malachite_nz/integer_vector/arithmetic/
multi_crt.rs

1// Copyright © 2026 Mikhail Hogrefe
2//
3// This file is part of Malachite.
4//
5// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
6// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
7// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.
8
9use crate::integer::Integer;
10use crate::integer_vector::IntegerVector;
11use crate::natural_vector::arithmetic::multi_crt::{
12    ElementCombiner, map_columns, multi_crt_combiner,
13};
14use crate::platform::Limb;
15use malachite_base::unsigned_vector::UnsignedVector;
16
17impl IntegerVector {
18    /// Combines vectors of residues modulo pairwise-coprime word-sized moduli into the vector whose
19    /// every element is the representative of smallest absolute value that is congruent to each of
20    /// its residues, returning `None` if the moduli are unusable.
21    ///
22    /// `residues[j]` holds the residues of every element modulo `moduli[j]`, so element $i$ of the
23    /// result is the combination of `residues[0][i]`, `residues[1][i]`, and so on, as
24    /// [`Integer::multi_balanced_crt`] would compute it. Each element $x$ of the result satisfies
25    /// $-M/2 < x \leq M/2$, where $M$ is the product of the moduli, so a tie at $M/2$ is positive.
26    /// The work that depends only on the moduli is done once, not once per element. The residues
27    /// must be already reduced, and the moduli are unusable under the conditions of
28    /// [`Integer::multi_balanced_crt`]: with one modulus, if it is 0; with more, if any is 0 or 1
29    /// or two are not coprime.
30    ///
31    /// For the representatives in $[0, M)$ instead, use
32    /// [`NaturalVector::multi_crt`](crate::natural_vector::NaturalVector::multi_crt).
33    ///
34    /// # Worst-case complexity
35    /// $T(n, d) = O(n (\log n)^3 \log\log n + dn (\log n)^2 \log\log n)$
36    ///
37    /// $M(n, d) = O(n \log n + dn)$
38    ///
39    /// where $T$ is time, $M$ is additional memory, $n$ is the number of significant bits of the
40    /// product of the moduli, and $d$ is the dimension of the residue vectors.
41    ///
42    /// # Panics
43    /// Panics if `moduli` is empty, if the number of residue vectors differs from the number of
44    /// moduli, if the residue vectors do not all have the same dimension, or if, when the moduli
45    /// are usable, any residue is greater than or equal to its modulus.
46    ///
47    /// # Examples
48    /// ```
49    /// use core::str::FromStr;
50    /// use malachite_base::unsigned_vector::UnsignedVector;
51    /// use malachite_nz::integer_vector::IntegerVector;
52    ///
53    /// // 23 is 2 mod 3, 3 mod 5, and 2 mod 7; 6 is 0, 1, and 6; and -5 is 1, 0, and 2.
54    /// let residues = [
55    ///     UnsignedVector::from_str("(2, 0, 1)").unwrap(),
56    ///     UnsignedVector::from_str("(3, 1, 0)").unwrap(),
57    ///     UnsignedVector::from_str("(2, 6, 2)").unwrap(),
58    /// ];
59    /// assert_eq!(
60    ///     IntegerVector::multi_balanced_crt(&[3, 5, 7], &residues)
61    ///         .unwrap()
62    ///         .to_string(),
63    ///     "(23, 6, -5)"
64    /// );
65    ///
66    /// // 4 and 6 are not coprime.
67    /// assert!(IntegerVector::multi_balanced_crt(&[4, 6], &residues[..2]).is_none());
68    /// ```
69    ///
70    /// This is equivalent to `_fmpz_vec_multi_CRT_ui` from `fmpz_vec/multi_CRT_ui.c`, FLINT 3.6.0,
71    /// with sign = 1 and the residues required to be reduced.
72    pub fn multi_balanced_crt(moduli: &[Limb], residues: &[UnsignedVector<Limb>]) -> Option<Self> {
73        Some(Self {
74            elements: match multi_crt_combiner(moduli, residues)? {
75                // A residue above half the modulus is closer to zero once the modulus is
76                // subtracted; at exactly half, it stays positive.
77                ElementCombiner::Single(m) => residues[0]
78                    .elements
79                    .iter()
80                    .map(|&r| {
81                        if r > m >> 1 {
82                            -Integer::from(m - r)
83                        } else {
84                            Integer::from(r)
85                        }
86                    })
87                    .collect(),
88                ElementCombiner::Comb(comb) => {
89                    map_columns(residues, |rs| comb.combine_balanced(rs))
90                }
91            },
92        })
93    }
94}
malachite_nz/integer_vector/arithmetic/multi_crt.rs

malachite_nz/integer_vector/arithmetic/
multi_crt.rs
