bnum

Arbitrary precision, fixed-size signed and unsigned integer types for Rust.

Overview

The aim of this crate is to provide integer types of arbitrary fixed size which behave exactly like Rust's primitive integer types: u8, i8, u16, i16, etc. Nearly all methods defined on Rust's signed and unsigned primitive integers are defined bnum's signed and unsigned integers. Additionally, some other useful methods are provided, mostly inspired by the BigInt and BigUint types from the num_bigint crate.

This crate uses Rust's const generics to allow creation of integers of arbitrary size that can be determined at compile time. Unsigned integers are stored as an array of digits (primitive unsigned integers) of length N. This means all bnum integers can be stored on the stack, as they are fixed size. Signed integers are simply stored as an unsigned integer in two's complement.

bnum defines 4 unsigned integer types: each uses a different primitive integer as its digit type. BUint uses u64 as its digit, BUintD32 uses u32, BUintD16 uses u16 and BUintD8 uses u8. The signed integer types, BInt, BIntD32, BIntD16 and BIntD8 are represented by these unsigned integers respectively.

BUint and BInt are the fastest as they store (and so operate on) the least number of digits for a given bit size. However, the drawback is that the bit size must be a multiple of 64 (bitsize = N * 64). This is why other integer types are provided as well, as they allow the bit size to be a multiple of 32, 16, or 8 instead. When choosing which of these types to use, determine which of 64, 32, 16, 8 is the largest multiple of the desired bit size, and use the corresponding type. For example, if you wanted a 96-bit unsigned integer, 32 is the largest multiple of 96 out of these, so use BUintD32<3>. A 40-bit signed integer would be BIntD8<5>.

bnum can be used in no_std environments, provided a global default allocator is configured.

Important: bug in v0.1.0

In version 0.1.0, the from_be and to_be methods on all integers were implemented incorrectly. This problem was fixed in 0.2.0 (the next version). If you are using 0.1.0, either update to a later version or do not use these methods.

Installation

To install and use bnum, simply add the following line to your Cargo.toml file in the [dependencies] section:

bnum = "0.8.1"

Or, to enable various bnum features as well, add for example this line instead:

bnum = { version = "0.8.1", features = ["rand"] } # enables the "rand" feature

Example Usage

NB: the examples in the documentation use specific type aliases (e.g. U256, U512, or I256, I512) to give examples of correct usage for most methods. There is nothing special about these types in particular: all methods that are shown with these are implemented for all unsigned/signed bnum integers for any value of N.

// As of version 0.6.0, you can now parse integers from string slices at compile time with the const methods `from_str_radix` or `parse_str_radix`:
use bnum::types::{U256, I256};
use bnum::errors::ParseIntError;

// `parse_str_radix` returns an integer, and panics if the string fails to parse
const UINT_FROM_DECIMAL_STR: U256 = U256::parse_str_radix("12345678901234567890", 10);

// If you are not sure that the string will successfully parse, you can use `from_str_radix` which returns a `Result`
const RESULT_INT_FROM_HEXA_STR: Result<I256, ParseIntError> = I256::from_str_radix("-1234567890abcdef", 16);

assert_eq!(format!("{}", UINT_FROM_DECIMAL_STR), "12345678901234567890");
assert_eq!(format!("{:x}", RESULT_INT_FROM_HEXA_STR.unwrap().abs()), "1234567890abcdef");

// Calculate the `n`th Fibonacci number, using the type alias `U512`.

use bnum::types::U512; // `U512` is a type alias for a `BUint` which contains 8 `u64` digits

// Calculate the nth Fibonacci number
fn fibonacci(n: usize) -> U512 {
    let mut f_n: U512 = U512::ZERO; // or `U512::from(0u8)`
    let mut f_n_next: U512 = U512::ONE; // or `U512::from(1u8)`

    for _ in 0..n {
        let temp = f_n_next;
        f_n_next += f_n;
        f_n = temp;
    }

    f_n
}

let n = 100;
let f_n = fibonacci(n);

println!("The {}th Fibonacci number is {}", n, f_n);
// Prints "The 100th Fibonacci number is 354224848179261915075"

assert_eq!(f_n, U512::from_str_radix("354224848179261915075", 10).unwrap());

// Construct an 80-bit signed integer
// Out of [64, 32, 16, 8], 16 is the largest multiple of 80, so use `BIntD16`
use bnum::BIntD16;

type I80 = BIntD16<5>; // 80 / 16 = 5

let neg_one = I80::NEG_ONE;
assert_eq!(neg_one.count_ones(), 80); // signed integers are stored in two's complement so `-1` is represented as `111111...`

Features

Fuzzing

The arbitrary feature derives the Arbitrary trait from the arbitrary crate. Note: currently, this feature cannot be used with no_std (see https://github.com/rust-fuzz/arbitrary/issues/38).

Random Number Generation

The rand feature allows creation of random bnum integers via the rand crate.

Serialization and Deserialization

The serde feature enables serialization and deserialization of bnum integers via the serde and serde_big_array crates.

num_traits and num_integer trait implementations

The numtraits feature includes implementations of traits from the num_traits and num_integer crates, e.g. AsPrimitive, Signed, Integer and Roots.

Nightly features

Some functionality in this crate currently only works with the Nightly Rust compiler. The nightly feature enables this functionality, at the cost of only being able to compile on nightly. The nightly features that this crate uses are generic_const_exprs, const_trait_impl and const_option_ext.

Activating the nightly feature will enable the from_be_bytes, from_le_bytes, from_ne_bytes, to_be_bytes, to_le_bytes and to_ne_bytes methods on bnum's unsigned and signed integers and will make nearly every method defined in the library const (although as of v0.8.0, most methods are already const on stable).

Testing

This crate is tested with the quickcheck crate as well as with specific edge cases. The outputs of methods are compared to the outputs of the equivalent methods of primitive integers to ensure that the behaviour is identical.

Documentation

If a method is not documented explicitly, it will have a link to the equivalent method defined on primitive Rust integers (since the methods have the same functionality).

NB: bnum is currently pre-1.0.0. As per the Semantic Versioning guidelines, the public API may contain breaking changes while it is in this stage. However, as the API is designed to be as similar as possible to the API of Rust's primitive integers, it is unlikely that there will be a large number of breaking changes.

Known Issues

At the moment, the From trait is implemented for bnum's integers, from all the Rust primitive integers. However, this behaviour is not quite correct. For example, if a 24-bit wide unsigned integer were created (BUintD8<3>), this should not implement From<u32>, etc. and should implement TryFrom<u32> instead. To ensure correct behaviour, the FromPrimitive trait from the num_traits crate can be used instead, as this will always return an Option rather than the integer itself.

The num_traits::NumCast trait is implemented for bnum's integers but will panic if its method from is called, as it is not possible to guarantee a correct conversion, due to trait bounds enforced by NumCast. This trait should therefore never be used on bnum's integers. The implementation exists only to allow implementation of the num_traits::PrimInt trait for bnum's integers.

Future Work

This library aims to provide arbitrary, fixed precision equivalents of Rust's 3 built-in number types: signed integers, unsigned integers and floats. Signed and unsigned integers have been implemented and fully tested, and will aim to keep up to date with Rust's integer interface. (e.g. when a new method is implemented on a Rust primitive integer, this library will attempt to keep in step to include that method as well. This includes nightly-only methods.)

Currently, arbitrary precision fixed size floats are being worked on but are incomplete. Most of the basic methods, such as arithmetic and classification, have been implemented, but at the moment there is no implementation of the transcendental floating point methods such as sin, exp, log, etc.

Additionally, a proc macro for parsing numeric values will be developed at some point, which will allow easier creation of large constant values for bnum's numeric types.

Licensing

bnum is licensed under either the MIT license or the Apache License 2.0.