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 // 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.
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