Generalized exponential integral En

I worked on this function during my Google Summer of Code internship. Relevant PR: cupy/cupy#6790.

The expression for expn is defined by:

Note: n ≥ 0 and real x ≥ 0.

More about expn in CuPy Documentation: https://docs.cupy.dev/en/stable/reference/generated/cupyx.scipy.special.expn.html#cupyx.scipy.special.expn

Key Notes:

• The function expn defined here is numerically stable and all the features are tested using GoogleTests.
• In CuPy this function is implemented by calling ufuncs for speedy implementation in GPU.
• We achieved nearly 40x times faster results in CuPy.
• Intiliatty, in the CuPy loop unrolling technique, was used in the polevl definition for compile-time optimization to get better speed. But we changed the implementation with a runtime argument as required by the function.

Acknowledgement

Thanks to my mentor Masayuki Takagi for his guidance, for reviewing my work, and for giving valuable suggestions in PR.