Elementary functions worklist

[fredrik-johansson]

Things to do in the future:

• Move all elementary function internals to a separate module since it's a lot of code that doesn't need to be visible in arb.h
• Right now the call sequence to dispatch to different algorithms is a bit of labyrinth. It would make sense to clean this up and have good interfaces for all algorithms (not restricted to an arf_t argument, no implicit restrictions like |x| < 1) for easy comparison
• Much stronger test code
• Better Taylor series code for small arguments
• Very carefully benchmark different combinations of precision and argument
• Optimize memory usage
• Maybe make caching/lookup table limits configurable at runtime
• Add high-precision rectangular splitting code for log and atan and use with direct argument reduction at appropriate precisions instead of Newton iteration
• When caching multiple logarithms/arctangents, we compute log(2) and pi as a byproduct. We could then update the cached values of those constants
• Optimize non-primary functions (asin, sinh, ...)
• Optimize nth roots
• Optimize for low precision (1-2 words)
• Deduplicate binary splitting code
• Add fmpq versions
• Optimize roots of unity
• Maybe reduce the precision of the lookup tables since the cutoffs for all functions are much lower than 4608 bits now
• Look into parallelizing parts that remain serial
• Optimize pi computation
• Add functions for jets of elementary functions
• Try a hybrid RS+BB algorithm (one or two BB steps followed by RS)