[IronPython] Math accuracy?

[Keith J. Farmer]

Here's a *VERY* naïve solution (ie, a 4am solution) for complex ^ positiveInt.  It could be improved by generating the binomial expansion directly for n and avoiding a bunch of extra Complex64 instantiations.

IronPython 0.9.1 on .NET 2.0.50215.44

Copyright (c) Microsoft Corporation. All rights reserved.

>>> a = 1j

>>> a ** 2

(-1+0j)

>>> a ** 1

1j

>>> a ** 0

(1+0j)

>>> a ** 3

-1j

>>> a ** 4

(1+0j)

-----

Keith J. Farmer

kfarmer at thuban.org

 

            public Complex64 Power(Complex64 y)

            {

                  double a = real;

                  double b = imag;

                  double c = y.real;

                  double d = y.imag;

 

                  if (Math.Truncate(c) == c && d == 0 && c >= 0)

                  {

                        switch ((int) c)

                        {

                              case 0: 

                                    return new Complex64(1, 0);

                              case 1:

                                    return this;

                              case 2:

                                    {

                                          double newReal = a * a - b * b;

                                          double newImaginary = 2 * a * b;

 

                                          return new Complex64(newReal, newImaginary);

                                    }

                              default:

                                    {

                                          double newReal = a * a - b * b;

                                          double newImaginary = 2 * a * b;

 

                                          return (new Complex64(newReal, newImaginary)) * this.Power(new Complex64(c-2, 0));

                                    }

                        }

                  }

 

                  double powers = a * a + b * b;

                  double arg = Math.Atan2(b, a);

                  double mul = Math.Pow(powers, c / 2) * Math.Pow(Math.E, -d * arg);

                  double common = c * arg + .5 * d * Math.Log(powers, Math.E);

 

                  return new Complex64(mul * Math.Cos(common), mul * Math.Sin(common));

            }

 

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