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 5 package cmplx 6 7 import "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. 49 func 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