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/* e_sinhl.c -- long double version of e_sinh.c.
* Conversion to long double by Ulrich Drepper,
* Cygnus Support, drepper@cygnus.com.
*/
/*
* ====================================================
* 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>
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, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
/* __ieee754_sinhl(x)
* Method :
* mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
* 1. Replace x by |x| (sinhl(-x) = -sinhl(x)).
* 2.
* E + E/(E+1)
* 0 <= x <= 25 : sinhl(x) := --------------, E=expm1l(x)
* 2
*
* 25 <= x <= lnovft : sinhl(x) := expl(x)/2
* lnovft <= x <= ln2ovft: sinhl(x) := expl(x/2)/2 * expl(x/2)
* ln2ovft < x : sinhl(x) := x*shuge (overflow)
*
* Special cases:
* sinhl(x) is |x| if x is +INF, -INF, or NaN.
* only sinhl(0)=0 is exact for finite x.
*/
#include "math.h"
#include "math_private.h"
#ifdef __STDC__
static const long double one = 1.0, shuge = 1.0e4931L,
ovf_thresh = 1.1357216553474703894801348310092223067821E4L;
#else
static long double one = 1.0, shuge = 1.0e4931L,
ovf_thresh = 1.1357216553474703894801348310092223067821E4L;
#endif
#ifdef __STDC__
long double
__ieee754_sinhl (long double x)
#else
long double
__ieee754_sinhl (x)
long double x;
#endif
{
long double t, w, h;
u_int32_t jx, ix;
ieee854_long_double_shape_type u;
/* Words of |x|. */
u.value = x;
jx = u.parts32.w0;
ix = jx & 0x7fffffff;
/* x is INF or NaN */
if (ix >= 0x7fff0000)
return x + x;
h = 0.5;
if (jx & 0x80000000)
h = -h;
/* Absolute value of x. */
u.parts32.w0 = ix;
/* |x| in [0,40], return sign(x)*0.5*(E+E/(E+1))) */
if (ix <= 0x40044000)
{
if (ix < 0x3fc60000) /* |x| < 2^-57 */
if (shuge + x > one)
return x; /* sinh(tiny) = tiny with inexact */
t = __expm1l (u.value);
if (ix < 0x3fff0000)
return h * (2.0 * t - t * t / (t + one));
return h * (t + t / (t + one));
}
/* |x| in [40, log(maxdouble)] return 0.5*exp(|x|) */
if (ix <= 0x400c62e3) /* 11356.375 */
return h * __ieee754_expl (u.value);
/* |x| in [log(maxdouble), overflowthreshold]
Overflow threshold is log(2 * maxdouble). */
if (u.value <= ovf_thresh)
{
w = __ieee754_expl (0.5 * u.value);
t = h * w;
return t * w;
}
/* |x| > overflowthreshold, sinhl(x) overflow */
return x * shuge;
}
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