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/* @(#)s_asinh.c 1.3 95/01/18 */
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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 SunSoft, 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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/* asinh(x)
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* Method :
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* Based on
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* asinh(x) = sign(x) * log [ |x| + ieee_sqrt(x*x+1) ]
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* we have
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* asinh(x) := x if 1+x*x=1,
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* := sign(x)*(ieee_log(x)+ln2)) for large |x|, else
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* := sign(x)*ieee_log(2|x|+1/(|x|+ieee_sqrt(x*x+1))) if|x|>2, else
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* := sign(x)*ieee_log1p(|x| + x^2/(1 + ieee_sqrt(1+x^2)))
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*/
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#include "fdlibm.h"
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#ifdef __STDC__
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static const double
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#else
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static double
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#endif
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one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
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ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
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huge= 1.00000000000000000000e+300;
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#ifdef __STDC__
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double asinh(double x)
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#else
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double asinh(x)
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double x;
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#endif
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{
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double t,w;
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int hx,ix;
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hx = __HI(x);
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ix = hx&0x7fffffff;
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if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */
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if(ix< 0x3e300000) { /* |x|<2**-28 */
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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>0x41b00000) { /* |x| > 2**28 */
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w = __ieee754_log(ieee_fabs(x))+ln2;
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} else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */
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t = ieee_fabs(x);
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w = __ieee754_log(2.0*t+one/(ieee_sqrt(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 =ieee_log1p(ieee_fabs(x)+t/(one+ieee_sqrt(one+t)));
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}
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if(hx>0) return w; else return -w;
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}
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