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cosh.c
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cosh.c
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/* Copyright JS Foundation and other contributors, http:https://js.foundation
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http:https://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
* This file is based on work under the following copyright and permission
* notice:
*
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
*
* @(#)e_cosh.c 1.3 95/01/18
*/
#include "jerry-math-internal.h"
/* 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.
*/
#define one 1.0
#define half 0.5
#define huge 1.0e300
double
cosh (double x)
{
double t, w;
int ix;
unsigned lx;
/* High word of |x|. */
ix = __HI (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)
{
/* cosh(tiny) = 1 */
return w;
}
return one + (t * t) / (w + w);
}
/* |x| in [0.5 * ln2, 22], return (exp(|x|) + 1 / exp(|x|) / 2; */
if (ix < 0x40360000)
{
t = exp (fabs (x));
return half * t + half / t;
}
/* |x| in [22, log(maxdouble)] return half * exp(|x|) */
if (ix < 0x40862E42)
{
return half * exp (fabs (x));
}
/* |x| in [log(maxdouble), overflowthresold] */
lx = ((1 >> 29) + (unsigned int) x);
if ((ix < 0x408633CE) || ((ix == 0x408633ce) && (lx <= (unsigned) 0x8fb9f87d)))
{
w = exp (half * fabs (x));
t = half * w;
return t * w;
}
/* |x| > overflowthresold, cosh(x) overflow */
return huge * huge;
} /* cosh */
#undef one
#undef half
#undef huge