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      1 /*	$NetBSD: n_acosh.c,v 1.6 2003/08/07 16:44:50 agc Exp $	*/
      2 /*
      3  * Copyright (c) 1985, 1993
      4  *	The Regents of the University of California.  All rights reserved.
      5  *
      6  * Redistribution and use in source and binary forms, with or without
      7  * modification, are permitted provided that the following conditions
      8  * are met:
      9  * 1. Redistributions of source code must retain the above copyright
     10  *    notice, this list of conditions and the following disclaimer.
     11  * 2. Redistributions in binary form must reproduce the above copyright
     12  *    notice, this list of conditions and the following disclaimer in the
     13  *    documentation and/or other materials provided with the distribution.
     14  * 3. Neither the name of the University nor the names of its contributors
     15  *    may be used to endorse or promote products derived from this software
     16  *    without specific prior written permission.
     17  *
     18  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
     19  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
     20  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
     21  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
     22  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
     23  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
     24  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
     25  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
     26  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
     27  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
     28  * SUCH DAMAGE.
     29  */
     30 
     31 #ifndef lint
     32 #if 0
     33 static char sccsid[] = "@(#)acosh.c	8.1 (Berkeley) 6/4/93";
     34 #endif
     35 #endif /* not lint */
     36 
     37 /* ACOSH(X)
     38  * RETURN THE INVERSE HYPERBOLIC COSINE OF X
     39  * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS)
     40  * CODED IN C BY K.C. NG, 2/16/85;
     41  * REVISED BY K.C. NG on 3/6/85, 3/24/85, 4/16/85, 8/17/85.
     42  *
     43  * Required system supported functions :
     44  *	sqrt(x)
     45  *
     46  * Required kernel function:
     47  *	log1p(x) 		...return log(1+x)
     48  *
     49  * Method :
     50  *	Based on
     51  *		acosh(x) = log [ x + sqrt(x*x-1) ]
     52  *	we have
     53  *		acosh(x) := log1p(x)+ln2,	if (x > 1.0E20); else
     54  *		acosh(x) := log1p( sqrt(x-1) * (sqrt(x-1) + sqrt(x+1)) ) .
     55  *	These formulae avoid the over/underflow complication.
     56  *
     57  * Special cases:
     58  *	acosh(x) is NaN with signal if x<1.
     59  *	acosh(NaN) is NaN without signal.
     60  *
     61  * Accuracy:
     62  *	acosh(x) returns the exact inverse hyperbolic cosine of x nearly
     63  *	rounded. In a test run with 512,000 random arguments on a VAX, the
     64  *	maximum observed error was 3.30 ulps (units of the last place) at
     65  *	x=1.0070493753568216 .
     66  *
     67  * Constants:
     68  * The hexadecimal values are the intended ones for the following constants.
     69  * The decimal values may be used, provided that the compiler will convert
     70  * from decimal to binary accurately enough to produce the hexadecimal values
     71  * shown.
     72  */
     73 
     74 #define _LIBM_STATIC
     75 #include "mathimpl.h"
     76 
     77 vc(ln2hi, 6.9314718055829871446E-1  ,7217,4031,0000,f7d0,   0, .B17217F7D00000)
     78 vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
     79 
     80 ic(ln2hi, 6.9314718036912381649E-1,  -1, 1.62E42FEE00000)
     81 ic(ln2lo, 1.9082149292705877000E-10,-33, 1.A39EF35793C76)
     82 
     83 #ifdef vccast
     84 #define    ln2hi    vccast(ln2hi)
     85 #define    ln2lo    vccast(ln2lo)
     86 #endif
     87 
     88 double
     89 acosh(double x)
     90 {
     91 	double t,big=1.E20; /* big+1==big */
     92 
     93 #if !defined(__vax__)&&!defined(tahoe)
     94 	if(x!=x) return(x);	/* x is NaN */
     95 #endif	/* !defined(__vax__)&&!defined(tahoe) */
     96 
     97     /* return log1p(x) + log(2) if x is large */
     98 	if(x>big) {t=log1p(x)+ln2lo; return(t+ln2hi);}
     99 
    100 	t=sqrt(x-1.0);
    101 	return(log1p(t*(t+sqrt(x+1.0))));
    102 }
    103