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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)
}