Using https://docs.rs/num-bigint/latest/num_bigint/ in units conversion

[younies]

We would like to check the feasibility for using num bigint in order to represent the numerator and denominator for the conversion factors.

1. Supporting std can be turned off
2. The data stored in a vector of Bigdigit Vec<BigDigit> and we can choose the type BigDigit to be u32 or u64. See the snippet of the code bellow
3. It supports the basic calculation operations such as mul, div and mod.

mod big_digit {
    /// A [`BigDigit`] is a [`BigUint`]'s composing element.
    #[cfg(not(u64_digit))]
    pub(crate) type BigDigit = u32;
    #[cfg(u64_digit)]
    pub(crate) type BigDigit = u64;

[sffc]

I think the latest PR uses fraction::GenericFraction<num_bigint::BigUint> which seems good to me.

[sffc]

Discuss with:

• @younies
• @sffc
• @robertbastian

Optional:

• @Manishearth

[sffc]

• @robertbastian - the num crates seem more polished
• @younies - I like GenericFraction at least for data generation because I can use BigUInt for the numerator and denominator (which allows us to keep the sign bit separately) and it's easy to get the bytes from them. For runtime, maybe we could use something different.
• @robertbastian - There is fraction::Ratio and also num_rational::Ratio
• @robertbastian - There is num_rational::BigRational, which is just Ratio<BigInt>. You can store the sign externally in order to be extra sure, and you are already storing the sign externally
• @sffc It is worth trying BigRational to see if it works
• @echeran Also, it looks like BigRational implements the Signed trait (by being an alias for Ratio<T>), which has methods like abs, signum, is_positive
• @sffc Also, note that BigIntegers are slower than floating point values. But that it is a separate point.
• @robertbastian Did you say that u64 is not big enough, @younies?
• @sffc It is not big enough to store u64 divided by u64. We can convert to an f64.
• @robertbastian Is that precise enough?
• @sffc Precision is the tradeoff. But we should give users that choice.
• @younies I will try the num_rational create including the BigRational. And I can provide APIs that allow users to choose the types and level of precision.

Conclusion: try num_rational::Ratio<BigInt> in a new PR. Convert to (Sign, num_rational::Ratio<BigUint>) when serializing.