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