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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::integer_polynomial::arithmetic::square_truncated::square_truncated_ref;
use crate::natural_polynomial::NaturalPolynomial;
use malachite_base::num::arithmetic::traits::SquareAssign;
use malachite_base::polynomial::{SquareTruncated, SquareTruncatedAssign};
impl SquareTruncated for NaturalPolynomial {
type Output = Self;
/// Squares an [`NaturalPolynomial`], keeping only the coefficients of $x^i$ for $i$ less than
/// `len`, taking it by value.
///
/// $$
/// f(p, n) = p^2 \bmod x^n.
/// $$
///
/// The polynomial need not already be truncated: this is the square of its image modulo $x^n$,
/// so only its first `len` coefficients are read.
///
/// # Worst-case complexity
/// $T(n, m) = O(n(m + \log n) \log (nm) \log\log (nm))$
///
/// $M(n, m) = O(n(m + \log n) \log (nm))$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `len`, and $m$ is the largest number of
/// significant bits of any of the first `len` coefficients of the polynomial.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::polynomial::SquareTruncated;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// assert_eq!(
/// (NaturalPolynomial::from_str("x^2+3*x+2").unwrap())
/// .square_truncated(3)
/// .to_string(),
/// "13*x^2+12*x+4"
/// );
/// // The cross terms combine with the square of the linear coefficient.
/// assert_eq!(
/// (NaturalPolynomial::from_str("x^2+x+1").unwrap())
/// .square_truncated(3)
/// .to_string(),
/// "3*x^2+2*x+1"
/// );
/// ```
///
/// This is equivalent to `fmpz_poly_sqrlow` from `fmpz_poly/sqrlow.c`, FLINT 3.6.0.
#[inline]
fn square_truncated(mut self, len: u64) -> Self {
self.square_truncated_assign(len);
self
}
}
impl SquareTruncated for &NaturalPolynomial {
type Output = NaturalPolynomial;
/// Squares an [`NaturalPolynomial`], keeping only the coefficients of $x^i$ for $i$ less than
/// `len`, taking it by reference.
///
/// $$
/// f(p, n) = p^2 \bmod x^n.
/// $$
///
/// The polynomial need not already be truncated: this is the square of its image modulo $x^n$,
/// so only its first `len` coefficients are read.
///
/// # Worst-case complexity
/// $T(n, m) = O(n(m + \log n) \log (nm) \log\log (nm))$
///
/// $M(n, m) = O(n(m + \log n) \log (nm))$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `len`, and $m$ is the largest number of
/// significant bits of any of the first `len` coefficients of the polynomial.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::polynomial::SquareTruncated;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// assert_eq!(
/// (&NaturalPolynomial::from_str("x^2+3*x+2").unwrap())
/// .square_truncated(3)
/// .to_string(),
/// "13*x^2+12*x+4"
/// );
/// // The cross terms combine with the square of the linear coefficient.
/// assert_eq!(
/// (&NaturalPolynomial::from_str("x^2+x+1").unwrap())
/// .square_truncated(3)
/// .to_string(),
/// "3*x^2+2*x+1"
/// );
/// ```
///
/// This is equivalent to `fmpz_poly_sqrlow` from `fmpz_poly/sqrlow.c`, FLINT 3.6.0.
#[inline]
fn square_truncated(self, len: u64) -> NaturalPolynomial {
NaturalPolynomial {
coefficients: square_truncated_ref(&self.coefficients, len),
}
}
}
impl SquareTruncatedAssign for NaturalPolynomial {
/// Squares an [`NaturalPolynomial`] in place, keeping only the coefficients of $x^i$ for $i$
/// less than `len`.
///
/// $$
/// p \gets p^2 \bmod x^n.
/// $$
///
/// # Worst-case complexity
/// $T(n, m) = O(n(m + \log n) \log (nm) \log\log (nm))$
///
/// $M(n, m) = O(n(m + \log n) \log (nm))$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `len`, and $m$ is the largest number of
/// significant bits of any of the first `len` coefficients of the polynomial.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::polynomial::SquareTruncatedAssign;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// let mut p = NaturalPolynomial::from_str("x^2+3*x+2").unwrap();
/// p.square_truncated_assign(3);
/// assert_eq!(p.to_string(), "13*x^2+12*x+4");
/// ```
///
/// This is equivalent to `fmpz_poly_sqrlow` from `fmpz_poly/sqrlow.c`, FLINT 3.6.0.
#[inline]
fn square_truncated_assign(&mut self, len: u64) {
// The square of a constant is computed in place.
if len != 0
&& let [c] = self.coefficients.as_mut_slice()
{
c.square_assign();
} else {
self.coefficients = square_truncated_ref(&self.coefficients, len);
}
}
}