This is a Python implementation of the Helfgott-Thompson algorithm for computing the Mertens function.
Their original C++ code is available at https://arxiv.org/abs/2101.08773. The process of converting it to this code was roughly the following:
- Combine the four C++ files into a single file.
- Remove the pragmas that made it parallel.
- Translate it line-by-line directly into Python3. There are some hiccups here related to pointer arithmetic, negative arguments in the division and remainder operations, and bit-twiddling on fixed-length vs arbitrary-length integers.
- In some cases where a function is invoked only once, inline that function.
- Make some further changes so that it plays more nicely with the interpreter, such as splitting the compound data types into multiple non-compound types.
Most original comments were copied mostly verbatim, and a few of my own were added.
At some future point, I will attempt to put the parallelism back in, but for now, this is a single-threaded program.
No attempt has been made to tune the tunable parameters.