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// Copyright © 2026 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::natural::Natural;
use crate::natural_polynomial::NaturalPolynomial;
use malachite_base::num::arithmetic::traits::{HeightRef, ModIsReduced};
use malachite_base::num::basic::traits::Zero;
impl ModIsReduced<Natural> for NaturalPolynomial {
/// Returns whether a [`NaturalPolynomial`] is reduced modulo a [`Natural`] $m$; in other words,
/// whether every one of its coefficients is less than $m$.
///
/// Asking that of every coefficient is asking it of the largest, so this is a comparison
/// against the polynomial's [`height`](HeightRef::height_ref). The height is one of the
/// coefficients, so it is borrowed rather than built. The zero polynomial has no coefficients
/// and is reduced modulo every $m$.
///
/// $m$ cannot be zero.
///
/// $f(p, m) = (\max_i p_i < m)$.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// coefficients.
///
/// # Panics
/// Panics if `m` is 0.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModIsReduced;
/// use malachite_base::num::basic::traits::One;
/// use malachite_nz::natural::Natural;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// // The coefficients are 2, 3, and 1, so 4 is large enough and 3 is not.
/// let p = NaturalPolynomial::from_str("x^2+3*x+2").unwrap();
/// assert_eq!(p.mod_is_reduced(&Natural::from(4u32)), true);
/// assert_eq!(p.mod_is_reduced(&Natural::from(3u32)), false);
///
/// // The zero polynomial is reduced modulo everything.
/// assert_eq!(
/// NaturalPolynomial::from_str("0")
/// .unwrap()
/// .mod_is_reduced(&Natural::ONE),
/// true
/// );
/// ```
#[inline]
fn mod_is_reduced(&self, m: &Natural) -> bool {
assert_ne!(*m, Natural::ZERO);
self.height_ref() < m
}
}