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use crate::natural::InnerNatural::{Large, Small};
use crate::natural::Natural;
use crate::platform::Limb;
use malachite_base::num::basic::integers::PrimitiveInt;
use malachite_base::num::logic::traits::LeadingZeros;
use malachite_base::slices::slice_leading_zeros;
use std::cmp::Ordering;
use std::mem::swap;
// Interpreting two equal-length slices of `Limb`s as the limbs (in ascending order) of two
// `Natural`s, compares the two `Natural`s.
//
// # Worst-case complexity
// $T(n) = O(n)$
//
// $M(n) = O(1)$
//
// where $T$ is time, $M$ is additional memory, and $n$ is `xs.len()`.
//
// This is equivalent to `mpn_cmp` from `gmp.h`, GMP 6.2.1.
//
// # Panics
// Panics if `xs` and `ys` have different lengths.
pub_crate_test! {limbs_cmp_same_length(xs: &[Limb], ys: &[Limb]) -> Ordering {
assert_eq!(xs.len(), ys.len());
xs.iter().rev().cmp(ys.iter().rev())
}}
// Interpreting two slices of `Limb`s as the limbs (in ascending order) of two `Natural`s, compares
// the two `Natural`s. Neither limb slice can contain trailing zeros.
//
// # Worst-case complexity
// $T(n) = O(n)$
//
// $M(n) = O(1)$
//
// where $T$ is time, $M$ is additional memory, and $n$ is `min(xs.len(), ys.len())`.
//
// # Panics
// Panics if the last element of `xs` or `ys` is zero.
pub_crate_test! {limbs_cmp(xs: &[Limb], ys: &[Limb]) -> Ordering {
assert_ne!(xs.last(), Some(&0));
assert_ne!(ys.last(), Some(&0));
xs.len()
.cmp(&ys.len())
.then_with(|| limbs_cmp_same_length(xs, ys))
}}
// Interpreting two slices of `Limb`s as the limbs (in ascending order) of two `Natural`s, returns
// their normalized comparison. See `Natural::cmp_normalized` for details.
//
// # Worst-case complexity
// $T(n) = O(n)$
//
// $M(n) = O(1)$
//
// where $T$ is time, $M$ is additional memory, and $n$ is `min(xs.len(), ys.len())`.
//
// # Panics
// Panics if either `xs` or `ys` is empty, or if the last element of `xs` or `ys` is zero.
pub_test! {limbs_cmp_normalized(xs: &[Limb], ys: &[Limb]) -> Ordering {
let mut xs = &xs[slice_leading_zeros(xs)..];
let mut ys = &ys[slice_leading_zeros(ys)..];
let mut xs_leading = LeadingZeros::leading_zeros(*xs.last().unwrap());
assert_ne!(xs_leading, Limb::WIDTH);
let mut ys_leading = LeadingZeros::leading_zeros(*ys.last().unwrap());
assert_ne!(ys_leading, Limb::WIDTH);
let mut xs_len = xs.len();
let mut ys_len = ys.len();
let mut swapped = false;
match xs_leading.cmp(&ys_leading) {
Ordering::Equal => {
return match xs_len.cmp(&ys_len) {
Ordering::Equal => limbs_cmp_same_length(xs, ys),
Ordering::Less => {
let leading_cmp = limbs_cmp_same_length(xs, &ys[ys_len - xs_len..]);
if leading_cmp == Ordering::Greater {
Ordering::Greater
} else {
Ordering::Less
}
}
Ordering::Greater => {
let leading_cmp = limbs_cmp_same_length(&xs[xs_len - ys_len..], ys);
if leading_cmp == Ordering::Less {
Ordering::Less
} else {
Ordering::Greater
}
}
};
}
Ordering::Less => {
swap(&mut xs, &mut ys);
swap(&mut xs_leading, &mut ys_leading);
swap(&mut xs_len, &mut ys_len);
swapped = true;
}
_ => {}
}
let xs_shift = xs_leading - ys_leading;
let comp_xs_shift = Limb::WIDTH - xs_shift;
let mut xs_i = xs_len - 1;
let mut ys_i = ys_len - 1;
loop {
let y = ys[ys_i];
let xs_hi = xs[xs_i];
let xs_lo = if xs_i == 0 { 0 } else { xs[xs_i - 1] };
let x = (xs_hi << xs_shift) | (xs_lo >> comp_xs_shift);
let cmp = x.cmp(&y);
if cmp != Ordering::Equal {
return if swapped { cmp.reverse() } else { cmp };
}
if xs_i == 0 {
return if ys_i == 0 {
Ordering::Equal
} else if swapped {
Ordering::Greater
} else {
Ordering::Less
};
} else if ys_i == 0 {
return if swapped {
Ordering::Less
} else {
Ordering::Greater
};
}
xs_i -= 1;
ys_i -= 1;
}
}}
impl PartialOrd for Natural {
/// Compares two [`Natural`]s.
///
/// See the documentation for the [`Ord`] implementation.
#[inline]
fn partial_cmp(&self, other: &Natural) -> Option<Ordering> {
Some(self.cmp(other))
}
}
impl Ord for Natural {
/// Compares two [`Natural`]s.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is
/// `min(self.significant_bits(), other.significant_bits())`.
///
/// # Examples
/// ```
/// use malachite_nz::natural::Natural;
///
/// assert!(Natural::from(123u32) > Natural::from(122u32));
/// assert!(Natural::from(123u32) >= Natural::from(122u32));
/// assert!(Natural::from(123u32) < Natural::from(124u32));
/// assert!(Natural::from(123u32) <= Natural::from(124u32));
/// ```
fn cmp(&self, other: &Natural) -> Ordering {
if std::ptr::eq(self, other) {
return Ordering::Equal;
}
match (self, other) {
(&Natural(Small(ref x)), &Natural(Small(ref y))) => x.cmp(y),
(&Natural(Small(_)), &Natural(Large(_))) => Ordering::Less,
(&Natural(Large(_)), &Natural(Small(_))) => Ordering::Greater,
(&Natural(Large(ref xs)), &Natural(Large(ref ys))) => limbs_cmp(xs, ys),
}
}
}
impl Natural {
/// Returns a result of a comparison between two [`Natural`]s as if each had been multiplied by
/// some power of 2 to bring it into the interval $[1, 2)$.
///
/// That is, the comparison is equivalent to a comparison between $f(x)$ and $f(y)$, where
/// $$
/// f(n) = n2^{\lfloor\log_2 n \rfloor}.
/// $$
///
/// The multiplication is not actually performed.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is
/// `min(self.significant_bits(), other.significant_bits())`.
///
/// # Panics
/// Panics if either argument is zero.
///
/// # Examples
/// ```
/// use malachite_nz::natural::Natural;
/// use std::cmp::Ordering;
///
/// // 1 == 1.0 * 2^0, 4 == 1.0 * 2^2
/// // 1.0 == 1.0
/// assert_eq!(Natural::from(1u32).cmp_normalized(&Natural::from(4u32)), Ordering::Equal);
///
/// // 5 == 1.25 * 2^2, 6 == 1.5 * 2^2
/// // 1.25 < 1.5
/// assert_eq!(Natural::from(5u32).cmp_normalized(&Natural::from(6u32)), Ordering::Less);
///
/// // 3 == 1.5 * 2^1, 17 == 1.0625 * 2^4
/// // 1.5 > 1.0625
/// assert_eq!(Natural::from(3u32).cmp_normalized(&Natural::from(17u32)), Ordering::Greater);
///
/// // 9 == 1.125 * 2^3, 36 == 1.125 * 2^5
/// // 1.125 == 1.125
/// assert_eq!(Natural::from(9u32).cmp_normalized(&Natural::from(36u32)), Ordering::Equal);
/// ```
pub fn cmp_normalized(&self, other: &Natural) -> Ordering {
assert_ne!(*self, 0);
assert_ne!(*other, 0);
if std::ptr::eq(self, other) {
return Ordering::Equal;
}
match (self, other) {
(&Natural(Small(x)), &Natural(Small(y))) => {
let leading_x = x.leading_zeros();
let leading_y = y.leading_zeros();
match leading_x.cmp(&leading_y) {
Ordering::Equal => x.cmp(&y),
Ordering::Less => x.cmp(&(y << (leading_y - leading_x))),
Ordering::Greater => (x << (leading_x - leading_y)).cmp(&y),
}
}
(&Natural(Small(x)), &Natural(Large(ref ys))) => limbs_cmp_normalized(&[x], ys),
(&Natural(Large(ref xs)), &Natural(Small(y))) => limbs_cmp_normalized(xs, &[y]),
(&Natural(Large(ref xs)), &Natural(Large(ref ys))) => limbs_cmp_normalized(xs, ys),
}
}
}