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Source file src/math/cmplx/pow.go

     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			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	

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