first shot at TAHOE.

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

/* 
* 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.
*/

#ifndef lint
static char sccsid[] =
"@(#)acosh.c    1.2 (Berkeley) 8/21/85; 1.3 (ucb.elefunt) %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 */
/* static double */
/* 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)
#else   /* IEEE double */
static double
ln2hi  =  6.9314718036912381649E-1    , /*Hex  2^ -1   *  1.62E42FEE00000 */
ln2lo  =  1.9082149292705877000E-10   ; /*Hex  2^-33   *  1.A39EF35793C76 */
#endif

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

   /* 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))));
}