[MPS] Adding lgamma, digamma, and polygamma implementations (#106292)
Fixes issue mentioned in #77764
e.g. https://github.com/pytorch/pytorch/issues/77764#issuecomment-1654111744
Adds MPS support for the following ops:
- lgamma
- mvlgamma
- digamma
- polygamma
The lgamma fucntion does not yet have an MPS backend implementation. I've added one using a custom metal kernel (following John D. Cook's c++ implementation of the log gamma function: https://www.johndcook.com/blog/cpp_gamma/). For the backward pass op, I've added a digamma kernel that follows the cpu+cuda digamma implementation, and for the backward pass of the digamma op, I've added a polygamma + trigamma kernel following, again, the cpu+cuda implementations.
NOTE:
The cpu implementation of the polygamma function incorrectly (as far as I can tell) outputs a finite number for order = 1 and x in the negative integers. The mps implementation correctly outputs infinite. (see https://github.com/pytorch/pytorch/issues/106692)
The polygamma tests currently don't pass because of the error in the cpu+cuda kernels, but also because there are smallish discrepancies near the negative integers between the cpu+cuda and the mps polygamma and trigamma kernels. I'm not sure exactly why this is, but let me know if the discrepancies are too big.
Pull Request resolved: https://github.com/pytorch/pytorch/pull/106292
Approved by: https://github.com/kulinseth
