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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 the Gelfond–Schneider constant, $2^{\sqrt 2}$, 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.)
///
/// $$
/// x = 2^{\sqrt 2}+\varepsilon.
/// $$
/// - 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
/// $T(n) = O(n^{3/2} \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// 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 (gelfond_schneider_constant, o) =
/// Float::gelfond_schneider_constant_prec_round(100, Floor);
/// assert_eq!(
/// gelfond_schneider_constant.to_string(),
/// "2.6651441426902251886502972498731"
/// );
/// assert_eq!(o, Less);
///
/// let (gelfond_schneider_constant, o) =
/// Float::gelfond_schneider_constant_prec_round(100, Ceiling);
/// assert_eq!(
/// gelfond_schneider_constant.to_string(),
/// "2.6651441426902251886502972498762"
/// );
/// assert_eq!(o, Greater);
/// ```
pub fn gelfond_schneider_constant_prec_round(prec: u64, rm: RoundingMode) -> (Self, Ordering) {
let mut working_prec = prec + 10;
let mut increment = Limb::WIDTH;
loop {
let (sqrt_2_lo, sqrt_2_hi) =
floor_and_ceiling(Self::sqrt_2_prec_round(working_prec, Floor));
// 2^x is increasing, so 2^sqrt_2_lo <= 2^sqrt(2) <= 2^sqrt_2_hi.
let (gelfond_schneider_constant_lo, mut o_lo) = Self::from_float_prec_round(
Self::power_of_2_of_float_round(sqrt_2_lo, Floor).0,
prec,
rm,
);
let (gelfond_schneider_constant_hi, mut o_hi) = Self::from_float_prec_round(
Self::power_of_2_of_float_round(sqrt_2_hi, 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 && gelfond_schneider_constant_lo == gelfond_schneider_constant_hi {
return (gelfond_schneider_constant_lo, o_lo);
}
working_prec += increment;
increment = working_prec >> 1;
}
}
/// Returns an approximation of the Gelfond–Schneider constant, $2^{\sqrt 2}$, 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.)
///
/// $$
/// x = 2^{\sqrt 2}+\varepsilon.
/// $$
/// - $|\varepsilon| < 2^{-p+1}$.
///
/// 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 (gelfond_schneider_constant, o) = Float::gelfond_schneider_constant_prec(1);
/// assert_eq!(gelfond_schneider_constant.to_string(), "2.0");
/// assert_eq!(o, Less);
///
/// let (gelfond_schneider_constant, o) = Float::gelfond_schneider_constant_prec(10);
/// assert_eq!(gelfond_schneider_constant.to_string(), "2.6641");
/// assert_eq!(o, Less);
///
/// let (gelfond_schneider_constant, o) = Float::gelfond_schneider_constant_prec(100);
/// assert_eq!(
/// gelfond_schneider_constant.to_string(),
/// "2.6651441426902251886502972498731"
/// );
/// assert_eq!(o, Less);
/// ```
#[inline]
pub fn gelfond_schneider_constant_prec(prec: u64) -> (Self, Ordering) {
Self::gelfond_schneider_constant_prec_round(prec, Nearest)
}
}