#include "FEATURE/uwin" #if !_UWIN || _lib_asinh void _STUB_asinh(){} #else /* * 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. 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 extern 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); } #endif