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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::Float;
use core::cmp::Ordering;
use malachite_base::rounding_modes::RoundingMode::{self, *};
impl Float {
/// Returns an approximation of the square root of 3, with the given precision and rounded using
/// the given [`RoundingMode`]. An [`Ordering`] is also returned, indicating whether the rounded
/// value is less than or greater than the exact value of the constant. (Since the constant is
/// irrational, the rounded value is never equal to the exact value.)
///
/// $$
/// x = \sqrt{3}+\varepsilon.
/// $$
/// - If $m$ is not `Nearest`, then $|\varepsilon| < 2^{-p+1}$.
/// - If $m$ is `Nearest`, then $|\varepsilon| < 2^{-p}$.
///
/// The constant is irrational and algebraic.
///
/// The output has precision `prec`.
///
/// # 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 `prec`.
///
/// # Panics
/// Panics if `prec` is zero or if `rm` is `Exact`.
///
/// # Examples
/// ```
/// use malachite_base::rounding_modes::RoundingMode::*;
/// use malachite_float::Float;
/// use std::cmp::Ordering::*;
///
/// let (sqrt_3, o) = Float::sqrt_3_prec_round(100, Floor);
/// assert_eq!(sqrt_3.to_string(), "1.732050807568877293527446341505");
/// assert_eq!(o, Less);
///
/// let (sqrt_3, o) = Float::sqrt_3_prec_round(100, Ceiling);
/// assert_eq!(sqrt_3.to_string(), "1.732050807568877293527446341506");
/// assert_eq!(o, Greater);
/// ```
#[inline]
pub fn sqrt_3_prec_round(prec: u64, rm: RoundingMode) -> (Self, Ordering) {
Self::sqrt_prec_round(const { Self::const_from_unsigned(3) }, prec, rm)
}
/// Returns an approximation of the square root of 3, with the given precision and rounded to
/// the nearest [`Float`] of that precision. An [`Ordering`] is also returned, indicating
/// whether the rounded value is less than or greater than the exact value of the constant.
/// (Since the constant is irrational, the rounded value is never equal to the exact value.)
///
/// $$
/// x = \sqrt{3}+\varepsilon.
/// $$
/// - $|\varepsilon| < 2^{-p}$.
///
/// The constant is irrational and algebraic.
///
/// The output has precision `prec`.
///
/// # 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 `prec`.
///
/// # Panics
/// Panics if `prec` is zero.
///
/// # Examples
/// ```
/// use malachite_float::Float;
/// use std::cmp::Ordering::*;
///
/// let (sqrt_3, o) = Float::sqrt_3_prec(1);
/// assert_eq!(sqrt_3.to_string(), "2.0");
/// assert_eq!(o, Greater);
///
/// let (sqrt_3, o) = Float::sqrt_3_prec(10);
/// assert_eq!(sqrt_3.to_string(), "1.732");
/// assert_eq!(o, Greater);
///
/// let (sqrt_3, o) = Float::sqrt_3_prec(100);
/// assert_eq!(sqrt_3.to_string(), "1.732050807568877293527446341506");
/// assert_eq!(o, Greater);
/// ```
#[inline]
pub fn sqrt_3_prec(prec: u64) -> (Self, Ordering) {
Self::sqrt_3_prec_round(prec, Nearest)
}
}