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, andComplex
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 1.26.1 news (2024-09-11)
- Bug fix: implementations of
CompleteRound
were wrongly usingprec_t
instead ofu32
for CompleteRound::Prec (issue 72).
Version 1.26.0 news (2024-08-30)
- Bug fix:
Complete
was not implemented but documented for incomplete values produced by the following methods (issue 69): - Float::get_significand is now usable in const context.
- The experimental feature
nightly-float
was added (issue 68).
Other releases
Details on other releases can be found in RELEASES.md.
Quick example
use ;
let mut int = new;
assert_eq!;
int.assign;
assert_eq!;
let decimal = "98_765_432_109_876_543_210";
int.assign;
assert!;
let hex_160 = "ffff0000ffff0000ffff0000ffff0000ffff0000";
int.assign;
assert_eq!;
int = - 1;
assert_eq!;
- Integer::new creates a new
Integer
intialized to zero. - To assign values to Rug types, we use the
Assign
trait and its methodAssign::assign
. We do not use the assignment operator=
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::parse and Integer::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.
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
use Integer;
let a = from;
let b = 5 - a;
assert_eq!;
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
use Integer;
let = ;
let incomplete = &a - &b;
// This would fail to compile: assert_eq!(incomplete, -10);
let sub = from;
assert_eq!;
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.
Using Rug
Rug is available on crates.io. To use Rug in your crate, add it as a dependency inside Cargo.toml:
[]
= "1.26"
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, which needs some setup to build; the gmp-mpfr-sys documentation has some details on usage under GNU/Linux, macOS and Windows.
Optional features
The Rug crate has six optional features:
integer
, enabled by default. Required for theInteger
type and its supporting features.rational
, enabled by default. Required for theRational
number type and its supporting features. This feature requires theinteger
feature.float
, enabled by default. Required for theFloat
type and its supporting features.complex
, enabled by default. Required for theComplex
number type and its supporting features. This feature requires thefloat
feature.rand
, enabled by default. Required for theRandState
type and its supporting features. This feature requires theinteger
feature.std
, enabled by default. This is for features that are not possible underno_std
, such as methods that returnString
or the implementation of theError
trait.serde
, disabled by default. This provides serialization support for theInteger
,Rational
,Float
andComplex
number types, providing that they are enabled. This feature requires thestd
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:
[]
= "1.26"
= false
= ["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 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.
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.)nightly-float
, disabled by default. This requires the nightly compiler, and implements some operations with the experimentalf16
andf128
primitives. (The plan is to always implement the operations and remove this experimental feature once the primitives are stabilized.)