malachite_nz/natural/logic/

or.rs

// Copyright © 2025 Mikhail Hogrefe
//
// Uses code adopted from the GNU MP Library.
//
//      Copyright © 1991-2018 Free Software Foundation, Inc.
//
// 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::natural::InnerNatural::{Large, Small};
use crate::natural::Natural;
use crate::platform::Limb;
use alloc::vec::Vec;
use core::mem::swap;
use core::ops::{BitOr, BitOrAssign};

// Interpreting a slice of `Limb`s as the limbs (in ascending order) of a `Natural`, returns the
// limbs of the bitwise or of the `Natural` and a `Limb`. `xs` cannot be empty.
//
// # 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 fn limbs_or_limb(xs: &[Limb], y: Limb) -> Vec<Limb> {
    let mut result = xs.to_vec();
    limbs_or_limb_in_place(&mut result, y);
    result
}

// Interpreting a slice of `Limb`s as the limbs (in ascending order) of a `Natural`, writes the
// limbs of the bitwise or of the `Natural` and a `Limb` to an output slice. The output slice must
// be at least as long as the input slice. `xs` cannot be empty.
//
// # 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 `out` is shorter than `xs` or if `xs` is empty.
pub_test! {limbs_or_limb_to_out(out: &mut [Limb], xs: &[Limb], y: Limb) {
    out[..xs.len()].copy_from_slice(xs);
    limbs_or_limb_in_place(out, y);
}}

// Interpreting a slice of `Limb`s as the limbs (in ascending order) of a `Natural`, writes the
// limbs of the bitwise or of the `Natural` and a `Limb` to the input slice. `xs` cannot be empty.
//
// # Worst-case complexity
// Constant time and additional memory.
//
// # Panics
// Panics if `xs` is empty.
pub_test! {limbs_or_limb_in_place(xs: &mut [Limb], y: Limb) {
    xs[0] |= y;
}}

// Interpreting two equal-length slices of `Limb`s as the limbs (in ascending order) of two
// `Natural`s, returns a `Vec` of the limbs of the bitwise or of the `Natural`s. The length of the
// result is the length of one of the input slices.
//
// # 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` and `ys` have different lengths.
//
// This is equivalent to `mpn_ior_n` from `gmp-impl.h`, GMP 6.2.1, where `rp` is returned.
pub_test! {limbs_or_same_length(xs: &[Limb], ys: &[Limb]) -> Vec<Limb> {
    assert_eq!(xs.len(), ys.len());
    xs.iter().zip(ys.iter()).map(|(x, y)| x | y).collect()
}}

// Interpreting two slices of `Limb`s as the limbs (in ascending order) of two `Natural`s, returns a
// `Vec` of the limbs of the bitwise or of the `Natural`s. The length of the result is the length of
// the longer input slice.
//
// # Worst-case complexity
// $T(n) = O(n)$
//
// $M(n) = O(n)$
//
// where $T$ is time, $M$ is additional memory, and $n$ is `max(xs.len(), ys.len())`.
//
// This is equivalent to `mpz_ior` from `mpz/ior.c`, GMP 6.2.1, where `res` is returned and both
// inputs are non-negative.
pub_test! {limbs_or(xs: &[Limb], ys: &[Limb]) -> Vec<Limb> {
    let xs_len = xs.len();
    let ys_len = ys.len();
    let mut result;
    if xs_len >= ys_len {
        result = limbs_or_same_length(&xs[..ys_len], ys);
        result.extend_from_slice(&xs[ys_len..]);
    } else {
        result = limbs_or_same_length(xs, &ys[..xs_len]);
        result.extend_from_slice(&ys[xs_len..]);
    }
    result
}}

// Interpreting two equal-length slices of `Limb`s as the limbs (in ascending order) of two
// `Natural`s, writes the limbs of the bitwise or of the `Natural`s to an output slice. The output
// must be at least as long as one of the input slices.
//
// # 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` and `ys` have different lengths or if `out` is too short.
//
// This is equivalent to `mpn_ior_n` from `gmp-impl.h`, GMP 6.2.1.
pub_test! {limbs_or_same_length_to_out(out: &mut [Limb], xs: &[Limb], ys: &[Limb]) {
    let len = xs.len();
    assert_eq!(len, ys.len());
    assert!(out.len() >= len);
    for (out_x, (x, y)) in out.iter_mut().zip(xs.iter().zip(ys.iter())) {
        *out_x = x | y;
    }
}}

// Interpreting two slices of `Limb`s as the limbs (in ascending order) of two `Natural`s, writes
// the limbs of the bitwise or of the `Natural`s to an output slice. The output must be at least as
// long as the longer input slice.
//
// # Worst-case complexity
// $T(n) = O(n)$
//
// $M(n) = O(1)$
//
// where $T$ is time, $M$ is additional memory, and $n$ is `max(xs.len(), ys.len())`.
//
// # Panics
// Panics if `out` is too short.
//
// This is equivalent to `mpz_ior` from `mpz/ior.c`, GMP 6.2.1, where both inputs are non-negative.
pub_test! {limbs_or_to_out(out: &mut [Limb], xs: &[Limb], ys: &[Limb]) {
    let xs_len = xs.len();
    let ys_len = ys.len();
    if xs_len >= ys_len {
        assert!(out.len() >= xs_len);
        limbs_or_same_length_to_out(out, &xs[..ys_len], ys);
        out[ys_len..xs_len].copy_from_slice(&xs[ys_len..]);
    } else {
        assert!(out.len() >= ys_len);
        limbs_or_same_length_to_out(out, xs, &ys[..xs_len]);
        out[xs_len..ys_len].copy_from_slice(&ys[xs_len..]);
    }
}}

// Interpreting two equal-length slices of `Limb`s as the limbs (in ascending order) of two
// `Natural`s, writes the limbs of the bitwise or of the `Natural`s to the first (left) slice.
//
// # 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` and `ys` have different lengths.
//
// This is equivalent to `mpn_ior_n` from `gmp-impl.h`, GMP 6.2.1, where `rp == up`.
pub_test! {limbs_or_same_length_in_place_left(xs: &mut [Limb], ys: &[Limb]) {
    assert_eq!(xs.len(), ys.len());
    for (x, &y) in xs.iter_mut().zip(ys.iter()) {
        *x |= y;
    }
}}

// Interpreting a `Vec` of `Limb`s and a slice of `Limb`s as the limbs (in ascending order) of two
// `Natural`s, writes the limbs of the bitwise or of the `Natural`s to the `Vec`. If `ys` is longer
// than `xs`, `xs` will be extended.
//
// # Worst-case complexity
// $T(n) = O(n)$
//
// $M(n) = O(n)$
//
// where $T$ is time, $M$ is additional memory, and $n$ is `ys.len()`.
//
// This is equivalent to `mpz_ior` from `mpz/ior.c`, GMP 6.2.1, where `res == op1` and both inputs
// are non-negative.
pub_test! {limbs_or_in_place_left(xs: &mut Vec<Limb>, ys: &[Limb]) {
    let xs_len = xs.len();
    let ys_len = ys.len();
    if xs_len >= ys_len {
        limbs_or_same_length_in_place_left(&mut xs[..ys_len], ys);
    } else {
        limbs_or_same_length_in_place_left(xs, &ys[..xs_len]);
        xs.extend_from_slice(&ys[xs_len..]);
    }
}}

// Interpreting two `Vec`s of `Limb`s as the limbs (in ascending order) of two `Natural`s, writes
// the limbs of the bitwise or of the `Natural`s to the longer slice (or the first one, if they are
// equally long). Returns a `bool` which is `false` when the output is to the first slice and `true`
// when it's to the second slice.
//
// # 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())`.
//
// This is equivalent to `mpz_ior` from `mpz/ior.c`, GMP 6.2.1, where both inputs are non-negative
// and the result is written to the longer input slice.
pub_test! {limbs_or_in_place_either(xs: &mut [Limb], ys: &mut [Limb]) -> bool {
    let xs_len = xs.len();
    let ys_len = ys.len();
    let right = xs_len < ys_len;
    if right {
        limbs_or_same_length_in_place_left(&mut ys[..xs_len], xs);
    } else {
        limbs_or_same_length_in_place_left(&mut xs[..ys_len], ys);
    }
    right
}}

impl Natural {
    #[inline]
    fn or_limb(mut self, other: Limb) -> Natural {
        self.or_assign_limb(other);
        self
    }

    fn or_limb_ref(&self, other: Limb) -> Natural {
        Natural(match self {
            Natural(Small(small)) => Small(small | other),
            Natural(Large(limbs)) => Large(limbs_or_limb(limbs, other)),
        })
    }

    fn or_assign_limb(&mut self, other: Limb) {
        match self {
            Natural(Small(small)) => *small |= other,
            Natural(Large(limbs)) => limbs_or_limb_in_place(limbs, other),
        }
    }
}

impl BitOr<Natural> for Natural {
    type Output = Natural;

    /// Takes the bitwise or of two [`Natural`]s, taking both by value.
    ///
    /// $$
    /// f(x, y) = x \vee y.
    /// $$
    ///
    /// # 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_base::num::arithmetic::traits::Pow;
    /// use malachite_base::num::basic::traits::One;
    /// use malachite_nz::natural::Natural;
    ///
    /// assert_eq!(Natural::from(123u32) | Natural::from(456u32), 507);
    /// assert_eq!(
    ///     Natural::from(10u32).pow(12) | (Natural::from(10u32).pow(12) - Natural::ONE),
    ///     1000000004095u64
    /// );
    /// ```
    #[inline]
    fn bitor(mut self, other: Natural) -> Natural {
        self |= other;
        self
    }
}

impl<'a> BitOr<&'a Natural> for Natural {
    type Output = Natural;

    /// Takes the bitwise or of two [`Natural`]s, taking the first by value and the second by
    /// reference.
    ///
    /// $$
    /// f(x, y) = x \vee y.
    /// $$
    ///
    /// # Worst-case complexity
    /// $T(n) = O(n)$
    ///
    /// $M(n) = O(n)$
    ///
    /// where $T$ is time, $M$ is additional memory, and $n$ is `other.significant_bits()`.
    ///
    /// # Examples
    /// ```
    /// use malachite_base::num::arithmetic::traits::Pow;
    /// use malachite_base::num::basic::traits::One;
    /// use malachite_nz::natural::Natural;
    ///
    /// assert_eq!(Natural::from(123u32) | &Natural::from(456u32), 507);
    /// assert_eq!(
    ///     Natural::from(10u32).pow(12) | &(Natural::from(10u32).pow(12) - Natural::ONE),
    ///     1000000004095u64
    /// );
    /// ```
    #[inline]
    fn bitor(mut self, other: &'a Natural) -> Natural {
        self |= other;
        self
    }
}

impl BitOr<Natural> for &Natural {
    type Output = Natural;

    /// Takes the bitwise or of two [`Natural`]s, taking the first by reference and the second by
    /// value.
    ///
    /// $$
    /// f(x, y) = x \vee y.
    /// $$
    ///
    /// # 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::traits::One;
    /// use malachite_nz::natural::Natural;
    ///
    /// assert_eq!(&Natural::from(123u32) | Natural::from(456u32), 507);
    /// assert_eq!(
    ///     &Natural::from(10u32).pow(12) | (Natural::from(10u32).pow(12) - Natural::ONE),
    ///     1000000004095u64
    /// );
    /// ```
    #[inline]
    fn bitor(self, mut other: Natural) -> Natural {
        other |= self;
        other
    }
}

impl BitOr<&Natural> for &Natural {
    type Output = Natural;

    /// Takes the bitwise or of two [`Natural`]s, taking both by reference.
    ///
    /// $$
    /// f(x, y) = x \vee y.
    /// $$
    ///
    /// # Worst-case complexity
    /// $T(n) = O(n)$
    ///
    /// $M(n) = O(n)$
    ///
    /// where $T$ is time, $M$ is additional memory, and $n$ is `max(self.significant_bits(),
    /// other.significant_bits())`.
    ///
    /// # Examples
    /// ```
    /// use malachite_base::num::arithmetic::traits::Pow;
    /// use malachite_base::num::basic::traits::One;
    /// use malachite_nz::natural::Natural;
    ///
    /// assert_eq!(&Natural::from(123u32) | &Natural::from(456u32), 507);
    /// assert_eq!(
    ///     &Natural::from(10u32).pow(12) | &(Natural::from(10u32).pow(12) - Natural::ONE),
    ///     1000000004095u64
    /// );
    /// ```
    fn bitor(self, other: &Natural) -> Natural {
        match (self, other) {
            (x, &Natural(Small(y))) => x.or_limb_ref(y),
            (&Natural(Small(x)), y) => y.or_limb_ref(x),
            (Natural(Large(xs)), Natural(Large(ys))) => Natural(Large(limbs_or(xs, ys))),
        }
    }
}

impl BitOrAssign<Natural> for Natural {
    /// Bitwise-ors a [`Natural`] with another [`Natural`] in place, taking the [`Natural`] on the
    /// right-hand side by value.
    ///
    /// # 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_base::num::basic::traits::Zero;
    /// use malachite_nz::natural::Natural;
    ///
    /// let mut x = Natural::ZERO;
    /// x |= Natural::from(0x0000000fu32);
    /// x |= Natural::from(0x00000f00u32);
    /// x |= Natural::from(0x000f_0000u32);
    /// x |= Natural::from(0x0f000000u32);
    /// assert_eq!(x, 0x0f0f_0f0f);
    /// ```
    fn bitor_assign(&mut self, mut other: Natural) {
        match (&mut *self, &mut other) {
            (_, Natural(Small(y))) => self.or_assign_limb(*y),
            (Natural(Small(x)), _) => *self = other.or_limb(*x),
            (Natural(Large(xs)), Natural(Large(ys))) => {
                if limbs_or_in_place_either(xs, ys) {
                    swap(xs, ys);
                }
            }
        }
    }
}

impl<'a> BitOrAssign<&'a Natural> for Natural {
    /// Bitwise-ors a [`Natural`] with another [`Natural`] in place, taking the [`Natural`] on the
    /// right-hand side by reference.
    ///
    /// # Worst-case complexity
    /// $T(n) = O(n)$
    ///
    /// $M(n) = O(n)$
    ///
    /// where $T$ is time, $M$ is additional memory, and $n$ is `other.significant_bits()`.
    ///
    /// # Examples
    /// ```
    /// use malachite_base::num::basic::traits::Zero;
    /// use malachite_nz::natural::Natural;
    ///
    /// let mut x = Natural::ZERO;
    /// x |= &Natural::from(0x0000000fu32);
    /// x |= &Natural::from(0x00000f00u32);
    /// x |= &Natural::from(0x000f_0000u32);
    /// x |= &Natural::from(0x0f000000u32);
    /// assert_eq!(x, 0x0f0f_0f0f);
    /// ```
    fn bitor_assign(&mut self, other: &'a Natural) {
        match (&mut *self, other) {
            (_, Natural(Small(y))) => self.or_assign_limb(*y),
            (Natural(Small(x)), _) => *self = other.or_limb_ref(*x),
            (Natural(Large(xs)), Natural(Large(ys))) => {
                limbs_or_in_place_left(xs, ys);
            }
        }
    }
}