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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

// Atan2 returns the arc tangent of y/x, using
// the signs of the two to determine the quadrant
// of the return value.
//
// Special cases are (in order):
//      Atan2(y, NaN) = NaN
//      Atan2(NaN, x) = NaN
//      Atan2(+0, x>=0) = +0
//      Atan2(-0, x>=0) = -0
//      Atan2(+0, x<=-0) = +Pi
//      Atan2(-0, x<=-0) = -Pi
//      Atan2(y>0, 0) = +Pi/2
//      Atan2(y<0, 0) = -Pi/2
//      Atan2(+Inf, +Inf) = +Pi/4
//      Atan2(-Inf, +Inf) = -Pi/4
//      Atan2(+Inf, -Inf) = 3Pi/4
//      Atan2(-Inf, -Inf) = -3Pi/4
//      Atan2(y, +Inf) = 0
//      Atan2(y>0, -Inf) = +Pi
//      Atan2(y<0, -Inf) = -Pi
//      Atan2(+Inf, x) = +Pi/2
//      Atan2(-Inf, x) = -Pi/2

//extern atan2
func libc_atan2(float64, float64) float64

func Atan2(y, x float64) float64 {
        return libc_atan2(y, x)
}

func atan2(y, x float64) float64 {
        // special cases
        switch {
        case IsNaN(y) || IsNaN(x):
                return NaN()
        case y == 0:
                if x >= 0 && !Signbit(x) {
                        return Copysign(0, y)
                }
                return Copysign(Pi, y)
        case x == 0:
                return Copysign(Pi/2, y)
        case IsInf(x, 0):
                if IsInf(x, 1) {
                        switch {
                        case IsInf(y, 0):
                                return Copysign(Pi/4, y)
                        default:
                                return Copysign(0, y)
                        }
                }
                switch {
                case IsInf(y, 0):
                        return Copysign(3*Pi/4, y)
                default:
                        return Copysign(Pi, y)
                }
        case IsInf(y, 0):
                return Copysign(Pi/2, y)
        }

        // Call atan and determine the quadrant.
        q := Atan(y / x)
        if x < 0 {
                if q <= 0 {
                        return q + Pi
                }
                return q - Pi
        }
        return q
}