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// Copyright © 2026 Mikhail Hogrefe
//
// Uses code adopted from the GNU MPFR Library.
//
// Copyright 1999, 2001-2024 Free Software Foundation, Inc.
//
// Contributed by the AriC and Caramba projects, INRIA.
//
// 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 $\pi/4$, 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.)
///
/// $$
/// x = \pi/4+\varepsilon.
/// $$
/// - If $m$ is not `Nearest`, then $|\varepsilon| < 2^{-p}$.
/// - If $m$ is `Nearest`, then $|\varepsilon| < 2^{-p-1}$.
///
/// The constant is irrational and transcendental.
///
/// The output has precision `prec`.
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n (\log n)^2)$
///
/// 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 (pi_over_4, o) = Float::pi_over_4_prec_round(100, Floor);
/// assert_eq!(pi_over_4.to_string(), "0.78539816339744830961566084582");
/// assert_eq!(o, Less);
///
/// let (pi_over_4, o) = Float::pi_over_4_prec_round(100, Ceiling);
/// assert_eq!(pi_over_4.to_string(), "0.7853981633974483096156608458206");
/// assert_eq!(o, Greater);
/// ```
#[inline]
pub fn pi_over_4_prec_round(prec: u64, rm: RoundingMode) -> (Self, Ordering) {
let (pi, o) = Self::pi_prec_round(prec, rm);
(pi >> 2u32, o)
}
/// Returns an approximation of $\pi/4$, 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.)
///
/// $$
/// x = \pi/4+\varepsilon.
/// $$
/// - $|\varepsilon| < 2^{-p-1}$.
///
/// The constant is irrational and transcendental.
///
/// The output has precision `prec`.
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n (\log n)^2)$
///
/// 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 (pi_over_4, o) = Float::pi_over_4_prec(1);
/// assert_eq!(pi_over_4.to_string(), "1.0");
/// assert_eq!(o, Greater);
///
/// let (pi_over_4, o) = Float::pi_over_4_prec(10);
/// assert_eq!(pi_over_4.to_string(), "0.785");
/// assert_eq!(o, Less);
///
/// let (pi_over_4, o) = Float::pi_over_4_prec(100);
/// assert_eq!(pi_over_4.to_string(), "0.78539816339744830961566084582");
/// assert_eq!(o, Less);
/// ```
#[inline]
pub fn pi_over_4_prec(prec: u64) -> (Self, Ordering) {
Self::pi_over_4_prec_round(prec, Nearest)
}
}