2014-12-04 18:41:16 +01:00
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/* @(#)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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/* 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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2014-12-04 19:02:39 +01:00
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#include <openlibm.h>
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2014-12-04 18:41:16 +01:00
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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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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,i0,i1;
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/* Words of |x|. */
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GET_LDOUBLE_WORDS(jx,i0,i1,x);
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ix = jx&0x7fff;
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/* x is INF or NaN */
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if(ix==0x7fff) return x+x;
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h = 0.5;
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if (jx & 0x8000) h = -h;
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/* |x| in [0,25], return sign(x)*0.5*(E+E/(E+1))) */
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if (ix < 0x4003 || (ix == 0x4003 && i0 <= 0xc8000000)) { /* |x|<25 */
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if (ix<0x3fdf) /* |x|<2**-32 */
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if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
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t = expm1l(fabsl(x));
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if(ix<0x3fff) 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 [25, log(maxdouble)] return 0.5*exp(|x|) */
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if (ix < 0x400c || (ix == 0x400c && i0 < 0xb17217f7))
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return h*expl(fabsl(x));
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/* |x| in [log(maxdouble), overflowthreshold] */
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if (ix<0x400c || (ix == 0x400c && (i0 < 0xb174ddc0
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|| (i0 == 0xb174ddc0
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&& i1 <= 0x31aec0ea)))) {
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w = expl(0.5*fabsl(x));
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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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