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// Copyright © 2024 Mikhail Hogrefe
//
// This file is part of Malachite.
//
// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.
use crate::integer::Integer;
use crate::natural::arithmetic::add::limbs_slice_add_limb_in_place;
use crate::natural::conversion::to_limbs::LimbIterator;
use crate::natural::logic::not::limbs_not_in_place;
use crate::natural::Natural;
use crate::platform::Limb;
use alloc::vec::Vec;
use malachite_base::num::arithmetic::traits::{IsPowerOf2, UnsignedAbs};
use malachite_base::num::basic::integers::PrimitiveInt;
use malachite_base::num::conversion::traits::{ExactFrom, WrappingFrom};
use malachite_base::slices::slice_leading_zeros;
// Given the limbs of the absolute value of an `Integer`, in ascending order, returns the two's
// complement limbs. The input limbs should not be all zero.
//
// # Worst-case complexity
// $T(n) = O(n)$
//
// $M(n) = O(n)$
//
// where $T$ is time, $M$ is additional memory, and $n$ is `xs.len()`.
pub_crate_test! {limbs_twos_complement(xs: &[Limb]) -> Vec<Limb> {
let i = slice_leading_zeros(xs);
let mut result = vec![0; i];
if i != xs.len() {
result.push(xs[i].wrapping_neg());
for x in &xs[i + 1..] {
result.push(!x);
}
}
result
}}
// Given the limbs of a non-negative `Integer`, in ascending order, checks whether the most
// significant bit is `false`; if it isn't, appends an extra zero bit. This way the `Integer`'s
// non-negativity is preserved in its limbs.
//
// # Worst-case complexity
// Constant time and additional memory.
pub_test! {limbs_maybe_sign_extend_non_negative_in_place(xs: &mut Vec<Limb>) {
if let Some(last) = xs.last() {
if last.get_highest_bit() {
// Sign-extend with an extra 0 limb to indicate a positive Integer
xs.push(0);
}
}
}}
// Given the limbs of the absolute value of an `Integer`, in ascending order, converts the limbs to
// two's complement. Returns whether there is a carry left over from the two's complement conversion
// process.
//
// # Worst-case complexity
// $T(n) = O(n)$
//
// $M(n) = O(1)$
//
// where $T$ is time, $M$ is additional memory, and $n$ is `xs.len()`.
pub_crate_test! {limbs_twos_complement_in_place(xs: &mut [Limb]) -> bool {
limbs_not_in_place(xs);
limbs_slice_add_limb_in_place(xs, 1)
}}
// Given the limbs of the absolute value of a negative `Integer`, in ascending order, converts the
// limbs to two's complement and checks whether the most significant bit is `true`; if it isn't,
// appends an extra `Limb::MAX` bit. This way the `Integer`'s negativity is preserved in its limbs.
// The limbs cannot be empty or contain only zeros.
//
// # Worst-case complexity
// $T(n) = O(n)$
//
// $M(n) = O(1)$
//
// where $T$ is time, $M$ is additional memory, and $n$ is `xs.len()`.
//
// # Panics
// Panics if `xs` contains only zeros.
pub_test! {limbs_twos_complement_and_maybe_sign_extend_negative_in_place(xs: &mut Vec<Limb>) {
assert!(!limbs_twos_complement_in_place(xs));
if let Some(last) = xs.last() {
if !last.get_highest_bit() {
// Sign-extend with an extra !0 limb to indicate a negative Integer
xs.push(Limb::MAX);
}
}
}}
#[derive(Clone, Copy, Debug, Eq, Hash, PartialEq)]
pub struct NegativeLimbIterator<'a>(NLIterator<'a>);
// A double-ended iterator over the two's complement [limbs](crate#limbs) of the negative of an
// [`Integer`].
//
// The forward order is ascending (least-significant first). There may be at most one
// most-significant `Limb::MAX` limb.
#[derive(Clone, Copy, Debug, Eq, Hash, PartialEq)]
struct NLIterator<'a> {
pub(crate) limbs: LimbIterator<'a>,
first_nonzero_index: Option<usize>,
}
impl<'a> NLIterator<'a> {
fn get(&self, index: u64) -> Limb {
let index = usize::exact_from(index);
if index >= self.limbs.len() {
// We're indexing into the infinite suffix of Limb::MAXs
Limb::MAX
} else {
for i in 0..index {
if self.limbs[i] != 0 {
return !self.limbs[index];
}
}
self.limbs[index].wrapping_neg()
}
}
}
impl<'a> Iterator for NLIterator<'a> {
type Item = Limb;
// A function to iterate through the two's complement limbs of the negative of a `Natural` in
// ascending order (least-significant first).
//
// # Worst-case complexity
// Constant time and additional memory.
fn next(&mut self) -> Option<Limb> {
let previous_i = self.limbs.i;
self.limbs.next().map(|limb| {
if let Some(first_nonzero_index) = self.first_nonzero_index {
if previous_i <= u64::wrapping_from(first_nonzero_index) {
limb.wrapping_neg()
} else {
!limb
}
} else {
if limb != 0 {
self.first_nonzero_index = Some(usize::exact_from(previous_i));
}
limb.wrapping_neg()
}
})
}
// A function that returns the length of the negative limbs iterator; that is, the `Natural`'s
// negative limb count (this is the same as its limb count). The format is (lower bound,
// Option<upper bound>), but in this case it's trivial to always have an exact bound.
//
// # Worst-case complexity
// Constant time and additional memory.
#[inline]
fn size_hint(&self) -> (usize, Option<usize>) {
self.limbs.size_hint()
}
}
impl<'a> DoubleEndedIterator for NLIterator<'a> {
// A function to iterate through the two's complement limbs of the negative of a `Natural` in
// descending order (most-significant first). This is worst-case linear since the first
// `next_back` call needs to determine the index of the least-significant nonzero limb.
//
// # Worst-case complexity
// $T(n) = O(n)$
//
// $M(n) = O(1)$
//
// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
fn next_back(&mut self) -> Option<Limb> {
let previous_j = self.limbs.j;
self.limbs.next_back().map(|limb| {
if self.first_nonzero_index.is_none() {
let mut i = 0;
while self.limbs[i] == 0 {
i += 1;
}
self.first_nonzero_index = Some(i);
}
let first_nonzero_index = self.first_nonzero_index.unwrap();
if previous_j <= u64::wrapping_from(first_nonzero_index) {
limb.wrapping_neg()
} else {
!limb
}
})
}
}
trait SignExtendedLimbIterator: DoubleEndedIterator<Item = Limb> {
const EXTENSION: Limb;
fn needs_sign_extension(&self) -> bool;
fn iterate_forward(&mut self, extension_checked: &mut bool) -> Option<Limb> {
let next = self.next();
if next.is_none() {
if *extension_checked {
None
} else {
*extension_checked = true;
if self.needs_sign_extension() {
Some(Self::EXTENSION)
} else {
None
}
}
} else {
next
}
}
fn iterate_backward(&mut self, extension_checked: &mut bool) -> Option<Limb> {
if !*extension_checked {
*extension_checked = true;
if self.needs_sign_extension() {
return Some(Self::EXTENSION);
}
}
self.next_back()
}
}
impl<'a> SignExtendedLimbIterator for LimbIterator<'a> {
const EXTENSION: Limb = 0;
fn needs_sign_extension(&self) -> bool {
self[self.limb_count - 1].get_highest_bit()
}
}
impl<'a> SignExtendedLimbIterator for NLIterator<'a> {
const EXTENSION: Limb = Limb::MAX;
fn needs_sign_extension(&self) -> bool {
let mut i = 0;
while self.limbs[i] == 0 {
i += 1;
}
let last_limb_index = self.limbs.limb_count - 1;
let last_limb = self.limbs[last_limb_index];
let twos_complement_limb = if i == last_limb_index {
last_limb.wrapping_neg()
} else {
!last_limb
};
!twos_complement_limb.get_highest_bit()
}
}
/// A double-ended iterator over the twos-complement [limbs](crate#limbs) of an [`Integer`].
///
/// The forward order is ascending (least-significant first). The most significant bit of the most
/// significant limb corresponds to the sign of the [`Integer`]; `false` for non-negative and `true`
/// for negative. This means that there may be a single most-significant sign-extension limb that is
/// 0 or `Limb::MAX`.
///
/// This struct also supports retrieving limbs by index. This functionality is completely
/// independent of the iterator's state. Indexing the implicit leading limbs is allowed.
#[derive(Clone, Copy, Debug, Eq, Hash, PartialEq)]
pub enum TwosComplementLimbIterator<'a> {
Zero,
Positive(LimbIterator<'a>, bool),
Negative(NegativeLimbIterator<'a>, bool),
}
impl<'a> TwosComplementLimbIterator<'a> {
/// A function to retrieve twos-complement [limbs](crate#limbs) by index. Indexing at or above
/// the limb count returns zero or `Limb::MAX` limbs, depending on the sign of the `[Integer`].
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::Pow;
/// use malachite_base::num::basic::integers::PrimitiveInt;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_nz::integer::Integer;
/// use malachite_nz::platform::Limb;
///
/// if Limb::WIDTH == u32::WIDTH {
/// assert_eq!(Integer::ZERO.twos_complement_limbs().get(0), 0);
///
/// // 2^64 - 10^12 = 4294967063 * 2^32 + 727379968
/// let negative_trillion = -Integer::from(10u32).pow(12);
/// let limbs = negative_trillion.twos_complement_limbs();
/// assert_eq!(limbs.get(0), 727379968);
/// assert_eq!(limbs.get(1), 4294967063);
/// assert_eq!(limbs.get(2), 4294967295);
/// assert_eq!(limbs.get(100), 4294967295);
/// }
/// ```
pub fn get(&self, index: u64) -> Limb {
match *self {
TwosComplementLimbIterator::Zero => 0,
TwosComplementLimbIterator::Positive(ref limbs, _) => limbs[usize::exact_from(index)],
TwosComplementLimbIterator::Negative(ref limbs, _) => limbs.0.get(index),
}
}
}
impl<'a> Iterator for TwosComplementLimbIterator<'a> {
type Item = Limb;
/// A function to iterate through the twos-complement [limbs](crate#limbs) of an [`Integer`] in
/// ascending order (least-significant first). The last limb may be a sign-extension limb.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::Pow;
/// use malachite_base::num::basic::integers::PrimitiveInt;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_nz::integer::Integer;
/// use malachite_nz::platform::Limb;
///
/// if Limb::WIDTH == u32::WIDTH {
/// assert_eq!(Integer::ZERO.twos_complement_limbs().next(), None);
///
/// // 2^64 - 10^12 = 4294967063 * 2^32 + 727379968
/// let negative_trillion = -Integer::from(10u32).pow(12);
/// let mut limbs = negative_trillion.twos_complement_limbs();
/// assert_eq!(limbs.next(), Some(727379968));
/// assert_eq!(limbs.next(), Some(4294967063));
/// assert_eq!(limbs.next(), None);
/// }
/// ```
fn next(&mut self) -> Option<Limb> {
match *self {
TwosComplementLimbIterator::Zero => None,
TwosComplementLimbIterator::Positive(ref mut limbs, ref mut extension_checked) => {
limbs.iterate_forward(extension_checked)
}
TwosComplementLimbIterator::Negative(ref mut limbs, ref mut extension_checked) => {
limbs.0.iterate_forward(extension_checked)
}
}
}
}
impl<'a> DoubleEndedIterator for TwosComplementLimbIterator<'a> {
/// A function to iterate through the twos-complement [limbs](crate#limbs) of an [`Integer`] in
/// descending order (most-significant first). The first limb may be a sign-extension limb.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::Pow;
/// use malachite_base::num::basic::integers::PrimitiveInt;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_nz::integer::Integer;
/// use malachite_nz::platform::Limb;
///
/// if Limb::WIDTH == u32::WIDTH {
/// assert_eq!(Integer::ZERO.twos_complement_limbs().next_back(), None);
///
/// // 2^64 - 10^12 = 4294967063 * 2^32 + 727379968
/// let negative_trillion = -Integer::from(10u32).pow(12);
/// let mut limbs = negative_trillion.twos_complement_limbs();
/// assert_eq!(limbs.next_back(), Some(4294967063));
/// assert_eq!(limbs.next_back(), Some(727379968));
/// assert_eq!(limbs.next_back(), None);
/// }
/// ```
fn next_back(&mut self) -> Option<Limb> {
match *self {
TwosComplementLimbIterator::Zero => None,
TwosComplementLimbIterator::Positive(ref mut limbs, ref mut extension_checked) => {
limbs.iterate_backward(extension_checked)
}
TwosComplementLimbIterator::Negative(ref mut limbs, ref mut extension_checked) => {
limbs.0.iterate_backward(extension_checked)
}
}
}
}
impl Natural {
/// Returns a double-ended iterator over the two's complement limbs of the negative of a
/// [`Natural`]. The forward order is ascending, so that less significant limbs appear first.
/// There may be at most one trailing `Limb::MAX` limb going forward, or leading `Limb::MAX`
/// limb going backward. The [`Natural`] cannot be zero.
///
/// # Worst-case complexity
/// Constant time and additional memory.
fn negative_limbs(&self) -> NegativeLimbIterator {
assert_ne!(*self, 0, "Cannot get negative limbs of 0.");
NegativeLimbIterator(NLIterator {
limbs: self.limbs(),
first_nonzero_index: None,
})
}
}
impl Integer {
/// Returns the [limbs](crate#limbs) of an [`Integer`], in ascending order, so that less
/// significant limbs have lower indices in the output vector.
///
/// The limbs are in two's complement, and the most significant bit of the limbs indicates the
/// sign; if the bit is zero, the [`Integer`] is positive, and if the bit is one it is negative.
/// There are no trailing zero limbs if the [`Integer`] is positive or trailing `Limb::MAX`
/// limbs if the [`Integer`] is negative, except as necessary to include the correct sign bit.
/// Zero is a special case: it contains no limbs.
///
/// This function borrows `self`. If taking ownership of `self` is possible,
/// [`into_twos_complement_limbs_asc`](`Self::into_twos_complement_limbs_asc`) is more
/// efficient.
///
/// This function is more efficient than
/// [`to_twos_complement_limbs_desc`](`Self::to_twos_complement_limbs_desc`).
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::Pow;
/// use malachite_base::num::basic::integers::PrimitiveInt;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_nz::integer::Integer;
/// use malachite_nz::platform::Limb;
///
/// if Limb::WIDTH == u32::WIDTH {
/// assert!(Integer::ZERO.to_twos_complement_limbs_asc().is_empty());
/// assert_eq!(Integer::from(123).to_twos_complement_limbs_asc(), &[123]);
/// assert_eq!(
/// Integer::from(-123).to_twos_complement_limbs_asc(),
/// &[4294967173]
/// );
/// // 10^12 = 232 * 2^32 + 3567587328
/// assert_eq!(
/// Integer::from(10u32).pow(12).to_twos_complement_limbs_asc(),
/// &[3567587328, 232]
/// );
/// assert_eq!(
/// (-Integer::from(10u32).pow(12)).to_twos_complement_limbs_asc(),
/// &[727379968, 4294967063]
/// );
/// }
/// ```
pub fn to_twos_complement_limbs_asc(&self) -> Vec<Limb> {
let mut limbs = self.abs.to_limbs_asc();
if self.sign {
limbs_maybe_sign_extend_non_negative_in_place(&mut limbs);
} else {
limbs_twos_complement_and_maybe_sign_extend_negative_in_place(&mut limbs);
}
limbs
}
/// Returns the [limbs](crate#limbs) of an [`Integer`], in descending order, so that less
/// significant limbs have higher indices in the output vector.
///
/// The limbs are in two's complement, and the most significant bit of the limbs indicates the
/// sign; if the bit is zero, the [`Integer`] is positive, and if the bit is one it is negative.
/// There are no leading zero limbs if the [`Integer`] is non-negative or leading `Limb::MAX`
/// limbs if the [`Integer`] is negative, except as necessary to include the correct sign bit.
/// Zero is a special case: it contains no limbs.
///
/// This is similar to how `BigInteger`s in Java are represented.
///
/// This function borrows `self`. If taking ownership of `self` is possible,
/// [`into_twos_complement_limbs_desc`](`Self::into_twos_complement_limbs_desc`) is more
/// efficient.
///
/// This function is less efficient than
/// [`to_twos_complement_limbs_asc`](`Self::to_twos_complement_limbs_asc`).
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::Pow;
/// use malachite_base::num::basic::integers::PrimitiveInt;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_nz::integer::Integer;
/// use malachite_nz::platform::Limb;
///
/// if Limb::WIDTH == u32::WIDTH {
/// assert!(Integer::ZERO.to_twos_complement_limbs_desc().is_empty());
/// assert_eq!(Integer::from(123).to_twos_complement_limbs_desc(), &[123]);
/// assert_eq!(
/// Integer::from(-123).to_twos_complement_limbs_desc(),
/// &[4294967173]
/// );
/// // 10^12 = 232 * 2^32 + 3567587328
/// assert_eq!(
/// Integer::from(10u32).pow(12).to_twos_complement_limbs_desc(),
/// &[232, 3567587328]
/// );
/// assert_eq!(
/// (-Integer::from(10u32).pow(12)).to_twos_complement_limbs_desc(),
/// &[4294967063, 727379968]
/// );
/// }
/// ```
pub fn to_twos_complement_limbs_desc(&self) -> Vec<Limb> {
let mut xs = self.to_twos_complement_limbs_asc();
xs.reverse();
xs
}
/// Returns the [limbs](crate#limbs) of an [`Integer`], in ascending order, so that less
/// significant limbs have lower indices in the output vector.
///
/// The limbs are in two's complement, and the most significant bit of the limbs indicates the
/// sign; if the bit is zero, the [`Integer`] is positive, and if the bit is one it is negative.
/// There are no trailing zero limbs if the [`Integer`] is positive or trailing `Limb::MAX`
/// limbs if the [`Integer`] is negative, except as necessary to include the correct sign bit.
/// Zero is a special case: it contains no limbs.
///
/// This function takes ownership of `self`. If it's necessary to borrow `self` instead, use
/// [`to_twos_complement_limbs_asc`](`Self::to_twos_complement_limbs_asc`).
///
/// This function is more efficient than
/// [`into_twos_complement_limbs_desc`](`Self::into_twos_complement_limbs_desc`).
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::Pow;
/// use malachite_base::num::basic::integers::PrimitiveInt;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_nz::integer::Integer;
/// use malachite_nz::platform::Limb;
///
/// if Limb::WIDTH == u32::WIDTH {
/// assert!(Integer::ZERO.into_twos_complement_limbs_asc().is_empty());
/// assert_eq!(Integer::from(123).into_twos_complement_limbs_asc(), &[123]);
/// assert_eq!(
/// Integer::from(-123).into_twos_complement_limbs_asc(),
/// &[4294967173]
/// );
/// // 10^12 = 232 * 2^32 + 3567587328
/// assert_eq!(
/// Integer::from(10u32)
/// .pow(12)
/// .into_twos_complement_limbs_asc(),
/// &[3567587328, 232]
/// );
/// assert_eq!(
/// (-Integer::from(10u32).pow(12)).into_twos_complement_limbs_asc(),
/// &[727379968, 4294967063]
/// );
/// }
/// ```
pub fn into_twos_complement_limbs_asc(self) -> Vec<Limb> {
let mut xs = self.abs.into_limbs_asc();
if self.sign {
limbs_maybe_sign_extend_non_negative_in_place(&mut xs);
} else {
limbs_twos_complement_and_maybe_sign_extend_negative_in_place(&mut xs);
}
xs
}
/// Returns the [limbs](crate#limbs) of an [`Integer`], in descending order, so that less
/// significant limbs have higher indices in the output vector.
///
/// The limbs are in two's complement, and the most significant bit of the limbs indicates the
/// sign; if the bit is zero, the [`Integer`] is positive, and if the bit is one it is negative.
/// There are no leading zero limbs if the [`Integer`] is non-negative or leading `Limb::MAX`
/// limbs if the [`Integer`] is negative, except as necessary to include the correct sign bit.
/// Zero is a special case: it contains no limbs.
///
/// This is similar to how `BigInteger`s in Java are represented.
///
/// This function takes ownership of `self`. If it's necessary to borrow `self` instead, use
/// [`to_twos_complement_limbs_desc`](`Self::to_twos_complement_limbs_desc`).
///
/// This function is less efficient than
/// [`into_twos_complement_limbs_asc`](`Self::into_twos_complement_limbs_asc`).
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::Pow;
/// use malachite_base::num::basic::integers::PrimitiveInt;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_nz::integer::Integer;
/// use malachite_nz::platform::Limb;
///
/// if Limb::WIDTH == u32::WIDTH {
/// assert!(Integer::ZERO.into_twos_complement_limbs_desc().is_empty());
/// assert_eq!(Integer::from(123).into_twos_complement_limbs_desc(), &[123]);
/// assert_eq!(
/// Integer::from(-123).into_twos_complement_limbs_desc(),
/// &[4294967173]
/// );
/// // 10^12 = 232 * 2^32 + 3567587328
/// assert_eq!(
/// Integer::from(10u32)
/// .pow(12)
/// .into_twos_complement_limbs_desc(),
/// &[232, 3567587328]
/// );
/// assert_eq!(
/// (-Integer::from(10u32).pow(12)).into_twos_complement_limbs_desc(),
/// &[4294967063, 727379968]
/// );
/// }
/// ```
pub fn into_twos_complement_limbs_desc(self) -> Vec<Limb> {
let mut xs = self.into_twos_complement_limbs_asc();
xs.reverse();
xs
}
/// Returns a double-ended iterator over the twos-complement [limbs](crate#limbs) of an
/// [`Integer`].
///
/// The forward order is ascending, so that less significant limbs appear first. There may be a
/// most-significant sign-extension limb.
///
/// If it's necessary to get a [`Vec`] of all the twos_complement limbs, consider using
/// [`to_twos_complement_limbs_asc`](`Self::to_twos_complement_limbs_asc`),
/// [`to_twos_complement_limbs_desc`](`Self::to_twos_complement_limbs_desc`),
/// [`into_twos_complement_limbs_asc`](`Self::into_twos_complement_limbs_asc`), or
/// [`into_twos_complement_limbs_desc`](`Self::into_twos_complement_limbs_desc`) instead.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// ```
/// use itertools::Itertools;
/// use malachite_base::num::arithmetic::traits::Pow;
/// use malachite_base::num::basic::integers::PrimitiveInt;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_nz::integer::Integer;
/// use malachite_nz::platform::Limb;
///
/// if Limb::WIDTH == u32::WIDTH {
/// assert!(Integer::ZERO.twos_complement_limbs().next().is_none());
/// assert_eq!(
/// Integer::from(123).twos_complement_limbs().collect_vec(),
/// &[123]
/// );
/// assert_eq!(
/// Integer::from(-123).twos_complement_limbs().collect_vec(),
/// &[4294967173]
/// );
/// // 10^12 = 232 * 2^32 + 3567587328
/// assert_eq!(
/// Integer::from(10u32)
/// .pow(12)
/// .twos_complement_limbs()
/// .collect_vec(),
/// &[3567587328, 232]
/// );
/// // Sign-extension for a non-negative `Integer`
/// assert_eq!(
/// Integer::from(4294967295i64)
/// .twos_complement_limbs()
/// .collect_vec(),
/// &[4294967295, 0]
/// );
/// assert_eq!(
/// (-Integer::from(10u32).pow(12))
/// .twos_complement_limbs()
/// .collect_vec(),
/// &[727379968, 4294967063]
/// );
/// // Sign-extension for a negative `Integer`
/// assert_eq!(
/// (-Integer::from(4294967295i64))
/// .twos_complement_limbs()
/// .collect_vec(),
/// &[1, 4294967295]
/// );
///
/// assert!(Integer::ZERO.twos_complement_limbs().next_back().is_none());
/// assert_eq!(
/// Integer::from(123)
/// .twos_complement_limbs()
/// .rev()
/// .collect_vec(),
/// &[123]
/// );
/// assert_eq!(
/// Integer::from(-123)
/// .twos_complement_limbs()
/// .rev()
/// .collect_vec(),
/// &[4294967173]
/// );
/// // 10^12 = 232 * 2^32 + 3567587328
/// assert_eq!(
/// Integer::from(10u32)
/// .pow(12)
/// .twos_complement_limbs()
/// .rev()
/// .collect_vec(),
/// &[232, 3567587328]
/// );
/// // Sign-extension for a non-negative `Integer`
/// assert_eq!(
/// Integer::from(4294967295i64)
/// .twos_complement_limbs()
/// .rev()
/// .collect_vec(),
/// &[0, 4294967295]
/// );
/// assert_eq!(
/// (-Integer::from(10u32).pow(12))
/// .twos_complement_limbs()
/// .rev()
/// .collect_vec(),
/// &[4294967063, 727379968]
/// );
/// // Sign-extension for a negative `Integer`
/// assert_eq!(
/// (-Integer::from(4294967295i64))
/// .twos_complement_limbs()
/// .rev()
/// .collect_vec(),
/// &[4294967295, 1]
/// );
/// }
/// ```
pub fn twos_complement_limbs(&self) -> TwosComplementLimbIterator {
if *self == 0 {
TwosComplementLimbIterator::Zero
} else if self.sign {
TwosComplementLimbIterator::Positive(self.abs.limbs(), false)
} else {
TwosComplementLimbIterator::Negative(self.abs.negative_limbs(), false)
}
}
/// Returns the number of twos-complement limbs of an [`Integer`]. There may be a
/// most-significant sign-extension limb, which is included in the count.
///
/// Zero has 0 limbs.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::{Pow, PowerOf2};
/// use malachite_base::num::basic::integers::PrimitiveInt;
/// use malachite_base::num::basic::traits::{One, Zero};
/// use malachite_nz::integer::Integer;
/// use malachite_nz::platform::Limb;
///
/// if Limb::WIDTH == u32::WIDTH {
/// assert_eq!(Integer::ZERO.twos_complement_limb_count(), 0);
/// assert_eq!(Integer::from(123u32).twos_complement_limb_count(), 1);
/// assert_eq!(Integer::from(10u32).pow(12).twos_complement_limb_count(), 2);
///
/// let n = Integer::power_of_2(Limb::WIDTH - 1);
/// assert_eq!((&n - Integer::ONE).twos_complement_limb_count(), 1);
/// assert_eq!(n.twos_complement_limb_count(), 2);
/// assert_eq!((&n + Integer::ONE).twos_complement_limb_count(), 2);
/// assert_eq!((-(&n - Integer::ONE)).twos_complement_limb_count(), 1);
/// assert_eq!((-&n).twos_complement_limb_count(), 1);
/// assert_eq!((-(&n + Integer::ONE)).twos_complement_limb_count(), 2);
/// }
/// ```
pub fn twos_complement_limb_count(&self) -> u64 {
if *self == 0 {
return 0;
}
let abs_limbs_count = self.unsigned_abs_ref().limb_count();
let highest_bit_of_highest_limb =
self.unsigned_abs().limbs()[usize::exact_from(abs_limbs_count - 1)].get_highest_bit();
if highest_bit_of_highest_limb
&& (*self > 0 || (*self < 0 && !self.unsigned_abs_ref().is_power_of_2()))
{
abs_limbs_count + 1
} else {
abs_limbs_count
}
}
}