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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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#include <math.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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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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DEF_STD(sinhl); |