no-std fix

Fixed-point number types

2 releases

Uses old Rust 2015

 0.1.1 Nov 20, 2017 May 17, 2017

#17 in #integer-arithmetic

21KB
383 lines

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.

~155KB