| // 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)) | |
| } | |