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104 lines
3.1 KiB
C
104 lines
3.1 KiB
C
/* @(#)e_sinh.c 5.1 93/09/24 */
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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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/*
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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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/* 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 <openlibm.h>
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#include "math_private.h"
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static const long double one = 1.0, shuge = 1.0e4931L,
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ovf_thresh = 1.1357216553474703894801348310092223067821E4L;
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long double
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sinhl(long double x)
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{
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long double t, w, h;
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u_int32_t jx, ix;
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ieee_quad_shape_type u;
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/* Words of |x|. */
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u.value = x;
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jx = u.parts32.mswhi;
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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 = 0.5;
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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.parts32.mswhi = 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 = expm1l (u.value);
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if (ix < 0x3fff0000)
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return h * (2.0 * 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 * expl (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 = expl (0.5 * 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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