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Source file src/math/cmplx/log.go

Documentation: math/cmplx

  // 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 natural logarithm
  //
  // DESCRIPTION:
  //
  // Returns complex logarithm to the base e (2.718...) of
  // the complex argument z.
  //
  // If
  //       z = x + iy, r = sqrt( x**2 + y**2 ),
  // then
  //       w = log(r) + i arctan(y/x).
  //
  // The arctangent ranges from -PI to +PI.
  //
  // ACCURACY:
  //
  //                      Relative error:
  // arithmetic   domain     # trials      peak         rms
  //    DEC       -10,+10      7000       8.5e-17     1.9e-17
  //    IEEE      -10,+10     30000       5.0e-15     1.1e-16
  //
  // Larger relative error can be observed for z near 1 +i0.
  // In IEEE arithmetic the peak absolute error is 5.2e-16, rms
  // absolute error 1.0e-16.
  
  // Log returns the natural logarithm of x.
  func Log(x complex128) complex128 {
  	return complex(math.Log(Abs(x)), Phase(x))
  }
  
  // Log10 returns the decimal logarithm of x.
  func Log10(x complex128) complex128 {
  	return math.Log10E * Log(x)
  }
  

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