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      1 /*	$NetBSD: n_asinh.c,v 1.7 2008/04/29 15:10:02 uwe Exp $	*/
      2 /*
      3  * Copyright (c) 1985, 1993
      4  *	The Regents of the University of California.  All rights reserved.
      5  *
      6  * Redistribution and use in source and binary forms, with or without
      7  * modification, are permitted provided that the following conditions
      8  * are met:
      9  * 1. Redistributions of source code must retain the above copyright
     10  *    notice, this list of conditions and the following disclaimer.
     11  * 2. Redistributions in binary form must reproduce the above copyright
     12  *    notice, this list of conditions and the following disclaimer in the
     13  *    documentation and/or other materials provided with the distribution.
     14  * 3. Neither the name of the University nor the names of its contributors
     15  *    may be used to endorse or promote products derived from this software
     16  *    without specific prior written permission.
     17  *
     18  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
     19  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
     20  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
     21  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
     22  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
     23  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
     24  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
     25  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
     26  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
     27  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
     28  * SUCH DAMAGE.
     29  */
     30 
     31 #ifndef lint
     32 #if 0
     33 static char sccsid[] = "@(#)asinh.c	8.1 (Berkeley) 6/4/93";
     34 #endif
     35 #endif /* not lint */
     36 
     37 /* ASINH(X)
     38  * RETURN THE INVERSE HYPERBOLIC SINE OF X
     39  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
     40  * CODED IN C BY K.C. NG, 2/16/85;
     41  * REVISED BY K.C. NG on 3/7/85, 3/24/85, 4/16/85.
     42  *
     43  * Required system supported functions :
     44  *	copysign(x,y)
     45  *	sqrt(x)
     46  *
     47  * Required kernel function:
     48  *	log1p(x) 		...return log(1+x)
     49  *
     50  * Method :
     51  *	Based on
     52  *		asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
     53  *	we have
     54  *	asinh(x) := x  if  1+x*x=1,
     55  *		 := sign(x)*(log1p(x)+ln2))	 if sqrt(1+x*x)=x, else
     56  *		 := sign(x)*log1p(|x| + |x|/(1/|x| + sqrt(1+(1/|x|)^2)) )
     57  *
     58  * Accuracy:
     59  *	asinh(x) returns the exact inverse hyperbolic sine of x nearly rounded.
     60  *	In a test run with 52,000 random arguments on a VAX, the maximum
     61  *	observed error was 1.58 ulps (units in the last place).
     62  *
     63  * Constants:
     64  * The hexadecimal values are the intended ones for the following constants.
     65  * The decimal values may be used, provided that the compiler will convert
     66  * from decimal to binary accurately enough to produce the hexadecimal values
     67  * shown.
     68  */
     69 #define _LIBM_STATIC
     70 #include "mathimpl.h"
     71 
     72 vc(ln2hi, 6.9314718055829871446E-1  ,7217,4031,0000,f7d0,   0, .B17217F7D00000)
     73 vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
     74 
     75 ic(ln2hi, 6.9314718036912381649E-1,   -1, 1.62E42FEE00000)
     76 ic(ln2lo, 1.9082149292705877000E-10, -33, 1.A39EF35793C76)
     77 
     78 #ifdef vccast
     79 #define    ln2hi    vccast(ln2hi)
     80 #define    ln2lo    vccast(ln2lo)
     81 #endif
     82 
     83 double
     84 asinh(double x)
     85 {
     86 	double t,s;
     87 	static const double	small=1.0E-10,	/* fl(1+small*small) == 1 */
     88 				big  =1.0E20,	/* fl(1+big) == big */
     89 				one  =1.0   ;
     90 
     91 #if !defined(__vax__)&&!defined(tahoe)
     92 	if(x!=x) return(x);	/* x is NaN */
     93 #endif	/* !defined(__vax__)&&!defined(tahoe) */
     94 	if((t=copysign(x,one))>small)
     95 	    if(t<big) {
     96 	     	s=one/t; return(copysign(log1p(t+t/(s+sqrt(one+s*s))),x)); }
     97 	    else	/* if |x| > big */
     98 		{s=log1p(t)+ln2lo; return(copysign(s+ln2hi,x));}
     99 	else	/* if |x| < small */
    100 	    return(x);
    101 }
    102