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54 lines
1.5 KiB
C
54 lines
1.5 KiB
C
/* @(#)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 <openlibm.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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}
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