Pnum32

[eschnett]

Thanks for your presentation today -- very cool.

I managed to easily extend your package to provide a type Pnum32 as well. I couldn't really expand the exponent range (that doesn't work with Rational), and initializing the exacts array takes a long time. Apart from this, the new type works just fine and is quite efficient:

julia> @time findroots(x->x^2-2, pb32"everything") |> Pnums.print_decimal
(-1.4142135977745056, -1.4142135381698608)
(1.4142135381698608, 1.4142135977745056)
  0.019251 seconds (285.87 k allocations: 4.816 MB)

If I calculate correctly, this type has even more precision than Float32.

Getting around the exacts limitation would probably require two steps:

• Don't store all values; instead, use a function that calculates them just-in time.
• Don't use Rational to represent them; instead, represent them by Rational with an exponent. That will require either handling rounding during addition, or using BigInt if necessary.

[jwmerrill]

That's awesome. I'm glad you were able to dive in and extend things reasonably easily.

I think avoiding actually storing the exacts is a good idea, as long as you've chosen then in a way that it's reasonably easy to do binary search on their ordered values.

Not sure what to do about extending the exponent.