Arbitrary precision, fixed-size signed and unsigned integer types for Rust.
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>
.
- Zero dependencies by default:
bnum
does not depend on any other crates by default. Support for crates such asrand
andserde
can be enabled with crate features. no-std
compatible:bnum
can be used inno_std
environments, provided that thearbitrary
andquickcheck
features are not enabled.- Compile-time integer parsing: the
from_str_radix
andparse_str_radix
methods onbnum
integers areconst
, which allows parsing of integers from string slices at compile time. Note that this is more powerful than compile-time parsing of integer literals. This is because it allows parsing of strings in all radices from2
to36
inclusive instead of just2
,8
,10
and16
. Additionally, the string to be parsed does not have to be a literal: it could, for example, be obtained viainclude_str!("...")
, orenv!("...")
. const
evaluation: nearly all methods defined onbnum
integers areconst
, which allows complex compile-time calculations.
To install and use bnum
, simply add the following line to your Cargo.toml
file in the [dependencies]
section:
bnum = "0.9.0"
Or, to enable various bnum
features as well, add for example this line instead:
bnum = { version = "0.9.0", features = ["rand"] } # enables the "rand" feature
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 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...`
The arbitrary
feature derives the Arbitrary
trait from the arbitrary
crate. Note: currently, this feature cannot be used with no_std
(see rust-fuzz/arbitrary#38).
The rand
feature allows creation of random bnum
integers via the rand
crate.
The serde
feature enables serialization and deserialization of bnum
integers via the serde
and serde_big_array
crates.
The numtraits
feature includes implementations of traits from the num_traits
and num_integer
crates, e.g. AsPrimitive
, Signed
, Integer
and Roots
.
The quickcheck
feature enables the Arbitrary
trait from the quickcheck
crate. Note: currently, this feature cannot be used with no_std
(see rust-fuzz/arbitrary#38).
The zeroize
feature enables the Zeroize
trait from the zeroize
crate.
The valuable
feature enables the Valuable
trait from the valuable
crate.
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 the unchecked_...
methods const
. This comes at the cost of only being able to compile on nightly. The nightly features that this uses are generic_const_exprs
, const_trait_impl
and const_option_ext
.
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.
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.
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.
The short list of bugs in previous versions can be found at changes/prior-bugs.md
.
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.
bnum
is licensed under either the MIT license or the Apache License 2.0.