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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.
* ====================================================
*/
/*
FUNCTION
<<asinh>>, <<asinhf>>---inverse hyperbolic sine
INDEX
asinh
INDEX
asinhf
ANSI_SYNOPSIS
#include <math.h>
double asinh(double <[x]>);
float asinhf(float <[x]>);
TRAD_SYNOPSIS
#include <math.h>
double asinh(<[x]>)
double <[x]>;
float asinhf(<[x]>)
float <[x]>;
DESCRIPTION
<<asinh>> calculates the inverse hyperbolic sine of <[x]>.
<<asinh>> is defined as
@ifinfo
. sgn(<[x]>) * log(abs(<[x]>) + sqrt(1+<[x]>*<[x]>))
@end ifinfo
@tex
$$sign(x) \times ln\Bigl(|x| + \sqrt{1+x^2}\Bigr)$$
@end tex
<<asinhf>> is identical, other than taking and returning floats.
RETURNS
<<asinh>> and <<asinhf>> return the calculated value.
PORTABILITY
Neither <<asinh>> nor <<asinhf>> are ANSI C.
*/
/* 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"
#ifndef _DOUBLE_IS_32BITS
#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;
__int32_t hx,ix;
GET_HIGH_WORD(hx,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 = 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; else return -w;
}
#endif /* _DOUBLE_IS_32BITS */
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