@varunagrawal : this looks excellent. I'll leave the question of (re)naming of GncHelper to @dellaert . My only comment/suggestion would be to add a few more unit tests. This is a quite basic functionality and it we get it wrong, it might be very hard to debug in downstream applications.

I looked at various implementations from both Boost and GCEM to understand how Halley's algorithm worked and how to deal with different datatypes effectively, but I wrote this pretty much on my own.

After some thought, I am considering these changes:

1. Rename GncHelpers to chiSquaredInverse.hpp.
2. Move it to nonlinear/internal since it is mostly for internal usage.
3. Unit test each individual function. I read up on how Boost does this and will do similar things.
4. Improve docs as I go along.

I looked at various implementations from both Boost and GCEM to understand how Halley's algorithm worked and how to deal with different datatypes effectively, but I wrote this pretty much on my own.

After some thought, I am considering these changes:

1. Rename GncHelpers to chiSquaredInverse.hpp.
2. Move it to nonlinear/internal since it is mostly for internal usage.
3. Unit test each individual function. I read up on how Boost does this and will do similar things.
4. Improve docs as I go along.

Sounds good. Please do document the above. Having straight copies of code from boost where possible would be preferable as those functions would not have to be unit-tested, and it is acceptable under their license.

...with attribution, of course

I wanted to give a quick update on this:

1. Adding code from Boost was getting really unwieldy, resulting in copy-paste of over a dozen files for computing the incomplete gamma function (this is used to compute the chi-squared inverse easily). This code was also getting far too complicated for long-term maintenance.
2. I did some looking around and found cephes which gives us everything we need in a really lightweight C library. Moreover scipy uses cephes for their implementation of the incomplete gamma inverse function so it is production grade.
3. Cephes is released under a very liberal license which makes bundling it under 3rdparty really easy.
4. As a result, I added cephes to 3rdparty and got it compiling. The overall PR now is much simpler with much of the work being offloaded to cephes.

Cephes license can be found here: https://smath.com/en-US/view/CephesMathLibrary/license