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use integer::conversion::to_twos_complement_limbs::limbs_twos_complement_in_place;
use malachite_base::num::arithmetic::traits::{
ModPowerOf2, ModPowerOf2Assign, NegModPowerOf2, NegModPowerOf2Assign, RemPowerOf2,
RemPowerOf2Assign, ShrRound,
};
use malachite_base::num::basic::integers::PrimitiveInt;
use malachite_base::num::basic::traits::Zero;
use malachite_base::num::conversion::traits::{ExactFrom, WrappingFrom};
use malachite_base::rounding_modes::RoundingMode;
use malachite_base::slices::slice_set_zero;
use natural::InnerNatural::{Large, Small};
use natural::Natural;
use platform::Limb;
// Interpreting a slice of `Limb`s as the limbs (in ascending order) of a `Natural`, returns the
// limbs of the `Natural` mod two raised to `pow`. Equivalently, retains only the least-significant
// `pow` bits.
//
// # Worst-case complexity
// $T(n) = O(n)$
//
// $M(n) = O(n)$
//
// where $T$ is time, $M$ is additional memory, and $n$ is `pow`.
//
// This is equivalent to `mpz_tdiv_r_2exp` from `mpz/tdiv_r_2exp.c`, GMP 6.2.1, where in is
// non-negative and the result is returned.
pub_test! {limbs_mod_power_of_2(xs: &[Limb], pow: u64) -> Vec<Limb> {
if pow == 0 {
return Vec::new();
}
let leftover_bits = pow & Limb::WIDTH_MASK;
let result_size = usize::exact_from(pow >> Limb::LOG_WIDTH);
if result_size >= xs.len() {
return xs.to_vec();
}
let mut result = xs[..result_size].to_vec();
if leftover_bits != 0 {
result.push(xs[result_size].mod_power_of_2(leftover_bits));
}
result
}}
// Interpreting a slice of `Limb`s as the limbs (in ascending order) of a `Natural`, writes the
// limbs of the `Natural` mod two raised to `pow` to the input slice. Equivalently, retains only
// the least-significant `pow` bits. If the upper limbs of the input slice are no longer needed,
// they are set to zero.
//
// # Worst-case complexity
// Constant time and additional memory.
//
// This is equivalent to `mpz_tdiv_r_2exp` from `mpz/tdiv_r_2exp.c`, GMP 6.2.1, where `in` is
// non-negative, `res == in`, and instead of possibly being truncated, the high limbs of `res` are
// possibly filled with zeros.
pub_crate_test! {limbs_slice_mod_power_of_2_in_place(xs: &mut [Limb], pow: u64) {
if pow == 0 {
slice_set_zero(xs);
return;
}
let new_size = usize::exact_from(pow.shr_round(Limb::LOG_WIDTH, RoundingMode::Ceiling));
if new_size > xs.len() {
return;
}
slice_set_zero(&mut xs[new_size..]);
let leftover_bits = pow & Limb::WIDTH_MASK;
if leftover_bits != 0 {
xs[new_size - 1].mod_power_of_2_assign(leftover_bits);
}
}}
// Interpreting a `Vec` of `Limb`s as the limbs (in ascending order) of a `Natural`, writes the
// limbs of the `Natural` mod two raised to `pow` to the input `Vec`. Equivalently, retains only
// the least-significant `pow` bits.
//
// # Worst-case complexity
// Constant time and additional memory.
//
// This is equivalent to `mpz_tdiv_r_2exp` from `mpz/tdiv_r_2exp.c`, GMP 6.2.1, where `in` is
// non-negative and `res == in`.
pub_crate_test! {limbs_vec_mod_power_of_2_in_place(xs: &mut Vec<Limb>, pow: u64) {
if pow == 0 {
xs.clear();
return;
}
let new_size = usize::exact_from(pow.shr_round(Limb::LOG_WIDTH, RoundingMode::Ceiling));
if new_size > xs.len() {
return;
}
xs.truncate(new_size);
let leftover_bits = pow & Limb::WIDTH_MASK;
if leftover_bits != 0 {
xs[new_size - 1].mod_power_of_2_assign(leftover_bits);
}
}}
// Interpreting a slice of `Limb`s as the limbs (in ascending order) of a `Natural`, returns the
// limbs of the negative of the `Natural` mod two raised to `pow`. Equivalently, takes the two's
// complement and retains only the least-significant `pow` bits.
//
// # Worst-case complexity
// $T(n) = O(n)$
//
// $M(n) = O(n)$
//
// where $T$ is time, $M$ is additional memory, and $n$ is `pow`.
//
// This is equivalent to `mpz_tdiv_r_2exp` from `mpz/tdiv_r_2exp.c`, GMP 6.2.1, where `in` is
// negative and the result is returned. `xs` is the limbs of `-in`.
pub_crate_test! {limbs_neg_mod_power_of_2(xs: &[Limb], pow: u64) -> Vec<Limb> {
let mut result = xs.to_vec();
limbs_neg_mod_power_of_2_in_place(&mut result, pow);
result
}}
// Interpreting a `Vec` of `Limb`s as the limbs (in ascending order) of a `Natural`, writes the
// limbs of the negative of the `Natural` mod two raised to `pow` to the input `Vec`. Equivalently,
// takes the two's complement and retains only the least-significant `pow` bits.
//
// # Worst-case complexity
// $T(n) = O(n)$
//
// $M(n) = O(n)$
//
// where $T$ is time, $M$ is additional memory, and $n$ is `pow`.
//
// This is equivalent to `mpz_tdiv_r_2exp` from `mpz/tdiv_r_2exp.c`, GMP 6.2.1, where `in` is
// negative and `res == in`. `xs` is the limbs of `-in`.
pub_crate_test! {limbs_neg_mod_power_of_2_in_place(xs: &mut Vec<Limb>, pow: u64) {
let new_size = usize::exact_from(pow.shr_round(Limb::LOG_WIDTH, RoundingMode::Ceiling));
xs.resize(new_size, 0);
limbs_twos_complement_in_place(xs);
let leftover_bits = pow & Limb::WIDTH_MASK;
if leftover_bits != 0 {
xs[new_size - 1].mod_power_of_2_assign(leftover_bits);
}
}}
impl ModPowerOf2 for Natural {
type Output = Natural;
/// Divides a [`Natural`] by $2^k$, returning just the remainder. The [`Natural`] is taken by
/// value.
///
/// If the quotient were computed, the quotient and remainder would satisfy
/// $x = q2^k + r$ and $0 \leq r < 2^k$.
///
/// $$
/// f(x, k) = x - 2^k\left \lfloor \frac{x}{2^k} \right \rfloor.
/// $$
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::ModPowerOf2;
/// use malachite_nz::natural::Natural;
///
/// // 1 * 2^8 + 4 = 260
/// assert_eq!(Natural::from(260u32).mod_power_of_2(8), 4);
///
/// // 100 * 2^4 + 11 = 1611
/// assert_eq!(Natural::from(1611u32).mod_power_of_2(4), 11);
/// ```
#[inline]
fn mod_power_of_2(mut self, pow: u64) -> Natural {
self.mod_power_of_2_assign(pow);
self
}
}
impl<'a> ModPowerOf2 for &'a Natural {
type Output = Natural;
/// Divides a [`Natural`] by $2^k$, returning just the remainder. The [`Natural`] is taken by
/// reference.
///
/// If the quotient were computed, the quotient and remainder would satisfy
/// $x = q2^k + r$ and $0 \leq r < 2^k$.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `pow`.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::ModPowerOf2;
/// use malachite_nz::natural::Natural;
///
/// // 1 * 2^8 + 4 = 260
/// assert_eq!((&Natural::from(260u32)).mod_power_of_2(8), 4);
/// // 100 * 2^4 + 11 = 1611
/// assert_eq!((&Natural::from(1611u32)).mod_power_of_2(4), 11);
/// ```
fn mod_power_of_2(self, pow: u64) -> Natural {
match *self {
Natural(Small(ref small)) => Natural(Small(small.mod_power_of_2(pow))),
Natural(Large(ref limbs)) => {
Natural::from_owned_limbs_asc(limbs_mod_power_of_2(limbs, pow))
}
}
}
}
impl ModPowerOf2Assign for Natural {
/// Divides a [`Natural`]by $2^k$, replacing the [`Natural`] by the remainder.
///
/// If the quotient were computed, the quotient and remainder would satisfy
/// $x = q2^k + r$ and $0 \leq r < 2^k$.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::ModPowerOf2Assign;
/// use malachite_nz::natural::Natural;
///
/// // 1 * 2^8 + 4 = 260
/// let mut x = Natural::from(260u32);
/// x.mod_power_of_2_assign(8);
/// assert_eq!(x, 4);
///
/// // 100 * 2^4 + 11 = 1611
/// let mut x = Natural::from(1611u32);
/// x.mod_power_of_2_assign(4);
/// assert_eq!(x, 11);
/// ```
fn mod_power_of_2_assign(&mut self, pow: u64) {
match *self {
Natural(Small(ref mut small)) => small.mod_power_of_2_assign(pow),
Natural(Large(ref mut limbs)) => {
limbs_vec_mod_power_of_2_in_place(limbs, pow);
self.trim();
}
}
}
}
impl RemPowerOf2 for Natural {
type Output = Natural;
/// Divides a [`Natural`] by $2^k$, returning just the remainder. The [`Natural`] is taken by
/// value.
///
/// If the quotient were computed, the quotient and remainder would satisfy $x = q2^k + r$ and
/// $0 \leq r < 2^k$.
///
/// $$
/// f(x, k) = x - 2^k\left \lfloor \frac{x}{2^k} \right \rfloor.
/// $$
///
/// For [`Natural`]s, `rem_power_of_2` is equivalent to
/// [`mod_power_of_2`](ModPowerOf2::mod_power_of_2).
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::RemPowerOf2;
/// use malachite_nz::natural::Natural;
///
/// // 1 * 2^8 + 4 = 260
/// assert_eq!(Natural::from(260u32).rem_power_of_2(8), 4);
///
/// // 100 * 2^4 + 11 = 1611
/// assert_eq!(Natural::from(1611u32).rem_power_of_2(4), 11);
/// ```
#[inline]
fn rem_power_of_2(self, pow: u64) -> Natural {
self.mod_power_of_2(pow)
}
}
impl<'a> RemPowerOf2 for &'a Natural {
type Output = Natural;
/// Divides a [`Natural`] by $2^k$, returning just the remainder. The [`Natural`] is taken by
/// reference.
///
/// If the quotient were computed, the quotient and remainder would satisfy $x = q2^k + r$ and
/// $0 \leq r < 2^k$.
///
/// $$
/// f(x, k) = x - 2^k\left \lfloor \frac{x}{2^k} \right \rfloor.
/// $$
///
/// For [`Natural`]s, `rem_power_of_2` is equivalent to
/// [`mod_power_of_2`](ModPowerOf2::mod_power_of_2).
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `pow`.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::RemPowerOf2;
/// use malachite_nz::natural::Natural;
///
/// // 1 * 2^8 + 4 = 260
/// assert_eq!((&Natural::from(260u32)).rem_power_of_2(8), 4);
/// // 100 * 2^4 + 11 = 1611
/// assert_eq!((&Natural::from(1611u32)).rem_power_of_2(4), 11);
/// ```
#[inline]
fn rem_power_of_2(self, pow: u64) -> Natural {
self.mod_power_of_2(pow)
}
}
impl RemPowerOf2Assign for Natural {
/// Divides a [`Natural`] by $2^k$, replacing the first [`Natural`] by the remainder.
///
/// If the quotient were computed, the quotient and remainder would satisfy
/// $x = q2^k + r$ and $0 \leq r < 2^k$.
///
/// $$
/// x \gets x - 2^k\left \lfloor \frac{x}{2^k} \right \rfloor.
/// $$
///
/// For [`Natural`]s, `rem_power_of_2_assign` is equivalent to
/// [`mod_power_of_2_assign`](ModPowerOf2Assign::mod_power_of_2_assign).
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::RemPowerOf2Assign;
/// use malachite_nz::natural::Natural;
///
/// // 1 * 2^8 + 4 = 260
/// let mut x = Natural::from(260u32);
/// x.rem_power_of_2_assign(8);
/// assert_eq!(x, 4);
///
/// // 100 * 2^4 + 11 = 1611
/// let mut x = Natural::from(1611u32);
/// x.rem_power_of_2_assign(4);
/// assert_eq!(x, 11);
/// ```
#[inline]
fn rem_power_of_2_assign(&mut self, pow: u64) {
self.mod_power_of_2_assign(pow);
}
}
impl NegModPowerOf2 for Natural {
type Output = Natural;
/// Divides the negative of a [`Natural`] by a $2^k$, returning just
/// the remainder. The [`Natural`] is taken by value.
///
/// If the quotient were computed, the quotient and remainder would satisfy $x = q2^k - r$ and
/// $0 \leq r < 2^k$.
///
/// $$
/// f(x, k) = 2^k\left \lceil \frac{x}{2^k} \right \rceil - x.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `pow`.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::NegModPowerOf2;
/// use malachite_nz::natural::Natural;
///
/// // 2 * 2^8 - 252 = 260
/// assert_eq!(Natural::from(260u32).neg_mod_power_of_2(8), 252);
///
/// // 101 * 2^4 - 5 = 1611
/// assert_eq!(Natural::from(1611u32).neg_mod_power_of_2(4), 5);
/// ```
#[inline]
fn neg_mod_power_of_2(mut self, pow: u64) -> Natural {
self.neg_mod_power_of_2_assign(pow);
self
}
}
impl<'a> NegModPowerOf2 for &'a Natural {
type Output = Natural;
/// Divides the negative of a [`Natural`] by a $2^k$, returning just the remainder. The
/// [`Natural`] is taken by reference.
///
/// If the quotient were computed, the quotient and remainder would satisfy $x = q2^k - r$ and
/// $0 \leq r < 2^k$.
///
/// $$
/// f(x, k) = 2^k\left \lceil \frac{x}{2^k} \right \rceil - x.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `pow`.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::NegModPowerOf2;
/// use malachite_nz::natural::Natural;
///
/// // 2 * 2^8 - 252 = 260
/// assert_eq!((&Natural::from(260u32)).neg_mod_power_of_2(8), 252);
/// // 101 * 2^4 - 5 = 1611
/// assert_eq!((&Natural::from(1611u32)).neg_mod_power_of_2(4), 5);
/// ```
fn neg_mod_power_of_2(self, pow: u64) -> Natural {
match (self, pow) {
(natural_zero!(), _) => Natural::ZERO,
(_, pow) if pow <= Limb::WIDTH => {
Natural::from(Limb::wrapping_from(self).neg_mod_power_of_2(pow))
}
(Natural(Small(small)), pow) => {
Natural::from_owned_limbs_asc(limbs_neg_mod_power_of_2(&[*small], pow))
}
(Natural(Large(ref limbs)), pow) => {
Natural::from_owned_limbs_asc(limbs_neg_mod_power_of_2(limbs, pow))
}
}
}
}
impl NegModPowerOf2Assign for Natural {
/// Divides the negative of a [`Natural`] by $2^k$, returning just the remainder.
///
/// If the quotient were computed, the quotient and remainder would satisfy $x = q2^k - r$ and
/// $0 \leq r < 2^k$.
///
/// $$
/// x \gets 2^k\left \lceil \frac{x}{2^k} \right \rceil - x.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `pow`.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::NegModPowerOf2Assign;
/// use malachite_nz::natural::Natural;
///
/// // 2 * 2^8 - 252 = 260
/// let mut x = Natural::from(260u32);
/// x.neg_mod_power_of_2_assign(8);
/// assert_eq!(x, 252);
///
/// // 101 * 2^4 - 5 = 1611
/// let mut x = Natural::from(1611u32);
/// x.neg_mod_power_of_2_assign(4);
/// assert_eq!(x, 5);
/// ```
fn neg_mod_power_of_2_assign(&mut self, pow: u64) {
if *self == 0 {
} else if pow <= Limb::WIDTH {
*self = Natural::from(Limb::wrapping_from(&*self).neg_mod_power_of_2(pow));
} else {
let limbs = self.promote_in_place();
limbs_neg_mod_power_of_2_in_place(limbs, pow);
self.trim();
}
}
}