| // 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) | |
| } | |