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jeremybenn |
/* e_sinhl.c -- __float128 version of e_sinh.c.
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* Conversion to __float128 by Ulrich Drepper,
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* Cygnus Support, drepper@cygnus.com.
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*/
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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/* Changes for 128-bit __float128 are
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Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
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and are incorporated herein by permission of the author. The author
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reserves the right to distribute this material elsewhere under different
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copying permissions. These modifications are distributed here under
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the following terms:
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This library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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This library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with this library; if not, write to the Free Software
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Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
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/* __ieee754_sinhl(x)
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* Method :
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* mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
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* 1. Replace x by |x| (sinhl(-x) = -sinhl(x)).
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* 2.
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* E + E/(E+1)
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* 0 <= x <= 25 : sinhl(x) := --------------, E=expm1l(x)
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* 2
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*
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* 25 <= x <= lnovft : sinhl(x) := expl(x)/2
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* lnovft <= x <= ln2ovft: sinhl(x) := expl(x/2)/2 * expl(x/2)
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* ln2ovft < x : sinhl(x) := x*shuge (overflow)
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*
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* Special cases:
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* sinhl(x) is |x| if x is +INF, -INF, or NaN.
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* only sinhl(0)=0 is exact for finite x.
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*/
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#include "quadmath-imp.h"
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static const __float128 one = 1.0, shuge = 1.0e4931Q,
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ovf_thresh = 1.1357216553474703894801348310092223067821E4Q;
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__float128
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sinhq (__float128 x)
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{
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__float128 t, w, h;
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uint32_t jx, ix;
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ieee854_float128 u;
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/* Words of |x|. */
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u.value = x;
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jx = u.words32.w0;
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ix = jx & 0x7fffffff;
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/* x is INF or NaN */
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if (ix >= 0x7fff0000)
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return x + x;
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h = 0.5Q;
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if (jx & 0x80000000)
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h = -h;
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/* Absolute value of x. */
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u.words32.w0 = ix;
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/* |x| in [0,40], return sign(x)*0.5*(E+E/(E+1))) */
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if (ix <= 0x40044000)
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{
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if (ix < 0x3fc60000) /* |x| < 2^-57 */
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if (shuge + x > one)
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return x; /* sinh(tiny) = tiny with inexact */
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t = expm1q (u.value);
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if (ix < 0x3fff0000)
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return h * (2.0Q * t - t * t / (t + one));
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return h * (t + t / (t + one));
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}
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/* |x| in [40, log(maxdouble)] return 0.5*exp(|x|) */
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if (ix <= 0x400c62e3) /* 11356.375 */
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return h * expq (u.value);
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/* |x| in [log(maxdouble), overflowthreshold]
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Overflow threshold is log(2 * maxdouble). */
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if (u.value <= ovf_thresh)
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{
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w = expq (0.5Q * u.value);
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t = h * w;
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return t * w;
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}
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/* |x| > overflowthreshold, sinhl(x) overflow */
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return x * shuge;
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}
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