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// Copyright 2010 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 cmplx

import "math"

// The original C code, the long comment, and the constants

// below are from http://netlib.sandia.gov/cephes/c9x-complex/clog.c.

// The go code is a simplified version of the original C.

//

// 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

// Complex power function

//

// DESCRIPTION:

//

// Raises complex A to the complex Zth power.

// Definition is per AMS55 # 4.2.8,

// analytically equivalent to cpow(a,z) = cexp(z clog(a)).

//

// ACCURACY:

//

//                      Relative error:

// arithmetic   domain     # trials      peak         rms

//    IEEE      -10,+10     30000       9.4e-15     1.5e-15

// Pow returns x**y, the base-x exponential of y.

func Pow(x, y complex128) complex128 {

        modulus := Abs(x)

        if modulus == 0 {

                return complex(0, 0)

        }

        r := math.Pow(modulus, real(y))

        arg := Phase(x)

        theta := real(y) * arg

        if imag(y) != 0 {

                r *= math.Exp(-imag(y) * arg)

                theta += imag(y) * math.Log(modulus)

        }

        s, c := math.Sincos(theta)

        return complex(r*c, r*s)

}