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 ( float64) float64 {
	const (
		 = -8.750608600031904122785e-01
		 = -1.615753718733365076637e+01
		 = -7.500855792314704667340e+01
		 = -1.228866684490136173410e+02
		 = -6.485021904942025371773e+01
		 = +2.485846490142306297962e+01
		 = +1.650270098316988542046e+02
		 = +4.328810604912902668951e+02
		 = +4.853903996359136964868e+02
		 = +1.945506571482613964425e+02
	)
	 :=  * 
	 =  * ((((*+)*+)*+)* + ) / (((((+)*+)*+)*+)* + )
	 = * + 
	return 
}
satan reduces its argument (known to be positive) to the range [0, 0.66] and calls xatan.
func ( float64) float64 {
	const (
		 = 6.123233995736765886130e-17 // pi/2 = PIO2 + Morebits
		 = 2.41421356237309504880      // tan(3*pi/8)
	)
	if  <= 0.66 {
		return xatan()
	}
	if  >  {
		return Pi/2 - xatan(1/) + 
	}
	return Pi/4 + xatan((-1)/(+1)) + 0.5*
}
Atan returns the arctangent, in radians, of x. Special cases are: Atan(±0) = ±0 Atan(±Inf) = ±Pi/2
func ( float64) float64

func ( float64) float64 {
	if  == 0 {
		return 
	}
	if  > 0 {
		return satan()
	}
	return -satan(-)