| // 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 cmath |
| |
| 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 cmplx(math.Log(Abs(x)), Phase(x)) |
| } |
| |
| // Log10 returns the decimal logarithm of x. |
| func Log10(x complex128) complex128 { |
| return math.Log10E * Log(x) |
| } |