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/* @(#)s_asinh.c 5.1 93/09/24 */
/*
* ====================================================
* 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 "math.h"
#include "math_private.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 w;
int32_t hx,ix;
GET_HIGH_WORD(hx,x);
ix = hx&0x7fffffff;
if(__builtin_expect(ix< 0x3e300000, 0)) { /* |x|<2**-28 */
if(huge+x>one) return x; /* return x inexact except 0 */
}
if(__builtin_expect(ix>0x41b00000, 0)) { /* |x| > 2**28 */
if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */
w = __ieee754_log(fabs(x))+ln2;
} else {
double xa = fabs(x);
if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */
w = __ieee754_log(2.0*xa+one/(__ieee754_sqrt(xa*xa+one)+xa));
} else { /* 2.0 > |x| > 2**-28 */
double t = xa*xa;
w =__log1p(xa+t/(one+__ieee754_sqrt(one+t)));
}
}
return __copysign(w, x);
}
weak_alias (__asinh, asinh)
#ifdef NO_LONG_DOUBLE
strong_alias (__asinh, __asinhl)
weak_alias (__asinh, asinhl)
#endif
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