````// 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 {`
`	z := Log(x)`
`	return complex(math.Log10E*real(z), math.Log10E*imag(z))`
`}`
```