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//   [email protected]
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.
51func 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