106 lines
3.3 KiB
C
106 lines
3.3 KiB
C
/*
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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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/*
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* Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
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*
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* Permission to use, copy, modify, and distribute this software for any
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* purpose with or without fee is hereby granted, provided that the above
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* copyright notice and this permission notice appear in all copies.
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*
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* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
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* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
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* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
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* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
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* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
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* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
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* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
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*/
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/* 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 <openlibm_math.h>
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#include "math_private.h"
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static const long double one = 1.0, half = 0.5, huge = 1.0e4900L,
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ovf_thresh = 1.1357216553474703894801348310092223067821E4L;
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long double
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coshl(long double x)
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{
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long double t, w;
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int32_t ex;
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ieee_quad_shape_type u;
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u.value = x;
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ex = u.parts32.mswhi & 0x7fffffff;
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/* Absolute value of x. */
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u.parts32.mswhi = 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 = expm1l (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 = expl (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 * expl (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 = expl (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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