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.cpp

@@ -0,0 +1,88 @@
+/*++
+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
+
+--*/
+
+#include "math/dd/dd_fdd.h"
+
+namespace dd {
+
+    fdd::fdd(bdd_manager& manager, unsigned_vector&& vars)
+        : m_pos2var(std::move(vars))
+        , m_var2pos()
+        // , m(&manager)
+        , m_var(manager.mk_var(m_pos2var))
+    {
+        for (unsigned pos = 0; pos < m_pos2var.size(); ++pos) {
+            unsigned const var = m_pos2var[pos];
+            while (var >= m_var2pos.size())
+                m_var2pos.push_back(UINT_MAX);
+            m_var2pos[var] = pos;
+        }
+    }
+
+    unsigned fdd::var2pos(unsigned var) const {
+        return var < m_var2pos.size() ? m_var2pos[var] : UINT_MAX;
+    }
+
+    bool fdd::contains(bdd b, rational const& val) const {
+        while (!b.is_const()) {
+            unsigned const pos = var2pos(b.var());
+            SASSERT(pos != UINT_MAX && "Unexpected BDD variable");
+            b = val.get_bit(pos) ? b.hi() : b.lo();
+        }
+        return b.is_true();
+    }
+
+    find_t fdd::find(bdd b, rational& out_val) const {
+        out_val = 0;
+        if (b.is_false())
+            return find_t::empty;
+        bool is_unique = true;
+        unsigned num_vars = 0;
+        while (!b.is_true()) {
+            ++num_vars;
+            unsigned const pos = var2pos(b.var());
+            SASSERT(pos != UINT_MAX && "Unexpected BDD variable");
+            if (b.lo().is_false()) {
+                out_val += rational::power_of_two(pos);
+                b = b.hi();
+            }
+            else {
+                if (!b.hi().is_false())
+                    is_unique = false;
+                b = b.lo();
+            }
+        }
+        if (num_vars != num_bits())
+            is_unique = false;
+        return is_unique ? find_t::singleton : find_t::multiple;
+    }
+
+    std::ostream& operator<<(std::ostream& out, find_t x) {
+        switch (x) {
+        case find_t::empty:
+            return out << "empty";
+        case find_t::singleton:
+            return out << "singleton";
+        case find_t::multiple:
+            return out << "multiple";
+        }
+        UNREACHABLE();
+        return out;
+    }
+
+}