* Copyright (c) 1985 Regents of the University of California.
* Use and reproduction of this software are granted in accordance with
* the terms and conditions specified in the Berkeley Software License
* Agreement (in particular, this entails acknowledgement of the programs'
* source, and inclusion of this notice) with the additional understanding
* that 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 "sendbug 4bsd-bugs@BERKELEY", to the authors.
static char sccsid
[] = "@(#)acosh.c 1.1 (ELEFUNT) %G%";
* 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 :
* Required kernel function:
* log1p(x) ...return log(1+x)
* acosh(x) = log [ x + sqrt(x*x-1) ]
* 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.
* acosh(x) is NaN with signal if x<1.
* acosh(NaN) is NaN without signal.
* 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
* 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
#ifdef VAX /* VAX D format */
/* ln2hi = 6.9314718055829871446E-1 , Hex 2^ 0 * .B17217F7D00000 */
/* ln2lo = 1.6465949582897081279E-12 ; Hex 2^-39 * .E7BCD5E4F1D9CC */
static long ln2hix
[] = { 0x72174031, 0x0000f7d0};
static long ln2lox
[] = { 0xbcd52ce7, 0xd9cce4f1};
#define ln2hi (*(double*)ln2hix)
#define ln2lo (*(double*)ln2lox)
ln2hi
= 6.9314718036912381649E-1 , /*Hex 2^ -1 * 1.62E42FEE00000 */
ln2lo
= 1.9082149292705877000E-10 ; /*Hex 2^-33 * 1.A39EF35793C76 */
double log1p(),sqrt(),t
,big
=1.E20
; /* big+1==big */
if(x
!=x
) return(x
); /* x is NaN */
/* return log1p(x) + log(2) if x is large */
if(x
>big
) {t
=log1p(x
)+ln2lo
; return(t
+ln2hi
);}
return(log1p(t
*(t
+sqrt(x
+1.0))));