112 lines
3.6 KiB
C
112 lines
3.6 KiB
C
/*
|
|
* ====================================================
|
|
* 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
|
|
<https://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>
|
|
#include <libm-alias-finite.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;
|
|
}
|
|
libm_alias_finite (__ieee754_coshl, __coshl)
|