/numeric

Primary LanguageRust

Numeric

The numeric project is a mathematical framework for Rust. It contains math traits, implementations of number types such as big integers and fixed-point values, matrix and vector types, and more. It aims to be an efficient, well-designed, and comprehensive toolbox for many kinds of mathematical work in Rust.

Features

  • Extended integer types
    • U<N> - N-byte unsigned integer
    • I<N> - N-byte signed integer
    • BigInt - Unbounded signed integer
  • Extended real-valued types
    • F<N> - N-byte floating point value
    • P<N> - N-byte posit value
    • Fixed<T, N> - N-bit fixed point value stored as integer T
    • Decimal<T> - Real value number stored as integer T / T
  • Compounds, Matrices, and more
    • All T represent a numeric type of minimal bounds to be useful.
    • Vec<T, N> - N long vector
    • Matrix<T, N, M> - NxM matrix
    • Complex<T> - Imaginary value
    • Rotor<T, N> - N-dimension rotor
    • BiVector<T, N> - N-dimension bivector

FAQ

What about num_traits?

numeric's traits crate is very similar in some ways to num_traits, which may lead one to wonder why not just use that crate. In short, while num_traits aims to be good for working with generic numeric types, it falls short of what numeric requires. It has overly strict bounds on Real making it unsuitable for our use, and is missing many of the custom operator traits we require. While the first may someday in the far future be fixed by a breaking change, the latter issue is unlikely to ever change as it's not in scope for num_traits.

As such, the decision was made to work entirely through our own, more tailored base traits. On the other hand, support for num_traits is a desirable goal under a feature gate eventually, to allow other crates that use it to support numeric types transparently.

Design Thoughts

Ideas

  • Replace TaggedOffset with a TaggedPtr into the linked list
  • Use fetch_add in interner adder to prevent race conditions
  • Maybe we should change BigInt to IBig for consistency, and a potential future UBig.

Even More Number Types

  • P-adics
    • How do these get represented? Every useful one is infinite
    • May be useful to work with truncated representations, as long as they can produce outputs

Other Math Stuff

  • Rotors
  • Quaternions
  • All the math stuff I can imagine