Numbers: A generic wrapper to use *any* custom Numeric type!

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Hey guys! I am back from vacation, during which I had some great new ideas.

Numbers has been completely overhauled!

A release candidate for version five (v5.0.0-rc0) is now available on Hex. Please give it a whirl and let me know if you find any rough edges.

This is a major version release because the internal structure is completely changed (and some old exceptions that used to be thrown at certain times no longer exist):

  • Instead of one Numeric behaviours as previously, a whole set of Protocols is now used, so types are no longer required to implement all of the operations if only some of them make sense for a certain numeric type (and when you get into more niche mathematical realms like the realm of elliptic curves for instance, these things do happen very frequently).
  • Using protocols also means that libraries are no longer forced to use the (semi-arbitrarily) function names that Numbers uses for the different operations.
  • Dispatching based on (consolidated!) protocols also means that the library should be a lot more performant. Although I have not done any benchmarks, in the old version of the library there were a lot of extra run-time checks going on that are now unnecessary.
  • A new library called coerce now handles the optional coercion of data types. Previously, coercion was something that was completely handled at runtime. Now, most of it already happens at compile-time, meaning that coercion is probably a lot faster too. coerce also has a lot clearer, more explicit way to define coercions, which I am very happy about as well.
  • No longer ‘ad hoc’ Decimal support. Decimal is now an optional dependency with an explicit version number, and a Decimal-implementation of the protocols is made conditionally using Code.ensure_loaded?, so you’ll only need to add Numbers to e.g. your Phoenix project to get started. Since Numbers will automatically coerce integers and floats to decimals if the other number in an operation is a decimal, this might really increase the readability of your mathematical algorithms. Thanks to @ericmj for telling me about optional dependencies, and also for Decimal itself.

I am very eager for feedback! I feel Numbers is getting quite mature now. :grin:

A full-fledged version will be released as soon as I’m convinced there are no glaring oversights anymore, and I’ll update ComplexNum, Tensor, Rational and FunLand at the same time to support the new version as well.

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