feat(polynomial): add multivariate polynomials

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

src/util/polynomial/polynomial.h

@@ -0,0 +1,80 @@
+/*
+Copyright (c) 2013 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Author: Leonardo de Moura
+*/
+#include <utility>
+#include <algorithm>
+#include "util/rc.h"
+
+namespace lean {
+
+class power : public std::pair<unsigned, unsigned> {
+public:
+    typedef unsigned var;
+    power(var v, unsigned d):std::pair<var, unsigned>(v, d) {}
+    var get_var() const { return first; }
+    void set_var(var x) { first = x; }
+    unsigned degree() const { return second; }
+    unsigned & degree() { return second; }
+    struct lt_var {
+        bool operator()(power const & p1, power const & p2) const { return p1.get_var() < p2.get_var(); }
+    };
+    struct lt_degree {
+        bool operator()(power const & p1, power const & p2) const { return p1.degree() < p2.degree(); }
+    };
+};
+
+template<typename T>
+class monomial {
+    struct cell {
+        MK_LEAN_RC();
+        unsigned m_total_degree;
+        unsigned m_size;
+        unsigned m_hash;
+        power    m_powers[0];
+    };
+    cell * m_ptr;
+public:
+    monomial():m_ptr(nullptr) {}
+    monomial(monomial const & s):m_ptr(s.m_ptr) { if (m_ptr) m_ptr->inc_ref(); }
+    monomial(monomial && s):m_ptr(s.m_ptr) { s.m_ptr = nullptr; }
+    ~monomial() { if (m_ptr) m_ptr->dec_ref(); }
+
+    static monomial const & null();
+
+    friend void swap(monomial & a, monomial & b) { std::swap(a.m_ptr, b.m_ptr); }
+
+    void release() { if (m_ptr) m_ptr->dec_ref(); m_ptr = nullptr; }
+
+    monomial & operator=(monomial const & s) { LEAN_COPY_REF(monomial, s); }
+    monomial & operator=(monomial && s) { LEAN_MOVE_REF(monomial, s); }
+};
+
+template<typename T>
+class polynomial {
+    struct cell {
+        MK_LEAN_RC();
+        unsigned m_size:31;
+        unsigned m_lex_sorted:1;
+        T *        m_as;
+        monomial * m_ms;
+    };
+    cell * m_ptr;
+public:
+    polynomial():m_ptr(nullptr) {}
+    polynomial(polynomial const & s):m_ptr(s.m_ptr) { if (m_ptr) m_ptr->inc_ref(); }
+    polynomial(polynomial && s):m_ptr(s.m_ptr) { s.m_ptr = nullptr; }
+    ~polynomial() { if (m_ptr) m_ptr->dec_ref(); }
+
+    static polynomial const & null();
+
+    friend void swap(polynomial & a, polynomial & b) { std::swap(a.m_ptr, b.m_ptr); }
+
+    void release() { if (m_ptr) m_ptr->dec_ref(); m_ptr = nullptr; }
+
+    polynomial & operator=(polynomial const & s) { LEAN_COPY_REF(polynomial, s); }
+    polynomial & operator=(polynomial && s) { LEAN_MOVE_REF(polynomial, s); }
+};
+}