
__RCSID("$NetBSD: e_cosh.c,v 1.11 2002/05/26 22:01:49 wiz Exp $");
#endif

#if defined(_MSC_VER)           /* Handle Microsoft VC++ compiler specifics. */
  // C4756: overflow in constant arithmetic
  #pragma warning ( disable : 4756 )
#endif

/* __ieee754_cosh(x)
 * Method :
 * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
 *  1. Replace x by |x| (cosh(x) = cosh(-x)).
 *  2.
 *                                            [ exp(x) - 1 ]^2
 *      0        <= x <= ln2/2  :  cosh(x) := 1 + -------------------
 *                             2*exp(x)
 *
 *                                      exp(x) +  1/exp(x)
 *      ln2/2    <= x <= 22     :  cosh(x) := -------------------
 *                            2
 *      22       <= x <= lnovft :  cosh(x) := exp(x)/2
 *      lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)
 *      ln2ovft  <  x     :  cosh(x) := huge*huge (overflow)
 *
 * Special cases:
 *  cosh(x) is |x| if x is +INF, -INF, or NaN.
 *  only cosh(0)=1 is exact for finite x.
 */

#include "math.h"
#include "math_private.h"

static const double one = 1.0, half=0.5, huge = 1.0e300;

double
__ieee754_cosh(double x)
{
  double t,w;
  int32_t ix;
  u_int32_t lx;

    /* High word of |x|. */
  GET_HIGH_WORD(ix,x);
  ix &= 0x7fffffff;

    /* x is INF or NaN */
  if(ix>=0x7ff00000) return x*x;

    /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
  if(ix<0x3fd62e43) {
      t = expm1(fabs(x));
      w = one+t;
      if (ix<0x3c800000) return w;  /* cosh(tiny) = 1 */
      return one+(t*t)/(w+w);
  }

    /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
  if (ix < 0x40360000) {
    t = __ieee754_exp(fabs(x));
    return half*t+half/t;
  }

    /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
  if (ix < 0x40862E42)  return half*__ieee754_exp(fabs(x));

    /* |x| in [log(maxdouble), overflowthresold] */
  GET_LOW_WORD(lx,x);
  if (ix<0x408633CE ||
        ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
      w = __ieee754_exp(half*fabs(x));
      t = half*w;
      return t*w;
  }

    /* |x| > overflowthresold, cosh(x) overflow */
  return huge*huge;
}