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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.

        Atan returns the value of the arctangent of its

        argument in the range [-pi/2,pi/2].

        There are no error returns.

        Coefficients are #5077 from Hart & Cheney. (19.56D)

*/

// xatan evaluates a series valid in the

// range [-0.414...,+0.414...]. (tan(pi/8))

func xatan(arg float64) float64 {

        const (

                P4 = .161536412982230228262e2

                P3 = .26842548195503973794141e3

                P2 = .11530293515404850115428136e4

                P1 = .178040631643319697105464587e4

                P0 = .89678597403663861959987488e3

                Q4 = .5895697050844462222791e2

                Q3 = .536265374031215315104235e3

                Q2 = .16667838148816337184521798e4

                Q1 = .207933497444540981287275926e4

                Q0 = .89678597403663861962481162e3

        )

        sq := arg * arg

        value := ((((P4*sq+P3)*sq+P2)*sq+P1)*sq + P0)

        value = value / (((((sq+Q4)*sq+Q3)*sq+Q2)*sq+Q1)*sq + Q0)

        return value * arg

}

// satan reduces its argument (known to be positive)

// to the range [0,0.414...] and calls xatan.

func satan(arg float64) float64 {

        if arg < Sqrt2-1 {

                return xatan(arg)

        }

        if arg > Sqrt2+1 {

                return Pi/2 - xatan(1/arg)

        }

        return Pi/4 + xatan((arg-1)/(arg+1))

}

// Atan returns the arctangent of x.

//

// Special cases are:

//      Atan(±0) = ±0

//      Atan(±Inf) = ±Pi/2

//extern atan

func libc_atan(float64) float64

func Atan(x float64) float64 {

        return libc_atan(x)

}

func atan(x float64) float64 {

        if x == 0 {

                return x

        }

        if x > 0 {

                return satan(x)

        }

        return -satan(-x)

}