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

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

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

/* ASINH(X)
 * RETURN THE INVERSE HYPERBOLIC SINE 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 3/7/85, 3/24/85, 4/16/85.
 *
 * Required system supported functions :
 *      copysign(x,y)
 *      sqrt(x)
 *
 * Required kernel function:
 *      log1p(x)                ...return log(1+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)*(log1p(x)+ln2))      if sqrt(1+x*x)=x, else
 *               := sign(x)*log1p(|x| + |x|/(1/|x| + sqrt(1+(1/|x|)^2)) )
 *
 * Accuracy:
 *      asinh(x) returns the exact inverse hyperbolic sine of x nearly rounded.
 *      In a test run with 52,000 random arguments on a VAX, the maximum
 *      observed error was 1.58 ulps (units in the last place).
 *
 * 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 asinh(x)
double x;
{
        double t,s;
        const static double     small=1.0E-10,  /* fl(1+small*small) == 1 */
                                big  =1.0E20,   /* fl(1+big) == big */
                                one  =1.0   ;

#if !defined(vax)&&!defined(tahoe)
        if(x!=x) return(x);     /* x is NaN */
#endif  /* !defined(vax)&&!defined(tahoe) */
        if((t=copysign(x,one))>small)
            if(t<big) {
                s=one/t; return(copysign(log1p(t+t/(s+sqrt(one+s*s))),x)); }
            else        /* if |x| > big */
                {s=log1p(t)+ln2lo; return(copysign(s+ln2hi,x));}
        else    /* if |x| < small */
            return(x);
}