* Copyright (c) 1985 Regents of the University of California.
* Use and reproduction of this software are granted in accordance with
* the terms and conditions specified in the Berkeley Software License
* Agreement (in particular, this entails acknowledgement of the programs'
* source, and inclusion of this notice) with the additional understanding
* that all recipients should regard themselves as participants in an
* ongoing research project and hence should feel obligated to report
* their experiences (good or bad) with these elementary function codes,
* using "sendbug 4bsd-bugs@BERKELEY", to the authors.
static char sccsid
[] = "@(#)asinh.c 1.2 (Berkeley) 8/21/85";
* 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 :
* Required kernel function:
* log1p(x) ...return log(1+x)
* asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
* 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)) )
* 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).
* 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
#ifdef VAX /* VAX D format */
/* ln2hi = 6.9314718055829871446E-1 , Hex 2^ 0 * .B17217F7D00000 */
/* ln2lo = 1.6465949582897081279E-12 ; Hex 2^-39 * .E7BCD5E4F1D9CC */
static long ln2hix
[] = { 0x72174031, 0x0000f7d0};
static long ln2lox
[] = { 0xbcd52ce7, 0xd9cce4f1};
#define ln2hi (*(double*)ln2hix)
#define ln2lo (*(double*)ln2lox)
ln2hi
= 6.9314718036912381649E-1 , /*Hex 2^ -1 * 1.62E42FEE00000 */
ln2lo
= 1.9082149292705877000E-10 ; /*Hex 2^-33 * 1.A39EF35793C76 */
double copysign(),log1p(),sqrt(),t
,s
;
static double small
=1.0E-10, /* fl(1+small*small) == 1 */
big
=1.0E20
, /* fl(1+big) == big */
if(x
!=x
) return(x
); /* x is NaN */
if((t
=copysign(x
,one
))>small
)
s
=one
/t
; return(copysign(log1p(t
+t
/(s
+sqrt(one
+s
*s
))),x
)); }
{s
=log1p(t
)+ln2lo
; return(copysign(s
+ln2hi
,x
));}
else /* if |x| < small */