Fix

Fixed-point number types.

Documentation

lib.rs:

Fixed-point number types.

What?

Fixed-point is a number representation with a fixed number of digits before and after the radix point. This means that range is static rather than dynamic, as with floating-point. It also means that they can be represented as integers, with their scale tracked by the type system.

In this library, the scale of a Fix is represented as two type-level integers: the base and the exponent. Any underlying integer primitive can be used to store the number. Arithmetic can be performed on these numbers, and they can be converted to different scale exponents.

Why?

A classic example: let's sum 10 cents and 20 cents using floating-point. We expect a result of 30 cents.

assert_eq!(0.30, 0.10 + 0.20);

Wrong! We get an extra forty quintillionths of a dollar.

assertion failed: `(left == right)` (left: `0.3`, right: `0.30000000000000004`)'

This is due to neither 0.1 nor 0.2 being exactly representable in base-2, just as a third can't be represented exactly in base-10. With Fix, we can choose the precision we want in base-10, at compile-time. In this case, hundredths of a dollar will do.

use fix::aliases::si::Centi; // Fix<_, U10, N2>
assert_eq!(Centi::new(0_30), Centi::new(0_10) + Centi::new(0_20));

But decimal is inefficient for binary computers, right? Multiplying and dividing by 10 is slower than bit-shifting, but that's only needed when moving the point. With Fix, this is only done explicitly with the convert method.

use fix::aliases::si::{Centi, Milli};
assert_eq!(Milli::new(0_300), Centi::new(0_30).convert());

We can also choose a base-2 scale just as easily.

use fix::aliases::iec::{Kibi, Mebi};
assert_eq!(Kibi::new(1024), Mebi::new(1).convert());

It's also worth noting that the type-level scale changes when multiplying and dividing, avoiding any implicit conversion.

use fix::aliases::iec::{Gibi, Kibi, Mebi};
assert_eq!(Mebi::new(3), Gibi::new(6) / Kibi::new(2));

no_std

This crate is no_std.

i128 support

Support for u128 and i128 can be enabled on nightly Rust through the i128 Cargo feature.