Fixed Point Arithmetic

[4meta5]

This is a subtle difficulty when working with computers. Floating point arithmetic is nondeterminisic so the basic approach is to use a wrapper type that represents either 1_000_000 (Permill) or 1_000_000_000 (Perbill) times the given floating point value.

I've learned recently that this can get messy. I think it's worth doing a recipe on this.

• Permill in docs

• StackOverflow Question

• Fixed64

[4meta5]

common pattern

1. start by defining a closure that converts all relevant inputs to the Perbill or Permill parts form; context of computation matters
2. next define all relevant inputs in terms of this form using the above closure or any on-paper arithmetic
3. perform intermediate computation with these large numbers => be careful of overflow
4. convert using Per{bill, mill}::from_parts(arg.min(billion as u32)

testing

• test with floating point numbers to ensure precision (using staking/inflation for guidance)

[4meta5]

focusing on treasury for the time being, waiting for more progress here: pull 3456, issue 3189

[JoshOrndorff]

Maybe the recipe should be called Fixed Point Arithmetic.

[JoshOrndorff]

Closed in #196