14013051218

Committed 22 Mar 2025 10:46PM UTC coverage: 76.118% (-2.4%) from 78.482%

Build # 14013051218

Build Type

push

github

Committed by

vigna

Commit Message

Ported changes from zcs

Run Details

18 of 51 new or added lines in 3 files covered. (35.29%)

142 existing lines in 6 files now uncovered.

3984 of 5234 relevant lines covered (76.12%)

125756095.75 hits per line

Source File
Press 'n' to go to next uncovered line, 'b' for previous

84.02

/src/utils/mod2_sys.rs

/*
 *
 * SPDX-FileCopyrightText: 2025 Dario Moschetti
 * SPDX-FileCopyrightText: 2025 Sebastiano Vigna
 *
 * SPDX-License-Identifier: Apache-2.0 OR LGPL-2.1-or-later
 */

#![allow(unexpected_cfgs)]
#![allow(clippy::comparison_chain)]
use std::ptr;

use crate::{bit_vec, traits::Word};
use anyhow::{bail, ensure, Result};
use arbitrary_chunks::ArbitraryChunks;

/// An equation on `W::BITS`-dimensional vectors with coefficients in **F**₂.
#[derive(Clone, Debug)]
pub struct Modulo2Equation<W: Word = usize> {
    /// The variables in increasing order.
    vars: Vec<u32>,
    /// The constant term
    c: W,
}

/// A system of [equations](struct.Modulo2Equation.html).
#[derive(Clone, Debug)]
pub struct Modulo2System<W: Word = usize> {
    /// The number of variables.
    num_vars: usize,
    /// The equations in the system.
    equations: Vec<Modulo2Equation<W>>,
}

impl<W: Word> Modulo2Equation<W> {
    /// Creates a new equation with given variables constant term.
    ///
    /// # Safety
    ///
    /// The caller must ensure that the variables are sorted.
    pub unsafe fn from_parts(vars: Vec<u32>, c: W) -> Self {
        debug_assert!(vars.iter().is_sorted());
        Modulo2Equation { vars, c }
    }

    #[inline(always)]
    unsafe fn add_ptr(
        mut left: *const u32,
        left_end: *const u32,
        mut right: *const u32,
        right_end: *const u32,
        mut dst: *mut u32,
    ) -> *mut u32 {
        while left != left_end && right != right_end {
            let less = *left <= *right;
            let more = *left >= *right;

            let src = if less { left } else { right };
            *dst = *src;

            left = left.add(less as usize);
            right = right.add(more as usize);
            dst = dst.add((less ^ more) as usize);
        }

        let rem_left = left_end.offset_from(left) as usize;
        ptr::copy_nonoverlapping(left, dst, rem_left);
        dst = dst.add(rem_left);
        let rem_right = right_end.offset_from(right) as usize;
        ptr::copy_nonoverlapping(right, dst, rem_right);
        dst = dst.add(rem_right);
        dst
    }

    pub fn add(&mut self, other: &Modulo2Equation<W>) {
        let left_range = self.vars.as_ptr_range();
        let left = left_range.start;
        let left_end = left_range.end;
        let right_range = other.vars.as_ptr_range();
        let right = right_range.start;
        let right_end = right_range.end;
        let mut vars = Vec::with_capacity(self.vars.len() + other.vars.len());
        let dst = vars.as_mut_ptr();

        unsafe {
            let copied =
                Self::add_ptr(left, left_end, right, right_end, dst).offset_from(dst) as usize;
            vars.set_len(copied);
        }

        self.vars = vars;
        self.c ^= other.c;
    }

    /// Checks whether the equation is unsolvable.
    fn is_unsolvable(&self) -> bool {
        self.vars.is_empty() && self.c != W::ZERO
    }

    /// Checks whether the equation is an identity.
    fn is_identity(&self) -> bool {
        self.vars.is_empty() && self.c == W::ZERO
    }

    /// Evaluates the XOR of the values associated to the given variables.
    fn eval_vars(vars: impl AsRef<[u32]>, values: impl AsRef<[W]>) -> W {
        let mut sum = W::ZERO;
        for &var in vars.as_ref() {
            sum ^= values.as_ref()[var as usize];
        }
        sum
    }
}

impl<W: Word> Modulo2System<W> {
    pub fn new(num_vars: usize) -> Self {
        Modulo2System {
            num_vars,
            equations: vec![],
        }
    }

    pub fn num_vars(&self) -> usize {
        self.num_vars
    }

    pub fn num_equations(&self) -> usize {
        self.equations.len()
    }

    /// Creates a new `Modulo2System` from existing equations.
    ///
    /// # Safety
    ///
    /// The caller must ensure that variables in each equation match the number
    /// of variables in the system.
    pub unsafe fn from_parts(num_vars: usize, equations: Vec<Modulo2Equation<W>>) -> Self {
        Modulo2System {
            num_vars,
            equations,
        }
    }

    /// Adds an equation to the system.
    pub fn push(&mut self, equation: Modulo2Equation<W>) {
        self.equations.push(equation);
    }

    /// Checks if a given solution satisfies the system of equations.
    pub fn check(&self, solution: &[W]) -> bool {
        assert_eq!(solution.len(), self.num_vars, "The number of variables in the solution ({}) does not match the number of variables in the system ({})", solution.len(), self.num_vars);
        self.equations
            .iter()
            .all(|eq| eq.c == Modulo2Equation::<W>::eval_vars(&eq.vars, solution))
    }

    /// Puts the system into echelon form.
    fn echelon_form(&mut self) -> Result<()> {
        let equations = &mut self.equations;
        if equations.is_empty() {
            return Ok(());
        }
        'main: for i in 0..equations.len() - 1 {
            ensure!(!equations[i].vars.is_empty());
            for j in i + 1..equations.len() {
                // SAFETY: to add the two equations, multiple references to the vector
                // of equations are needed, one of which is mutable
                let eq_j = unsafe { &*(&equations[j] as *const Modulo2Equation<W>) };
                let eq_i = &mut equations[i];

                let first_var_j = eq_j.vars[0];

                if eq_i.vars[0] == first_var_j {
                    eq_i.add(eq_j);
                    if eq_i.is_unsolvable() {
                        bail!("System is unsolvable");
                    }
                    if eq_i.is_identity() {
                        continue 'main;
                    }
                }

                if eq_i.vars[0] > first_var_j {
                    equations.swap(i, j)
                }
            }
        }
        Ok(())
    }

    /// Solves the system using Gaussian elimination.
    pub fn gaussian_elimination(&mut self) -> Result<Vec<W>> {
        self.echelon_form()?;
        let mut solution = vec![W::ZERO; self.num_vars];
        self.equations
            .iter()
            .rev()
            .filter(|eq| !eq.is_identity())
            .for_each(|eq| {
                solution[eq.vars[0] as usize] =
                    eq.c ^ Modulo2Equation::<W>::eval_vars(&eq.vars, &solution);
            });
        Ok(solution)
    }

    /// Builds the data structures needed for lazy Gaussian elimination.
    ///
    /// This method returns the variable-to-equation mapping, the weight of each
    /// variable (the number of equations in which it appears), and the priority
    /// of each equation (the number of variables in it). The
    /// variable-to-equation mapping is materialized as a vector of mutable
    /// slices, each of which points inside a provided backing vector. This
    /// approach greatly reduces the number of allocations.
    fn setup<'a>(
        &self,
        backing: &'a mut Vec<usize>,
    ) -> (Vec<&'a mut [usize]>, Vec<usize>, Vec<usize>) {
        let mut weight = vec![0; self.num_vars];
        let mut priority = vec![0; self.equations.len()];

        let mut total_vars = 0;
        for (i, equation) in self.equations.iter().enumerate() {
            priority[i] = equation.vars.len();
            total_vars += equation.vars.len();
            for &var in &equation.vars {
                weight[var as usize] += 1;
            }
        }

        backing.resize(total_vars, 0);
        let mut var_to_eq: Vec<&mut [usize]> = Vec::with_capacity(self.num_vars);

        backing.arbitrary_chunks_mut(&weight).for_each(|chunk| {
            var_to_eq.push(chunk);
        });

        let mut pos = vec![0usize; self.num_vars];
        for (i, equation) in self.equations.iter().enumerate() {
            for &var in &equation.vars {
                let var = var as usize;
                var_to_eq[var][pos[var]] = i;
                pos[var] += 1;
            }
        }

        (var_to_eq, weight, priority)
    }

    /// Solves the system using lazy Gaussian elimination.
    pub fn lazy_gaussian_elimination(&mut self) -> Result<Vec<W>> {
        let num_vars = self.num_vars;
        let num_equations = self.equations.len();

        if num_equations == 0 {
            return Ok(vec![W::ZERO; num_vars]);
        }

        let mut backing = vec![];
        let (var_to_eqs, mut weight, mut priority);
        (var_to_eqs, weight, priority) = self.setup(&mut backing);

        let mut variables = vec![0; num_vars];
        {
            let mut count = vec![0; num_equations + 1];

            for x in 0..num_vars {
                count[weight[x]] += 1
            }
            for i in 1..count.len() {
                count[i] += count[i - 1]
            }
            for i in (0..num_vars).rev() {
                count[weight[i]] -= 1;
                variables[count[weight[i]]] = i;
            }
        }

        let mut equation_list: Vec<usize> = (0..priority.len())
            .rev()
            .filter(|&x| priority[x] <= 1)
            .collect();

        let mut dense = vec![];
        let mut solved = vec![];
        let mut pivots = vec![];

        let equations = &mut self.equations;
        let mut idle = bit_vec![true; num_vars];

        let mut remaining = equations.len();

        while remaining != 0 {
            if equation_list.is_empty() {
                let mut var = variables.pop().unwrap();
                while weight[var] == 0 {
                    var = variables.pop().unwrap()
                }
                idle.set(var, false);
                var_to_eqs[var].as_ref().iter().for_each(|&eq| {
                    priority[eq] -= 1;
                    if priority[eq] == 1 {
                        equation_list.push(eq)
                    }
                });
            } else {
                remaining -= 1;
                let first = equation_list.pop().unwrap();

                if priority[first] == 0 {
                    let equation = &mut equations[first];
                    if equation.is_unsolvable() {
                        bail!("System is unsolvable")
                    }
                    if equation.is_identity() {
                        continue;
                    }
                    dense.push(equation.to_owned());
                } else if priority[first] == 1 {
                    // SAFETY: to add the equations, multiple references to the vector
                    // of equations are needed, one of which is mutable
                    let equation = unsafe { &*(&equations[first] as *const Modulo2Equation<W>) };

                    let pivot = equation
                        .vars
                        .iter()
                        .copied()
                        .find(|x| idle.get(*x as usize))
                        .expect("Missing expected idle variable in equation");
                    pivots.push(pivot as usize);
                    solved.push(first);
                    weight[pivot as usize] = 0;
                    var_to_eqs[pivot as usize]
                        .as_ref()
                        .iter()
                        .filter(|&&eq_idx| eq_idx != first)
                        .for_each(|&eq| {
                            equations[eq].add(equation);

                            priority[eq] -= 1;
                            if priority[eq] == 1 {
                                equation_list.push(eq)
                            }
                        });
                }
            }
        }

        // SAFETY: the usage of the method is safe, as the equations have the
        // right number of variables
        let mut dense_system = unsafe { Modulo2System::from_parts(num_vars, dense) };
        let mut solution = dense_system.gaussian_elimination()?;

        for i in 0..solved.len() {
            let eq = &equations[solved[i]];
            let pivot = pivots[i];
            assert!(solution[pivot] == W::ZERO);
            solution[pivot] = eq.c ^ Modulo2Equation::<W>::eval_vars(&eq.vars, &solution);
        }

        Ok(solution)
    }
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_add_ptr() {
        let a = [0, 1, 3, 4];
        let b = [0, 2, 4, 5];
        let mut c = Vec::with_capacity(a.len() + b.len());

        let ra = a.as_ptr_range();
        let rb = b.as_ptr_range();
        let mut dst = c.as_mut_ptr();
        unsafe {
            dst = Modulo2Equation::<u32>::add_ptr(ra.start, ra.end, rb.start, rb.end, dst);
            assert_eq!(dst.offset_from(c.as_ptr()), 4);
            c.set_len(4);
            assert_eq!(c, vec![1, 2, 3, 5]);
        }
    }

    #[test]
    fn test_equation_builder() {
        let eq = unsafe { Modulo2Equation::from_parts(vec![0, 1, 2], 3_usize) };
        assert_eq!(eq.vars.len(), 3);
        assert_eq!(eq.vars.to_vec(), vec![0, 1, 2]);
    }

    #[test]
    fn test_equation_addition() {
        let mut eq0 = unsafe { Modulo2Equation::from_parts(vec![1, 4, 9], 3_usize) };
        let eq1 = unsafe { Modulo2Equation::from_parts(vec![1, 4, 10], 3_usize) };
        eq0.add(&eq1);
        assert_eq!(eq0.vars, vec![9, 10]);
        assert_eq!(eq0.c, 0);
    }

    #[test]
    fn test_system_one_equation() {
        let mut system = Modulo2System::<usize>::new(2);
        let eq = unsafe { Modulo2Equation::from_parts(vec![0], 3_usize) };
        system.push(eq);
        let solution = system.lazy_gaussian_elimination();
        assert!(solution.is_ok());
        assert!(system.check(&solution.unwrap()));
    }

    #[test]
    fn test_impossible_system() {
        let mut system = Modulo2System::<usize>::new(1);
        let eq0 = unsafe { Modulo2Equation::from_parts(vec![0], 0_usize) };
        system.push(eq0);
        let eq1 = unsafe { Modulo2Equation::from_parts(vec![0], 1_usize) };
        system.push(eq1);
        let solution = system.lazy_gaussian_elimination();
        assert!(solution.is_err());
    }

    #[test]
    fn test_redundant_system() {
        let mut system = Modulo2System::<usize>::new(1);
        let eq0 = unsafe { Modulo2Equation::from_parts(vec![0], 0_usize) };
        system.push(eq0);
        let eq1 = unsafe { Modulo2Equation::from_parts(vec![0], 0_usize) };
        system.push(eq1);
        let solution = system.lazy_gaussian_elimination();
        assert!(solution.is_ok());
        assert!(system.check(&solution.unwrap()));
    }

    #[test]
    fn test_small_system() {
        let mut system = Modulo2System::<usize>::new(11);
        let mut eq = unsafe { Modulo2Equation::from_parts(vec![1, 4, 10], 0) };
        system.push(eq);
        eq = unsafe { Modulo2Equation::from_parts(vec![1, 4, 9], 2) };
        system.push(eq);
        eq = unsafe { Modulo2Equation::from_parts(vec![0, 6, 8], 0) };
        system.push(eq);
        eq = unsafe { Modulo2Equation::from_parts(vec![0, 6, 9], 1) };
        system.push(eq);
        eq = unsafe { Modulo2Equation::from_parts(vec![2, 4, 8], 2) };
        system.push(eq);
        eq = unsafe { Modulo2Equation::from_parts(vec![2, 6, 10], 0) };
        system.push(eq);

        let solution = system.lazy_gaussian_elimination();
        assert!(solution.is_ok());
        assert!(system.check(&solution.unwrap()));
    }

    #[test]
    fn test_var_to_vec_builder() {
        let system = unsafe {
            Modulo2System::from_parts(
                11,
                vec![
                    Modulo2Equation::from_parts(vec![1, 4, 10], 0_usize),
                    Modulo2Equation::from_parts(vec![1, 4, 9], 1),
                    Modulo2Equation::from_parts(vec![0, 6, 8], 2),
                    Modulo2Equation::from_parts(vec![0, 6, 9], 3),
                    Modulo2Equation::from_parts(vec![2, 4, 8], 4),
                    Modulo2Equation::from_parts(vec![2, 6, 10], 5),
                ],
            )
        };
        let mut backing: Vec<usize> = vec![];
        let (var_to_eqs, _weight, _priority) = system.setup(&mut backing);
        let expected_res = vec![
            vec![2, 3],
            vec![0, 1],
            vec![4, 5],
            vec![],
            vec![0, 1, 4],
            vec![],
            vec![2, 3, 5],
            vec![],
            vec![2, 4],
            vec![1, 3],
            vec![0, 5],
        ];
        var_to_eqs
            .iter()
            .zip(expected_res.iter())
            .for_each(|(v, e)| v.iter().zip(e.iter()).for_each(|(x, y)| assert_eq!(x, y)));
    }
}

1	/*
2	*
3	* SPDX-FileCopyrightText: 2025 Dario Moschetti
4	* SPDX-FileCopyrightText: 2025 Sebastiano Vigna
5	*
6	* SPDX-License-Identifier: Apache-2.0 OR LGPL-2.1-or-later
7	*/
8
9	#![allow(unexpected_cfgs)]
10	#![allow(clippy::comparison_chain)]
11	use std::ptr;
12
13	use crate::{bit_vec, traits::Word};
14	use anyhow::{bail, ensure, Result};
15	use arbitrary_chunks::ArbitraryChunks;
16
17	/// An equation on `W::BITS`-dimensional vectors with coefficients in F₂.
18	#[derive(Clone, Debug)]
19	pub struct Modulo2Equation<W: Word = usize> {
20	/// The variables in increasing order.
21	vars: Vec<u32>,
22	/// The constant term
23	c: W,
24	}
25
26	/// A system of [equations](struct.Modulo2Equation.html).
27	#[derive(Clone, Debug)]
28	pub struct Modulo2System<W: Word = usize> {
29	/// The number of variables.
30	num_vars: usize,
31	/// The equations in the system.
32	equations: Vec<Modulo2Equation<W>>,
33	}
34
35	impl<W: Word> Modulo2Equation<W> {
36	/// Creates a new equation with given variables constant term.
37	///
38	/// # Safety
39	///
40	/// The caller must ensure that the variables are sorted.
41	pub unsafe fn from_parts(vars: Vec<u32>, c: W) -> Self {	729,845✔
42	debug_assert!(vars.iter().is_sorted());	1,459,690✔
43	Modulo2Equation { vars, c }
44	}
45
46	#[inline(always)]
47	unsafe fn add_ptr(	1,844,470✔
48	mut left: *const u32,
49	left_end: *const u32,
50	mut right: *const u32,
51	right_end: *const u32,
52	mut dst: *mut u32,
53	) -> *mut u32 {
54	while left != left_end && right != right_end {	2,120,280,318✔
55	let less = left <= right;	1,059,009,695✔
56	let more = left >= right;	1,059,009,695✔
57
58	let src = if less { left } else { right };	1,059,009,695✔
59	dst = src;	×
60
61	left = left.add(less as usize);	×
62	right = right.add(more as usize);	×
63	dst = dst.add((less ^ more) as usize);	×
64	}
65
66	let rem_left = left_end.offset_from(left) as usize;	1,844,470✔
67	ptr::copy_nonoverlapping(left, dst, rem_left);	1,844,470✔
68	dst = dst.add(rem_left);	1,844,470✔
69	let rem_right = right_end.offset_from(right) as usize;	1,844,470✔
70	ptr::copy_nonoverlapping(right, dst, rem_right);	1,844,470✔
71	dst = dst.add(rem_right);	1,844,470✔
72	dst	1,844,470✔
73	}
74
75	pub fn add(&mut self, other: &Modulo2Equation<W>) {	1,844,469✔
76	let left_range = self.vars.as_ptr_range();	1,844,469✔
77	let left = left_range.start;	1,844,469✔
78	let left_end = left_range.end;	1,844,469✔
79	let right_range = other.vars.as_ptr_range();	1,844,469✔
80	let right = right_range.start;	1,844,469✔
81	let right_end = right_range.end;	1,844,469✔
82	let mut vars = Vec::with_capacity(self.vars.len() + other.vars.len());	1,844,469✔
83	let dst = vars.as_mut_ptr();	1,844,469✔
84
85	unsafe {
86	let copied =	1,844,469✔
87	Self::add_ptr(left, left_end, right, right_end, dst).offset_from(dst) as usize;	1,844,469✔
88	vars.set_len(copied);	1,844,469✔
89	}
90
91	self.vars = vars;	1,844,469✔
92	self.c ^= other.c;	1,844,469✔
93	}
94
95	/// Checks whether the equation is unsolvable.
96	fn is_unsolvable(&self) -> bool {	705,901✔
97	self.vars.is_empty() && self.c != W::ZERO	706,343✔
98	}
99
100	/// Checks whether the equation is an identity.
101	fn is_identity(&self) -> bool {	723,846✔
102	self.vars.is_empty() && self.c == W::ZERO	723,847✔
103	}
104
105	/// Evaluates the XOR of the values associated to the given variables.
106	fn eval_vars(vars: impl AsRef<[u32]>, values: impl AsRef<[W]>) -> W {	595,087✔
107	let mut sum = W::ZERO;	595,087✔
108	for &var in vars.as_ref() {	304,723,364✔
109	sum ^= values.as_ref()[var as usize];	×
110	}
111	sum	595,087✔
112	}
113	}
114
115	impl<W: Word> Modulo2System<W> {
116	pub fn new(num_vars: usize) -> Self {	4✔
117	Modulo2System {
118	num_vars,
119	equations: vec![],	4✔
120	}
121	}
122
123	pub fn num_vars(&self) -> usize {	×
124	self.num_vars	×
125	}
126
127	pub fn num_equations(&self) -> usize {	25✔
128	self.equations.len()	25✔
129	}
130
131	/// Creates a new `Modulo2System` from existing equations.
132	///
133	/// # Safety
134	///
135	/// The caller must ensure that variables in each equation match the number
136	/// of variables in the system.
137	pub unsafe fn from_parts(num_vars: usize, equations: Vec<Modulo2Equation<W>>) -> Self {	598✔
138	Modulo2System {
139	num_vars,
140	equations,
141	}
142	}
143
144	/// Adds an equation to the system.
145	pub fn push(&mut self, equation: Modulo2Equation<W>) {	11✔
146	self.equations.push(equation);	11✔
147	}
148
149	/// Checks if a given solution satisfies the system of equations.
150	pub fn check(&self, solution: &[W]) -> bool {	3✔
151	assert_eq!(solution.len(), self.num_vars, "The number of variables in the solution ({}) does not match the number of variables in the system ({})", solution.len(), self.num_vars);	3✔
152	self.equations	3✔
153	.iter()
154	.all(\|eq\| eq.c == Modulo2Equation::<W>::eval_vars(&eq.vars, solution))	15✔
155	}
156
157	/// Puts the system into echelon form.
158	fn echelon_form(&mut self) -> Result<()> {	132✔
159	let equations = &mut self.equations;	132✔
160	if equations.is_empty() {	132✔
161	return Ok(());	2✔
162	}
163	'main: for i in 0..equations.len() - 1 {	19,807✔
164	ensure!(!equations[i].vars.is_empty());	19,807✔
165	for j in i + 1..equations.len() {	14,572,192✔
166	// SAFETY: to add the two equations, multiple references to the vector
167	// of equations are needed, one of which is mutable
168	let eq_j = unsafe { &(&equations[j] as const Modulo2Equation<W>) };	14,552,385✔
169	let eq_i = &mut equations[i];	14,552,385✔
170
171	let first_var_j = eq_j.vars[0];	14,552,385✔
172
173	if eq_i.vars[0] == first_var_j {	14,552,385✔
174	eq_i.add(eq_j);	679,900✔
175	if eq_i.is_unsolvable() {	679,900✔
176	bail!("System is unsolvable");	104✔
177	}
178	if eq_i.is_identity() {	679,796✔
UNCOV 179	continue 'main;	×
180	}
181	}
182
183	if eq_i.vars[0] > first_var_j {	14,552,281✔
184	equations.swap(i, j)	9,731,869✔
185	}
186	}
187	}
188	Ok(())	26✔
189	}
190
191	/// Solves the system using Gaussian elimination.
192	pub fn gaussian_elimination(&mut self) -> Result<Vec<W>> {	132✔
193	self.echelon_form()?;	236✔
194	let mut solution = vec![W::ZERO; self.num_vars];	28✔
195	self.equations	28✔
196	.iter()
197	.rev()
198	.filter(\|eq\| !eq.is_identity())	18,414✔
199	.for_each(\|eq\| {	18,386✔
200	solution[eq.vars[0] as usize] =	18,386✔
201	eq.c ^ Modulo2Equation::<W>::eval_vars(&eq.vars, &solution);	18,386✔
202	});
203	Ok(solution)	×
204	}
205
206	/// Builds the data structures needed for lazy Gaussian elimination.
207	///
208	/// This method returns the variable-to-equation mapping, the weight of each
209	/// variable (the number of equations in which it appears), and the priority
210	/// of each equation (the number of variables in it). The
211	/// variable-to-equation mapping is materialized as a vector of mutable
212	/// slices, each of which points inside a provided backing vector. This
213	/// approach greatly reduces the number of allocations.
214	fn setup<'a>(	470✔
215	&self,
216	backing: &'a mut Vec<usize>,
217	) -> (Vec<&'a mut [usize]>, Vec<usize>, Vec<usize>) {
218	let mut weight = vec![0; self.num_vars];	470✔
219	let mut priority = vec![0; self.equations.len()];	470✔
220
221	let mut total_vars = 0;	470✔
222	for (i, equation) in self.equations.iter().enumerate() {	730,312✔
223	priority[i] = equation.vars.len();	×
224	total_vars += equation.vars.len();	×
225	for &var in &equation.vars {	5,108,874✔
226	weight[var as usize] += 1;	×
227	}
228	}
229
230	backing.resize(total_vars, 0);	470✔
231	let mut var_to_eq: Vec<&mut [usize]> = Vec::with_capacity(self.num_vars);	470✔
232
233	backing.arbitrary_chunks_mut(&weight).for_each(\|chunk\| {	1,385,596✔
234	var_to_eq.push(chunk);	1,385,126✔
235	});
236
237	let mut pos = vec![0usize; self.num_vars];	470✔
238	for (i, equation) in self.equations.iter().enumerate() {	730,312✔
239	for &var in &equation.vars {	5,108,874✔
240	let var = var as usize;	×
241	var_to_eq[var][pos[var]] = i;	×
242	pos[var] += 1;	×
243	}
244	}
245
246	(var_to_eq, weight, priority)	470✔
247	}
248
249	/// Solves the system using lazy Gaussian elimination.
250	pub fn lazy_gaussian_elimination(&mut self) -> Result<Vec<W>> {	469✔
251	let num_vars = self.num_vars;	469✔
252	let num_equations = self.equations.len();	469✔
253
254	if num_equations == 0 {	469✔
255	return Ok(vec![W::ZERO; num_vars]);	×
256	}
257
258	let mut backing = vec![];	469✔
259	let (var_to_eqs, mut weight, mut priority);	469✔
260	(var_to_eqs, weight, priority) = self.setup(&mut backing);	469✔
261
262	let mut variables = vec![0; num_vars];	469✔
263	{
264	let mut count = vec![0; num_equations + 1];	469✔
265
266	for x in 0..num_vars {	1,385,115✔
267	count[weight[x]] += 1	×
268	}
269	for i in 1..count.len() {	729,836✔
270	count[i] += count[i - 1]	×
271	}
272	for i in (0..num_vars).rev() {	1,385,115✔
273	count[weight[i]] -= 1;	×
274	variables[count[weight[i]]] = i;	×
275	}
276	}
277
278	let mut equation_list: Vec<usize> = (0..priority.len())	×
279	.rev()
280	.filter(\|&x\| priority[x] <= 1)	729,836✔
281	.collect();
282
283	let mut dense = vec![];	×
284	let mut solved = vec![];	×
285	let mut pivots = vec![];	×
286
287	let equations = &mut self.equations;	×
288	let mut idle = bit_vec![true; num_vars];	×
289
290	let mut remaining = equations.len();	×
291
292	while remaining != 0 {	735,847✔
293	if equation_list.is_empty() {	735,715✔
294	let mut var = variables.pop().unwrap();	45,565✔
295	while weight[var] == 0 {	648,797✔
296	var = variables.pop().unwrap()	603,232✔
297	}
298	idle.set(var, false);	45,565✔
299	var_to_eqs[var].as_ref().iter().for_each(\|&eq\| {	300,471✔
300	priority[eq] -= 1;	254,906✔
301	if priority[eq] == 1 {	254,906✔
302	equation_list.push(eq)	47,743✔
303	}
304	});
305	} else {
306	remaining -= 1;	690,150✔
307	let first = equation_list.pop().unwrap();	690,150✔
308
309	if priority[first] == 0 {	690,150✔
310	let equation = &mut equations[first];	26,001✔
311	if equation.is_unsolvable() {	26,001✔
312	bail!("System is unsolvable")	337✔
313	}
314	if equation.is_identity() {	25,664✔
315	continue;	1✔
316	}
317	dense.push(equation.to_owned());	25,663✔
318	} else if priority[first] == 1 {	1,328,298✔
319	// SAFETY: to add the equations, multiple references to the vector
320	// of equations are needed, one of which is mutable
321	let equation = unsafe { &(&equations[first] as const Modulo2Equation<W>) };	664,149✔
322
323	let pivot = equation	664,149✔
324	.vars	664,149✔
325	.iter()
326	.copied()
327	.find(\|x\| idle.get(*x as usize))	148,920,030✔
328	.expect("Missing expected idle variable in equation");
329	pivots.push(pivot as usize);	664,149✔
330	solved.push(first);	664,149✔
331	weight[pivot as usize] = 0;	664,149✔
332	var_to_eqs[pivot as usize]	664,149✔
333	.as_ref()
334	.iter()
335	.filter(\|&&eq_idx\| eq_idx != first)	3,157,015✔
336	.for_each(\|&eq\| {	1,828,717✔
337	equations[eq].add(equation);	1,164,568✔
338
339	priority[eq] -= 1;	1,164,568✔
340	if priority[eq] == 1 {	1,164,568✔
341	equation_list.push(eq)	643,216✔
342	}
343	});
344	}
345	}
346	}
347
348	// SAFETY: the usage of the method is safe, as the equations have the
349	// right number of variables
350	let mut dense_system = unsafe { Modulo2System::from_parts(num_vars, dense) };	132✔
351	let mut solution = dense_system.gaussian_elimination()?;	132✔
352
353	for i in 0..solved.len() {	576,692✔
354	let eq = &equations[solved[i]];	576,692✔
355	let pivot = pivots[i];	576,692✔
356	assert!(solution[pivot] == W::ZERO);	576,692✔
357	solution[pivot] = eq.c ^ Modulo2Equation::<W>::eval_vars(&eq.vars, &solution);	576,692✔
358	}
359
360	Ok(solution)	28✔
361	}
362	}
363
364	#[cfg(test)]
365	mod tests {
366	use super::*;
367
368	#[test]
369	fn test_add_ptr() {
370	let a = [0, 1, 3, 4];
371	let b = [0, 2, 4, 5];
372	let mut c = Vec::with_capacity(a.len() + b.len());
373
374	let ra = a.as_ptr_range();
375	let rb = b.as_ptr_range();
376	let mut dst = c.as_mut_ptr();
377	unsafe {
378	dst = Modulo2Equation::<u32>::add_ptr(ra.start, ra.end, rb.start, rb.end, dst);
379	assert_eq!(dst.offset_from(c.as_ptr()), 4);
380	c.set_len(4);
381	assert_eq!(c, vec![1, 2, 3, 5]);
382	}
383	}
384
385	#[test]
386	fn test_equation_builder() {
387	let eq = unsafe { Modulo2Equation::from_parts(vec![0, 1, 2], 3_usize) };
388	assert_eq!(eq.vars.len(), 3);
389	assert_eq!(eq.vars.to_vec(), vec![0, 1, 2]);
390	}
391
392	#[test]
393	fn test_equation_addition() {
394	let mut eq0 = unsafe { Modulo2Equation::from_parts(vec![1, 4, 9], 3_usize) };
395	let eq1 = unsafe { Modulo2Equation::from_parts(vec![1, 4, 10], 3_usize) };
396	eq0.add(&eq1);
397	assert_eq!(eq0.vars, vec![9, 10]);
398	assert_eq!(eq0.c, 0);
399	}
400
401	#[test]
402	fn test_system_one_equation() {
403	let mut system = Modulo2System::<usize>::new(2);
404	let eq = unsafe { Modulo2Equation::from_parts(vec![0], 3_usize) };
405	system.push(eq);
406	let solution = system.lazy_gaussian_elimination();
407	assert!(solution.is_ok());
408	assert!(system.check(&solution.unwrap()));
409	}
410
411	#[test]
412	fn test_impossible_system() {
413	let mut system = Modulo2System::<usize>::new(1);
414	let eq0 = unsafe { Modulo2Equation::from_parts(vec![0], 0_usize) };
415	system.push(eq0);
416	let eq1 = unsafe { Modulo2Equation::from_parts(vec![0], 1_usize) };
417	system.push(eq1);
418	let solution = system.lazy_gaussian_elimination();
419	assert!(solution.is_err());
420	}
421
422	#[test]
423	fn test_redundant_system() {
424	let mut system = Modulo2System::<usize>::new(1);
425	let eq0 = unsafe { Modulo2Equation::from_parts(vec![0], 0_usize) };
426	system.push(eq0);
427	let eq1 = unsafe { Modulo2Equation::from_parts(vec![0], 0_usize) };
428	system.push(eq1);
429	let solution = system.lazy_gaussian_elimination();
430	assert!(solution.is_ok());
431	assert!(system.check(&solution.unwrap()));
432	}
433
434	#[test]
435	fn test_small_system() {
436	let mut system = Modulo2System::<usize>::new(11);
437	let mut eq = unsafe { Modulo2Equation::from_parts(vec![1, 4, 10], 0) };
438	system.push(eq);
439	eq = unsafe { Modulo2Equation::from_parts(vec![1, 4, 9], 2) };
440	system.push(eq);
441	eq = unsafe { Modulo2Equation::from_parts(vec![0, 6, 8], 0) };
442	system.push(eq);
443	eq = unsafe { Modulo2Equation::from_parts(vec![0, 6, 9], 1) };
444	system.push(eq);
445	eq = unsafe { Modulo2Equation::from_parts(vec![2, 4, 8], 2) };
446	system.push(eq);
447	eq = unsafe { Modulo2Equation::from_parts(vec![2, 6, 10], 0) };
448	system.push(eq);
449
450	let solution = system.lazy_gaussian_elimination();
451	assert!(solution.is_ok());
452	assert!(system.check(&solution.unwrap()));
453	}
454
455	#[test]
456	fn test_var_to_vec_builder() {
457	let system = unsafe {
458	Modulo2System::from_parts(
459	11,
460	vec![
461	Modulo2Equation::from_parts(vec![1, 4, 10], 0_usize),
462	Modulo2Equation::from_parts(vec![1, 4, 9], 1),
463	Modulo2Equation::from_parts(vec![0, 6, 8], 2),
464	Modulo2Equation::from_parts(vec![0, 6, 9], 3),
465	Modulo2Equation::from_parts(vec![2, 4, 8], 4),
466	Modulo2Equation::from_parts(vec![2, 6, 10], 5),
467	],
468	)
469	};
470	let mut backing: Vec<usize> = vec![];
471	let (var_to_eqs, _weight, _priority) = system.setup(&mut backing);
472	let expected_res = vec![
473	vec![2, 3],
474	vec![0, 1],
475	vec![4, 5],
476	vec![],
477	vec![0, 1, 4],
478	vec![],
479	vec![2, 3, 5],
480	vec![],
481	vec![2, 4],
482	vec![1, 3],
483	vec![0, 5],
484	];
485	var_to_eqs
486	.iter()
487	.zip(expected_res.iter())
488	.for_each(\|(v, e)\| v.iter().zip(e.iter()).for_each(\|(x, y)\| assert_eq!(x, y)));
489	}
490	}

vigna / sux-rs / 14013051218

Source File Press 'n' to go to next uncovered line, 'b' for previous

Source File
Press 'n' to go to next uncovered line, 'b' for previous