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authorRoland McGrath <roland@gnu.org>1995-02-18 01:27:10 +0000
committerRoland McGrath <roland@gnu.org>1995-02-18 01:27:10 +0000
commit28f540f45bbacd939bfd07f213bcad2bf730b1bf (patch)
tree15f07c4c43d635959c6afee96bde71fb1b3614ee /sysdeps/generic/acosh.c
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+/*
+ * 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[] = "@(#)acosh.c	8.1 (Berkeley) 6/4/93";
+#endif /* not lint */
+
+/* ACOSH(X)
+ * RETURN THE INVERSE HYPERBOLIC COSINE 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 3/6/85, 3/24/85, 4/16/85, 8/17/85.
+ *
+ * Required system supported functions :
+ *	sqrt(x)
+ *
+ * Required kernel function:
+ *	log1p(x) 		...return log(1+x)
+ *
+ * Method :
+ *	Based on 
+ *		acosh(x) = log [ x + sqrt(x*x-1) ]
+ *	we have
+ *		acosh(x) := log1p(x)+ln2,	if (x > 1.0E20); else		
+ *		acosh(x) := log1p( sqrt(x-1) * (sqrt(x-1) + sqrt(x+1)) ) .
+ *	These formulae avoid the over/underflow complication.
+ *
+ * Special cases:
+ *	acosh(x) is NaN with signal if x<1.
+ *	acosh(NaN) is NaN without signal.
+ *
+ * Accuracy:
+ *	acosh(x) returns the exact inverse hyperbolic cosine of x nearly 
+ *	rounded. In a test run with 512,000 random arguments on a VAX, the
+ *	maximum observed error was 3.30 ulps (units of the last place) at
+ *	x=1.0070493753568216 .
+ *
+ * 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 acosh(x)
+double x;
+{	
+	double t,big=1.E20; /* big+1==big */
+
+#if !defined(vax)&&!defined(tahoe)
+	if(x!=x) return(x);	/* x is NaN */
+#endif	/* !defined(vax)&&!defined(tahoe) */
+
+    /* return log1p(x) + log(2) if x is large */
+	if(x>big) {t=log1p(x)+ln2lo; return(t+ln2hi);} 
+
+	t=sqrt(x-1.0);
+	return(log1p(t*(t+sqrt(x+1.0))));
+}