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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 natural logarithm

//

// DESCRIPTION:

//

// Returns complex logarithm to the base e (2.718...) of

// the complex argument z.

//

// If

//       z = x + iy, r = sqrt( x**2 + y**2 ),

// then

//       w = log(r) + i arctan(y/x).

//

// The arctangent ranges from -PI to +PI.

//

// ACCURACY:

//

//                      Relative error:

// arithmetic   domain     # trials      peak         rms

//    DEC       -10,+10      7000       8.5e-17     1.9e-17

//    IEEE      -10,+10     30000       5.0e-15     1.1e-16

//

// Larger relative error can be observed for z near 1 +i0.

// In IEEE arithmetic the peak absolute error is 5.2e-16, rms

// absolute error 1.0e-16.

// Log returns the natural logarithm of x.

func Log(x complex128) complex128 {

        return complex(math.Log(Abs(x)), Phase(x))

}

// Log10 returns the decimal logarithm of x.

func Log10(x complex128) complex128 {

        return math.Log10E * Log(x)

}