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+
+/* @(#)e_atanh.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ *
+ */
+
+/*
+FUNCTION
+ <<atanh>>, <<atanhf>>---inverse hyperbolic tangent
+
+INDEX
+ atanh
+INDEX
+ atanhf
+
+ANSI_SYNOPSIS
+ #include <math.h>
+ double atanh(double <[x]>);
+ float atanhf(float <[x]>);
+
+TRAD_SYNOPSIS
+ #include <math.h>
+ double atanh(<[x]>)
+ double <[x]>;
+
+ float atanhf(<[x]>)
+ float <[x]>;
+
+DESCRIPTION
+ <<atanh>> calculates the inverse hyperbolic tangent of <[x]>.
+
+ <<atanhf>> is identical, other than taking and returning
+ <<float>> values.
+
+RETURNS
+ <<atanh>> and <<atanhf>> return the calculated value.
+
+ If
+ @ifinfo
+ |<[x]>|
+ @end ifinfo
+ @tex
+ $|x|$
+ @end tex
+ is greater than 1, the global <<errno>> is set to <<EDOM>> and
+ the result is a NaN. A <<DOMAIN error>> is reported.
+
+ If
+ @ifinfo
+ |<[x]>|
+ @end ifinfo
+ @tex
+ $|x|$
+ @end tex
+ is 1, the global <<errno>> is set to <<EDOM>>; and the result is
+ infinity with the same sign as <<x>>. A <<SING error>> is reported.
+
+ You can modify the error handling for these routines using
+ <<matherr>>.
+
+PORTABILITY
+ Neither <<atanh>> nor <<atanhf>> are ANSI C.
+
+QUICKREF
+ atanh - pure
+ atanhf - pure
+
+
+*/
+
+/* atanh(x)
+ * Method :
+ * 1.Reduced x to positive by atanh(-x) = -atanh(x)
+ * 2.For x>=0.5
+ * 1 2x x
+ * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
+ * 2 1 - x 1 - x
+ *
+ * For x<0.5
+ * atanh(x) = 0.5*log1p(2x+2x*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.
+ *
+ */
+
+#include "fdlibm.h"
+
+#ifndef _DOUBLE_IS_32BITS
+
+#ifdef __STDC__
+static const double one = 1.0, huge = 1e300;
+#else
+static double one = 1.0, huge = 1e300;
+#endif
+
+#ifdef __STDC__
+static const double zero = 0.0;
+#else
+static double zero = 0.0;
+#endif
+
+#ifdef __STDC__
+ double atanh(double x)
+#else
+ double atanh(x)
+ double x;
+#endif
+{
+ double t;
+ __int32_t hx,ix;
+ __uint32_t lx;
+ EXTRACT_WORDS(hx,lx,x);
+ ix = hx&0x7fffffff;
+ if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
+ return (x-x)/(x-x);
+ if(ix==0x3ff00000)
+ return x/zero;
+ if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */
+ SET_HIGH_WORD(x,ix);
+ if(ix<0x3fe00000) { /* x < 0.5 */
+ t = x+x;
+ t = 0.5*log1p(t+t*x/(one-x));
+ } else
+ t = 0.5*log1p((x+x)/(one-x));
+ if(hx>=0) return t; else return -t;
+}
+
+#endif /* defined(_DOUBLE_IS_32BITS) */