1 // Copyright 2010 The Go Authors. All rights reserved. 2 // Use of this source code is governed by a BSD-style 3 // license that can be found in the LICENSE file. 4 5 package cmplx 6 7 import "math" 8 9 // The original C code, the long comment, and the constants 10 // below are from http://netlib.sandia.gov/cephes/c9x-complex/clog.c. 11 // The go code is a simplified version of the original C. 12 // 13 // Cephes Math Library Release 2.8: June, 2000 14 // Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier 15 // 16 // The readme file at http://netlib.sandia.gov/cephes/ says: 17 // Some software in this archive may be from the book _Methods and 18 // Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster 19 // International, 1989) or from the Cephes Mathematical Library, a 20 // commercial product. In either event, it is copyrighted by the author. 21 // What you see here may be used freely but it comes with no support or 22 // guarantee. 23 // 24 // The two known misprints in the book are repaired here in the 25 // source listings for the gamma function and the incomplete beta 26 // integral. 27 // 28 // Stephen L. Moshier 29 // [email protected] 30 31 // Complex natural logarithm 32 // 33 // DESCRIPTION: 34 // 35 // Returns complex logarithm to the base e (2.718...) of 36 // the complex argument z. 37 // 38 // If 39 // z = x + iy, r = sqrt( x**2 + y**2 ), 40 // then 41 // w = log(r) + i arctan(y/x). 42 // 43 // The arctangent ranges from -PI to +PI. 44 // 45 // ACCURACY: 46 // 47 // Relative error: 48 // arithmetic domain # trials peak rms 49 // DEC -10,+10 7000 8.5e-17 1.9e-17 50 // IEEE -10,+10 30000 5.0e-15 1.1e-16 51 // 52 // Larger relative error can be observed for z near 1 +i0. 53 // In IEEE arithmetic the peak absolute error is 5.2e-16, rms 54 // absolute error 1.0e-16. 55 56 // Log returns the natural logarithm of x. 57 func Log(x complex128) complex128 { 58 return complex(math.Log(Abs(x)), Phase(x)) 59 } 60 61 // Log10 returns the decimal logarithm of x. 62 func Log10(x complex128) complex128 { 63 z := Log(x) 64 return complex(math.Log10E*real(z), math.Log10E*imag(z)) 65 } 66