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/* origin: FreeBSD /usr/src/lib/msun/src/s_asinh.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, 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 "libm.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;
int32_t hx,ix;
GET_HIGH_WORD(hx, x);
ix = hx & 0x7fffffff;
if (ix >= 0x7ff00000) /* x is inf or NaN */
return x+x;
if (ix < 0x3e300000) { /* |x| < 2**-28 */
/* return x inexact except 0 */
if (huge+x > one)
return x;
}
if (ix > 0x41b00000) { /* |x| > 2**28 */
w = log(fabs(x)) + ln2;
} else if (ix > 0x40000000) { /* 2**28 > |x| > 2.0 */
t = fabs(x);
w = 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;
return -w;
}
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