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https://github.com/Z3Prover/z3
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updates to sorting networks
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner
parent
3c4ac9aee5
commit
edb3569599
18 changed files with 2070 additions and 170 deletions
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@ -24,6 +24,28 @@ Notes:
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#ifndef SORTING_NETWORK_H_
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#define SORTING_NETWORK_H_
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enum sorting_network_encoding {
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grouped_at_most_1,
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bimander_at_most_1,
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ordered_at_most_1
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};
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inline std::ostream& operator<<(std::ostream& out, sorting_network_encoding enc) {
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switch (enc) {
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case grouped_at_most_1: return out << "grouped";
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case bimander_at_most_1: return out << "bimander";
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case ordered_at_most_1: return out << "ordered";
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}
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return out << "???";
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}
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struct sorting_network_config {
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sorting_network_encoding m_encoding;
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sorting_network_config() {
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m_encoding = grouped_at_most_1;
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}
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};
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template <typename Ext>
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class sorting_network {
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typedef typename Ext::vector vect;
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@ -88,7 +110,7 @@ Notes:
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}
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public:
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sorting_network(Ext& ext):
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sorting_network(Ext& ext):
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m_ext(ext),
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m_current(&m_currentv),
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m_next(&m_nextv)
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@ -121,6 +143,7 @@ Notes:
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class psort_nw {
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typedef typename psort_expr::literal literal;
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typedef typename psort_expr::literal_vector literal_vector;
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sorting_network_config m_cfg;
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class vc {
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unsigned v; // number of vertices
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@ -185,7 +208,7 @@ Notes:
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}
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};
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psort_nw(psort_expr& c): ctx(c) {}
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psort_nw(psort_expr& c, sorting_network_config const& cfg): ctx(c), m_cfg(cfg) {}
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literal ge(bool full, unsigned k, unsigned n, literal const* xs) {
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if (k > n) {
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@ -220,7 +243,17 @@ Notes:
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else if (k == 1) {
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literal_vector ors;
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// scoped_stats _ss(m_stats, k, n);
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return mk_at_most_1(full, n, xs, ors, false);
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switch (m_cfg.m_encoding) {
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case grouped_at_most_1:
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return mk_at_most_1(full, n, xs, ors, false);
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case bimander_at_most_1:
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return mk_at_most_1_bimander(full, n, xs, ors);
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case ordered_at_most_1:
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return mk_ordered_atmost_1(full, n, xs);
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default:
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UNREACHABLE();
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return xs[0];
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}
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}
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else {
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SASSERT(2*k <= n);
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@ -278,7 +311,7 @@ Notes:
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if (n == 1) {
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return ors[0];
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}
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literal result = fresh();
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literal result = fresh("or");
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add_implies_or(result, n, ors);
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add_or_implies(result, n, ors);
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return result;
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@ -317,15 +350,26 @@ Notes:
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if (ands.size() == 1) {
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return ands[0];
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}
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literal result = fresh();
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literal result = fresh("and");
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add_implies_and(result, ands);
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add_and_implies(result, ands);
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return result;
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}
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literal mk_exactly_1(bool full, unsigned n, literal const* xs) {
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TRACE("pb", tout << "exactly 1 with " << n << " arguments " << (full?"full":"not full") << "\n";);
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literal_vector ors;
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literal r1 = mk_at_most_1(full, n, xs, ors, true);
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literal r1;
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switch (m_cfg.m_encoding) {
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case grouped_at_most_1:
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r1 = mk_at_most_1(full, n, xs, ors, true);
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break;
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case bimander_at_most_1:
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r1 = mk_at_most_1_bimander(full, n, xs, ors);
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break;
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case ordered_at_most_1:
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return mk_ordered_exactly_1(full, n, xs);
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}
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if (full) {
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r1 = mk_and(r1, mk_or(ors));
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@ -340,12 +384,8 @@ Notes:
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TRACE("pb_verbose", tout << (full?"full":"partial") << " ";
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for (unsigned i = 0; i < n; ++i) tout << xs[i] << " ";
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tout << "\n";);
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if (n >= 4 && false) {
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return mk_at_most_1_bimander(full, n, xs, ors);
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}
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literal_vector in(n, xs);
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literal result = fresh();
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literal result = fresh("at-most-1");
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unsigned inc_size = 4;
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literal_vector ands;
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ands.push_back(result);
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@ -387,7 +427,7 @@ Notes:
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// xs[0] + ... + xs[n-1] <= 1 => and_x
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if (full) {
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literal and_i = fresh();
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literal and_i = fresh("and");
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for (unsigned i = 0; i < n; ++i) {
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literal_vector lits;
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lits.push_back(and_i);
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@ -407,29 +447,6 @@ Notes:
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}
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#if 0
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literal result = fresh();
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// result => xs[0] + ... + xs[n-1] <= 1
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for (unsigned i = 0; i < n; ++i) {
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for (unsigned j = i + 1; j < n; ++j) {
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add_clause(ctx.mk_not(result), ctx.mk_not(xs[i]), ctx.mk_not(xs[j]));
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}
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}
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// xs[0] + ... + xs[n-1] <= 1 => result
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for (unsigned i = 0; i < n; ++i) {
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literal_vector lits;
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lits.push_back(result);
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for (unsigned j = 0; j < n; ++j) {
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if (j != i) lits.push_back(xs[j]);
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}
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add_clause(lits);
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}
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return result;
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#endif
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#if 1
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// r <=> and( or(!xi,!xj))
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//
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literal_vector ands;
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@ -439,30 +456,100 @@ Notes:
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}
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}
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return mk_and(ands);
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#else
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// r <=> or (and !x_{j != i})
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literal_vector ors;
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for (unsigned i = 0; i < n; ++i) {
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literal_vector ands;
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for (unsigned j = 0; j < n; ++j) {
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if (j != i) {
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ands.push_back(ctx.mk_not(xs[j]));
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}
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}
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ors.push_back(mk_and(ands));
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}
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return mk_or(ors);
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#endif
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}
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literal mk_ordered_exactly_1(bool full, unsigned n, literal const* xs) {
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return mk_ordered_1(full, true, n, xs);
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}
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literal mk_ordered_atmost_1(bool full, unsigned n, literal const* xs) {
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return mk_ordered_1(full, false, n, xs);
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}
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literal mk_ordered_1(bool full, bool is_eq, unsigned n, literal const* xs) {
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if (n <= 1 && !is_eq) return ctx.mk_true();
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if (n == 0) {
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return ctx.mk_false();
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}
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if (n == 1) {
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return xs[0];
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}
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// y0 -> y1
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// x0 -> y0
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// x1 -> y1
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// r, y0 -> ~x1
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// r, y1 -> ~x2
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// r -> x3 | y1
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// r -> ~x3 | ~y1
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// x0,x1,x2, .., x_{n-1}, x_n
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// y0,y1,y2, .., y_{n-1}
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// y_i -> y_{i+1} i = 0, ..., n - 2
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// x_i -> y_i i = 0, ..., n - 1
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// r, y_i -> ~x_{i+1} i = 0, ..., n - 1
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// exactly 1:
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// r -> x_n | y_{n-1}
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// full (exactly 1):
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// two_i -> y_i & x_{i+1}
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// zero -> ~x_n
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// zero -> ~y_{n-1}
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// r | zero | two_0 | ... | two_{n-1}
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// full atmost 1:
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// r | two | two_0 | ... | two_{n-1}
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literal r = fresh("ordered");
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literal_vector ys;
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for (unsigned i = 0; i + 1 < n; ++i) {
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ys.push_back(fresh("y"));
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}
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for (unsigned i = 0; i + 2 < n; ++i) {
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add_clause(ctx.mk_not(ys[i]), ys[i + 1]);
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}
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for (unsigned i = 0; i + 1 < n; ++i) {
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add_clause(ctx.mk_not(xs[i]), ys[i]);
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add_clause(ctx.mk_not(r), ctx.mk_not(ys[i]), ctx.mk_not(xs[i + 1]));
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}
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add_clause(ctx.mk_not(r), ys[n-2], xs[n-1]);
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add_clause(ctx.mk_not(r), ctx.mk_not(ys[n-2]), ctx.mk_not(xs[n-1]));
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for (unsigned i = 1; i < n - 1; ++i) {
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add_clause(ctx.mk_not(ys[i]), xs[i], ys[i-1]);
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}
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add_clause(ctx.mk_not(ys[0]), xs[0]);
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if (full) {
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literal_vector twos;
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for (unsigned i = 0; i < n - 1; ++i) {
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twos.push_back(fresh("two"));
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}
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add_clause(ctx.mk_not(twos[0]), ys[0]);
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add_clause(ctx.mk_not(twos[0]), xs[1]);
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for (unsigned i = 1; i < n - 1; ++i) {
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add_clause(ctx.mk_not(twos[i]), ys[i], twos[i-1]);
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add_clause(ctx.mk_not(twos[i]), xs[i + 1], twos[i-1]);
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}
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if (is_eq) {
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literal zero = fresh("zero");
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add_clause(ctx.mk_not(zero), ctx.mk_not(xs[n-1]));
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add_clause(ctx.mk_not(zero), ctx.mk_not(ys[n-2]));
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add_clause(r, zero, twos.back());
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}
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else {
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add_clause(r, twos.back());
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}
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}
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return r;
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}
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//
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literal mk_at_most_1_bimander(bool full, unsigned n, literal const* xs, literal_vector& ors) {
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if (full) {
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return mk_at_most_1(full, n, xs, ors, true);
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}
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literal_vector in(n, xs);
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literal result = fresh();
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literal result = fresh("bimander");
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unsigned inc_size = 2;
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literal_vector ands;
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for (unsigned i = 0; i < n; i += inc_size) {
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@ -477,7 +564,7 @@ Notes:
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}
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literal_vector bits;
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for (unsigned k = 0; k < nbits; ++k) {
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bits.push_back(fresh());
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bits.push_back(fresh("bit"));
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}
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for (unsigned i = 0; i < ors.size(); ++i) {
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for (unsigned k = 0; k < nbits; ++k) {
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@ -539,9 +626,9 @@ Notes:
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return ctx.mk_min(a, b);
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}
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literal fresh() {
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literal fresh(char const* n) {
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m_stats.m_num_compiled_vars++;
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return ctx.fresh();
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return ctx.fresh(n);
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}
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void add_clause(literal l1, literal l2, literal l3) {
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literal lits[3] = { l1, l2, l3 };
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@ -558,7 +645,6 @@ Notes:
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m_stats.m_num_compiled_clauses++;
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m_stats.m_num_clause_vars += n;
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literal_vector tmp(n, ls);
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TRACE("pb_verbose", for (unsigned i = 0; i < n; ++i) tout << ls[i] << " "; tout << "\n";);
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ctx.mk_clause(n, tmp.c_ptr());
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}
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@ -925,7 +1011,7 @@ Notes:
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SASSERT(b <= c);
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SASSERT(a + b >= c);
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for (unsigned i = 0; i < c; ++i) {
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out.push_back(fresh());
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out.push_back(fresh("dsmerge"));
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}
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if (m_t != GE) {
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for (unsigned i = 0; i < a; ++i) {
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@ -983,7 +1069,7 @@ Notes:
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SASSERT(m <= n);
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literal_vector lits;
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for (unsigned i = 0; i < m; ++i) {
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out.push_back(fresh());
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out.push_back(fresh("dsort"));
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}
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if (m_t != GE) {
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for (unsigned k = 1; k <= m; ++k) {
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