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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 crate::InnerFloat::Finite;
use alloc::vec;
use core::cmp::Ordering::{self, *};
use malachite_base::iterators::thue_morse_sequence;
use malachite_base::num::arithmetic::traits::{NegModPowerOf2, PowerOf2};
use malachite_base::num::basic::integers::PrimitiveInt;
use malachite_base::num::basic::traits::OneHalf;
use malachite_base::rounding_modes::RoundingMode::{self, *};
use malachite_nz::natural::{Natural, bit_to_limb_count_ceiling};
use malachite_nz::platform::Limb;
#[cfg(feature = "32_bit_limbs")]
const LIMB_0: Limb = 0xd32d2cd2;
#[cfg(feature = "32_bit_limbs")]
const LIMB_1: Limb = 0x2cd2d32c;
#[cfg(not(feature = "32_bit_limbs"))]
const LIMB_0: Limb = 0xd32d2cd32cd2d32c;
#[cfg(not(feature = "32_bit_limbs"))]
const LIMB_1: Limb = 0x2cd2d32cd32d2cd2;
impl Float {
/// Returns an approximation of the Prouhet-Thue-Morse constant, 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.)
///
/// The Prouhet-Thue-Morse constant is the real number whose bits are the Thue-Morse sequence.
/// That is,
/// $$
/// \tau = \sum_{k=0}^\infty\frac{t_n}{2^{n+1}}+\varepsilon,
/// where $t_n$ is the Thue-Morse sequence.
/// $$
/// - If $m$ is not `Nearest`, then $|\varepsilon| < 2^{-p-1}$.
/// - If $m$ is `Nearest`, then $|\varepsilon| < 2^{-p-2}$.
///
/// An alternative expression, from <https://mathworld.wolfram.com/Thue-MorseConstant.html>, is
/// $$
/// \tau = \frac{1}{4}\left[2-\prod_{k=0}^\infty\left(1-\frac{1}{2^{2^k}}\right)\right].
/// $$
///
/// The constant is irrational and transcendental.
///
/// The output has precision `prec`.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// 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 (tmc, o) = Float::prouhet_thue_morse_constant_prec_round(100, Floor);
/// assert_eq!(tmc.to_string(), "0.4124540336401075977833613682584");
/// assert_eq!(o, Less);
///
/// let (tmc, o) = Float::prouhet_thue_morse_constant_prec_round(100, Ceiling);
/// assert_eq!(tmc.to_string(), "0.4124540336401075977833613682588");
/// assert_eq!(o, Greater);
/// ```
pub fn prouhet_thue_morse_constant_prec_round(prec: u64, rm: RoundingMode) -> (Self, Ordering) {
assert_ne!(prec, 0);
assert_ne!(rm, Exact);
// If the result is 1/2 then the exponent is 0 rather than -1, so we handle that case
// separately.
if prec == 1 && (rm == Nearest || rm == Ceiling || rm == Up) {
return (Self::ONE_HALF, Greater);
} else if prec == 2 && (rm == Ceiling || rm == Up) {
// TODO implement const_from_unsigned_prec_times_power_of_2
return (Self::one_half_prec(2), Greater);
}
let len = bit_to_limb_count_ceiling(prec);
let mut limbs = vec![0; len];
let mut tms = thue_morse_sequence();
for (i, b) in (0..len).rev().zip(&mut tms) {
limbs[i] = if b {
limbs[i + 1] |= 1;
LIMB_1
} else {
LIMB_0
};
}
let lsb = Limb::power_of_2(prec.neg_mod_power_of_2(Limb::LOG_WIDTH));
let mut next_tms = false;
if lsb == 1 {
next_tms = tms.next().unwrap();
if next_tms {
limbs[0] |= 1;
}
}
let increment = match rm {
Up | Ceiling => true,
Down | Floor => false,
Nearest => match lsb {
1 => !next_tms,
2 => tms.next().unwrap(),
_ => limbs[0] & (lsb >> 1) != 0,
},
Exact => unreachable!(),
};
limbs[0] &= !(lsb - 1);
let mut significand = Natural::from_owned_limbs_asc(limbs);
if increment {
significand += Natural::from(lsb);
}
(
Self(Finite {
sign: true,
exponent: -1,
precision: prec,
significand,
}),
if increment { Greater } else { Less },
)
}
/// Returns an approximation of the Prouhet-Thue-Morse constant, 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.)
///
/// The Prouhet-Thue-Morse constant is the real number whose bits are the Thue-Morse sequence.
/// That is,
/// $$
/// \tau = \sum_{k=0}^\infty\frac{t_n}{2^{n+1}}+\varepsilon,
/// $$
/// where $t_n$ is the Thue-Morse sequence.
/// - $|\varepsilon| < 2^{-p-2}$.
///
/// An alternative expression, from <https://mathworld.wolfram.com/Thue-MorseConstant.html>, is
/// $$
/// \tau = \frac{1}{4}\left[2-\prod_{k=0}^\infty\left(1-\frac{1}{2^{2^k}}\right)\right].
/// $$
///
/// The constant is irrational and transcendental.
///
/// The output has precision `prec`.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// 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 (tmc, o) = Float::prouhet_thue_morse_constant_prec(1);
/// assert_eq!(tmc.to_string(), "0.5");
/// assert_eq!(o, Greater);
///
/// let (tmc, o) = Float::prouhet_thue_morse_constant_prec(10);
/// assert_eq!(tmc.to_string(), "0.4126");
/// assert_eq!(o, Greater);
///
/// let (tmc, o) = Float::prouhet_thue_morse_constant_prec(100);
/// assert_eq!(tmc.to_string(), "0.4124540336401075977833613682584");
/// assert_eq!(o, Less);
/// ```
#[inline]
pub fn prouhet_thue_morse_constant_prec(prec: u64) -> (Self, Ordering) {
Self::prouhet_thue_morse_constant_prec_round(prec, Nearest)
}
}