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# Source file src/math/cmplx/pow.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 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  //	Pow(0, ±0) returns 1+0i
48  //	Pow(0, c) for real(c)<0 returns Inf+0i if imag(c) is zero, otherwise Inf+Inf i.
49  func Pow(x, y complex128) complex128 {
50  	if x == 0 { // Guaranteed also true for x == -0.
51  		if IsNaN(y) {
52  			return NaN()
53  		}
54  		r, i := real(y), imag(y)
55  		switch {
56  		case r == 0:
57  			return 1
58  		case r < 0:
59  			if i == 0 {
60  				return complex(math.Inf(1), 0)
61  			}
62  			return Inf()
63  		case r > 0:
64  			return 0
65  		}
66  		panic("not reached")
67  	}
68  	modulus := Abs(x)
69  	if modulus == 0 {
70  		return complex(0, 0)
71  	}
72  	r := math.Pow(modulus, real(y))
73  	arg := Phase(x)
74  	theta := real(y) * arg
75  	if imag(y) != 0 {
76  		r *= math.Exp(-imag(y) * arg)
77  		theta += imag(y) * math.Log(modulus)
78  	}
79  	s, c := math.Sincos(theta)
80  	return complex(r*c, r*s)
81  }
82
```

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