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