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 5package cmplx 6 7import "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// moshier@na-net.ornl.gov 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. 57func Log(x complex128) complex128 { 58 return complex(math.Log(Abs(x)), Phase(x)) 59} 60 61// Log10 returns the decimal logarithm of x. 62func Log10(x complex128) complex128 { 63 z := Log(x) 64 return complex(math.Log10E*real(z), math.Log10E*imag(z)) 65} 66