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/* @(#)s_asinh.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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/* asinhl(x) |
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* Method : |
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* Based on |
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* asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ] |
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* we have |
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* asinhl(x) := x if 1+x*x=1, |
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* := signl(x)*(logl(x)+ln2)) for large |x|, else |
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* := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else |
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* := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2))) |
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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 |
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one = 1.000000000000000000000e+00L, /* 0x3FFF, 0x00000000, 0x00000000 */ |
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ln2 = 6.931471805599453094287e-01L, /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */ |
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huge= 1.000000000000000000e+4900L; |
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long double |
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asinhl(long double x) |
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{ |
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long double t,w; |
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int32_t hx,ix; |
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GET_LDOUBLE_EXP(hx,x); |
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ix = hx&0x7fff; |
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if(ix==0x7fff) return x+x; /* x is inf or NaN */ |
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if(ix< 0x3fde) { /* |x|<2**-34 */ |
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if(huge+x>one) return x; /* return x inexact except 0 */ |
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} |
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if(ix>0x4020) { /* |x| > 2**34 */ |
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w = logl(fabsl(x))+ln2; |
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} else if (ix>0x4000) { /* 2**34 > |x| > 2.0 */ |
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t = fabsl(x); |
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w = logl(2.0*t+one/(sqrtl(x*x+one)+t)); |
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} else { /* 2.0 > |x| > 2**-28 */ |
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t = x*x; |
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w =log1pl(fabsl(x)+t/(one+sqrtl(one+t))); |
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} |
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if(hx&0x8000) return -w; else return w; |
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} |