add directory gnu

gnu/glibc/glibc-1.03/math/bsd/common_source/acosh.c

@@ -0,0 +1,88 @@
+/*
+ * Copyright (c) 1985 Regents of the University of California.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms are permitted provided
+ * that: (1) source distributions retain this entire copyright notice and
+ * comment, and (2) distributions including binaries display the following
+ * acknowledgement:  ``This product includes software developed by the
+ * University of California, Berkeley and its contributors'' in the
+ * documentation or other materials provided with the distribution and in
+ * all advertising materials mentioning features or use of this software.
+ * 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 ``AS IS'' AND WITHOUT ANY EXPRESS OR IMPLIED
+ * WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED WARRANTIES OF
+ * MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
+ */
+
+#ifndef lint
+static char sccsid[] = "@(#)acosh.c	5.6 (Berkeley) 10/9/90";
+#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))));
+}