/*

 * ====================================================

 * 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.

 * ====================================================

 */

/* Changes for 128-bit long double are

   Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>

   and are incorporated herein by permission of the author.  The author

   reserves the right to distribute this material elsewhere under different

   copying permissions.  These modifications are distributed here under

   the following terms:

    This library is free software; you can redistribute it and/or

    modify it under the terms of the GNU Lesser General Public

    License as published by the Free Software Foundation; either

    version 2.1 of the License, or (at your option) any later version.

    This library is distributed in the hope that it will be useful,

    but WITHOUT ANY WARRANTY; without even the implied warranty of

    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

    Lesser General Public License for more details.

    You should have received a copy of the GNU Lesser General Public

    License along with this library; if not, see

    <http://www.gnu.org/licenses/>.  */

/* __ieee754_coshl(x)

 * Method :

 * mathematically coshl(x) if defined to be (exp(x)+exp(-x))/2

 *      1. Replace x by |x| (coshl(x) = coshl(-x)).

 *      2.

 *                                                      [ exp(x) - 1 ]^2

 *          0        <= x <= ln2/2  :  coshl(x) := 1 + -------------------

 *                                                         2*exp(x)

 *

 *                                                 exp(x) +  1/exp(x)

 *          ln2/2    <= x <= 22     :  coshl(x) := -------------------

 *                                                         2

 *          22       <= x <= lnovft :  coshl(x) := expl(x)/2

 *          lnovft   <= x <= ln2ovft:  coshl(x) := expl(x/2)/2 * expl(x/2)

 *          ln2ovft  <  x           :  coshl(x) := huge*huge (overflow)

 *

 * Special cases:

 *      coshl(x) is |x| if x is +INF, -INF, or NaN.

 *      only coshl(0)=1 is exact for finite x.

 */

#include <math.h>

#include <math_private.h>

static const _Float128 one = 1.0, half = 0.5, huge = L(1.0e4900),

ovf_thresh = L(1.1357216553474703894801348310092223067821E4);

_Float128

__ieee754_coshl (_Float128 x)

{

  _Float128 t, w;

  int32_t ex;

  ieee854_long_double_shape_type u;

  u.value = x;

  ex = u.parts32.w0 & 0x7fffffff;

  /* Absolute value of x.  */

  u.parts32.w0 = ex;

  /* x is INF or NaN */

  if (ex >= 0x7fff0000)

    return x * x;

  /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */

  if (ex < 0x3ffd62e4) /* 0.3465728759765625 */

    {

      if (ex < 0x3fb80000) /* |x| < 2^-116 */

	return one;		/* cosh(tiny) = 1 */

      t = __expm1l (u.value);

      w = one + t;

      return one + (t * t) / (w + w);

    }

  /* |x| in [0.5*ln2,40], return (exp(|x|)+1/exp(|x|)/2; */

  if (ex < 0x40044000)

    {

      t = __ieee754_expl (u.value);

      return half * t + half / t;

    }

  /* |x| in [22, ln(maxdouble)] return half*exp(|x|) */

  if (ex <= 0x400c62e3) /* 11356.375 */

    return half * __ieee754_expl (u.value);

  /* |x| in [log(maxdouble), overflowthresold] */

  if (u.value <= ovf_thresh)

    {

      w = __ieee754_expl (half * u.value);

      t = half * w;

      return t * w;

    }

  /* |x| > overflowthresold, cosh(x) overflow */

  return huge * huge;

}

strong_alias (__ieee754_coshl, __coshl_finite)