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//! Definitions of [UBig].
//!
//! Conversion from internal representations including [Buffer][crate::buffer::Buffer], [TypedRepr], [TypedReprRef]
//! to [UBig] is not implemented, the designed way to construct UBig from them is first convert them
//! into [Repr], and then directly construct from the [Repr]. This restriction is set to make
//! the source type explicit.
use crate::repr::{Repr, TypedRepr, TypedReprRef};
/// An unsigned arbitrary precision integer.
///
/// This struct represents an arbitrarily large unsigned integer. Technically the size of the integer
/// is bounded by the memory size, but it's enough for practical use on modern devices.
///
/// # Parsing and printing
///
/// To create a [UBig] instance, there are three ways:
/// 1. Use predifined constants (e.g. [UBig::ZERO], [UBig::ONE]).
/// 1. Use the literal macro `ubig!` defined in the [`dashu-macro`](https://docs.rs/dashu-macros/latest/dashu_macros/) crate.
/// 1. Parse from a string.
///
/// Parsing from either literal or string supports representation with base 2~36.
///
/// For printing, the [UBig] type supports common formatting traits ([Display][core::fmt::Display],
/// [Debug][core::fmt::Debug], [LowerHex][core::fmt::LowerHex], etc.). Specially, printing huge number
/// using [Debug][core::fmt::Debug] will conveniently omit the middle digits of the number, only print
/// the least and most significant (decimal) digits.
///
/// ```
/// # use dashu_int::{error::ParseError, UBig, Word};
/// // parsing
/// let a = UBig::from(408580953453092208335085386466371u128);
/// let b = UBig::from(0x1231abcd4134u64);
/// let c = UBig::from_str_radix("a2a123bbb127779cccc123", 32)?;
/// let d = UBig::from_str_radix("1231abcd4134", 16)?;
/// assert_eq!(a, c);
/// assert_eq!(b, d);
///
/// // printing
/// assert_eq!(format!("{}", UBig::from(12u8)), "12");
/// assert_eq!(format!("{:#X}", UBig::from(0xabcdu16)), "0xABCD");
/// if Word::BITS == 64 {
/// // number of digits to display depends on the word size
/// assert_eq!(
/// format!("{:?}", UBig::ONE << 1000),
/// "1071508607186267320..4386837205668069376"
/// );
/// }
/// # Ok::<(), ParseError>(())
/// ```
///
/// # Memory
///
/// Integers that fit in a [DoubleWord][crate::DoubleWord] will be inlined on stack and
/// no heap allocation will be invoked. For large integers, they will be represented as
/// an array of [Word][crate::Word]s, and stored on heap.
///
/// Note that the [UBig] struct has a niche bit, therefore it can be used within simple
/// enums with no memory overhead.
///
/// ```
/// # use dashu_int::UBig;
/// use core::mem::size_of;
/// assert_eq!(size_of::<UBig>(), size_of::<Option<UBig>>());
/// ```
#[derive(Eq, Hash, PartialEq)]
#[repr(transparent)]
pub struct UBig(pub(crate) Repr);
impl UBig {
/// Get the representation of UBig.
#[inline]
pub(crate) fn repr(&self) -> TypedReprRef<'_> {
self.0.as_typed()
}
/// Convert into representation.
#[inline]
pub(crate) fn into_repr(self) -> TypedRepr {
self.0.into_typed()
}
/// [UBig] with value 0
pub const ZERO: Self = Self(Repr::zero());
/// [UBig] with value 1
pub const ONE: Self = Self(Repr::one());
/// Get the raw representation in [Word][crate::Word]s.
///
/// If the number is zero, then empty slice will be returned.
///
/// # Examples
///
/// ```
/// # use dashu_int::{UBig, Word};
/// assert_eq!(UBig::ZERO.as_words(), &[] as &[Word]);
/// assert_eq!(UBig::ONE.as_words(), &[1]);
/// ```
#[inline]
pub fn as_words(&self) -> &[crate::Word] {
let (sign, words) = self.0.as_sign_slice();
debug_assert!(matches!(sign, crate::Sign::Positive));
words
}
/// Create a UBig from a single [Word][crate::Word].
///
/// # Examples
///
/// ```
/// # use dashu_int::UBig;
/// const ZERO: UBig = UBig::from_word(0);
/// assert_eq!(ZERO, UBig::ZERO);
/// const ONE: UBig = UBig::from_word(1);
/// assert_eq!(ONE, UBig::ONE);
/// ```
#[inline]
pub const fn from_word(word: crate::Word) -> Self {
Self(Repr::from_word(word))
}
/// Create a UBig from a [DoubleWord][crate::DoubleWord].
///
/// # Examples
///
/// ```
/// # use dashu_int::UBig;
/// const ZERO: UBig = UBig::from_dword(0);
/// assert_eq!(ZERO, UBig::ZERO);
/// const ONE: UBig = UBig::from_dword(1);
/// assert_eq!(ONE, UBig::ONE);
/// ```
#[inline]
pub const fn from_dword(dword: crate::DoubleWord) -> Self {
Self(Repr::from_dword(dword))
}
/// Convert a sequence of [Word][crate::Word]s into a UBig
///
/// # Examples
///
/// ```
/// # use dashu_int::{UBig, Word};
/// assert_eq!(UBig::from_words(&[] as &[Word]), UBig::ZERO);
/// assert_eq!(UBig::from_words(&[1]), UBig::ONE);
/// assert_eq!(UBig::from_words(&[1, 1]), (UBig::ONE << Word::BITS as usize) + UBig::ONE);
/// ```
#[inline]
pub fn from_words(words: &[crate::Word]) -> Self {
Self(Repr::from_buffer(words.into()))
}
/// Check whether the value is 0
///
/// # Examples
///
/// ```
/// # use dashu_int::UBig;
/// assert!(UBig::ZERO.is_zero());
/// assert!(!UBig::ONE.is_zero());
/// ```
#[inline]
pub const fn is_zero(&self) -> bool {
self.0.is_zero()
}
/// Check whether the value is 1
///
/// # Examples
///
/// ```
/// # use dashu_int::UBig;
/// assert!(!UBig::ZERO.is_one());
/// assert!(UBig::ONE.is_one());
/// ```
#[inline]
pub const fn is_one(&self) -> bool {
self.0.is_one()
}
}
// This custom implementation is necessary due to https://github.com/rust-lang/rust/issues/98374
impl Clone for UBig {
#[inline]
fn clone(&self) -> UBig {
UBig(self.0.clone())
}
#[inline]
fn clone_from(&mut self, source: &UBig) {
self.0.clone_from(&source.0)
}
}
#[cfg(test)]
mod tests {
use super::*;
use crate::buffer::Buffer;
impl UBig {
/// Capacity in Words.
#[inline]
pub(crate) fn capacity(&self) -> usize {
self.0.capacity()
}
}
#[test]
fn test_buffer_to_ubig() {
let buf = Buffer::allocate(5);
let num = UBig(Repr::from_buffer(buf));
assert_eq!(num, UBig::ZERO);
let mut buf = Buffer::allocate(5);
buf.push(7);
let num = UBig(Repr::from_buffer(buf));
assert_eq!(num, UBig::from(7u8));
let mut buf = Buffer::allocate(100);
buf.push(7);
buf.push(0);
buf.push(0);
let num = UBig(Repr::from_buffer(buf));
assert_eq!(num, UBig::from(7u8));
let mut buf = Buffer::allocate(5);
buf.push(1);
buf.push(2);
buf.push(3);
buf.push(4);
let num = UBig(Repr::from_buffer(buf));
assert_eq!(num.capacity(), 7);
let mut buf = Buffer::allocate(100);
buf.push(1);
buf.push(2);
buf.push(3);
buf.push(4);
let num = UBig(Repr::from_buffer(buf));
assert_eq!(num.capacity(), 6);
}
#[test]
fn test_clone() {
let a = UBig::from(5u8);
assert_eq!(a.clone(), a);
let a = gen_ubig(10);
let b = a.clone();
assert_eq!(a, b);
assert_eq!(a.capacity(), b.capacity());
}
#[test]
fn test_clone_from() {
let num: UBig = gen_ubig(10);
let mut a = UBig::from(3u8);
a.clone_from(&num);
assert_eq!(a, num);
let b = UBig::from(7u8);
a.clone_from(&b);
assert_eq!(a, b);
a.clone_from(&b);
assert_eq!(a, b);
let mut a = gen_ubig(9);
let prev_cap = a.capacity();
a.clone_from(&num);
// the buffer should be reused, 9 is close enough to 10.
assert_eq!(a.capacity(), prev_cap);
assert_ne!(a.capacity(), num.capacity());
let mut a = gen_ubig(3);
let prev_cap = a.capacity();
a.clone_from(&num);
// the buffer should now be reallocated, it's too Small.
assert_ne!(a.capacity(), prev_cap);
assert_eq!(a.capacity(), num.capacity());
let mut a = gen_ubig(100);
let prev_cap = a.capacity();
a.clone_from(&num);
// the buffer should now be reallocated, it's too large.
assert_ne!(a.capacity(), prev_cap);
assert_eq!(a.capacity(), num.capacity());
}
fn gen_ubig(num_words: u16) -> UBig {
let mut buf = Buffer::allocate(num_words.into());
for i in 0..num_words {
buf.push(i.into());
}
UBig(Repr::from_buffer(buf))
}
}