errors-and-erasures universal decoding + fast encoding

[lrq3000]

Hi there,

I needed a fast pure-python implementation of Reed-Solomon, and since I wanted it to be as resilient as possible, I did a big rewrite of this library to add the following features:

• full support of errors-and-erasures decoding (it already worked before using Forney syndrome, but now it's not even necessary, and I worked the edge cases so that it always decodes correctly, and I also added the management of erasures in the API).
• support universal parametrization (we can now specify the parameters of the GF field and the FCR so that this lib is now compatible with almost any other RS codec)
• fast encoding/decoding (with PyPy 2.5 or Cython, the latter being about 2x faster than PyPy on pure-python). You can expect an encoding speed of > 3 MB/s.
• Added very strict unit tests, one being called "CrossValidation" which tests lots of different combinations of GF fields, RS parameters and errors/erasures to check that they all decode correctly (this is a good sanity check that the RS codec works correctly and is universal, and it's not slow to compute).
• Added lots of comments!

I'm finishing updating the tutorial on wikiversity, so that you can check it out to better understand the code.

[lrq3000]

The Travis build fails because of Cython. I'm not really used to Travis so I don't know how to fix that... But I've found this that may be of help: https://github.com/msabramo/cython-test

[lrq3000]

Ok finally fixed the compatibility issues without hitting the performance. Only PyPy fails, and it's only because it can't run the Cython extension (this is normal, PyPy is not yet compatible with Cython), and I don't know how to configure Travis to exclude the cython test only when in the pypy env, but I have set the pypy env as failure acceptable, so the final build is not affected. To summary, PyPy runs ok, the build is completely OK.

[tomerfiliba]

thanks