118 lines
3.9 KiB
C
118 lines
3.9 KiB
C
/* asinh.c - 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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01c,14oct92,jdi made asinh() nomanual.
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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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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/TAHOE 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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* asinh - compute the inverse hyperbolic sine of <x>
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*
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* ASINH(X)
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* RETURN THE INVERSE HYPERBOLIC SINE OF X
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* DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
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* CODED IN C BY K.C. NG, 2/16/85;
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* REVISED BY K.C. NG on 3/7/85, 3/24/85, 4/16/85.
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*
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* Required system supported functions are copysign(x,y) and sqrt(x).
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*
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* Required kernel function is log1p(x) ...return log(1+x)
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*
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* Method :
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* Based on
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* .CS
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* asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
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* .CE
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* we have
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* .CS
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* asinh(x) := x if 1+x*x=1,
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* := sign(x)*(log1p(x)+ln2)) if sqrt(1+x*x)=x, else
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* := sign(x)*log1p(|x| + |x|/(1/|x| + sqrt(1+(1/|x|)^2)) )
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* .CE
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*
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* asinh(x) returns the exact inverse hyperbolic sine of x nearly rounded.
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* In a test run with 52,000 random arguments on a VAX, the maximum
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* observed error was 1.58 ulps (units in the last place).
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* The hexadecimal values are the intended ones for the following constants.
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* The decimal values may be used, provided that the compiler will convert
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* from decimal to binary accurately enough to produce the hexadecimal values
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* shown.
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*
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* NOMANUAL
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*/
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double asinh(x)
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double x;
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{
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double copysign(),log1p(),sqrt(),t,s;
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static double small=1.0E-10, /* fl(1+small*small) == 1 */
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big =1.0E20, /* fl(1+big) == big */
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one =1.0 ;
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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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if((t=copysign(x,one))>small)
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if(t<big) {
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s=one/t; return(copysign(log1p(t+t/(s+sqrt(one+s*s))),x)); }
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else /* if |x| > big */
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{s=log1p(t)+ln2lo; return(copysign(s+ln2hi,x));}
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else /* if |x| < small */
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return(x);
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}
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