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+// Copyright 2009 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package math
+
+/*
+	Floating-point arctangent.
+*/
+
+// The original C code, the long comment, and the constants below were
+// from http://netlib.sandia.gov/cephes/cmath/atan.c, available from
+// http://www.netlib.org/cephes/cmath.tgz.
+// The go code is a version of the original C.
+//
+// atan.c
+// Inverse circular tangent (arctangent)
+//
+// SYNOPSIS:
+// double x, y, atan();
+// y = atan( x );
+//
+// DESCRIPTION:
+// Returns radian angle between -pi/2 and +pi/2 whose tangent is x.
+//
+// Range reduction is from three intervals into the interval from zero to 0.66.
+// The approximant uses a rational function of degree 4/5 of the form
+// x + x**3 P(x)/Q(x).
+//
+// ACCURACY:
+//                      Relative error:
+// arithmetic   domain    # trials  peak     rms
+//    DEC       -10, 10   50000     2.4e-17  8.3e-18
+//    IEEE      -10, 10   10^6      1.8e-16  5.0e-17
+//
+// Cephes Math Library Release 2.8:  June, 2000
+// Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
+//
+// The readme file at http://netlib.sandia.gov/cephes/ says:
+//    Some software in this archive may be from the book _Methods and
+// Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
+// International, 1989) or from the Cephes Mathematical Library, a
+// commercial product. In either event, it is copyrighted by the author.
+// What you see here may be used freely but it comes with no support or
+// guarantee.
+//
+//   The two known misprints in the book are repaired here in the
+// source listings for the gamma function and the incomplete beta
+// integral.
+//
+//   Stephen L. Moshier
+//   moshier@na-net.ornl.gov
+
+// xatan evaluates a series valid in the range [0, 0.66].
+func xatan(x float64) float64 {
+	const (
+		P0 = -8.750608600031904122785e-01
+		P1 = -1.615753718733365076637e+01
+		P2 = -7.500855792314704667340e+01
+		P3 = -1.228866684490136173410e+02
+		P4 = -6.485021904942025371773e+01
+		Q0 = +2.485846490142306297962e+01
+		Q1 = +1.650270098316988542046e+02
+		Q2 = +4.328810604912902668951e+02
+		Q3 = +4.853903996359136964868e+02
+		Q4 = +1.945506571482613964425e+02
+	)
+	z := x * x
+	z = z * ((((P0*z+P1)*z+P2)*z+P3)*z + P4) / (((((z+Q0)*z+Q1)*z+Q2)*z+Q3)*z + Q4)
+	z = x*z + x
+	return z
+}
+
+// satan reduces its argument (known to be positive)
+// to the range [0, 0.66] and calls xatan.
+func satan(x float64) float64 {
+	const (
+		Morebits = 6.123233995736765886130e-17 // pi/2 = PIO2 + Morebits
+		Tan3pio8 = 2.41421356237309504880      // tan(3*pi/8)
+	)
+	if x <= 0.66 {
+		return xatan(x)
+	}
+	if x > Tan3pio8 {
+		return Pi/2 - xatan(1/x) + Morebits
+	}
+	return Pi/4 + xatan((x-1)/(x+1)) + 0.5*Morebits
+}
+
+// Atan returns the arctangent, in radians, of x.
+//
+// Special cases are:
+//      Atan(±0) = ±0
+//      Atan(±Inf) = ±Pi/2
+func Atan(x float64) float64 {
+	if haveArchAtan {
+		return archAtan(x)
+	}
+	return atan(x)
+}
+
+func atan(x float64) float64 {
+	if x == 0 {
+		return x
+	}
+	if x > 0 {
+		return satan(x)
+	}
+	return -satan(-x)
+}