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/* @(#)s_asinh.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* asinh(x)
* Method :
* Based on
* asinh(x) = sign(x) * log [ |x| + ieee_sqrt(x*x+1) ]
* we have
* asinh(x) := x if 1+x*x=1,
* := sign(x)*(ieee_log(x)+ln2)) for large |x|, else
* := sign(x)*ieee_log(2|x|+1/(|x|+ieee_sqrt(x*x+1))) if|x|>2, else
* := sign(x)*ieee_log1p(|x| + x^2/(1 + ieee_sqrt(1+x^2)))
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
huge= 1.00000000000000000000e+300;
#ifdef __STDC__
double asinh(double x)
#else
double asinh(x)
double x;
#endif
{
double t,w;
int hx,ix;
hx = __HI(x);
ix = hx&0x7fffffff;
if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */
if(ix< 0x3e300000) { /* |x|<2**-28 */
if(huge+x>one) return x; /* return x inexact except 0 */
}
if(ix>0x41b00000) { /* |x| > 2**28 */
w = __ieee754_log(ieee_fabs(x))+ln2;
} else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */
t = ieee_fabs(x);
w = __ieee754_log(2.0*t+one/(ieee_sqrt(x*x+one)+t));
} else { /* 2.0 > |x| > 2**-28 */
t = x*x;
w =ieee_log1p(ieee_fabs(x)+t/(one+ieee_sqrt(one+t)));
}
if(hx>0) return w; else return -w;
}
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