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/* @(#)e_cosh.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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/* 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 "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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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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u_int32_t mx,lx; |
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/* High word of |x|. */ |
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GET_LDOUBLE_WORDS(ex,mx,lx,x); |
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ex &= 0x7fff; |
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/* x is INF or NaN */ |
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if(ex==0x7fff) 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 < 0x3ffd || (ex == 0x3ffd && mx < 0xb17217f7u)) { |
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t = expm1l(fabsl(x)); |
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w = one+t; |
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if (ex<0x3fbc) 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*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ |
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if (ex < 0x4003 || (ex == 0x4003 && mx < 0xb0000000u)) { |
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t = expl(fabsl(x)); |
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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 < 0x400c || (ex == 0x400c && mx < 0xb1700000u)) |
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return half*expl(fabsl(x)); |
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/* |x| in [log(maxdouble), log(2*maxdouble)) */ |
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if (ex == 0x400c && (mx < 0xb174ddc0u |
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|| (mx == 0xb174ddc0u && lx < 0x31aec0ebu))) |
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{ |
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w = expl(half*fabsl(x)); |
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t = half*w; |
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return t*w; |
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} |
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/* |x| >= log(2*maxdouble), cosh(x) overflow */ |
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return huge*huge; |
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} |
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DEF_STD(coshl); |