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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

func isOddInt(x float64) bool {
        xi, xf := Modf(x)
        return xf == 0 && int64(xi)&1 == 1
}

// Special cases taken from FreeBSD's /usr/src/lib/msun/src/e_pow.c
// updated by IEEE Std. 754-2008 "Section 9.2.1 Special values".

// Pow returns x**y, the base-x exponential of y.
//
// Special cases are (in order):
//      Pow(x, ±0) = 1 for any x
//      Pow(1, y) = 1 for any y
//      Pow(x, 1) = x for any x
//      Pow(NaN, y) = NaN
//      Pow(x, NaN) = NaN
//      Pow(±0, y) = ±Inf for y an odd integer < 0
//      Pow(±0, -Inf) = +Inf
//      Pow(±0, +Inf) = +0
//      Pow(±0, y) = +Inf for finite y < 0 and not an odd integer
//      Pow(±0, y) = ±0 for y an odd integer > 0
//      Pow(±0, y) = +0 for finite y > 0 and not an odd integer
//      Pow(-1, ±Inf) = 1
//      Pow(x, +Inf) = +Inf for |x| > 1
//      Pow(x, -Inf) = +0 for |x| > 1
//      Pow(x, +Inf) = +0 for |x| < 1
//      Pow(x, -Inf) = +Inf for |x| < 1
//      Pow(+Inf, y) = +Inf for y > 0
//      Pow(+Inf, y) = +0 for y < 0
//      Pow(-Inf, y) = Pow(-0, -y)
//      Pow(x, y) = NaN for finite x < 0 and finite non-integer y
func Pow(x, y float64) float64 {
        switch {
        case y == 0 || x == 1:
                return 1
        case y == 1:
                return x
        case y == 0.5:
                return Sqrt(x)
        case y == -0.5:
                return 1 / Sqrt(x)
        case IsNaN(x) || IsNaN(y):
                return NaN()
        case x == 0:
                switch {
                case y < 0:
                        if isOddInt(y) {
                                return Copysign(Inf(1), x)
                        }
                        return Inf(1)
                case y > 0:
                        if isOddInt(y) {
                                return x
                        }
                        return 0
                }
        case IsInf(y, 0):
                switch {
                case x == -1:
                        return 1
                case (Abs(x) < 1) == IsInf(y, 1):
                        return 0
                default:
                        return Inf(1)
                }
        case IsInf(x, 0):
                if IsInf(x, -1) {
                        return Pow(1/x, -y) // Pow(-0, -y)
                }
                switch {
                case y < 0:
                        return 0
                case y > 0:
                        return Inf(1)
                }
        }

        absy := y
        flip := false
        if absy < 0 {
                absy = -absy
                flip = true
        }
        yi, yf := Modf(absy)
        if yf != 0 && x < 0 {
                return NaN()
        }
        if yi >= 1<<63 {
                return Exp(y * Log(x))
        }

        // ans = a1 * 2**ae (= 1 for now).
        a1 := 1.0
        ae := 0

        // ans *= x**yf
        if yf != 0 {
                if yf > 0.5 {
                        yf--
                        yi++
                }
                a1 = Exp(yf * Log(x))
        }

        // ans *= x**yi
        // by multiplying in successive squarings
        // of x according to bits of yi.
        // accumulate powers of two into exp.
        x1, xe := Frexp(x)
        for i := int64(yi); i != 0; i >>= 1 {
                if i&1 == 1 {
                        a1 *= x1
                        ae += xe
                }
                x1 *= x1
                xe <<= 1
                if x1 < .5 {
                        x1 += x1
                        xe--
                }
        }

        // ans = a1*2**ae
        // if flip { ans = 1 / ans }
        // but in the opposite order
        if flip {
                a1 = 1 / a1
                ae = -ae
        }
        return Ldexp(a1, ae)
}