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https://github.com/Z3Prover/z3
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intblast with lazy expansion of shl, ashr, lshr
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner
parent
50e0fd3ba6
commit
d0a59f3740
10 changed files with 321 additions and 83 deletions
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@ -205,58 +205,117 @@ namespace arith {
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add_clause(dgez, neg);
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}
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bool solver::check_band_term(app* n) {
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bool solver::check_bv_term(app* n) {
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unsigned sz;
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expr* x, * y;
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expr* _x, * _y;
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if (!ctx.is_relevant(expr2enode(n)))
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return true;
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VERIFY(a.is_band(n, sz, x, y));
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expr_ref vx(m), vy(m),vn(m);
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if (!get_value(expr2enode(x), vx) || !get_value(expr2enode(y), vy) || !get_value(expr2enode(n), vn)) {
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rational valn, valx, valy;
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bool is_int;
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VERIFY(a.is_band(n, sz, _x, _y) || a.is_shl(n, sz, _x, _y) || a.is_ashr(n, sz, _x, _y) || a.is_lshr(n, sz, _x, _y));
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if (!get_value(expr2enode(_x), vx) || !get_value(expr2enode(_y), vy) || !get_value(expr2enode(n), vn)) {
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IF_VERBOSE(2, verbose_stream() << "could not get value of " << mk_pp(n, m) << "\n");
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found_unsupported(n);
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return true;
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}
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rational valn, valx, valy;
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bool is_int;
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if (!a.is_numeral(vn, valn, is_int) || !is_int || !a.is_numeral(vx, valx, is_int) || !is_int || !a.is_numeral(vy, valy, is_int) || !is_int) {
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IF_VERBOSE(2, verbose_stream() << "could not get value of " << mk_pp(n, m) << "\n");
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found_unsupported(n);
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return true;
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}
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// verbose_stream() << "band: " << mk_pp(n, m) << " " << valn << " := " << valx << "&" << valy << "\n";
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rational N = rational::power_of_two(sz);
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valx = mod(valx, N);
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valy = mod(valy, N);
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expr_ref x(a.mk_mod(_x, a.mk_int(N)), m);
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expr_ref y(a.mk_mod(_y, a.mk_int(N)), m);
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SASSERT(0 <= valn && valn < N);
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// x mod 2^{i + 1} >= 2^i means the i'th bit is 1.
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auto bitof = [&](expr* x, unsigned i) {
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expr_ref r(m);
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r = a.mk_ge(a.mk_mod(x, a.mk_int(rational::power_of_two(i+1))), a.mk_int(rational::power_of_two(i)));
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return mk_literal(r);
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};
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for (unsigned i = 0; i < sz; ++i) {
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bool xb = valx.get_bit(i);
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bool yb = valy.get_bit(i);
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bool nb = valn.get_bit(i);
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if (xb && yb && !nb)
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add_clause(~bitof(x, i), ~bitof(y, i), bitof(n, i));
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else if (nb && !xb)
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add_clause(~bitof(n, i), bitof(x, i));
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else if (nb && !yb)
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add_clause(~bitof(n, i), bitof(y, i));
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else
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continue;
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if (a.is_band(n)) {
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IF_VERBOSE(2, verbose_stream() << "band: " << mk_bounded_pp(n, m) << " " << valn << " := " << valx << "&" << valy << "\n");
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for (unsigned i = 0; i < sz; ++i) {
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bool xb = valx.get_bit(i);
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bool yb = valy.get_bit(i);
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bool nb = valn.get_bit(i);
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if (xb && yb && !nb)
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add_clause(~bitof(x, i), ~bitof(y, i), bitof(n, i));
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else if (nb && !xb)
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add_clause(~bitof(n, i), bitof(x, i));
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else if (nb && !yb)
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add_clause(~bitof(n, i), bitof(y, i));
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else
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continue;
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return false;
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}
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}
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if (a.is_shl(n)) {
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SASSERT(valy >= 0);
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if (valy >= sz || valy == 0)
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return true;
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unsigned k = valy.get_unsigned();
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sat::literal eq = eq_internalize(n, a.mk_mod(a.mk_mul(_x, a.mk_int(rational::power_of_two(k))), a.mk_int(N)));
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if (s().value(eq) == l_true)
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return true;
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add_clause(~eq_internalize(y, a.mk_int(k)), eq);
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IF_VERBOSE(2, verbose_stream() << "shl: " << mk_bounded_pp(n, m) << " " << valn << " := " << valx << " << " << valy << "\n");
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return false;
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}
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if (a.is_lshr(n)) {
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SASSERT(valy >= 0);
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if (valy >= sz || valy == 0)
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return true;
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unsigned k = valy.get_unsigned();
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sat::literal eq = eq_internalize(n, a.mk_idiv(x, a.mk_int(rational::power_of_two(k))));
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if (s().value(eq) == l_true)
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return true;
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add_clause(~eq_internalize(y, a.mk_int(k)), eq);
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IF_VERBOSE(2, verbose_stream() << "lshr: " << mk_bounded_pp(n, m) << " " << valn << " := " << valx << " >>l " << valy << "\n");
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return false;
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}
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if (a.is_ashr(n)) {
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SASSERT(valy >= 0);
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if (valy >= sz || valy == 0)
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return true;
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unsigned k = valy.get_unsigned();
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sat::literal signx = mk_literal(a.mk_ge(x, a.mk_int(N/2)));
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sat::literal eq;
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expr* xdiv2k;
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switch (s().value(signx)) {
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case l_true:
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// x < 0 & y = k -> n = (x div 2^k - 2^{N-k}) mod 2^N
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xdiv2k = a.mk_idiv(x, a.mk_int(rational::power_of_two(k)));
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eq = eq_internalize(n, a.mk_mod(a.mk_add(xdiv2k, a.mk_int(-rational::power_of_two(sz - k))), a.mk_int(N)));
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if (s().value(eq) == l_true)
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return true;
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break;
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case l_false:
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// x >= 0 & y = k -> n = x div 2^k
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xdiv2k = a.mk_idiv(x, a.mk_int(rational::power_of_two(k)));
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eq = eq_internalize(n, xdiv2k);
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if (s().value(eq) == l_true)
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return true;
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break;
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case l_undef:
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ctx.mark_relevant(signx);
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return false;
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}
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add_clause(~eq_internalize(y, a.mk_int(k)), ~signx, eq);
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return false;
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}
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return true;
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}
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bool solver::check_band_terms() {
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for (app* n : m_band_terms) {
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if (!check_band_term(n)) {
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++m_stats.m_band_axioms;
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bool solver::check_bv_terms() {
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for (app* n : m_bv_terms) {
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if (!check_bv_term(n)) {
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++m_stats.m_bv_axioms;
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return false;
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}
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}
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@ -268,15 +327,43 @@ namespace arith {
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* x&y <= x
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* x&y <= y
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*/
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void solver::mk_band_axiom(app* n) {
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void solver::mk_bv_axiom(app* n) {
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unsigned sz;
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expr* x, * y;
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VERIFY(a.is_band(n, sz, x, y));
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expr* _x, * _y;
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VERIFY(a.is_band(n, sz, _x, _y) || a.is_shl(n, sz, _x, _y) || a.is_ashr(n, sz, _x, _y) || a.is_lshr(n, sz, _x, _y));
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rational N = rational::power_of_two(sz);
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add_clause(mk_literal(a.mk_ge(n, a.mk_int(0))));
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add_clause(mk_literal(a.mk_le(n, a.mk_int(N - 1))));
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add_clause(mk_literal(a.mk_le(n, a.mk_mod(x, a.mk_int(N)))));
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add_clause(mk_literal(a.mk_le(n, a.mk_mod(y, a.mk_int(N)))));
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expr_ref x(a.mk_mod(_x, a.mk_int(N)), m);
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expr_ref y(a.mk_mod(_y, a.mk_int(N)), m);
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if (a.is_band(n)) {
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add_clause(mk_literal(a.mk_ge(n, a.mk_int(0))));
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add_clause(mk_literal(a.mk_le(n, a.mk_int(N - 1))));
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add_clause(mk_literal(a.mk_le(n, x)));
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add_clause(mk_literal(a.mk_le(n, y)));
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}
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else if (a.is_shl(n)) {
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// y >= sz => n = 0
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// y = 0 => n = x
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add_clause(~mk_literal(a.mk_ge(y, a.mk_int(sz))), mk_literal(m.mk_eq(n, a.mk_int(0))));
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add_clause(~mk_literal(a.mk_eq(y, a.mk_int(0))), mk_literal(m.mk_eq(n, x)));
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}
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else if (a.is_lshr(n)) {
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// y >= sz => n = 0
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// y = 0 => n = x
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add_clause(~mk_literal(a.mk_ge(y, a.mk_int(sz))), mk_literal(m.mk_eq(n, a.mk_int(0))));
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add_clause(~mk_literal(a.mk_eq(y, a.mk_int(0))), mk_literal(m.mk_eq(n, x)));
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}
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else if (a.is_ashr(n)) {
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// y >= sz & x < 2^{sz-1} => n = 0
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// y >= sz & x >= 2^{sz-1} => n = -1
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// y = 0 => n = x
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auto signx = mk_literal(a.mk_ge(x, a.mk_int(N/2)));
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add_clause(~mk_literal(a.mk_ge(a.mk_mod(y, a.mk_int(N)), a.mk_int(sz))), signx, mk_literal(m.mk_eq(n, a.mk_int(0))));
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add_clause(~mk_literal(a.mk_ge(a.mk_mod(y, a.mk_int(N)), a.mk_int(sz))), ~signx, mk_literal(m.mk_eq(n, a.mk_int(N-1))));
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add_clause(~mk_literal(a.mk_eq(a.mk_mod(y, a.mk_int(N)), a.mk_int(0))), mk_literal(m.mk_eq(n, x)));
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}
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else
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UNREACHABLE();
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}
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void solver::mk_bound_axioms(api_bound& b) {
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