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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, floor_and_ceiling};
use core::cmp::Ordering::{self, *};
use malachite_base::num::basic::integers::PrimitiveInt;
use malachite_base::rounding_modes::RoundingMode::{self, *};
use malachite_nz::platform::Limb;
impl Float {
/// Returns an approximation of Gelfond's constant, $e^\pi$, 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.)
///
/// $$
/// x = e^\pi+\varepsilon.
/// $$
/// - If $m$ is not `Nearest`, then $|\varepsilon| < 2^{-p+5}$.
/// - If $m$ is `Nearest`, then $|\varepsilon| < 2^{-p+4}$.
///
/// The constant is irrational and transcendental.
///
/// The output has precision `prec`.
///
/// # Worst-case complexity
/// $T(n) = O(n^{3/2} \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// 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 (gelfonds_constant, o) = Float::gelfonds_constant_prec_round(100, Floor);
/// assert_eq!(
/// gelfonds_constant.to_string(),
/// "23.140692632779269005729086367940"
/// );
/// assert_eq!(o, Less);
///
/// let (gelfonds_constant, o) = Float::gelfonds_constant_prec_round(100, Ceiling);
/// assert_eq!(
/// gelfonds_constant.to_string(),
/// "23.140692632779269005729086367965"
/// );
/// assert_eq!(o, Greater);
/// ```
pub fn gelfonds_constant_prec_round(prec: u64, rm: RoundingMode) -> (Self, Ordering) {
let mut working_prec = prec + 10;
let mut increment = Limb::WIDTH;
loop {
let (pi_lo, pi_hi) = floor_and_ceiling(Self::pi_prec_round(working_prec, Floor));
// exp is increasing, so exp(pi_lo) <= exp(pi) <= exp(pi_hi).
let (gelfonds_constant_lo, mut o_lo) =
Self::from_float_prec_round(pi_lo.exp_round(Floor).0, prec, rm);
let (gelfonds_constant_hi, mut o_hi) =
Self::from_float_prec_round(pi_hi.exp_round(Ceiling).0, prec, rm);
if o_lo == Equal {
o_lo = o_hi;
}
if o_hi == Equal {
o_hi = o_lo;
}
if o_lo == o_hi && gelfonds_constant_lo == gelfonds_constant_hi {
return (gelfonds_constant_lo, o_lo);
}
working_prec += increment;
increment = working_prec >> 1;
}
}
/// Returns an approximation of Gelfond's constant, $e^\pi$, 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.)
///
/// $$
/// x = e^\pi+\varepsilon.
/// $$
/// - $|\varepsilon| < 2^{-p+4}$.
///
/// The constant is irrational and transcendental.
///
/// The output has precision `prec`.
///
/// # Worst-case complexity
/// $T(n) = O(n^{3/2} \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// 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 (gelfonds_constant, o) = Float::gelfonds_constant_prec(1);
/// assert_eq!(gelfonds_constant.to_string(), "16.0");
/// assert_eq!(o, Less);
///
/// let (gelfonds_constant, o) = Float::gelfonds_constant_prec(10);
/// assert_eq!(gelfonds_constant.to_string(), "23.156");
/// assert_eq!(o, Greater);
///
/// let (gelfonds_constant, o) = Float::gelfonds_constant_prec(100);
/// assert_eq!(
/// gelfonds_constant.to_string(),
/// "23.140692632779269005729086367940"
/// );
/// assert_eq!(o, Less);
/// ```
#[inline]
pub fn gelfonds_constant_prec(prec: u64) -> (Self, Ordering) {
Self::gelfonds_constant_prec_round(prec, Nearest)
}
}