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// Copyright © 2026 Mikhail Hogrefe
//
// Uses code adopted from the GNU MPFR Library.
//
// Copyright 1999-2024 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::num::arithmetic::traits::{Sqrt, Square};
use malachite_base::num::basic::integers::PrimitiveInt;
use malachite_base::num::conversion::traits::ExactFrom;
use malachite_base::rounding_modes::RoundingMode::{self, *};
use malachite_nz::natural::arithmetic::float_extras::float_can_round;
use malachite_nz::platform::Limb;
impl Float {
/// Returns an approximation of $\pi$, 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.)
///
/// $$
/// x = \pi+\varepsilon.
/// $$
/// - If $m$ is not `Nearest`, then $|\varepsilon| < 2^{-p+2}$.
/// - 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, o) = Float::pi_prec_round(100, Floor);
/// assert_eq!(pi.to_string(), "3.141592653589793238462643383279");
/// assert_eq!(o, Less);
///
/// let (pi, o) = Float::pi_prec_round(100, Ceiling);
/// assert_eq!(pi.to_string(), "3.141592653589793238462643383282");
/// assert_eq!(o, Greater);
/// ```
///
// This is mpfr_const_pi_internal from const_pi.c, MPFR 4.2.0.
#[inline]
pub fn pi_prec_round(prec: u64, rm: RoundingMode) -> (Self, Ordering) {
// we need 9 * 2 ^ kmax - 4 >= px + 2 * kmax + 8
let mut kmax = 2;
while ((prec + 2 * kmax + 12) / 9) >> kmax != 0 {
kmax += 1;
}
// guarantees no recomputation for px <= 10000
let mut working_prec = prec + 3 * kmax + 14;
let mut increment = Limb::WIDTH;
loop {
let mut a = Self::one_prec(working_prec);
let mut big_a = a.clone();
let mut big_b = Self::one_half_prec(working_prec);
let mut big_d = Self::one_prec(working_prec) >> 2;
let mut k = 0;
loop {
let s = (&big_a + &big_b) >> 2;
a = (a + big_b.sqrt()) >> 1;
big_a = (&a).square();
big_b = (&big_a - s) << 1;
let mut s = &big_a - &big_b;
assert!(s < 1u32);
let ip = i64::exact_from(working_prec);
let cancel = if s == 0 {
ip
} else {
i64::from(-s.get_exponent().unwrap())
};
s <<= k;
big_d -= s;
// stop when |A_k - B_k| <= 2 ^ (k - p) i.e. cancel >= p - k
if cancel >= ip - i64::exact_from(k) {
break;
}
k += 1;
}
let pi: Self = big_b / big_d;
if float_can_round(
pi.significand_ref().unwrap(),
working_prec - (k << 1) - 8,
prec,
rm,
) {
return Self::from_float_prec_round(pi, prec, rm);
}
working_prec += kmax + increment;
increment = working_prec >> 1;
}
}
/// Returns an approximation of $\pi$, 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.)
///
/// $$
/// x = \pi+\varepsilon.
/// $$
/// - $|\varepsilon| < 2^{-p+1}$.
///
/// 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, o) = Float::pi_prec(1);
/// assert_eq!(pi.to_string(), "4.0");
/// assert_eq!(o, Greater);
///
/// let (pi, o) = Float::pi_prec(10);
/// assert_eq!(pi.to_string(), "3.141");
/// assert_eq!(o, Less);
///
/// let (pi, o) = Float::pi_prec(100);
/// assert_eq!(pi.to_string(), "3.141592653589793238462643383279");
/// assert_eq!(o, Less);
/// ```
#[inline]
pub fn pi_prec(prec: u64) -> (Self, Ordering) {
Self::pi_prec_round(prec, Nearest)
}
}