asinh.c File Reference

#include "prim.h"
#include "math.h"

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Functions
double	asinh (double x)
	Inverse hyperbolic sine function. More...

Variables
static const double	one = 1.00000000000000000000e+00
static const double	ln2 = 6.93147180559945286227e-01
static const double	huge = 1.00000000000000000000e+300

Function Documentation

double asinh

(

double

x

)

Inverse hyperbolic sine function.

Version

1.3

Date

95/01/18

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)))

Copyright

Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 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.

Definition at line 73 of file asinh.c.

References huge, ln2, log1p(), one, and sqrt().

Referenced by RealNumber::HypArcCosecant(), and RealNumber::HypArcSine().

{
    double t,w;
    sword 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;
}

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Variable Documentation

const double huge = 1.00000000000000000000e+300

static

Definition at line 50 of file asinh.c.

Referenced by asinh().

const double ln2 = 6.93147180559945286227e-01

static

Definition at line 49 of file asinh.c.

Referenced by asinh().

const double one = 1.00000000000000000000e+00

static

Definition at line 48 of file asinh.c.

Referenced by asinh().