License issue with src/operator/contrib/erfinv-inl.h

[mseth10]

This file has a comment that states "Code is a direct translation of the erfinv m file in matlab version 2.0.”
https://github.com/apache/incubator-mxnet/blob/dba682a57812b49a222c04297224921393ea90bb/src/operator/contrib/erfinv-inl.h#L61-L62
Since Matlab is not open source software, it's basically a Category X software.

Proposed Solution

There are two commonly used methods for implementing the inverse error function:

• Initial approximation followed by two steps of Newton's method
  • Used by MATLAB (current implementation) - Category X license
  • Also used by Scilab (GPL license - also Category X): https://github.com/scilab/scilab/blob/master/scilab/modules/special_functions/macros/erfinv.sci
• Rational approximation of percentage points of normal distribution
  Used by SciPy (new BSD license): https://github.com/scipy/scipy/blob/master/scipy/special/cephes/erfinv.c

We can modify MXNet's erfinv function to use SciPy's implementation as SciPy's license is Apache compliant.

[szha]

Is the performance comparable between the translated solution and the scipy's implementation?

[mseth10]

Is the performance comparable between the translated solution and the scipy's implementation?

I can check for performance after getting SciPy's implementation to work and then post the results here.

[mseth10]

Do we have inverse normal distribution function in MXNet? Something similar to https://github.com/scipy/scipy/blob/master/scipy/special/cephes/ndtri.c @szha @leezu

[szha]

I don't recall if we have one

[mseth10]

Fixed by #20517