# Source file src/math/cmplx/log.go

## Documentation: math/cmplx

```     1  // Copyright 2010 The Go Authors. All rights reserved.
2  // Use of this source code is governed by a BSD-style
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  	return math.Log10E * Log(x)
64  }
65
```

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