Additional BDD operations; BDD vectors and finite domain abstraction

src/math/dd/dd_fdd.h

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+/*++
+Copyright (c) 2021 Microsoft Corporation
+
+Module Name:
+
+    dd_fdd
+
+Abstract:
+
+    Finite domain abstraction for using BDDs as sets of integers, inspired by BuDDy's fdd module.
+
+Author:
+
+    Jakob Rath 2021-04-20
+    Nikolaj Bjorner (nbjorner) 2021-04-20
+
+--*/
+#pragma once
+
+#include "math/dd/dd_bdd.h"
+#include "util/vector.h"
+#include "util/rational.h"
+
+namespace dd {
+
+    enum class find_t { empty, singleton, multiple };
+    std::ostream& operator<<(std::ostream& out, find_t x);
+
+    /**
+     * Finite domain abstraction over BDDs.
+     */
+    class fdd {
+        unsigned_vector m_pos2var;  // pos -> BDD var
+        unsigned_vector m_var2pos;  // var -> pos (pos = place number in the bit representation, 0 is LSB's place)
+        bdd_manager*    m;
+        bddv            m_var;
+
+        static unsigned_vector seq(unsigned count, unsigned start = 0, unsigned step = 1) {
+            unsigned_vector result;
+            unsigned k = start;
+            for (unsigned i = 0; i < count; ++i, k += step)
+                result.push_back(k);
+            return result;
+        }
+
+        unsigned var2pos(unsigned var) const;
+
+        bool contains(bdd const& b, bool_vector const& value) const;
+
+        rational bits2rational(bool_vector const& v) const;
+
+        bool_vector rational2bits(rational const& r) const;
+
+    public:
+        /** Initialize FDD using BDD variables from 0 to num_bits-1. */
+        fdd(bdd_manager& manager, unsigned num_bits, unsigned start = 0, unsigned step = 1) : fdd(manager, seq(num_bits, start, step)) { }
+        fdd(bdd_manager& manager, unsigned_vector const& vars) : fdd(manager, unsigned_vector(vars)) { }
+        fdd(bdd_manager& manager, unsigned_vector&& vars);
+
+        unsigned num_bits() const { return m_pos2var.size(); }
+        unsigned_vector const& bdd_vars() const { return m_pos2var; }
+
+        bddv const& var() const { return m_var; }
+
+        /** Equivalent to var() != 0 */
+        bdd non_zero() const;
+
+        /** Checks whether the integer val is contained in the BDD when viewed as set of integers.
+         * Precondition: the bdd only contains variables managed by this fdd.
+         */
+        bool contains(bdd b, rational const& val) const;
+
+        /** Returns an integer contained in the BDD, if any, and whether the BDD is a singleton.
+         * Precondition: the bdd only contains variables managed by this fdd.
+         */
+        find_t find(bdd b, rational& out_val) const;
+
+        /** Like find, but returns hint if it is contained in the BDD. */
+        find_t find_hint(bdd b, rational const& hint, rational& out_val) const;
+
+        /*
+         * find largest value at lo or above such that bdd b evaluates to true
+         * at lo and all values between.
+         * dually, find smallest value below hi that evaluates b to true
+         * and all values between the value and hi also evaluate b to true.
+         * \param b - a bdd using variables from this
+         * \param lo/hi - bound to be traversed.
+         * \return false if b is false at lo/hi
+         * \pre variables in b are a subset of variables from the fdd
+         */
+        bool sup(bdd const& b, bool_vector& lo) const;
+
+        bool inf(bdd const& b, bool_vector& hi) const;
+
+        bool sup(bdd const& b, rational& lo) const;
+
+        bool inf(bdd const& b, rational& hi) const;
+
+        /*
+        * Find the min-max satisfying assignment.
+        * \pre b is not false.
+        */
+        rational max(bdd b) const;
+
+        rational min(bdd b) const;
+    };
+
+}