115 lines
3.6 KiB
C
115 lines
3.6 KiB
C
/* acosh.c - ANSI math routines */
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/* Copyright 1992 Wind River Systems, Inc. */
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/*
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modification history
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--------------------
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01d,14oct92,jdi made acosh() nomanual.
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01c,13oct92,jdi mangen fixes
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01b,20sep92,smb documentation additions
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01a,08jul92,smb documentation
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*/
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/*
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DESCRIPTION
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* Copyright (c) 1985 Regents of the University of California.
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms are permitted
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* provided that the above copyright notice and this paragraph are
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* duplicated in all such forms and that any documentation,
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* advertising materials, and other materials related to such
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* distribution and use acknowledge that the software was developed
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* by the University of California, Berkeley. The name of the
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* University may not be used to endorse or promote products derived
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* from this software without specific prior written permission.
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* THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
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* IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
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* WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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*
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* All recipients should regard themselves as participants in an ongoing
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* research project and hence should feel obligated to report their
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* experiences (good or bad) with these elementary function codes, using
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* the sendbug(8) program, to the authors.
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*
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SEE ALSO: American National Standard X3.159-1989
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NOMANUAL
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*/
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#include "vxWorks.h"
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#include "math.h"
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#if defined(vax)||defined(tahoe) /* VAX D format */
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#ifdef vax
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#define _0x(A,B) 0x/**/A/**/B
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#else /* vax */
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#define _0x(A,B) 0x/**/B/**/A
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#endif /* vax */
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/* static double */
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/* ln2hi = 6.9314718055829871446E-1 , Hex 2^ 0 * .B17217F7D00000 */
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/* ln2lo = 1.6465949582897081279E-12 ; Hex 2^-39 * .E7BCD5E4F1D9CC */
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static long ln2hix[] = { _0x(7217,4031), _0x(0000,f7d0)};
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static long ln2lox[] = { _0x(bcd5,2ce7), _0x(d9cc,e4f1)};
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#define ln2hi (*(double*)ln2hix)
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#define ln2lo (*(double*)ln2lox)
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#else /* defined(vax)||defined(tahoe) */
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static double
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ln2hi = 6.9314718036912381649E-1 , /*Hex 2^ -1 * 1.62E42FEE00000 */
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ln2lo = 1.9082149292705877000E-10 ; /*Hex 2^-33 * 1.A39EF35793C76 */
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#endif /* defined(vax)||defined(tahoe) */
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/*****************************************************************************
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*
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* acosh - compute the inverse hyperbolic cosine of <x>
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*
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* This routine returns the inverse hyperbolic cosine of <x>
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* in double precision (VAX D Format 56 BITS, IEEE Double 53 BITS).
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*
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* Required system support function: sqrt()
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*
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* Required kernel function:
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* .CS
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* log1p(x) ...return log(1+x)
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* .CE
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*
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* Based on acosh(x) = log [ x + sqrt(x*x-1) ] we have
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* .CS
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* acosh(x) := log1p(x)+ln2, if (x > 1.0E20); else
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* acosh(x) := log1p( sqrt(x-1) * (sqrt(x-1) + sqrt(x+1)) ) .
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* .CE
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* These formulae avoid the over/underflow complication.
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*
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* Special cases are acosh(x) is NaN with signal if x<1 and acosh(NaN)
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* is NaN without signal.
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*
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* RETURNS: The inverse hyperbolic cosine of <x>.
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* It returns the exact inverse hyperbolic cosine of <x> nearly
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* rounded. In a test run with 512,000 random arguments on a VAX, the
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* maximum observed error was 3.30 ulps (units of the last place) at
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* x=1.0070493753568216.
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*
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* INTERNAL
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* Coded IN C BY K.C. NG, 2/16/85;
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* Revised BY K.C. NG on 3/6/85, 3/24/85, 4/16/85, 8/17/85.
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*
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* NOMANUAL
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*/
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double acosh(x)
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double x;
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{
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double log1p(),sqrt(),t,big=1.E20; /* big+1==big */
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#if !defined(vax)&&!defined(tahoe)
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if(x!=x) return(x); /* x is NaN */
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#endif /* !defined(vax)&&!defined(tahoe) */
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/* return log1p(x) + log(2) if x is large */
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if(x>big) {t=log1p(x)+ln2lo; return(t+ln2hi);}
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t=sqrt(x-1.0);
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return(log1p(t*(t+sqrt(x+1.0))));
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}
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