diff options
| author | Rodney W. Grimes <rgrimes@FreeBSD.org> | 1994-05-27 05:00:24 +0000 | 
|---|---|---|
| committer | Rodney W. Grimes <rgrimes@FreeBSD.org> | 1994-05-27 05:00:24 +0000 | 
| commit | 58f0484fa251c266ede97b591b499fe3dd4f578e (patch) | |
| tree | 41932a7161f4cd72005330a9c69747e7bab2ee5b /lib/libm/common_source/asinh.c | |
| parent | fb49e767ba942f74b1cee8814e085e5f2615ac53 (diff) | |
Notes
Diffstat (limited to 'lib/libm/common_source/asinh.c')
| -rw-r--r-- | lib/libm/common_source/asinh.c | 101 | 
1 files changed, 101 insertions, 0 deletions
| diff --git a/lib/libm/common_source/asinh.c b/lib/libm/common_source/asinh.c new file mode 100644 index 000000000000..5db8d2ddf7f8 --- /dev/null +++ b/lib/libm/common_source/asinh.c @@ -0,0 +1,101 @@ +/* + * Copyright (c) 1985, 1993 + *	The Regents of the University of California.  All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 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 + * SUCH DAMAGE. + */ + +#ifndef lint +static char sccsid[] = "@(#)asinh.c	8.1 (Berkeley) 6/4/93"; +#endif /* not lint */ + +/* ASINH(X) + * RETURN THE INVERSE HYPERBOLIC SINE 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 3/7/85, 3/24/85, 4/16/85. + * + * Required system supported functions : + *	copysign(x,y) + *	sqrt(x) + * + * Required kernel function: + *	log1p(x) 		...return log(1+x) + * + * Method : + *	Based on  + *		asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] + *	we have + *	asinh(x) := x  if  1+x*x=1, + *		 := sign(x)*(log1p(x)+ln2))	 if sqrt(1+x*x)=x, else + *		 := sign(x)*log1p(|x| + |x|/(1/|x| + sqrt(1+(1/|x|)^2)) )   + * + * Accuracy: + *	asinh(x) returns the exact inverse hyperbolic sine of x nearly rounded. + *	In a test run with 52,000 random arguments on a VAX, the maximum  + *	observed error was 1.58 ulps (units in the last place). + * + * 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. + */ +#include "mathimpl.h" + +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) + +#ifdef vccast +#define    ln2hi    vccast(ln2hi) +#define    ln2lo    vccast(ln2lo) +#endif + +double asinh(x) +double x; +{	 +	double t,s; +	const static double	small=1.0E-10,	/* fl(1+small*small) == 1 */ +				big  =1.0E20,	/* fl(1+big) == big */ +				one  =1.0   ;	 + +#if !defined(vax)&&!defined(tahoe) +	if(x!=x) return(x);	/* x is NaN */ +#endif	/* !defined(vax)&&!defined(tahoe) */ +	if((t=copysign(x,one))>small)  +	    if(t<big) { +	     	s=one/t; return(copysign(log1p(t+t/(s+sqrt(one+s*s))),x)); } +	    else	/* if |x| > big */ +		{s=log1p(t)+ln2lo; return(copysign(s+ln2hi,x));} +	else	/* if |x| < small */ +	    return(x); +} | 
