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Source file src/math/cmplx/pow.go

  // 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.
  		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)
  }
  

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