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 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