# shithub: 9ferno

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```/* derived from /netlib/fdlibm */

/* @(#)s_asinh.c 1.3 95/01/18 */
/*
* ====================================================
*
* 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| + sqrt(x*x+1) ]
*	we have
*	asinh(x) := x  if  1+x*x=1,
*		 := sign(x)*(log(x)+ln2)) for large |x|, else
*		 := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
*		 := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
*/

#include "fdlibm.h"

static const double
one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
ln2 =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
Huge=  1.00000000000000000000e+300;

double asinh(double x)
{
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(fabs(x))+ln2;
} else if (ix>0x40000000) {	/* 2**28 > |x| > 2.0 */
t = fabs(x);
w = __ieee754_log(2.0*t+one/(sqrt(x*x+one)+t));
} else {		/* 2.0 > |x| > 2**-28 */
t = x*x;
w =log1p(fabs(x)+t/(one+sqrt(one+t)));
}
if(hx>0) return w; else return -w;
}
```