| // 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 cmath |
| |
| 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. |
| func Pow(x, y complex128) complex128 { |
| 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) |
| } |
