BDD vectors: add subtract and quot_rem, move finite domain abstraction out of bdd_manager (#5201)

* Coding style

* Simplify bddv class

* mk_eq: run loop from below

* Add unit test for bddv unsigned comparison

* Add test that shows contains_num/find_num fail after reordering

* Add BDD vector subtraction

* Call apply_rec in mk_ite_rec instead of apply

* Question about mk_quant

* Implement quot_rem over BDD vectors

* Move shl/shr to bddv

* Make unit test smaller

* Add class dd::fdd to manage association between BDDs and numbers

* Remove contains_num/find_num from bdd_manager

src/math/dd/dd_fdd.h

@@ -0,0 +1,69 @@
+/*++
+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:
+
+    Nikolaj Bjorner (nbjorner) 2021-04-20
+    Jakob Rath 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;  // NOTE: currently unused
+        bddv            m_var;
+
+        static unsigned_vector seq(unsigned count) {
+            unsigned_vector result;
+            for (unsigned i = 0; i < count; ++i)
+                result.push_back(i);
+            return result;
+        }
+
+        unsigned var2pos(unsigned var) const;
+
+    public:
+        /** Initialize FDD using BDD variables from 0 to num_bits-1. */
+        fdd(bdd_manager& manager, unsigned num_bits) : fdd(manager, seq(num_bits)) { }
+        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; }
+
+        /** 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;
+    };
+
+}