112 lines
3.5 KiB
C
112 lines
3.5 KiB
C
/* sinhq.c -- __float128 version of e_sinh.c.
|
|
* Conversion to __float128 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 __float128 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, write to the Free Software
|
|
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
|
|
|
|
/* sinhq(x)
|
|
* Method :
|
|
* mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
|
|
* 1. Replace x by |x| (sinhq(-x) = -sinhq(x)).
|
|
* 2.
|
|
* E + E/(E+1)
|
|
* 0 <= x <= 25 : sinhq(x) := --------------, E=expm1q(x)
|
|
* 2
|
|
*
|
|
* 25 <= x <= lnovft : sinhq(x) := expq(x)/2
|
|
* lnovft <= x <= ln2ovft: sinhq(x) := expq(x/2)/2 * expq(x/2)
|
|
* ln2ovft < x : sinhq(x) := x*shuge (overflow)
|
|
*
|
|
* Special cases:
|
|
* sinhq(x) is |x| if x is +INF, -INF, or NaN.
|
|
* only sinhq(0)=0 is exact for finite x.
|
|
*/
|
|
|
|
#include "quadmath-imp.h"
|
|
|
|
static const __float128 one = 1.0, shuge = 1.0e4931Q,
|
|
ovf_thresh = 1.1357216553474703894801348310092223067821E4Q;
|
|
|
|
__float128
|
|
sinhq (__float128 x)
|
|
{
|
|
__float128 t, w, h;
|
|
uint32_t jx, ix;
|
|
ieee854_float128 u;
|
|
|
|
/* Words of |x|. */
|
|
u.value = x;
|
|
jx = u.words32.w0;
|
|
ix = jx & 0x7fffffff;
|
|
|
|
/* x is INF or NaN */
|
|
if (ix >= 0x7fff0000)
|
|
return x + x;
|
|
|
|
h = 0.5Q;
|
|
if (jx & 0x80000000)
|
|
h = -h;
|
|
|
|
/* Absolute value of x. */
|
|
u.words32.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 = expm1q (u.value);
|
|
if (ix < 0x3fff0000)
|
|
return h * (2.0Q * 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 * expq (u.value);
|
|
|
|
/* |x| in [log(maxdouble), overflowthreshold]
|
|
Overflow threshold is log(2 * maxdouble). */
|
|
if (u.value <= ovf_thresh)
|
|
{
|
|
w = expq (0.5Q * u.value);
|
|
t = h * w;
|
|
return t * w;
|
|
}
|
|
|
|
/* |x| > overflowthreshold, sinhq(x) overflow */
|
|
return x * shuge;
|
|
}
|