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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::FloorSqrt;
use malachite_base::polynomial::{FloorL2Norm, L2NormSquared};
impl FloorL2Norm for &NaturalPolynomial {
type Output = Natural;
/// Computes the floor of a [`NaturalPolynomial`]'s $L^2$ norm: the floor of the square root of
/// the sum of the squares of its coefficients.
///
/// $$
/// f(p) = \left \lfloor \sqrt{\sum_i p_i^2} \right \rfloor.
/// $$
///
/// The exact square of the norm is [`l2_norm_squared`](L2NormSquared::l2_norm_squared).
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// coefficients.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::polynomial::FloorL2Norm;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// assert_eq!(
/// NaturalPolynomial::from_str("x^2+3*x+2")
/// .unwrap()
/// .floor_l2_norm(),
/// 3u32
/// );
/// assert_eq!(
/// NaturalPolynomial::from_str("0").unwrap().floor_l2_norm(),
/// 0u32
/// );
/// assert_eq!(
/// NaturalPolynomial::from_str("5").unwrap().floor_l2_norm(),
/// 5u32
/// );
/// ```
///
/// This is equivalent to `fmpz_poly_2norm` from `fmpz_poly/2norm.c`, FLINT 3.6.0.
#[inline]
fn floor_l2_norm(self) -> Natural {
self.l2_norm_squared().floor_sqrt()
}
}