- [crates.io](https://crates.io/crates/malachite-q)
- [docs.rs](https://docs.rs/malachite-base/latest/malachite_q/)
Rather than using this crate directly, use the
[`malachite`](https://crates.io/crates/malachite) meta-crate. It re-exports all of this crate's
public members.
In `malachite-q`'s doctests you will frequently see import paths beginning with
`malachite_q::`. When using the `malachite` crate, replace this part of the paths with
`malachite::`.
The import path of the `Rational` type is shortened to `malachite::Rational`.
# malachite-q
This crate defines
[`Rational`](https://docs.rs/malachite-q/latest/malachite_q/struct.Rational.html)s. The name of
this crate refers to the mathematical symbol for rational numbers, ℚ.
- There are many functions defined on
[`Rational`](https://docs.rs/malachite-q/latest/malachite_q/struct.Rational.html)s. These include
- All the ones you'd expect, like addition, subtraction, multiplication, and division;
- Functions related to conversion between
[`Rational`](https://docs.rs/malachite-q/latest/malachite_q/struct.Rational.html)s and other
kinds of numbers, including primitive floats;
- Functions for Diophantine approximation;
- Functions for expressing
[`Rational`](https://docs.rs/malachite-q/latest/malachite_q/struct.Rational.html)s in
scientific notation.
- The numerators and denominators of
[`Rational`](https://docs.rs/malachite-q/latest/malachite_q/struct.Rational.html)s are stored as
[`Natural`](https://docs.rs/malachite-nz/latest/malachite_nz/natural/struct.Natural.html)s, so
[`Rational`](https://docs.rs/malachite-q/latest/malachite_q/struct.Rational.html)s with small
numerators and denominators can be stored entirely on the stack.
- Most arithmetic involving
[`Rational`](https://docs.rs/malachite-q/latest/malachite_q/struct.Rational.html)s requires
(automatically) reducing the numerator and denominator. This is done very efficiently by using
the high performance GCD and exact division algorithms implemented by
[`Natural`](https://docs.rs/malachite-nz/latest/malachite_nz/natural/struct.Natural.html)s.
# Demos and benchmarks
This crate comes with a `bin` target that can be used for running demos and benchmarks.
- Almost all of the public functions in this crate have an associated demo. Running a demo
shows you a function's behavior on a large number of inputs. For example, to demo
[`Rational`](https://docs.rs/malachite-q/latest/malachite_q/struct.Rational.html) addition, you
can use the following command:
```text
cargo run --features bin_build --release -- -l 10000 -m exhaustive -d demo_rational_add
```
This command uses the `exhaustive` mode, which generates every possible input, generally
starting with the simplest input and progressing to more complex ones. Another mode is
`random`. The `-l` flag specifies how many inputs should be generated.
- You can use a similar command to run benchmarks. The following command benchmarks various
addition algorithms:
```text
cargo run --features bin_build --release -- -l 1000000 -m random -b \
benchmark_rational_add_algorithms -o gcd-bench.gp
```
or GCD implementations of other libraries:
```text
cargo run --features bin_build --release -- -l 1000000 -m random -b \
benchmark_rational_add_assign_library_comparison -o gcd-bench.gp
```
This creates a file called gcd-bench.gp. You can use gnuplot to create an SVG from it like
so:
```text
gnuplot -e "set terminal svg; l \"gcd-bench.gp\"" > gcd-bench.svg
```
The list of available demos and benchmarks is not documented anywhere; you must find them by
browsing through
[`bin_util/demo_and_bench`](https://github.com/mhogrefe/malachite/tree/master/malachite-q/src/bin_util/demo_and_bench).
# Features
- `32_bit_limbs`: Sets the type of `Limb` to
[`u32`](https://doc.rust-lang.org/nightly/std/primitive.u32.html) instead of the default,
[`u64`](https://doc.rust-lang.org/nightly/std/primitive.u64.html).
- `random`: This feature provides some functions for randomly generating values. It is off by
default to avoid pulling in some extra dependencies.
- `enable_serde`: Enables serialization and deserialization using [serde](`https://serde.rs/`).
- `test_build`: A large proportion of the code in this crate is only used for testing. For a
typical user, building this code would result in an unnecessarily long compilation time and
an unnecessarily large binary. My solution is to only build this code when the `test_build`
feature is enabled. If you want to run unit tests, you must enable `test_build`. However,
doctests don't require it, since they only test the public interface. Enabling this feature also
enables `random`.
- `bin_build`: This feature is used to build the code for demos and benchmarks, which also
takes a long time to build. Enabling this feature also enables `test_build` and `random`.
Malachite is developed by Mikhail Hogrefe. Thanks to b4D8, florian1345, konstin, Rowan Hart, YunWon Jeong, Park Joon-Kyu, Antonio Mamić, OliverNChalk, shekohex, and skycloudd for additional contributions.
Copyright © 2025 Mikhail Hogrefe