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# Source file src/math/cmplx/exp.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 exponential function
32  //
33  // DESCRIPTION:
34  //
35  // Returns the complex exponential of the complex argument z.
36  //
37  // If
38  //     z = x + iy,
39  //     r = exp(x),
40  // then
41  //     w = r cos y + i r sin y.
42  //
43  // ACCURACY:
44  //
45  //                      Relative error:
46  // arithmetic   domain     # trials      peak         rms
47  //    DEC       -10,+10      8700       3.7e-17     1.1e-17
48  //    IEEE      -10,+10     30000       3.0e-16     8.7e-17
49
50  // Exp returns e**x, the base-e exponential of x.
51  func Exp(x complex128) complex128 {
52  	switch re, im := real(x), imag(x); {
53  	case math.IsInf(re, 0):
54  		switch {
55  		case re > 0 && im == 0:
56  			return x
57  		case math.IsInf(im, 0) || math.IsNaN(im):
58  			if re < 0 {
59  				return complex(0, math.Copysign(0, im))
60  			} else {
61  				return complex(math.Inf(1.0), math.NaN())
62  			}
63  		}
64  	case math.IsNaN(re):
65  		if im == 0 {
66  			return complex(math.NaN(), im)
67  		}
68  	}
69  	r := math.Exp(real(x))
70  	s, c := math.Sincos(imag(x))
71  	return complex(r*c, r*s)
72  }
73
```

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