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jeremybenn |
/*
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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_coshl(x)
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* Method :
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* mathematically coshl(x) if defined to be (exp(x)+exp(-x))/2
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* 1. Replace x by |x| (coshl(x) = coshl(-x)).
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* 2.
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* [ exp(x) - 1 ]^2
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* 0 <= x <= ln2/2 : coshl(x) := 1 + -------------------
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* 2*exp(x)
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*
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* exp(x) + 1/exp(x)
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* ln2/2 <= x <= 22 : coshl(x) := -------------------
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* 2
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* 22 <= x <= lnovft : coshl(x) := expl(x)/2
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* lnovft <= x <= ln2ovft: coshl(x) := expl(x/2)/2 * expl(x/2)
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* ln2ovft < x : coshl(x) := huge*huge (overflow)
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*
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* Special cases:
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* coshl(x) is |x| if x is +INF, -INF, or NaN.
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* only coshl(0)=1 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 = 1.0Q, half = 0.5Q, huge = 1.0e4900Q,
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ovf_thresh = 1.1357216553474703894801348310092223067821E4Q;
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__float128
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coshq (__float128 x)
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{
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__float128 t, w;
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int32_t ex;
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ieee854_float128 u;
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u.value = x;
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ex = u.words32.w0 & 0x7fffffff;
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/* Absolute value of x. */
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u.words32.w0 = ex;
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/* x is INF or NaN */
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if (ex >= 0x7fff0000)
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return x * x;
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/* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */
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if (ex < 0x3ffd62e4) /* 0.3465728759765625 */
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{
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t = expm1q (u.value);
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w = one + t;
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if (ex < 0x3fb80000) /* |x| < 2^-116 */
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return w; /* cosh(tiny) = 1 */
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return one + (t * t) / (w + w);
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}
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/* |x| in [0.5*ln2,40], return (exp(|x|)+1/exp(|x|)/2; */
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if (ex < 0x40044000)
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{
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t = expq (u.value);
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return half * t + half / t;
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}
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/* |x| in [22, ln(maxdouble)] return half*exp(|x|) */
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if (ex <= 0x400c62e3) /* 11356.375 */
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return half * expq (u.value);
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/* |x| in [log(maxdouble), overflowthresold] */
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if (u.value <= ovf_thresh)
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{
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w = expq (half * u.value);
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t = half * w;
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return t * w;
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}
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/* |x| > overflowthresold, cosh(x) overflow */
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return huge * huge;
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}
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