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use crate::natural::InnerNatural::{Large, Small};
use crate::natural::Natural;
use crate::platform::Limb;
use malachite_base::num::arithmetic::traits::{
ArithmeticCheckedShl, NextPowerOf2, NextPowerOf2Assign,
};
use malachite_base::slices::{slice_set_zero, slice_test_zero};
// Interpreting a slice of `Limb`s as the limbs (in ascending order) of a `Natural`, returns the
// limbs of the smallest integer power of 2 greater than or equal to the `Natural`.
//
// This function assumes that `xs` is nonempty and the last (most significant) limb is nonzero.
//
// # Worst-case complexity
// $T(n) = O(n)$
//
// $M(n) = O(n)$
//
// where $T$ is time, $M$ is additional memory, and $n$ is `xs.len()`.
//
// # Panics
// Panics if `xs` is empty.
pub_test! {limbs_next_power_of_2(xs: &[Limb]) -> Vec<Limb> {
let (xs_last, xs_init) = xs.split_last().unwrap();
let mut out;
if let Some(x) = xs_last.checked_next_power_of_two() {
out = vec![0; xs_init.len()];
if x == *xs_last && !slice_test_zero(xs_init) {
if let Some(x) = x.arithmetic_checked_shl(1) {
out.push(x)
} else {
out.push(0);
out.push(1);
}
} else {
out.push(x);
}
} else {
out = vec![0; xs.len()];
out.push(1);
}
out
}}
// Interpreting a slice of `Limb`s as the limbs (in ascending order) of a `Natural`, writes the
// limbs of the smallest integer power of 2 greater than or equal to the `Natural` to the input
// slice. If the input slice is too small to hold the result, the limbs are all set to zero and the
// carry bit, `true`, is returned. Otherwise, `false` is returned.
//
// This function assumes that `xs` is nonempty and the last (most significant) limb is nonzero.
//
// # 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` is empty.
pub_test! {limbs_slice_next_power_of_2_in_place(xs: &mut [Limb]) -> bool {
let (xs_last, xs_init) = xs.split_last_mut().unwrap();
if let Some(x) = xs_last.checked_next_power_of_two() {
if x == *xs_last && !slice_test_zero(xs_init) {
slice_set_zero(xs_init);
if let Some(x) = x.arithmetic_checked_shl(1) {
*xs_last = x;
false
} else {
*xs_last = 0;
true
}
} else {
slice_set_zero(xs_init);
*xs_last = x;
false
}
} else {
slice_set_zero(xs_init);
*xs_last = 0;
true
}
}}
// Interpreting a `Vec` of `Limb`s as the limbs (in ascending order) of a `Natural`, writes the
// limbs of the smallest integer power of 2 greater than or equal to the `Natural` to the input
// `Vec`.
//
// This function assumes that `xs` is nonempty and the last (most significant) limb is nonzero.
//
// # Worst-case complexity
// $T(n) = O(n)$
//
// $M(n) = O(n)$ (only if the underlying [`Vec`] needs to reallocate)
//
// where $T$ is time, $M$ is additional memory, and $n$ is `xs.len()`.
//
// # Panics
// Panics if `xs` is empty.
pub_test! {limbs_vec_next_power_of_2_in_place(xs: &mut Vec<Limb>) {
if limbs_slice_next_power_of_2_in_place(xs) {
xs.push(1);
}
}}
impl NextPowerOf2 for Natural {
type Output = Natural;
/// Finds the smallest power of 2 greater than or equal to a [`Natural`]. The [`Natural`] is
/// taken by value.
///
/// $f(x) = 2^{\lceil \log_2 x \rceil}$.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$ (only if the underlying [`Vec`] needs to reallocate)
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::{NextPowerOf2, Pow};
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_nz::natural::Natural;
///
/// assert_eq!(Natural::ZERO.next_power_of_2(), 1);
/// assert_eq!(Natural::from(123u32).next_power_of_2(), 128);
/// assert_eq!(Natural::from(10u32).pow(12).next_power_of_2(), 1099511627776u64);
/// ```
#[inline]
fn next_power_of_2(mut self) -> Natural {
self.next_power_of_2_assign();
self
}
}
impl<'a> NextPowerOf2 for &'a Natural {
type Output = Natural;
/// Finds the smallest power of 2 greater than or equal to a [`Natural`]. The [`Natural`] is
/// taken by reference.
///
/// $f(x) = 2^{\lceil \log_2 x \rceil}$.
///
/// # 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
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::{NextPowerOf2, Pow};
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_nz::natural::Natural;
///
/// assert_eq!((&Natural::ZERO).next_power_of_2(), 1);
/// assert_eq!((&Natural::from(123u32)).next_power_of_2(), 128);
/// assert_eq!((&Natural::from(10u32).pow(12)).next_power_of_2(), 1099511627776u64);
/// ```
fn next_power_of_2(self) -> Natural {
Natural(match *self {
Natural(Small(small)) => {
if let Some(result) = small.checked_next_power_of_two() {
Small(result)
} else {
Large(vec![0, 1])
}
}
Natural(Large(ref limbs)) => Large(limbs_next_power_of_2(limbs)),
})
}
}
impl NextPowerOf2Assign for Natural {
/// Replaces a [`Natural`] with the smallest power of 2 greater than or equal to it.
///
/// $x \gets 2^{\lceil \log_2 x \rceil}$.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$ (only if the underlying [`Vec`] needs to reallocate)
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::{NextPowerOf2Assign, Pow};
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_nz::natural::Natural;
///
/// let mut x = Natural::ZERO;
/// x.next_power_of_2_assign();
/// assert_eq!(x, 1);
///
/// let mut x = Natural::from(123u32);
/// x.next_power_of_2_assign();
/// assert_eq!(x, 128);
///
/// let mut x = Natural::from(10u32).pow(12);
/// x.next_power_of_2_assign();
/// assert_eq!(x, 1099511627776u64);
/// ```
fn next_power_of_2_assign(&mut self) {
match *self {
Natural(Small(ref mut small)) => {
if let Some(pow) = small.checked_next_power_of_two() {
*small = pow;
} else {
*self = Natural(Large(vec![0, 1]));
}
}
Natural(Large(ref mut limbs)) => {
limbs_vec_next_power_of_2_in_place(limbs);
}
}
}
}