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/*
* ====================================================
* 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 contributed by
Stephen L. Moshier <moshier@na-net.ornl.gov> */
/* __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"
#ifdef __STDC__
static const long double one = 1.0, half = 0.5, huge = 1.0e4900L,
ovf_thresh = 1.1357216553474703894801348310092223067821E4L;
#else
static long double one = 1.0, half = 0.5, huge = 1.0e4900L,
ovf_thresh = 1.1357216553474703894801348310092223067821E4L;
#endif
#ifdef __STDC__
long double
__ieee754_coshl (long double x)
#else
long double
__ieee754_coshl (x)
long double x;
#endif
{
long double t, w;
int32_t ex;
u_int32_t mx, lx;
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 */
{
t = __expm1l (u.value);
w = one + t;
if (ex < 0x3fc60000) /* |x| < 2^-57 */
return w; /* cosh(tiny) = 1 */
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;
}
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