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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. 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) }