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Merge pull request #1862 from kbobyrev/arith_eq_solver-cleanup
[NFC] Cleanup arith_eq_solver.(cpp|h)
This commit is contained in:
Nikolaj Bjorner
GitHub
commit
55cc89b6bb
2 changed files with 78 additions and 81 deletions
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@ -12,14 +12,11 @@ Abstract:
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Author:
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Nikolaj Bjorner (nbjorner) 2012-02-25
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--*/
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#include "smt/arith_eq_solver.h"
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arith_eq_solver::~arith_eq_solver() {
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}
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arith_eq_solver::arith_eq_solver(ast_manager & m, params_ref const& p):
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m(m),
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m_params(p),
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@ -93,9 +90,9 @@ void arith_eq_solver::gcd_normalize(vector<numeral>& values) {
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if (g.is_zero() || g.is_one()) {
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return;
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}
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for (unsigned i = 0; i < values.size(); ++i) {
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values[i] = values[i] / g;
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SASSERT(values[i].is_int());
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for (auto &value : values) {
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value /= g;
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SASSERT(value.is_int());
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}
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}
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@ -116,9 +113,9 @@ unsigned arith_eq_solver::find_abs_min(vector<numeral>& values) {
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#ifdef _TRACE
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static void print_row(std::ostream& out, vector<rational> const& row) {
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for(unsigned i = 0; i < row.size(); ++i) {
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out << row[i] << " ";
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}
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for(unsigned i = 0; i < row.size(); ++i) {
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out << row[i] << " ";
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}
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out << "\n";
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}
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@ -165,7 +162,7 @@ bool arith_eq_solver::solve_integer_equation(
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bool& is_fresh
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)
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{
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TRACE("arith_eq_solver",
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TRACE("arith_eq_solver",
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tout << "solving: ";
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print_row(tout, values);
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);
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@ -174,31 +171,31 @@ bool arith_eq_solver::solve_integer_equation(
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//
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// Given:
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// a1*x1 + a2*x2 + .. + a_n*x_n + a_{n+1} = 0
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//
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//
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// Assume gcd(a1,..,a_n,a_{n+1}) = 1
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// Assume gcd(a1,...,a_n) divides a_{n+1} (eg. gcd(a1,..,an) = 1)
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//
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//
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// post-condition: values[index] = -1.
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//
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//
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// Let a_index be index of least absolute value.
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//
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// If |a_index| = 1, then return row and index.
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// Otherwise:
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// Let m = |a_index| + 1
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// Set
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//
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// m*x_index'
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// =
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//
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// m*x_index'
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// =
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// ((a1 mod_hat m)*x1 + (a2 mod_hat m)*x2 + .. + (a_n mod_hat m)*x_n + (k mod_hat m))
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// =
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// =
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// (a1'*x1 + a2'*x2 + .. (-)1*x_index + ...)
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//
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//
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// <=> Normalize signs so that sign to x_index is -1.
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// (-)a1'*x1 + (-)a2'*x2 + .. -1*x_index + ... + m*x_index' = 0
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//
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//
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// Return row, where the coefficient to x_index is implicit.
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// Instead used the coefficient 'm' at position 'index'.
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//
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//
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gcd_normalize(values);
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if (!gcd_test(values)) {
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@ -216,8 +213,8 @@ bool arith_eq_solver::solve_integer_equation(
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return true;
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}
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if (a.is_one()) {
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for (unsigned i = 0; i < values.size(); ++i) {
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values[i].neg();
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for (auto &value : values) {
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value.neg();
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}
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}
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is_fresh = !abs_a.is_one();
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@ -225,19 +222,19 @@ bool arith_eq_solver::solve_integer_equation(
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if (is_fresh) {
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numeral m = abs_a + numeral(1);
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for (unsigned i = 0; i < values.size(); ++i) {
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values[i] = mod_hat(values[i], m);
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for (auto &value : values) {
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value = mod_hat(value, m);
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}
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if (values[index].is_one()) {
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for (unsigned i = 0; i < values.size(); ++i) {
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values[i].neg();
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for (auto &value : values) {
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value.neg();
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}
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}
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SASSERT(values[index].is_minus_one());
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values[index] = m;
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}
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TRACE("arith_eq_solver",
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TRACE("arith_eq_solver",
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tout << "solved at index " << index << ": ";
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print_row(tout, values);
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);
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@ -253,7 +250,7 @@ void arith_eq_solver::substitute(
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)
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{
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SASSERT(1 <= index && index < s.size());
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TRACE("arith_eq_solver",
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TRACE("arith_eq_solver",
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tout << "substitute " << index << ":\n";
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print_row(tout, r);
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print_row(tout, s);
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@ -272,21 +269,21 @@ void arith_eq_solver::substitute(
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// s encodes an equation that contains a variable
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// with a unit coefficient.
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//
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// Let
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// Let
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// c = r[index]
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// s = s[index]*x + s'*y = 0
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// r = c*x + r'*y = 0
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//
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// =>
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//
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// =>
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//
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// 0
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// =
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// -sign(s[index])*c*s + r
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// =
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// =
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// -sign(s[index])*c*s + r
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// =
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// -s[index]*sign(s[index])*c*x - sign(s[index])*c*s'*y + c*x + r'*y
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// =
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// =
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// -c*x - sign(s[index])*c*s'*y + c*x + r'*y
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// =
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// =
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// -sign(s[index])*c*s'*y + r'*y
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//
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numeral sign_s = s[index].is_pos()?numeral(1):numeral(-1);
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@ -301,36 +298,36 @@ void arith_eq_solver::substitute(
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//
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// s encodes a substitution using an auxiliary variable.
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// the auxiliary variable is at position 'index'.
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//
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// Let
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//
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// Let
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// c = r[index]
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// s = s[index]*x + s'*y = 0
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// r = c*x + r'*y = 0
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//
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// s encodes : x |-> s[index]*x' + s'*y
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//
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// Set:
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// Set:
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//
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// r := c*s + r'*y
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//
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//
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r[index] = numeral(0);
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for (unsigned i = 0; i < r.size(); ++i) {
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r[i] += c*s[i];
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}
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}
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for (unsigned i = r.size(); i < s.size(); ++i) {
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r.push_back(c*s[i]);
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}
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}
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}
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TRACE("arith_eq_solver",
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TRACE("arith_eq_solver",
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tout << "result: ";
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print_row(tout, r);
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);
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}
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bool arith_eq_solver::solve_integer_equations(
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vector<row>& rows,
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vector<row>& rows,
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row& unsat_row
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)
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{
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@ -340,10 +337,10 @@ bool arith_eq_solver::solve_integer_equations(
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//
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// Naive integer equation solver where only units are eliminated.
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//
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//
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bool arith_eq_solver::solve_integer_equations_units(
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vector<row>& rows,
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vector<row>& rows,
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row& unsat_row
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)
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{
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@ -351,7 +348,7 @@ bool arith_eq_solver::solve_integer_equations_units(
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TRACE("arith_eq_solver", print_rows(tout << "solving:\n", rows););
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unsigned_vector todo, done;
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for (unsigned i = 0; i < rows.size(); ++i) {
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todo.push_back(i);
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row& r = rows[i];
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@ -360,9 +357,9 @@ bool arith_eq_solver::solve_integer_equations_units(
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unsat_row = r;
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TRACE("arith_eq_solver", print_row(tout << "input is unsat: ", unsat_row); );
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return false;
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}
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}
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}
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for (unsigned i = 0; i < todo.size(); ++i) {
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for (unsigned i = 0; i < todo.size(); ++i) {
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row& r = rows[todo[i]];
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gcd_normalize(r);
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if (!gcd_test(r)) {
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@ -388,7 +385,7 @@ bool arith_eq_solver::solve_integer_equations_units(
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todo.push_back(done[j]);
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done.erase(done.begin()+j);
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--j;
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}
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}
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}
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}
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else {
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@ -396,7 +393,7 @@ bool arith_eq_solver::solve_integer_equations_units(
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}
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}
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TRACE("arith_eq_solver",
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TRACE("arith_eq_solver",
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tout << ((done.size()<=1)?"solved ":"incomplete check ") << done.size() << "\n";
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for (unsigned i = 0; i < done.size(); ++i) {
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print_row(tout, rows[done[i]]);
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@ -411,12 +408,12 @@ bool arith_eq_solver::solve_integer_equations_units(
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//
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// Partial solver based on the omega test equalities.
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// unsatisfiability is not preserved when eliminating
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// unsatisfiability is not preserved when eliminating
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// auxiliary variables.
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//
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bool arith_eq_solver::solve_integer_equations_omega(
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vector<row> & rows,
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vector<row> & rows,
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row& unsat_row
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)
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{
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@ -460,16 +457,16 @@ bool arith_eq_solver::solve_integer_equations_omega(
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//
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// solved_row: -x_index + m*sigma + r1 = 0
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// unsat_row: k*sigma + r2 = 0
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//
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// <=>
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//
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//
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// <=>
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//
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// solved_row: -k*x_index + k*m*sigma + k*r1 = 0
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// unsat_row: m*k*sigma + m*r2 = 0
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//
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// =>
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//
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// m*k*sigma + m*r2 + k*x_index - k*m*sigma - k*r1 = 0
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//
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//
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for (unsigned l = 0; l < unsat_row.size(); ++l) {
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unsat_row[l] *= m;
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unsat_row[l] -= k*solved_row[l];
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@ -479,7 +476,7 @@ bool arith_eq_solver::solve_integer_equations_omega(
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}
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gcd_normalize(unsat_row);
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TRACE("arith_eq_solver",
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TRACE("arith_eq_solver",
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tout << "gcd: ";
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print_row(tout, solved_row);
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print_row(tout, unsat_row);
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@ -525,18 +522,18 @@ bool arith_eq_solver::solve_integer_equations_omega(
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//
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// Eliminate variables by searching for combination of rows where
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// the coefficients have gcd = 1.
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//
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// the coefficients have gcd = 1.
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//
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bool arith_eq_solver::solve_integer_equations_gcd(
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vector<row> & rows,
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vector<row> & rows,
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row& unsat_row
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)
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{
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{
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unsigned_vector live, useful, gcd_pos;
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vector<rational> gcds;
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rational u, v;
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if (rows.empty()) {
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return true;
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}
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@ -548,7 +545,7 @@ bool arith_eq_solver::solve_integer_equations_gcd(
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unsat_row = r;
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TRACE("arith_eq_solver", print_row(tout << "input is unsat: ", unsat_row); );
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return false;
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}
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}
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}
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unsigned max_column = rows[0].size();
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bool change = true;
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@ -579,7 +576,7 @@ bool arith_eq_solver::solve_integer_equations_gcd(
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if (j == live.size()) {
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continue;
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}
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change = true;
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// found gcd, now identify reduced set of rows with GCD = 1.
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g = abs(rows[live[j]][i]);
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@ -592,7 +589,7 @@ bool arith_eq_solver::solve_integer_equations_gcd(
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useful.push_back(gcd_pos[j]);
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g = gcd(g, gcds[j]);
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SASSERT(j == 0 || gcd(g,gcds[j-1]).is_one());
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}
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}
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}
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//
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// we now have a set "useful" of rows whose combined GCD = 1.
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@ -600,7 +597,7 @@ bool arith_eq_solver::solve_integer_equations_gcd(
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//
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row& r0 = rows[useful[0]];
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for (j = 1; j < useful.size(); ++j) {
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row& r1 = rows[useful[j]];
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row& r1 = rows[useful[j]];
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g = gcd(r0[i], r1[i], u, v);
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for (unsigned k = 0; k < max_column; ++k) {
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r0[k] = u*r0[k] + v*r1[k];
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@ -626,7 +623,7 @@ bool arith_eq_solver::solve_integer_equations_gcd(
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}
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}
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TRACE("arith_eq_solver",
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TRACE("arith_eq_solver",
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tout << ((live.size()<=1)?"solved ":"incomplete check ") << live.size() << "\n";
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for (unsigned i = 0; i < live.size(); ++i) {
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print_row(tout, rows[live[i]]);
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|
|
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@ -12,7 +12,7 @@ Abstract:
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Author:
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Nikolaj Bjorner (nbjorner) 2012-02-25
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--*/
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#ifndef ARITH_EQ_SOLVER_H_
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#define ARITH_EQ_SOLVER_H_
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@ -35,45 +35,45 @@ class arith_eq_solver {
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void prop_mod_const(expr * e, unsigned depth, numeral const& k, expr_ref& result);
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bool gcd_test(vector<numeral>& value);
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bool gcd_test(vector<numeral>& values);
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unsigned find_abs_min(vector<numeral>& values);
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void gcd_normalize(vector<numeral>& values);
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void substitute(vector<numeral>& r, vector<numeral> const& s, unsigned index);
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bool solve_integer_equations_units(
|
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vector<vector<numeral> > & rows,
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vector<vector<numeral> > & rows,
|
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vector<numeral>& unsat_row
|
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);
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bool solve_integer_equations_omega(
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vector<vector<numeral> > & rows,
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vector<vector<numeral> > & rows,
|
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vector<numeral>& unsat_row
|
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);
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void compute_hnf(vector<vector<numeral> >& A);
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bool solve_integer_equations_hermite(
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vector<vector<numeral> > & rows,
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vector<vector<numeral> > & rows,
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vector<numeral>& unsat_row
|
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);
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bool solve_integer_equations_gcd(
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vector<vector<numeral> > & rows,
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vector<vector<numeral> > & rows,
|
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vector<numeral>& unsat_row
|
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);
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public:
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arith_eq_solver(ast_manager & m, params_ref const& p = params_ref());
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~arith_eq_solver();
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~arith_eq_solver() = default;
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// Integer linear solver for a single equation.
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// The array values contains integer coefficients
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//
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//
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// Determine integer solutions to:
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//
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// a+k = 0
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//
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// where a = sum_i a_i*k_i
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//
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//
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typedef vector<numeral> row;
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typedef vector<row> matrix;
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|
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@ -90,14 +90,14 @@ public:
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// a+k = 0
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//
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// where a = sum_i a_i*k_i
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//
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//
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// Solution, if there is any, is returned as a substitution.
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// The return value is "true".
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// If there is no solution, then return "false".
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// together with equality "eq_unsat", such that
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//
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// eq_unsat = 0
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//
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//
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// is implied and is unsatisfiable over the integers.
|
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//
|
||||
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|
|
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Add a link
Reference in a new issue