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Merge pull request #1862 from kbobyrev/arith_eq_solver-cleanup

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[NFC] Cleanup arith_eq_solver.(cpp|h)
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Nikolaj Bjorner 2018-10-02 08:48:49 -07:00 committed by GitHub
parent cc312d2f68 a376a8d343
commit 55cc89b6bb
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2 changed files with 78 additions and 81 deletions
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135
src/smt/arith_eq_solver.cpp
View file

@ -12,14 +12,11 @@ Abstract:
Author: Author:
Nikolaj Bjorner (nbjorner) 2012-02-25 Nikolaj Bjorner (nbjorner) 2012-02-25
--*/ --*/
#include "smt/arith_eq_solver.h" #include "smt/arith_eq_solver.h"
arith_eq_solver::~arith_eq_solver() {
}
arith_eq_solver::arith_eq_solver(ast_manager & m, params_ref const& p): arith_eq_solver::arith_eq_solver(ast_manager & m, params_ref const& p):
m(m), m(m),
m_params(p), m_params(p),
@ -93,9 +90,9 @@ void arith_eq_solver::gcd_normalize(vector<numeral>& values) {
if (g.is_zero() || g.is_one()) { if (g.is_zero() || g.is_one()) {
return; return;
} }
for (unsigned i = 0; i < values.size(); ++i) { for (auto &value : values) {
values[i] = values[i] / g; value /= g;
SASSERT(values[i].is_int()); SASSERT(value.is_int());
} }
} }
@ -116,9 +113,9 @@ unsigned arith_eq_solver::find_abs_min(vector<numeral>& values) {
#ifdef _TRACE #ifdef _TRACE
static void print_row(std::ostream& out, vector<rational> const& row) { static void print_row(std::ostream& out, vector<rational> const& row) {
for(unsigned i = 0; i < row.size(); ++i) { for(unsigned i = 0; i < row.size(); ++i) {
out << row[i] << " "; out << row[i] << " ";
} }
out << "\n"; out << "\n";
} }
@ -165,7 +162,7 @@ bool arith_eq_solver::solve_integer_equation(
bool& is_fresh bool& is_fresh
) )
{ {
TRACE("arith_eq_solver", TRACE("arith_eq_solver",
tout << "solving: "; tout << "solving: ";
print_row(tout, values); print_row(tout, values);
); );
@ -174,31 +171,31 @@ bool arith_eq_solver::solve_integer_equation(
// //
// Given: // Given:
// a1*x1 + a2*x2 + .. + a_n*x_n + a_{n+1} = 0 // a1*x1 + a2*x2 + .. + a_n*x_n + a_{n+1} = 0
// //
// Assume gcd(a1,..,a_n,a_{n+1}) = 1 // Assume gcd(a1,..,a_n,a_{n+1}) = 1
// Assume gcd(a1,...,a_n) divides a_{n+1} (eg. gcd(a1,..,an) = 1) // Assume gcd(a1,...,a_n) divides a_{n+1} (eg. gcd(a1,..,an) = 1)
// //
// post-condition: values[index] = -1. // post-condition: values[index] = -1.
// //
// Let a_index be index of least absolute value. // Let a_index be index of least absolute value.
// //
// If |a_index| = 1, then return row and index. // If |a_index| = 1, then return row and index.
// Otherwise: // Otherwise:
// Let m = |a_index| + 1 // Let m = |a_index| + 1
// Set // Set
// //
// m*x_index' // m*x_index'
// = // =
// ((a1 mod_hat m)*x1 + (a2 mod_hat m)*x2 + .. + (a_n mod_hat m)*x_n + (k mod_hat m)) // ((a1 mod_hat m)*x1 + (a2 mod_hat m)*x2 + .. + (a_n mod_hat m)*x_n + (k mod_hat m))
// = // =
// (a1'*x1 + a2'*x2 + .. (-)1*x_index + ...) // (a1'*x1 + a2'*x2 + .. (-)1*x_index + ...)
// //
// <=> Normalize signs so that sign to x_index is -1. // <=> Normalize signs so that sign to x_index is -1.
// (-)a1'*x1 + (-)a2'*x2 + .. -1*x_index + ... + m*x_index' = 0 // (-)a1'*x1 + (-)a2'*x2 + .. -1*x_index + ... + m*x_index' = 0
// //
// Return row, where the coefficient to x_index is implicit. // Return row, where the coefficient to x_index is implicit.
// Instead used the coefficient 'm' at position 'index'. // Instead used the coefficient 'm' at position 'index'.
// //
gcd_normalize(values); gcd_normalize(values);
if (!gcd_test(values)) { if (!gcd_test(values)) {
@ -216,8 +213,8 @@ bool arith_eq_solver::solve_integer_equation(
return true; return true;
} }
if (a.is_one()) { if (a.is_one()) {
for (unsigned i = 0; i < values.size(); ++i) { for (auto &value : values) {
values[i].neg(); value.neg();
} }
} }
is_fresh = !abs_a.is_one(); is_fresh = !abs_a.is_one();
@ -225,19 +222,19 @@ bool arith_eq_solver::solve_integer_equation(
if (is_fresh) { if (is_fresh) {
numeral m = abs_a + numeral(1); numeral m = abs_a + numeral(1);
for (unsigned i = 0; i < values.size(); ++i) { for (auto &value : values) {
values[i] = mod_hat(values[i], m); value = mod_hat(value, m);
} }
if (values[index].is_one()) { if (values[index].is_one()) {
for (unsigned i = 0; i < values.size(); ++i) { for (auto &value : values) {
values[i].neg(); value.neg();
} }
} }
SASSERT(values[index].is_minus_one()); SASSERT(values[index].is_minus_one());
values[index] = m; values[index] = m;
} }
TRACE("arith_eq_solver", TRACE("arith_eq_solver",
tout << "solved at index " << index << ": "; tout << "solved at index " << index << ": ";
print_row(tout, values); print_row(tout, values);
); );
@ -253,7 +250,7 @@ void arith_eq_solver::substitute(
) )
{ {
SASSERT(1 <= index && index < s.size()); SASSERT(1 <= index && index < s.size());
TRACE("arith_eq_solver", TRACE("arith_eq_solver",
tout << "substitute " << index << ":\n"; tout << "substitute " << index << ":\n";
print_row(tout, r); print_row(tout, r);
print_row(tout, s); print_row(tout, s);
@ -272,21 +269,21 @@ void arith_eq_solver::substitute(
// s encodes an equation that contains a variable // s encodes an equation that contains a variable
// with a unit coefficient. // with a unit coefficient.
// //
// Let // Let
// c = r[index] // c = r[index]
// s = s[index]*x + s'*y = 0 // s = s[index]*x + s'*y = 0
// r = c*x + r'*y = 0 // r = c*x + r'*y = 0
// //
// => // =>
// //
// 0 // 0
// = // =
// -sign(s[index])*c*s + r // -sign(s[index])*c*s + r
// = // =
// -s[index]*sign(s[index])*c*x - sign(s[index])*c*s'*y + c*x + r'*y // -s[index]*sign(s[index])*c*x - sign(s[index])*c*s'*y + c*x + r'*y
// = // =
// -c*x - sign(s[index])*c*s'*y + c*x + r'*y // -c*x - sign(s[index])*c*s'*y + c*x + r'*y
// = // =
// -sign(s[index])*c*s'*y + r'*y // -sign(s[index])*c*s'*y + r'*y
// //
numeral sign_s = s[index].is_pos()?numeral(1):numeral(-1); numeral sign_s = s[index].is_pos()?numeral(1):numeral(-1);
@ -301,36 +298,36 @@ void arith_eq_solver::substitute(
// //
// s encodes a substitution using an auxiliary variable. // s encodes a substitution using an auxiliary variable.
// the auxiliary variable is at position 'index'. // the auxiliary variable is at position 'index'.
// //
// Let // Let
// c = r[index] // c = r[index]
// s = s[index]*x + s'*y = 0 // s = s[index]*x + s'*y = 0
// r = c*x + r'*y = 0 // r = c*x + r'*y = 0
// //
// s encodes : x |-> s[index]*x' + s'*y // s encodes : x |-> s[index]*x' + s'*y
// //
// Set: // Set:
// //
// r := c*s + r'*y // r := c*s + r'*y
// //
r[index] = numeral(0); r[index] = numeral(0);
for (unsigned i = 0; i < r.size(); ++i) { for (unsigned i = 0; i < r.size(); ++i) {
r[i] += c*s[i]; r[i] += c*s[i];
} }
for (unsigned i = r.size(); i < s.size(); ++i) { for (unsigned i = r.size(); i < s.size(); ++i) {
r.push_back(c*s[i]); r.push_back(c*s[i]);
} }
} }
TRACE("arith_eq_solver", TRACE("arith_eq_solver",
tout << "result: "; tout << "result: ";
print_row(tout, r); print_row(tout, r);
); );
} }
bool arith_eq_solver::solve_integer_equations( bool arith_eq_solver::solve_integer_equations(
vector<row>& rows, vector<row>& rows,
row& unsat_row row& unsat_row
) )
{ {
@ -340,10 +337,10 @@ bool arith_eq_solver::solve_integer_equations(
// //
// Naive integer equation solver where only units are eliminated. // Naive integer equation solver where only units are eliminated.
// //
bool arith_eq_solver::solve_integer_equations_units( bool arith_eq_solver::solve_integer_equations_units(
vector<row>& rows, vector<row>& rows,
row& unsat_row row& unsat_row
) )
{ {
@ -351,7 +348,7 @@ bool arith_eq_solver::solve_integer_equations_units(
TRACE("arith_eq_solver", print_rows(tout << "solving:\n", rows);); TRACE("arith_eq_solver", print_rows(tout << "solving:\n", rows););
unsigned_vector todo, done; unsigned_vector todo, done;
for (unsigned i = 0; i < rows.size(); ++i) { for (unsigned i = 0; i < rows.size(); ++i) {
todo.push_back(i); todo.push_back(i);
row& r = rows[i]; row& r = rows[i];
@ -360,9 +357,9 @@ bool arith_eq_solver::solve_integer_equations_units(
unsat_row = r; unsat_row = r;
TRACE("arith_eq_solver", print_row(tout << "input is unsat: ", unsat_row); ); TRACE("arith_eq_solver", print_row(tout << "input is unsat: ", unsat_row); );
return false; return false;
} }
} }
for (unsigned i = 0; i < todo.size(); ++i) { for (unsigned i = 0; i < todo.size(); ++i) {
row& r = rows[todo[i]]; row& r = rows[todo[i]];
gcd_normalize(r); gcd_normalize(r);
if (!gcd_test(r)) { if (!gcd_test(r)) {
@ -388,7 +385,7 @@ bool arith_eq_solver::solve_integer_equations_units(
todo.push_back(done[j]); todo.push_back(done[j]);
done.erase(done.begin()+j); done.erase(done.begin()+j);
--j; --j;
} }
} }
} }
else { else {
@ -396,7 +393,7 @@ bool arith_eq_solver::solve_integer_equations_units(
} }
} }
TRACE("arith_eq_solver", TRACE("arith_eq_solver",
tout << ((done.size()<=1)?"solved ":"incomplete check ") << done.size() << "\n"; tout << ((done.size()<=1)?"solved ":"incomplete check ") << done.size() << "\n";
for (unsigned i = 0; i < done.size(); ++i) { for (unsigned i = 0; i < done.size(); ++i) {
print_row(tout, rows[done[i]]); print_row(tout, rows[done[i]]);
@ -411,12 +408,12 @@ bool arith_eq_solver::solve_integer_equations_units(
// //
// Partial solver based on the omega test equalities. // Partial solver based on the omega test equalities.
// unsatisfiability is not preserved when eliminating // unsatisfiability is not preserved when eliminating
// auxiliary variables. // auxiliary variables.
// //
bool arith_eq_solver::solve_integer_equations_omega( bool arith_eq_solver::solve_integer_equations_omega(
vector<row> & rows, vector<row> & rows,
row& unsat_row row& unsat_row
) )
{ {
@ -460,16 +457,16 @@ bool arith_eq_solver::solve_integer_equations_omega(
// //
// solved_row: -x_index + m*sigma + r1 = 0 // solved_row: -x_index + m*sigma + r1 = 0
// unsat_row: k*sigma + r2 = 0 // unsat_row: k*sigma + r2 = 0
// //
// <=> // <=>
// //
// solved_row: -k*x_index + k*m*sigma + k*r1 = 0 // solved_row: -k*x_index + k*m*sigma + k*r1 = 0
// unsat_row: m*k*sigma + m*r2 = 0 // unsat_row: m*k*sigma + m*r2 = 0
// //
// => // =>
// //
// m*k*sigma + m*r2 + k*x_index - k*m*sigma - k*r1 = 0 // m*k*sigma + m*r2 + k*x_index - k*m*sigma - k*r1 = 0
// //
for (unsigned l = 0; l < unsat_row.size(); ++l) { for (unsigned l = 0; l < unsat_row.size(); ++l) {
unsat_row[l] *= m; unsat_row[l] *= m;
unsat_row[l] -= k*solved_row[l]; unsat_row[l] -= k*solved_row[l];
@ -479,7 +476,7 @@ bool arith_eq_solver::solve_integer_equations_omega(
} }
gcd_normalize(unsat_row); gcd_normalize(unsat_row);
TRACE("arith_eq_solver", TRACE("arith_eq_solver",
tout << "gcd: "; tout << "gcd: ";
print_row(tout, solved_row); print_row(tout, solved_row);
print_row(tout, unsat_row); print_row(tout, unsat_row);
@ -525,18 +522,18 @@ bool arith_eq_solver::solve_integer_equations_omega(
// //
// Eliminate variables by searching for combination of rows where // Eliminate variables by searching for combination of rows where
// the coefficients have gcd = 1. // the coefficients have gcd = 1.
// //
bool arith_eq_solver::solve_integer_equations_gcd( bool arith_eq_solver::solve_integer_equations_gcd(
vector<row> & rows, vector<row> & rows,
row& unsat_row row& unsat_row
) )
{ {
unsigned_vector live, useful, gcd_pos; unsigned_vector live, useful, gcd_pos;
vector<rational> gcds; vector<rational> gcds;
rational u, v; rational u, v;
if (rows.empty()) { if (rows.empty()) {
return true; return true;
} }
@ -548,7 +545,7 @@ bool arith_eq_solver::solve_integer_equations_gcd(
unsat_row = r; unsat_row = r;
TRACE("arith_eq_solver", print_row(tout << "input is unsat: ", unsat_row); ); TRACE("arith_eq_solver", print_row(tout << "input is unsat: ", unsat_row); );
return false; return false;
} }
} }
unsigned max_column = rows[0].size(); unsigned max_column = rows[0].size();
bool change = true; bool change = true;
@ -579,7 +576,7 @@ bool arith_eq_solver::solve_integer_equations_gcd(
if (j == live.size()) { if (j == live.size()) {
continue; continue;
} }
change = true; change = true;
// found gcd, now identify reduced set of rows with GCD = 1. // found gcd, now identify reduced set of rows with GCD = 1.
g = abs(rows[live[j]][i]); g = abs(rows[live[j]][i]);
@ -592,7 +589,7 @@ bool arith_eq_solver::solve_integer_equations_gcd(
useful.push_back(gcd_pos[j]); useful.push_back(gcd_pos[j]);
g = gcd(g, gcds[j]); g = gcd(g, gcds[j]);
SASSERT(j == 0 || gcd(g,gcds[j-1]).is_one()); SASSERT(j == 0 || gcd(g,gcds[j-1]).is_one());
} }
} }
// //
// we now have a set "useful" of rows whose combined GCD = 1. // we now have a set "useful" of rows whose combined GCD = 1.
@ -600,7 +597,7 @@ bool arith_eq_solver::solve_integer_equations_gcd(
// //
row& r0 = rows[useful[0]]; row& r0 = rows[useful[0]];
for (j = 1; j < useful.size(); ++j) { for (j = 1; j < useful.size(); ++j) {
row& r1 = rows[useful[j]]; row& r1 = rows[useful[j]];
g = gcd(r0[i], r1[i], u, v); g = gcd(r0[i], r1[i], u, v);
for (unsigned k = 0; k < max_column; ++k) { for (unsigned k = 0; k < max_column; ++k) {
r0[k] = u*r0[k] + v*r1[k]; r0[k] = u*r0[k] + v*r1[k];
@ -626,7 +623,7 @@ bool arith_eq_solver::solve_integer_equations_gcd(
} }
} }
TRACE("arith_eq_solver", TRACE("arith_eq_solver",
tout << ((live.size()<=1)?"solved ":"incomplete check ") << live.size() << "\n"; tout << ((live.size()<=1)?"solved ":"incomplete check ") << live.size() << "\n";
for (unsigned i = 0; i < live.size(); ++i) { for (unsigned i = 0; i < live.size(); ++i) {
print_row(tout, rows[live[i]]); print_row(tout, rows[live[i]]);

24
src/smt/arith_eq_solver.h
View file

@ -12,7 +12,7 @@ Abstract:
Author: Author:
Nikolaj Bjorner (nbjorner) 2012-02-25 Nikolaj Bjorner (nbjorner) 2012-02-25
--*/ --*/
#ifndef ARITH_EQ_SOLVER_H_ #ifndef ARITH_EQ_SOLVER_H_
#define ARITH_EQ_SOLVER_H_ #define ARITH_EQ_SOLVER_H_
@ -35,45 +35,45 @@ class arith_eq_solver {
void prop_mod_const(expr * e, unsigned depth, numeral const& k, expr_ref& result); void prop_mod_const(expr * e, unsigned depth, numeral const& k, expr_ref& result);
bool gcd_test(vector<numeral>& value); bool gcd_test(vector<numeral>& values);
unsigned find_abs_min(vector<numeral>& values); unsigned find_abs_min(vector<numeral>& values);
void gcd_normalize(vector<numeral>& values); void gcd_normalize(vector<numeral>& values);
void substitute(vector<numeral>& r, vector<numeral> const& s, unsigned index); void substitute(vector<numeral>& r, vector<numeral> const& s, unsigned index);
bool solve_integer_equations_units( bool solve_integer_equations_units(
vector<vector<numeral> > & rows, vector<vector<numeral> > & rows,
vector<numeral>& unsat_row vector<numeral>& unsat_row
); );
bool solve_integer_equations_omega( bool solve_integer_equations_omega(
vector<vector<numeral> > & rows, vector<vector<numeral> > & rows,
vector<numeral>& unsat_row vector<numeral>& unsat_row
); );
void compute_hnf(vector<vector<numeral> >& A); void compute_hnf(vector<vector<numeral> >& A);
bool solve_integer_equations_hermite( bool solve_integer_equations_hermite(
vector<vector<numeral> > & rows, vector<vector<numeral> > & rows,
vector<numeral>& unsat_row vector<numeral>& unsat_row
); );
bool solve_integer_equations_gcd( bool solve_integer_equations_gcd(
vector<vector<numeral> > & rows, vector<vector<numeral> > & rows,
vector<numeral>& unsat_row vector<numeral>& unsat_row
); );
public: public:
arith_eq_solver(ast_manager & m, params_ref const& p = params_ref()); arith_eq_solver(ast_manager & m, params_ref const& p = params_ref());
~arith_eq_solver(); ~arith_eq_solver() = default;
// Integer linear solver for a single equation. // Integer linear solver for a single equation.
// The array values contains integer coefficients // The array values contains integer coefficients
// //
// Determine integer solutions to: // Determine integer solutions to:
// //
// a+k = 0 // a+k = 0
// //
// where a = sum_i a_i*k_i // where a = sum_i a_i*k_i
// //
typedef vector<numeral> row; typedef vector<numeral> row;
typedef vector<row> matrix; typedef vector<row> matrix;
@ -90,14 +90,14 @@ public:
// a+k = 0 // a+k = 0
// //
// where a = sum_i a_i*k_i // where a = sum_i a_i*k_i
// //
// Solution, if there is any, is returned as a substitution. // Solution, if there is any, is returned as a substitution.
// The return value is "true". // The return value is "true".
// If there is no solution, then return "false". // If there is no solution, then return "false".
// together with equality "eq_unsat", such that // together with equality "eq_unsat", such that
// //
// eq_unsat = 0 // eq_unsat = 0
// //
// is implied and is unsatisfiable over the integers. // is implied and is unsatisfiable over the integers.
// //