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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::num::arithmetic::traits::{BellNumber, CheckedBellNumber};
// The Bell numbers grow superexponentially, so for every primitive width the entire range of
// representable values is a short hardcoded table, checked against OEIS A000110.
const BELL_NUMBERS_U8: [u8; 7] = [1, 1, 2, 5, 15, 52, 203];
const BELL_NUMBERS_U16: [u16; 10] = [1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147];
const BELL_NUMBERS_U32: [u32; 16] = [
1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213597, 27644437, 190899322,
1382958545,
];
const BELL_NUMBERS_U64: [u64; 26] = [
1,
1,
2,
5,
15,
52,
203,
877,
4140,
21147,
115975,
678570,
4213597,
27644437,
190899322,
1382958545,
10480142147,
82864869804,
682076806159,
5832742205057,
51724158235372,
474869816156751,
4506715738447323,
44152005855084346,
445958869294805289,
4638590332229999353,
];
const BELL_NUMBERS_U128: [u128; 43] = [
1,
1,
2,
5,
15,
52,
203,
877,
4140,
21147,
115975,
678570,
4213597,
27644437,
190899322,
1382958545,
10480142147,
82864869804,
682076806159,
5832742205057,
51724158235372,
474869816156751,
4506715738447323,
44152005855084346,
445958869294805289,
4638590332229999353,
49631246523618756274,
545717047936059989389,
6160539404599934652455,
71339801938860275191172,
846749014511809332450147,
10293358946226376485095653,
128064670049908713818925644,
1629595892846007606764728147,
21195039388640360462388656799,
281600203019560266563340426570,
3819714729894818339975525681317,
52868366208550447901945575624941,
746289892095625330523099540639146,
10738823330774692832768857986425209,
157450588391204931289324344702531067,
2351152507740617628200694077243788988,
35742549198872617291353508656626642567,
];
macro_rules! impl_bell_numbers {
($t:ident, $bs:ident) => {
impl CheckedBellNumber for $t {
/// Computes the $n$th Bell number: the number of ways to partition a set of $n$
/// elements.
///
/// If the result is too large to be represented, the function returns `None`.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// See [here](super::bell_number#checked_bell_number).
#[inline]
fn checked_bell_number(n: u64) -> Option<$t> {
$bs.get(usize::try_from(n).ok()?).copied()
}
}
impl BellNumber for $t {
/// Computes the $n$th Bell number: the number of ways to partition a set of $n$
/// elements.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Panics
/// Panics if the result is too large to be represented.
///
/// # Examples
/// See [here](super::bell_number#bell_number).
#[inline]
fn bell_number(n: u64) -> $t {
$t::checked_bell_number(n).unwrap()
}
}
};
}
impl_bell_numbers!(u8, BELL_NUMBERS_U8);
impl_bell_numbers!(u16, BELL_NUMBERS_U16);
impl_bell_numbers!(u32, BELL_NUMBERS_U32);
impl_bell_numbers!(u64, BELL_NUMBERS_U64);
impl_bell_numbers!(u128, BELL_NUMBERS_U128);
impl CheckedBellNumber for usize {
/// Computes the $n$th Bell number: the number of ways to partition a set of $n$ elements.
///
/// If the result is too large to be represented, the function returns `None`.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// See [here](super::bell_number#checked_bell_number).
#[inline]
fn checked_bell_number(n: u64) -> Option<Self> {
BELL_NUMBERS_U64
.get(Self::try_from(n).ok()?)
.and_then(|&b| Self::try_from(b).ok())
}
}
impl BellNumber for usize {
/// Computes the $n$th Bell number: the number of ways to partition a set of $n$ elements.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Panics
/// Panics if the result is too large to be represented.
///
/// # Examples
/// See [here](super::bell_number#bell_number).
#[inline]
fn bell_number(n: u64) -> Self {
Self::checked_bell_number(n).unwrap()
}
}