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 (a] 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 r, i := real(y), imag(y) 52 switch { 53 case r == 0: 54 return 1 55 case r < 0: 56 if i == 0 { 57 return complex(math.Inf(1), 0) 58 } 59 return Inf() 60 case r > 0: 61 return 0 62 } 63 panic("not reached") 64 } 65 modulus := Abs(x) 66 if modulus == 0 { 67 return complex(0, 0) 68 } 69 r := math.Pow(modulus, real(y)) 70 arg := Phase(x) 71 theta := real(y) * arg 72 if imag(y) != 0 { 73 r *= math.Exp(-imag(y) * arg) 74 theta += imag(y) * math.Log(modulus) 75 } 76 s, c := math.Sincos(theta) 77 return complex(r*c, r*s) 78 } 79
