add Berkeley specific copyright

[unix-history] / usr / src / lib / libm / common_source / acosh.c

/*
* Copyright (c) 1985 Regents of the University of California.
* All rights reserved.
*
* Redistribution and use in source and binary forms are permitted
* provided that this notice is preserved and that due credit is given
* to the University of California at Berkeley. The name of the University
* may not be used to endorse or promote products derived from this
* software without specific prior written permission. This software
* is provided ``as is'' without express or implied warranty.
*
* All recipients should regard themselves as participants in an ongoing
* research project and hence should feel obligated to report their
* experiences (good or bad) with these elementary function codes, using
* the sendbug(8) program, to the authors.
*/

#ifndef lint
static char sccsid[] = "@(#)acosh.c     5.2 (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.
*/

#if defined(vax)||defined(tahoe)        /* VAX D format */
#ifdef vax
#define _0x(A,B)        0x/**/A/**/B
#else   /* vax */
#define _0x(A,B)        0x/**/B/**/A
#endif  /* vax */
/* static double */
/* ln2hi  =  6.9314718055829871446E-1    , Hex  2^  0   *  .B17217F7D00000 */
/* ln2lo  =  1.6465949582897081279E-12   ; Hex  2^-39   *  .E7BCD5E4F1D9CC */
static long     ln2hix[] = { _0x(7217,4031), _0x(0000,f7d0)};
static long     ln2lox[] = { _0x(bcd5,2ce7), _0x(d9cc,e4f1)};
#define    ln2hi    (*(double*)ln2hix)
#define    ln2lo    (*(double*)ln2lox)
#else   /* defined(vax)||defined(tahoe) */
static double
ln2hi  =  6.9314718036912381649E-1    , /*Hex  2^ -1   *  1.62E42FEE00000 */
ln2lo  =  1.9082149292705877000E-10   ; /*Hex  2^-33   *  1.A39EF35793C76 */
#endif  /* defined(vax)||defined(tahoe) */

double acosh(x)
double x;
{       
       double log1p(),sqrt(),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))));
}