* Copyright (c) 1985 Regents of the University of California.
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. All advertising materials mentioning features or use of this software
* must display the following acknowledgement:
* This product includes software developed by the University of
* California, Berkeley and its contributors.
* 4. Neither the name of the University nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
static char sccsid
[] = "@(#)acosh.c 5.6 (Berkeley) 10/9/90";
* 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
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
)
#define ln2hi vccast(ln2hi)
#define ln2lo vccast(ln2lo)
double 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
);}
return(log1p(t
*(t
+sqrt(x
+1.0))));