Taichi: General power operator x ** y

[yuanming-hu]

Concisely describe the proposed feature
Allow using x ** y in Taichi kernels

Describe the solution you'd like
In the preprocessor, convert x ** y into ti.pow(x, y).
Add a binary operator pow to the IR and codegen.

Implementing this feature will help the contributor understand the Taichi compiler code structure. Assigning this task to our great intern @xumingkuan as a practice.

Issue raised here: https://forum.taichi.graphics/t/the-right-use-method-of-sqrt/68

[archibate]

What a great chance to dive into the Taichi compiler! May I have a try (just for exercise)?

[yuanming-hu]

Sure, thanks! Let's reduce some burden on @xumingkuan then.

[yuanming-hu]

If either of you guys are interested, we can also implement its gradients for differentiable programming:

d(x^y)/dx: https://www.wolframalpha.com/input/?i=d%28x%5Ey%29%2Fdx
d(x^y)/dy: https://www.wolframalpha.com/input/?i=d%28x%5Ey%29%2Fdy

Code to modify:

https://github.com/taichi-dev/taichi/blob/d76c64fc27d32daeb4446f204c2b8000877dea3a/taichi/transforms/make_adjoint.cpp#L184

[Psycho7]

Just passing by. Duplicated with #247?

[yuanming-hu]

This is nicely implemented by @archibate.