usr/src/lib/libm/common_source/acosh.c

/*
 * Copyright (c) 1985 Regents of the University of California.
 * All rights reserved.
 *
 * %sccs.include.redist.c%
 */

#ifndef lint
static char sccsid[] = "@(#)acosh.c     5.6 (Berkeley) %G%";
#endif /* not lint */

/* ACOSH(X)
 * RETURN THE INVERSE HYPERBOLIC COSINE OF X
 * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS)
 * CODED IN C BY K.C. NG, 2/16/85;
 * REVISED BY K.C. NG on 3/6/85, 3/24/85, 4/16/85, 8/17/85.
 *
 * Required system supported functions :
 *      sqrt(x)
 *
 * Required kernel function:
 *      log1p(x)                ...return log(1+x)
 *
 * Method :
 *      Based on
 *              acosh(x) = log [ x + sqrt(x*x-1) ]
 *      we have
 *              acosh(x) := log1p(x)+ln2,       if (x > 1.0E20); else
 *              acosh(x) := log1p( sqrt(x-1) * (sqrt(x-1) + sqrt(x+1)) ) .
 *      These formulae avoid the over/underflow complication.
 *
 * Special cases:
 *      acosh(x) is NaN with signal if x<1.
 *      acosh(NaN) is NaN without signal.
 *
 * Accuracy:
 *      acosh(x) returns the exact inverse hyperbolic cosine of x nearly
 *      rounded. In a test run with 512,000 random arguments on a VAX, the
 *      maximum observed error was 3.30 ulps (units of the last place) at
 *      x=1.0070493753568216 .
 *
 * Constants:
 * The hexadecimal values are the intended ones for the following constants.
 * The decimal values may be used, provided that the compiler will convert
 * from decimal to binary accurately enough to produce the hexadecimal values
 * shown.
 */

#include "mathimpl.h"

vc(ln2hi, 6.9314718055829871446E-1  ,7217,4031,0000,f7d0,   0, .B17217F7D00000)
vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)

ic(ln2hi, 6.9314718036912381649E-1,  -1, 1.62E42FEE00000)
ic(ln2lo, 1.9082149292705877000E-10,-33, 1.A39EF35793C76)

#ifdef vccast
#define    ln2hi    vccast(ln2hi)
#define    ln2lo    vccast(ln2lo)
#endif

double acosh(x)
double x;
{
        double t,big=1.E20; /* big+1==big */

#if !defined(vax)&&!defined(tahoe)
        if(x!=x) return(x);     /* x is NaN */
#endif  /* !defined(vax)&&!defined(tahoe) */

    /* return log1p(x) + log(2) if x is large */
        if(x>big) {t=log1p(x)+ln2lo; return(t+ln2hi);}

        t=sqrt(x-1.0);
        return(log1p(t*(t+sqrt(x+1.0))));
}