108 lines
2.3 KiB
C
108 lines
2.3 KiB
C
|
|
/* @(#)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
|
|
@ifnottex
|
|
. sgn(<[x]>) * log(abs(<[x]>) + sqrt(1+<[x]>*<[x]>))
|
|
@end ifnottex
|
|
@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 */
|