created_at2017-06-13 13:20:13.536882
updated_at2024-03-31 22:17:36.498655
descriptionArbitrary-precision integers, rational, floating-point and complex numbers based on GMP, MPFR and MPC.
Trevor Spiteri



# Arbitrary-precision numbers Rug provides integers and floating-point numbers with arbitrary precision and correct rounding: * [`Integer`] is a bignum integer with arbitrary precision, * [`Rational`] is a bignum rational number with arbitrary precision, * [`Float`] is a multi-precision floating-point number with correct rounding, and * [`Complex`] is a multi-precision complex number with correct rounding. Rug is a high-level interface to the following [GNU] libraries: * [GMP] for integers and rational numbers, * [MPFR] for floating-point numbers, and * [MPC] for complex numbers. Rug is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. See the full text of the [GNU LGPL] and [GNU GPL] for details. ## What’s new ### Version 1.24.1 news (2024-04-01) * Bug fix: when std is not enabled, a precondition for `slice::from_raw_parts` was being violated ([issue 63]). [issue 63]: ### Version 1.24.0 news (2024-01-25) * [`Float`][flo-1-24] now implements [AssignRound][assr-1-24]\<[bool][`bool`]>. * The following methods are now usable in const context: * [Float][flo-1-24]::[as\_neg][flo-an-1-24], [Float][flo-1-24]::[as\_abs][flo-aa-1-24] * [Complex][com-1-24]::[as\_neg][com-an-1-24], [Complex][com-1-24]::[as\_conj][com-ac-1-24], [Complex][com-1-24]::[as\_mul\_i][com-am-1-24] * [MiniInteger][mi-1-24]::[borrow][mi-b-1-24] * [MiniRational][mr-1-24]::[borrow][mr-b-1-24] * [MiniFloat][mf-1-24]::[borrow][mf-b-1-24] * [MiniComplex][mc-1-24]::[borrow][mc-b-1-24] * The `std` [optional feature][feat-1-24] was added ([issue 62]). The feature is enabled by default, and the crate will be compiled without the standard library (`no_std`) if the feature is disabled. * [`MiniRational`][mr-1-24] now implements * [From][`From`]\<[MiniInteger][mi-1-24]>, [Assign][ass-1-24]\<[MiniInteger][mi-1-24]> * [`MiniFloat`][mf-1-24] now implements * [From][`From`]\<[bool][`bool`]>, [Assign][ass-1-24]\<[bool][`bool`]> * [`MiniComplex`][mc-1-24] now implements * [From][`From`]\<[MiniFloat][mf-1-24]>, [Assign][ass-1-24]\<[MiniFloat][mf-1-24]> * [From][`From`]\<[(][tuple][MiniFloat][mf-1-24][,][tuple] [MiniFloat][mf-1-24][)][tuple]>, [Assign][ass-1-24]\<[(][tuple][MiniFloat][mf-1-24][,][tuple] [MiniFloat][mf-1-24][)][tuple]> * The following methods were added to [`MiniInteger`][mi-1-24]: * [`const_from_bool`][mi-bool-1-24] * [`const_from_i8`][mi-i8-1-24], [`const_from_i16`][mi-i16-1-24], [`const_from_i32`][mi-i32-1-24], [`const_from_i64`][mi-i64-1-24], [`const_from_i128`][mi-i128-1-24], [`const_from_isize`][mi-isize-1-24] * [`const_from_u8`][mi-u8-1-24], [`const_from_u16`][mi-u16-1-24], [`const_from_u32`][mi-u32-1-24], [`const_from_u64`][mi-u64-1-24], [`const_from_u128`][mi-u128-1-24], [`const_from_usize`][mi-usize-1-24] * The following method was added to [`MiniRational`][mr-1-24]: * [`const_from_integer`][mr-cfi-1-24] * The following methods were added to [`MiniFloat`][mf-1-24]: * [`const_from_bool`][mf-bool-1-24] * [`const_from_i8`][mf-i8-1-24], [`const_from_i16`][mf-i16-1-24], [`const_from_i32`][mf-i32-1-24], [`const_from_i64`][mf-i64-1-24], [`const_from_i128`][mf-i128-1-24], [`const_from_isize`][mf-isize-1-24] * [`const_from_u8`][mf-u8-1-24], [`const_from_u16`][mf-u16-1-24], [`const_from_u32`][mf-u32-1-24], [`const_from_u64`][mf-u64-1-24], [`const_from_u128`][mf-u128-1-24], [`const_from_usize`][mf-usize-1-24] * [`const_from_f32`][mf-f32-1-24], [`const_from_f64`][mf-f64-1-24] * [`const_from_special`][mf-cfs-1-24] * The following methods were added to [`MiniComplex`][mc-1-24]: * [`const_from_real`][mc-cfr-1-24], [`const_from_parts`][mc-cfp-1-24] * When the `num-traits` [experimental feature][feat-exp-1-24] is enabled, the following traits are implemented for [`Integer`][int-1-24]: * [`CheckedDiv`][nt-0-2-cd], [`CheckedRem`][nt-0-2-cr] * [`Euclid`][nt-0-2-e], [`CheckedEuclid`][nt-0-2-ce] #### Compatibility notes * The following methods no longer set the [MPFR NaN flag][sys-mpfr-sn-1-6] if a NaN is encountered: * [Float][flo-1-24]::[as\_neg][flo-an-1-24], [Float][flo-1-24]::[as\_abs][flo-aa-1-24] * [Complex][com-1-24]::[as\_neg][com-an-1-24], [Complex][com-1-24]::[as\_conj][com-ac-1-24], [Complex][com-1-24]::[as\_mul\_i][com-am-1-24] * Functionality that depends on `std` now requires the `std` feature to be enabled. While the `std` feature is enabled by default, it is now disabled if the crate’s default features are disabled in [*Cargo.toml*]. In this case, `std` must be added to the list of features to reenable the functionality. * The implementation of the deprecated [`SmallInteger`][smi-1-24], [`SmallRational`][smr-1-24], [`SmallFloat`][smf-1-24] and [`SmallComplex`][smc-1-24] was changed to remove [their soundness issue][issue 52]. They now allocate memory for the digits, though their whole point was to be non-allocating. [`From`]: [`bool`]: [ass-1-24]: [assr-1-24]: [com-1-24]: [com-ac-1-24]: [com-am-1-24]: [com-an-1-24]: [feat-1-24]: [feat-exp-1-24]: [flo-1-24]: [flo-aa-1-24]: [flo-an-1-24]: [int-1-24]: [issue 52]: [issue 62]: [mc-1-24]: [mc-b-1-24]: [mc-cfp-1-24]: [mc-cfr-1-24]: [mf-1-24]: [mf-b-1-24]: [mf-bool-1-24]: [mf-cfs-1-24]: [mf-f32-1-24]: [mf-f64-1-24]: [mf-i128-1-24]: [mf-i16-1-24]: [mf-i32-1-24]: [mf-i64-1-24]: [mf-i8-1-24]: [mf-isize-1-24]: [mf-u128-1-24]: [mf-u16-1-24]: [mf-u32-1-24]: [mf-u64-1-24]: [mf-u8-1-24]: [mf-usize-1-24]: [mi-1-24]: [mi-b-1-24]: [mi-bool-1-24]: [mi-i128-1-24]: [mi-i16-1-24]: [mi-i32-1-24]: [mi-i64-1-24]: [mi-i8-1-24]: [mi-isize-1-24]: [mi-u128-1-24]: [mi-u16-1-24]: [mi-u32-1-24]: [mi-u64-1-24]: [mi-u8-1-24]: [mi-usize-1-24]: [mr-1-24]: [mr-b-1-24]: [mr-cfi-1-24]: [nt-0-2-cd]: [nt-0-2-ce]: [nt-0-2-cr]: [nt-0-2-e]: [smc-1-24]: [smf-1-24]: [smi-1-24]: [smr-1-24]: [sys-mpfr-sn-1-6]: [tuple]: ### Other releases Details on other releases can be found in [**]. ## Quick example ```rust use rug::{Assign, Integer}; let mut int = Integer::new(); assert_eq!(int, 0); int.assign(14); assert_eq!(int, 14); let decimal = "98_765_432_109_876_543_210"; int.assign(Integer::parse(decimal).unwrap()); assert!(int > 100_000_000); let hex_160 = "ffff0000ffff0000ffff0000ffff0000ffff0000"; int.assign(Integer::parse_radix(hex_160, 16).unwrap()); assert_eq!(int.significant_bits(), 160); int = (int >> 128) - 1; assert_eq!(int, 0xfffe_ffff_u32); ``` * [Integer][`Integer`]::[new][`new`] creates a new [`Integer`] intialized to zero. * To assign values to Rug types, we use the [`Assign`] trait and its method [`Assign::assign`]. We do not use the [assignment operator `=`][assignment] as that would drop the left-hand-side operand and replace it with a right-hand-side operand of the same type, which is not what we want here. * Arbitrary precision numbers can hold numbers that are too large to fit in a primitive type. To assign such a number to the large types, we use strings rather than primitives; in the example this is done using [Integer][`Integer`]::[parse][`parse`] and [Integer][`Integer`]::[parse_radix][`parse_radix`]. * We can compare Rug types to primitive types or to other Rug types using the normal comparison operators, for example `int > 100_000_000`. * Most arithmetic operations are supported with Rug types and primitive types on either side of the operator, for example `int >> 128`. ## Using with primitive types With Rust primitive types, arithmetic operators usually operate on two values of the same type, for example `12i32 + 5i32`. Unlike primitive types, conversion to and from Rug types can be expensive, so the arithmetic operators are overloaded to work on many combinations of Rug types and primitives. More details are available in the [documentation][primitive types]. ## Operators Operators are overloaded to work on Rug types alone or on a combination of Rug types and Rust primitives. When at least one operand is an owned value of a Rug type, the operation will consume that value and return a value of the Rug type. For example ```rust use rug::Integer; let a = Integer::from(10); let b = 5 - a; assert_eq!(b, 5 - 10); ``` Here `a` is consumed by the subtraction, and `b` is an owned [`Integer`]. If on the other hand there are no owned Rug types and there are references instead, the returned value is not the final value, but an incomplete-computation value. For example ```rust use rug::Integer; let (a, b) = (Integer::from(10), Integer::from(20)); let incomplete = &a - &b; // This would fail to compile: assert_eq!(incomplete, -10); let sub = Integer::from(incomplete); assert_eq!(sub, -10); ``` Here `a` and `b` are not consumed, and `incomplete` is not the final value. It still needs to be converted or assigned into an [`Integer`]. This is covered in more detail in the documentation’s [*Incomplete-computation values*] section. More details on operators are available in the [documentation][operators]. ## Using Rug Rug is available on [][rug crate]. To use Rug in your crate, add it as a dependency inside [*Cargo.toml*]: ```toml [dependencies] rug = "1.24" ``` Rug requires rustc version 1.65.0 or later. Rug also depends on the [GMP], [MPFR] and [MPC] libraries through the low-level FFI bindings in the [gmp-mpfr-sys crate][sys crate], which needs some setup to build; the [gmp-mpfr-sys documentation][sys] has some details on usage under [GNU/Linux][sys gnu], [macOS][sys mac] and [Windows][sys win]. ## Optional features The Rug crate has six optional features: 1. `integer`, enabled by default. Required for the [`Integer`] type and its supporting features. 2. `rational`, enabled by default. Required for the [`Rational`] number type and its supporting features. This feature requires the `integer` feature. 3. `float`, enabled by default. Required for the [`Float`] type and its supporting features. 4. `complex`, enabled by default. Required for the [`Complex`] number type and its supporting features. This feature requires the `float` feature. 5. `rand`, enabled by default. Required for the [`RandState`] type and its supporting features. This feature requires the `integer` feature. 6. `std`, enabled by default. This is for features that are not possible under `no_std`, such as methods that return [`String`] or the implementation of the [`Error`] trait. 7. `serde`, disabled by default. This provides serialization support for the [`Integer`], [`Rational`], [`Float`] and [`Complex`] number types, providing that they are enabled. This feature requires the `std` feature and the [serde crate]. The first six optional features are enabled by default; to use features selectively, you can add the dependency like this to [*Cargo.toml*]: ```toml [dependencies.rug] version = "1.24" default-features = false features = ["integer", "float", "std"] ``` Here only the `integer`, `float` and `rand` features are enabled. If none of the features are selected, the [gmp-mpfr-sys crate][sys crate] is not required and thus not enabled. In that case, only the [`Assign`] trait and the traits that are in the [`ops`] module are provided by the crate. ## Experimental optional features It is not considered a breaking change if the following experimental features are removed. The removal of experimental features would however require a minor version bump. Similarly, on a minor version bump, optional dependencies can be updated to an incompatible newer version. 1. `num-traits`, disabled by default. This implements some traits from the [*num-traits* crate] and the [*num-integer* crate]. (The plan is to promote this to an optional feature once the [*num-traits* crate] and the [*num-integer* crate] reach version 1.0.0.) [*Cargo.toml*]: [*Incomplete-computation values*]: [**]: [*num-integer* crate]: [*num-traits* crate]: [GMP]: [GNU GPL]: [GNU LGPL]: [GNU]: [MPC]: [MPFR]: [`Assign::assign`]: [`Assign`]: [`Complex`]: [`Error`]: [`Float`]: [`Integer`]: [`RandState`]: [`Rational`]: [`String`]: [`new`]: [`ops`]: [`parse_radix`]: [`parse`]: [assignment]: [operators]: [primitive types]: [rug crate]: [serde crate]: [sys crate]: [sys gnu]: [sys mac]: [sys win]: [sys]:
Commit count: 1855

cargo fmt