initial import

sysdeps/generic/atanh.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[] = "@(#)atanh.c	8.1 (Berkeley) 6/4/93";
+#endif /* not lint */
+
+/* ATANH(X)
+ * RETURN THE HYPERBOLIC ARC TANGENT OF X
+ * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
+ * CODED IN C BY K.C. NG, 1/8/85; 
+ * REVISED BY K.C. NG on 2/7/85, 3/7/85, 8/18/85.
+ *
+ * Required kernel function:
+ *	log1p(x) 	...return log(1+x)
+ *
+ * Method :
+ *	Return 
+ *                          1              2x                          x
+ *		atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
+ *                          2             1 - x                      1 - x
+ *
+ * Special cases:
+ *	atanh(x) is NaN if |x| > 1 with signal;
+ *	atanh(NaN) is that NaN with no signal;
+ *	atanh(+-1) is +-INF with signal.
+ *
+ * Accuracy:
+ *	atanh(x) returns the exact hyperbolic arc tangent of x nearly rounded.
+ *	In a test run with 512,000 random arguments on a VAX, the maximum
+ *	observed error was 1.87 ulps (units in the last place) at
+ *	x= -3.8962076028810414000e-03.
+ */
+#include "mathimpl.h"
+
+#if defined(vax)||defined(tahoe)
+#include <errno.h>
+#endif	/* defined(vax)||defined(tahoe) */
+
+double atanh(x)
+double x;
+{
+	double z;
+	z = copysign(0.5,x);
+	x = copysign(x,1.0);
+#if defined(vax)||defined(tahoe)
+	if (x == 1.0) {
+	    return(copysign(1.0,z)*infnan(ERANGE));	/* sign(x)*INF */
+	}
+#endif	/* defined(vax)||defined(tahoe) */
+	x = x/(1.0-x);
+	return( z*log1p(x+x) );
+}