1// Copyright 2010 The Go Authors. All rights reserved. 2// Use of this source code is governed by a BSD-style 3// license that can be found in the LICENSE file. 4 5package cmplx 6 7import "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. 49func 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