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 power function
32//
33// DESCRIPTION:
34//
35// Raises complex A to the complex Zth power.
36// Definition is per AMS55 # 4.2.8,
37// analytically equivalent to cpow(a,z) = cexp(z clog(a)).
38//
39// ACCURACY:
40//
41//                      Relative error:
42// arithmetic   domain     # trials      peak         rms
43//    IEEE      -10,+10     30000       9.4e-15     1.5e-15
44
45// Pow returns x**y, the base-x exponential of y.
46// For generalized compatibility with [math.Pow]:
47//
48//	Pow(0, ±0) returns 1+0i
49//	Pow(0, c) for real(c)<0 returns Inf+0i if imag(c) is zero, otherwise Inf+Inf i.
50func Pow(x, y complex128) complex128 {
51	if x == 0 { // Guaranteed also true for x == -0.
52		if IsNaN(y) {
53			return NaN()
54		}
55		r, i := real(y), imag(y)
56		switch {
57		case r == 0:
58			return 1
59		case r < 0:
60			if i == 0 {
61				return complex(math.Inf(1), 0)
62			}
63			return Inf()
64		case r > 0:
65			return 0
66		}
67		panic("not reached")
68	}
69	modulus := Abs(x)
70	if modulus == 0 {
71		return complex(0, 0)
72	}
73	r := math.Pow(modulus, real(y))
74	arg := Phase(x)
75	theta := real(y) * arg
76	if imag(y) != 0 {
77		r *= math.Exp(-imag(y) * arg)
78		theta += imag(y) * math.Log(modulus)
79	}
80	s, c := math.Sincos(theta)
81	return complex(r*c, r*s)
82}
83