acosh.c File Reference

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

Include dependency graph for acosh.c:

Go to the source code of this file.

Functions
double	acosh (double x)
	Inverse hyperbolic cosine function. More...

Variables
static const double	one = 1.0
static const double	ln2 = 6.93147180559945286227e-01

Function Documentation

double acosh

(

double

x

)

Inverse hyperbolic cosine function.

Version

1.3

Date

95/01/18

Method :
 Based on
    acosh(x) = log [ x + sqrt(x*x-1) ]
 we have
    acosh(x) := log(x)+ln2, if x is large; else
    acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
    acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.

Special cases:
 acosh(x) is NaN with signal if x<1.
 acosh(NaN) is NaN without signal.

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 75 of file acosh.c.

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

Referenced by RealNumber::HypArcCosine(), and RealNumber::HypArcSecant().

{
    double t;
    sword hx, lx;
    GET_HIGH_WORD(hx,x);
    GET_LOW_WORD(lx,x);

    if(hx<0x3ff00000) {     /* x < 1 */
        return (x-x)/(x-x);
    } else if(hx >=0x41b00000) {    /* x > 2**28 */
        if(hx >=0x7ff00000) {   /* x is inf of NaN */
            return x+x;
        } else
            return log(x)+ln2;  /* acosh(huge)=log(2x) */
    } else if(((hx-0x3ff00000)|lx)==0) {
        return 0.0;         /* acosh(1) = 0 */
    } else if (hx > 0x40000000) {   /* 2**28 > x > 2 */
        t=x*x;
        return log(2.0*x-one/(x+sqrt(t-one)));
    } else {            /* 1<x<2 */
        t = x-one;
        return log1p(t+sqrt(2.0*t+t*t));
    }
}

Here is the call graph for this function:

Here is the caller graph for this function:

Variable Documentation

const double ln2 = 6.93147180559945286227e-01

static

Definition at line 49 of file acosh.c.

Referenced by acosh().

const double one = 1.0

static

Definition at line 48 of file acosh.c.

Referenced by acosh().