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// Copyright 2010 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package cmplx
import "math"
// The original C code, the long comment, and the constants
// below are from http://netlib.sandia.gov/cephes/c9x-complex/clog.c.
// The go code is a simplified version of the original C.
//
// Cephes Math Library Release 2.8: June, 2000
// Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
//
// The readme file at http://netlib.sandia.gov/cephes/ says:
// Some software in this archive may be from the book _Methods and
// Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
// International, 1989) or from the Cephes Mathematical Library, a
// commercial product. In either event, it is copyrighted by the author.
// What you see here may be used freely but it comes with no support or
// guarantee.
//
// The two known misprints in the book are repaired here in the
// source listings for the gamma function and the incomplete beta
// integral.
//
// Stephen L. Moshier
// moshier@na-net.ornl.gov
// Complex power function
//
// DESCRIPTION:
//
// Raises complex A to the complex Zth power.
// Definition is per AMS55 # 4.2.8,
// analytically equivalent to cpow(a,z) = cexp(z clog(a)).
//
// ACCURACY:
//
// Relative error:
// arithmetic domain # trials peak rms
// IEEE -10,+10 30000 9.4e-15 1.5e-15
// Pow returns x**y, the base-x exponential of y.
// For generalized compatibility with [math.Pow]:
//
// Pow(0, ±0) returns 1+0i
// Pow(0, c) for real(c)<0 returns Inf+0i if imag(c) is zero, otherwise Inf+Inf i.
func Pow(x, y complex128) complex128 {
if x == 0 { // Guaranteed also true for x == -0.
if IsNaN(y) {
return NaN()
}
r, i := real(y), imag(y)
switch {
case r == 0:
return 1
case r < 0:
if i == 0 {
return complex(math.Inf(1), 0)
}
return Inf()
case r > 0:
return 0
}
panic("not reached")
}
modulus := Abs(x)
if modulus == 0 {
return complex(0, 0)
}
r := math.Pow(modulus, real(y))
arg := Phase(x)
theta := real(y) * arg
if imag(y) != 0 {
r *= math.Exp(-imag(y) * arg)
theta += imag(y) * math.Log(modulus)
}
s, c := math.Sincos(theta)
return complex(r*c, r*s)
}