Merge branch 'opt' of https://github.com/NikolajBjorner/z3 into opt

src/api/dotnet/core/DummyContracts.cs

@@ -62,4 +62,4 @@ namespace System.Diagnostics.Contracts
         public static void EndContractBlock() { }
         public static T ValueAtReturn<T>(out T v) { T[] t = new T[1]; v = t[0]; return v; }
     }
-}
+}

src/api/dotnet/dotnet35/Example/App.config

@@ -3,4 +3,4 @@
     <startup> 
         <supportedRuntime version="v4.0" sku=".NETFramework,Version=v4.5.2" />
     </startup>
-</configuration>
+</configuration>

src/api/dotnet/dotnet35/Example/Example.csproj

@@ -75,4 +75,4 @@
   <Target Name="AfterBuild">
   </Target>
   -->
-</Project>
+</Project>

src/api/dotnet/dotnet35/Microsoft.Z3.NET35.csproj

@@ -344,4 +344,4 @@
     <None Include="packages.config" />
   </ItemGroup>
   <Import Project="$(MSBuildToolsPath)\Microsoft.CSharp.targets" />
-</Project>
+</Project>

src/api/dotnet/dotnet35/packages.config

@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="utf-8"?>
 <packages>
   <package id="Code.Contract" version="1.0.0" targetFramework="net35" />
-</packages>
+</packages>

src/api/python/setup.py

@@ -164,6 +164,6 @@ setup(
     package_data={
         'z3': [os.path.join('lib', '*'), os.path.join('include', '*.h'), os.path.join('include', 'c++', '*.h')]
     },
-    scripts=[os.path.join('bin', EXECUTABLE_FILE)],
+    data_files=[('bin',[os.path.join('bin',EXECUTABLE_FILE)])],
     cmdclass={'build': build, 'develop': develop, 'sdist': sdist, 'bdist_egg': bdist_egg},
 )

src/api/python/z3/z3.py

@@ -1300,8 +1300,10 @@ class BoolSortRef(SortRef):
         if isinstance(val, bool):
             return BoolVal(val, self.ctx)
         if __debug__:
-            _z3_assert(is_expr(val), "True, False or Z3 Boolean expression expected. Received %s" % val)
-            _z3_assert(self.eq(val.sort()), "Value cannot be converted into a Z3 Boolean value")
+            if not is_expr(val):
+               _z3_assert(is_expr(val), "True, False or Z3 Boolean expression expected. Received %s" % val)
+            if not self.eq(val.sort()):
+               _z3_assert(self.eq(val.sort()), "Value cannot be converted into a Z3 Boolean value")
         return val
 
     def subsort(self, other):

src/ast/arith_decl_plugin.h

@@ -305,6 +305,7 @@ public:
     MATCH_UNARY(is_uminus);
     MATCH_UNARY(is_to_real);
     MATCH_UNARY(is_to_int);
+    MATCH_UNARY(is_is_int);
     MATCH_BINARY(is_sub);
     MATCH_BINARY(is_add);
     MATCH_BINARY(is_mul);
@@ -377,6 +378,9 @@ public:
     app * mk_real(int i) {
         return mk_numeral(rational(i), false);
     }
+    app * mk_real(rational const& r) {
+        return mk_numeral(r, false);
+    }
     app * mk_le(expr * arg1, expr * arg2) const { return m_manager.mk_app(m_afid, OP_LE, arg1, arg2); }
     app * mk_ge(expr * arg1, expr * arg2) const { return m_manager.mk_app(m_afid, OP_GE, arg1, arg2); }
     app * mk_lt(expr * arg1, expr * arg2) const { return m_manager.mk_app(m_afid, OP_LT, arg1, arg2); }

src/ast/ast_pp_util.cpp

@@ -44,8 +44,11 @@ void ast_pp_util::display_decls(std::ostream& out) {
     }
     n = coll.get_num_decls();
     for (unsigned i = 0; i < n; ++i) {
-        ast_smt2_pp(out, coll.get_func_decls()[i], env);
-        out << "\n";
+        func_decl* f = coll.get_func_decls()[i];
+        if (f->get_family_id() == null_family_id) {
+            ast_smt2_pp(out, f, env);
+            out << "\n";
+        }
     }
 }
 

src/ast/rewriter/pb2bv_rewriter.cpp

@@ -26,6 +26,7 @@ Notes:
 #include"ast_pp.h"
 #include"lbool.h"
 #include"uint_set.h"
+#include"gparams.h"
 
 const unsigned g_primes[7] = { 2, 3, 5, 7, 11, 13, 17};
 
@@ -54,6 +55,8 @@ struct pb2bv_rewriter::imp {
         vector<rational> m_coeffs;
         bool m_keep_cardinality_constraints;
         bool m_keep_pb_constraints;
+        bool m_pb_num_system;
+        bool m_pb_totalizer;
         unsigned m_min_arity;
 
         template<lbool is_le>
@@ -114,23 +117,24 @@ struct pb2bv_rewriter::imp {
                 return expr_ref((is_le == l_false)?m.mk_true():m.mk_false(), m);
             }
 
-#if 0
-            expr_ref result(m);
-            switch (is_le) {
-            case l_true:  if (mk_le_tot(sz, args, k, result)) return result; else break;
-            case l_false: if (mk_ge_tot(sz, args, k, result)) return result; else break;
-            case l_undef: break;
+            if (m_pb_totalizer) {
+                expr_ref result(m);
+                switch (is_le) {
+                case l_true:  if (mk_le_tot(sz, args, k, result)) return result; else break;
+                case l_false: if (mk_ge_tot(sz, args, k, result)) return result; else break;
+                case l_undef: break;
+                }
+            }
+            
+            if (m_pb_num_system) {
+                expr_ref result(m);
+                switch (is_le) {
+                case l_true:  if (mk_le(sz, args, k, result)) return result; else break;
+                case l_false: if (mk_ge(sz, args, k, result)) return result; else break;
+                case l_undef: if (mk_eq(sz, args, k, result)) return result; else break;
+                }
             }
-#endif
 
-#if 0
-            expr_ref result(m);
-            switch (is_le) {
-            case l_true:  if (mk_le(sz, args, k, result)) return result; else break;
-            case l_false: if (mk_ge(sz, args, k, result)) return result; else break;
-            case l_undef: if (mk_eq(sz, args, k, result)) return result; else break;
-            }
-#endif
             // fall back to divide and conquer encoding.
             SASSERT(k.is_pos());
             expr_ref zero(m), bound(m);
@@ -397,22 +401,31 @@ struct pb2bv_rewriter::imp {
             for (unsigned j = 0; j + lim - 1 < out.size(); j += n) {
                 expr_ref tmp(m);
                 tmp = out[j + lim - 1];
-                if (j + n < out.size()) {
-                    tmp = m.mk_and(tmp, m.mk_not(out[j + n]));
+                if (j + n - 1 < out.size()) {
+                    tmp = m.mk_and(tmp, m.mk_not(out[j + n - 1]));
                 }
                 ors.push_back(tmp);
             }
             return ::mk_or(ors);
         }
 
+        // x0 + 5x1 + 3x2 >= k
+        // x0 x1 x1 -> s0 s1 s2
+        // s2 x1 x2 -> s3 s4 s5
+        // k = 7: s5 or (s4 & not s2 & s0)
+        // k = 6: s4
+        // k = 5: s4 or (s3 & not s2 & s1)
+        // k = 4: s4 or (s3 & not s2 & s0)
+        // k = 3: s3
+        // 
         bool mk_ge(unsigned sz, expr * const* args, rational bound, expr_ref& result) {
             if (!create_basis()) return false;
             if (!bound.is_unsigned()) return false;
             vector<rational> coeffs(m_coeffs);
             result = m.mk_true();
             expr_ref_vector carry(m), new_carry(m);
-            for (unsigned i = 0; i < m_base.size(); ++i) {
-                rational b_i = m_base[i];
+            m_base.push_back(bound + rational::one());
+            for (rational b_i : m_base) {
                 unsigned B   = b_i.get_unsigned();
                 unsigned d_i = (bound % b_i).get_unsigned();
                 bound = div(bound, b_i);                
@@ -425,16 +438,16 @@ struct pb2bv_rewriter::imp {
                     coeffs[j] = div(coeffs[j], b_i);
                 }
                 TRACE("pb", tout << "Carry: " << carry << "\n";
-                      for (unsigned j = 0; j < coeffs.size(); ++j) tout << coeffs[j] << " ";
+                      for (auto c : coeffs) tout << c << " ";
                       tout << "\n";
                       );
                 ptr_vector<expr> out;
                 m_sort.sorting(carry.size(), carry.c_ptr(), out);
-
+                
                 expr_ref gt = mod_ge(out, B, d_i + 1);
                 expr_ref ge = mod_ge(out, B, d_i);
                 result = mk_or(gt, mk_and(ge, result));                
-                TRACE("pb", tout << result << "\n";);
+                TRACE("pb", tout << "b: " << b_i << " d: " << d_i << " gt: " << gt << " ge: " << ge << " " << result << "\n";);
 
                 new_carry.reset();
                 for (unsigned j = B - 1; j < out.size(); j += B) {
@@ -443,11 +456,11 @@ struct pb2bv_rewriter::imp {
                 carry.reset();
                 carry.append(new_carry);
             }
-            TRACE("pb", tout << result << "\n";);
+            TRACE("pb", tout << "bound: " << bound << " Carry: " << carry << " result: " << result << "\n";);
             return true;
         }
 
-        expr_ref mk_and(expr_ref& a, expr_ref& b) {
+         expr_ref mk_and(expr_ref& a, expr_ref& b) {
             if (m.is_true(a)) return b;
             if (m.is_true(b)) return a;
             if (m.is_false(a)) return a;
@@ -491,6 +504,7 @@ struct pb2bv_rewriter::imp {
             for (unsigned i = 0; i < sz; ++i) {
                 m_coeffs.push_back(pb.get_coeff(f, i));
             }
+            CTRACE("pb", k.is_neg(), tout << expr_ref(m.mk_app(f, sz, args), m) << "\n";);
             SASSERT(!k.is_neg());
             switch (kind) {
             case OP_PB_GE:
@@ -567,6 +581,8 @@ struct pb2bv_rewriter::imp {
             m_args(m),
             m_keep_cardinality_constraints(false),
             m_keep_pb_constraints(false),
+            m_pb_num_system(false),
+            m_pb_totalizer(false),
             m_min_arity(2)
         {}
 
@@ -761,6 +777,14 @@ struct pb2bv_rewriter::imp {
         void keep_pb_constraints(bool f) {
             m_keep_pb_constraints = f;
         }
+
+        void pb_num_system(bool f) {
+            m_pb_num_system = f;
+        }
+
+        void pb_totalizer(bool f) {
+            m_pb_totalizer = f;
+        }
     };
 
     struct card2bv_rewriter_cfg : public default_rewriter_cfg {
@@ -774,6 +798,8 @@ struct pb2bv_rewriter::imp {
         card2bv_rewriter_cfg(imp& i, ast_manager & m):m_r(i, m) {}
         void keep_cardinality_constraints(bool f) { m_r.keep_cardinality_constraints(f); }
         void keep_pb_constraints(bool f) { m_r.keep_pb_constraints(f); }
+        void pb_num_system(bool f) { m_r.pb_num_system(f); }
+        void pb_totalizer(bool f) { m_r.pb_totalizer(f); }
     };
     
     class card_pb_rewriter : public rewriter_tpl<card2bv_rewriter_cfg> {
@@ -784,27 +810,62 @@ struct pb2bv_rewriter::imp {
             m_cfg(i, m) {}
         void keep_cardinality_constraints(bool f) { m_cfg.keep_cardinality_constraints(f); }
         void keep_pb_constraints(bool f) { m_cfg.keep_pb_constraints(f); }
+        void pb_num_system(bool f) { m_cfg.pb_num_system(f); }
+        void pb_totalizer(bool f) { m_cfg.pb_totalizer(f); }
     };
 
     card_pb_rewriter m_rw;
     
+    bool keep_cardinality() const {
+        params_ref const& p = m_params;
+        return 
+            p.get_bool("keep_cardinality_constraints", false) ||
+            p.get_bool("sat.cardinality.solver", false) ||
+            p.get_bool("cardinality.solver", false) || 
+            gparams::get_module("sat").get_bool("cardinality.solver", false) ||
+            keep_pb();
+    }
+
+    bool keep_pb() const {
+        params_ref const& p = m_params;
+        return 
+            p.get_bool("keep_pb_constraints", false) ||
+            p.get_bool("sat.pb.solver", false) ||
+            p.get_bool("pb.solver", false) ||
+            gparams::get_module("sat").get_bool("pb.solver", false);
+    }
+
+    bool pb_num_system() const {
+        return m_params.get_bool("pb_num_system", false);
+    }
+
+    bool pb_totalizer() const {
+        return m_params.get_bool("pb_totalizer", false);
+    }
+
     imp(ast_manager& m, params_ref const& p): 
         m(m), m_params(p), m_lemmas(m),
         m_fresh(m),
         m_num_translated(0), 
         m_rw(*this, m) {
-        m_rw.keep_cardinality_constraints(p.get_bool("keep_cardinality_constraints", false));
-        m_rw.keep_pb_constraints(p.get_bool("keep_pb_constraints", false));
+        m_rw.keep_cardinality_constraints(keep_cardinality());
+        m_rw.keep_pb_constraints(keep_pb());
+        m_rw.pb_num_system(pb_num_system());
+        m_rw.pb_totalizer(pb_totalizer());
     }
 
     void updt_params(params_ref const & p) {
         m_params.append(p);
-        m_rw.keep_cardinality_constraints(m_params.get_bool("keep_cardinality_constraints", false));
-        m_rw.keep_pb_constraints(m_params.get_bool("keep_pb_constraints", false));
+        m_rw.keep_cardinality_constraints(keep_cardinality());
+        m_rw.keep_pb_constraints(keep_pb());
+        m_rw.pb_num_system(pb_num_system());
+        m_rw.pb_totalizer(pb_totalizer());
     }
     void collect_param_descrs(param_descrs& r) const {
         r.insert("keep_cardinality_constraints", CPK_BOOL, "(default: true) retain cardinality constraints (don't bit-blast them) and use built-in cardinality solver");
         r.insert("keep_pb_constraints", CPK_BOOL, "(default: true) retain pb constraints (don't bit-blast them) and use built-in pb solver");
+        r.insert("pb_num_system", CPK_BOOL, "(default: false) use pb number system encoding");
+        r.insert("pb_totalizer", CPK_BOOL, "(default: false) use pb totalizer encoding");
     }
 
     unsigned get_num_steps() const { return m_rw.get_num_steps(); }

src/ast/rewriter/pb_rewriter.cpp

@@ -232,6 +232,7 @@ br_status pb_rewriter::mk_app_core(func_decl * f, unsigned num_args, expr * cons
     }    
 
     bool is_eq = f->get_decl_kind() == OP_PB_EQ;
+    br_status st = BR_DONE;
     
     pb_ast_rewriter_util pbu(m);
     pb_rewriter_util<pb_ast_rewriter_util> util(pbu);
@@ -249,11 +250,14 @@ br_status pb_rewriter::mk_app_core(func_decl * f, unsigned num_args, expr * cons
     default: {
         bool all_unit = true;
         unsigned sz = vec.size();
+        rational slack(0);
         m_args.reset();
         m_coeffs.reset();
         for (unsigned i = 0; i < sz; ++i) {
             m_args.push_back(vec[i].first);
             m_coeffs.push_back(vec[i].second);
+            SASSERT(vec[i].second.is_pos());
+            slack += vec[i].second;
             all_unit &= m_coeffs.back().is_one();
         }
         if (is_eq) {
@@ -271,7 +275,42 @@ br_status pb_rewriter::mk_app_core(func_decl * f, unsigned num_args, expr * cons
             result = mk_and(m, sz, m_args.c_ptr());
         }
         else {
-            result = m_util.mk_ge(sz, m_coeffs.c_ptr(), m_args.c_ptr(), k);
+            expr_ref_vector conj(m), disj(m);
+            for (unsigned i = 0; i < m_args.size(); ++i) {
+                rational& c = m_coeffs[i];
+                if (slack < c + k) {
+                    conj.push_back(m_args[i]);
+                    slack -= c;
+                    k -= c;
+                }
+                else if (c >= k) {
+                    slack -= c;
+                    disj.push_back(m_args[i]);
+                }
+                else {
+                    continue;
+                }
+                m_args[i] = m_args.back();
+                m_coeffs[i] = m_coeffs.back();
+                --i;
+                m_args.pop_back();
+                m_coeffs.pop_back();
+            }
+            sz = m_coeffs.size();
+            if (slack < k) {
+                conj.push_back(m.mk_false());
+            }
+            else if (k.is_pos() && sz > 0) {
+                conj.push_back(m_util.mk_ge(sz, m_coeffs.c_ptr(), m_args.c_ptr(), k));
+            }
+            result = mk_and(conj);
+            if (!disj.empty()) {
+                disj.push_back(result);
+                result = mk_or(disj);
+            }
+            if (!disj.empty() || conj.size() > 1) {
+                st = BR_REWRITE3;
+            }
         }
         break;
     }
@@ -286,7 +325,7 @@ br_status pb_rewriter::mk_app_core(func_decl * f, unsigned num_args, expr * cons
     TRACE("pb_validate",
           validate_rewrite(f, num_args, args, result););
           
-    return BR_DONE;
+    return st;
 }
 
 

src/ast/rewriter/seq_rewriter.cpp

@@ -440,24 +440,16 @@ br_status seq_rewriter::mk_app_core(func_decl * f, unsigned num_args, expr * con
  * (seq.unit (_ BitVector 8)) ==> String constant
  */
 br_status seq_rewriter::mk_seq_unit(expr* e, expr_ref& result) {
-    sort * s = m().get_sort(e);
     bv_util bvu(m());
-
-    if (is_sort_of(s, bvu.get_family_id(), BV_SORT)) {
-        // specifically we want (_ BitVector 8)
-        rational n_val;
-        unsigned int n_size;
-        if (bvu.is_numeral(e, n_val, n_size)) {
-            if (n_size == 8) {
-                // convert to string constant
-                char ch = (char)n_val.get_int32();
-                TRACE("seq", tout << "rewrite seq.unit of 8-bit value " << n_val.to_string() << " to string constant \"" << ch << "\"" << std::endl;);
-                char s_tmp[2] = {ch, '\0'};
-                symbol s(s_tmp);
-                result = m_util.str.mk_string(s);
-                return BR_DONE;
-            }
-        }
+    rational n_val;
+    unsigned int n_size;
+    // specifically we want (_ BitVector 8)
+    if (bvu.is_bv(e) && bvu.is_numeral(e, n_val, n_size) && n_size == 8) {
+        // convert to string constant
+        zstring str(n_val.get_unsigned());
+        TRACE("seq", tout << "rewrite seq.unit of 8-bit value " << n_val.to_string() << " to string constant \"" << str<< "\"" << std::endl;);
+        result = m_util.str.mk_string(str);
+        return BR_DONE;
     }
 
     return BR_FAILED;
@@ -1431,37 +1423,10 @@ br_status seq_rewriter::mk_re_star(expr* a, expr_ref& result) {
 }
 
 /*
- * (re.range c_1 c_n) = (re.union (str.to.re c1) (str.to.re c2) ... (str.to.re cn))
+ * (re.range c_1 c_n) 
  */
 br_status seq_rewriter::mk_re_range(expr* lo, expr* hi, expr_ref& result) {
     return BR_FAILED;
-    TRACE("seq", tout << "rewrite re.range [" << mk_pp(lo, m()) << " " << mk_pp(hi, m()) << "]\n";);
-    zstring str_lo, str_hi;
-    if (m_util.str.is_string(lo, str_lo) && m_util.str.is_string(hi, str_hi)) {
-        if (str_lo.length() == 1 && str_hi.length() == 1) {
-            unsigned int c1 = str_lo[0];
-            unsigned int c2 = str_hi[0];
-            if (c1 > c2) {
-                // exchange c1 and c2
-                unsigned int tmp = c1;
-                c2 = c1;
-                c1 = tmp;
-            }
-            zstring s(c1);
-            expr_ref acc(m_util.re.mk_to_re(m_util.str.mk_string(s)), m());
-            for (unsigned int ch = c1 + 1; ch <= c2; ++ch) {
-                zstring s_ch(ch);
-                expr_ref acc2(m_util.re.mk_to_re(m_util.str.mk_string(s_ch)), m());
-                acc = m_util.re.mk_union(acc, acc2);
-            }
-            result = acc;
-            return BR_REWRITE2;
-        } else {
-            m().raise_exception("string constants in re.range must have length 1");
-        }
-    }
-
-    return BR_FAILED;
 }
 
 /*
@@ -1506,6 +1471,7 @@ br_status seq_rewriter::mk_re_opt(expr* a, expr_ref& result) {
 }
 
 br_status seq_rewriter::mk_eq_core(expr * l, expr * r, expr_ref & result) {
+    TRACE("seq", tout << mk_pp(l, m()) << " = " << mk_pp(r, m()) << "\n";);
     expr_ref_vector lhs(m()), rhs(m()), res(m());
     bool changed = false;
     if (!reduce_eq(l, r, lhs, rhs, changed)) {

src/ast/seq_decl_plugin.cpp

@@ -876,6 +876,36 @@ bool seq_decl_plugin::is_value(app* e) const {
     }
 }
 
+bool seq_decl_plugin::are_equal(app* a, app* b) const {
+    if (a == b) return true;
+    // handle concatenations
+    return false;
+}
+
+bool seq_decl_plugin::are_distinct(app* a, app* b) const {
+    if (a == b) {
+        return false;
+    }
+    if (is_app_of(a, m_family_id, OP_STRING_CONST) &&
+        is_app_of(b, m_family_id, OP_STRING_CONST)) {
+        return true;
+    }
+    if (is_app_of(a, m_family_id, OP_SEQ_UNIT) && 
+        is_app_of(b, m_family_id, OP_SEQ_UNIT)) {
+        return true;
+    }
+    if (is_app_of(a, m_family_id, OP_SEQ_EMPTY) && 
+        is_app_of(b, m_family_id, OP_SEQ_UNIT)) {
+        return true;
+    }
+    if (is_app_of(b, m_family_id, OP_SEQ_EMPTY) && 
+        is_app_of(a, m_family_id, OP_SEQ_UNIT)) {
+        return true;
+    }    
+    return false;
+}
+
+
 expr* seq_decl_plugin::get_some_value(sort* s) {
     seq_util util(*m_manager);
     if (util.is_seq(s)) {

src/ast/seq_decl_plugin.h

@@ -182,7 +182,11 @@ public:
 
     virtual bool is_value(app * e) const;
 
-    virtual bool is_unique_value(app * e) const { return is_value(e); }
+    virtual bool is_unique_value(app * e) const { return false; }
+
+    virtual bool are_equal(app* a, app* b) const;
+
+    virtual bool are_distinct(app* a, app* b) const;
 
     virtual expr * get_some_value(sort * s);
 

src/interp/foci2.h

@@ -1,75 +0,0 @@
-/*++
-  Copyright (c) 2011 Microsoft Corporation
-
-  Module Name:
-
-  foci2.h
-
-  Abstract:
-
-  An interface class for foci2.   
-
-  Author:
-
-  Ken McMillan (kenmcmil)
-
-  Revision History:
-
-  --*/
-
-#ifndef FOCI2_H
-#define FOCI2_H
-
-#include <vector>
-#include <string>
-
-#ifdef _WINDOWS
-#define FOCI2_EXPORT __declspec(dllexport)
-#else
-#define FOCI2_EXPORT __attribute__ ((visibility ("default")))
-#endif
-
-class foci2 {
- public:
-    virtual ~foci2(){}
-
-    typedef int ast;
-    typedef int symb;
-
-    /** Built-in operators */
-    enum ops {
-        And = 0, Or, Not, Iff, Ite, Equal, Plus, Times, Floor, Leq, Div, Bool, Int, Array, Tsym, Fsym, Forall, Exists, Distinct, LastOp
-    };
-  
-    virtual symb mk_func(const std::string &s) = 0;
-    virtual symb mk_pred(const std::string &s) = 0;
-    virtual ast mk_op(ops op, const std::vector<ast> args) = 0;
-    virtual ast mk_op(ops op, ast) = 0;
-    virtual ast mk_op(ops op, ast, ast) = 0;
-    virtual ast mk_op(ops op, ast, ast, ast) = 0;
-    virtual ast mk_int(const std::string &) = 0;
-    virtual ast mk_rat(const std::string &) = 0;
-    virtual ast mk_true() = 0;
-    virtual ast mk_false() = 0;
-    virtual ast mk_app(symb,const std::vector<ast> args) = 0;
-  
-    virtual bool get_func(ast, symb &) = 0;
-    virtual bool get_pred(ast, symb &) = 0;
-    virtual bool get_op(ast, ops &) = 0;
-    virtual bool get_true(ast id) = 0;
-    virtual bool get_false(ast id) = 0;
-    virtual bool get_int(ast id, std::string &res) = 0;
-    virtual bool get_rat(ast id, std::string &res) = 0;
-    virtual const std::string &get_symb(symb) = 0;
-  
-    virtual int get_num_args(ast) = 0;
-    virtual ast get_arg(ast, int) = 0;
-  
-    virtual void show_ast(ast) = 0;
-  
-    virtual bool interpolate(const std::vector<ast> &frames, std::vector<ast> &itps, std::vector<int> parents) = 0;
-
-    FOCI2_EXPORT static foci2 *create(const std::string &);
-};
-
-#endif

src/interp/foci2stub/foci2.cpp

@@ -1,25 +0,0 @@
-/*++
-Copyright (c) 2011 Microsoft Corporation
-
-Module Name:
-
-    foci2.cpp
-
-Abstract:
-
-   Fake foci2, to be replaced
-
-Author:
-
-    Ken McMillan (kenmcmil)
-
-Revision History:
-
---*/
-
-
-#include "foci2.h"
-
-FOCI2_EXPORT foci2 *foci2::create(const std::string &){
-  return 0;
-}

src/interp/foci2stub/foci2.h

@@ -1,75 +0,0 @@
-/*++
-Copyright (c) 2011 Microsoft Corporation
-
-Module Name:
-
-    foci2.h
-
-Abstract:
-
-   An interface class for foci2.   
-
-Author:
-
-    Ken McMillan (kenmcmil)
-
-Revision History:
-
---*/
-
-#ifndef FOCI2_H
-#define FOCI2_H
-
-#include <vector>
-#include <string>
-
-#ifdef WIN32
-#define FOCI2_EXPORT __declspec(dllexport)
-#else
-#define FOCI2_EXPORT __attribute__ ((visibility ("default")))
-#endif
-
-class foci2 {
- public:
-  virtual ~foci2(){}
-
-  typedef int ast;
-  typedef int symb;
-
-  /** Built-in operators */
-  enum ops {
-    And = 0, Or, Not, Iff, Ite, Equal, Plus, Times, Floor, Leq, Div, Bool, Int, Array, Tsym, Fsym, Forall, Exists, Distinct, LastOp
-  };
-  
-  virtual symb mk_func(const std::string &s) = 0;
-  virtual symb mk_pred(const std::string &s) = 0;
-  virtual ast mk_op(ops op, const std::vector<ast> args) = 0;
-  virtual ast mk_op(ops op, ast) = 0;
-  virtual ast mk_op(ops op, ast, ast) = 0;
-  virtual ast mk_op(ops op, ast, ast, ast) = 0;
-  virtual ast mk_int(const std::string &) = 0;
-  virtual ast mk_rat(const std::string &) = 0;
-  virtual ast mk_true() = 0;
-  virtual ast mk_false() = 0;
-  virtual ast mk_app(symb,const std::vector<ast> args) = 0;
-  
-  virtual bool get_func(ast, symb &) = 0;
-  virtual bool get_pred(ast, symb &) = 0;
-  virtual bool get_op(ast, ops &) = 0;
-  virtual bool get_true(ast id) = 0;
-  virtual bool get_false(ast id) = 0;
-  virtual bool get_int(ast id, std::string &res) = 0;
-  virtual bool get_rat(ast id, std::string &res) = 0;
-  virtual const std::string &get_symb(symb) = 0;
-  
-  virtual int get_num_args(ast) = 0;
-  virtual ast get_arg(ast, int) = 0;
-  
-  virtual void show_ast(ast) = 0;
-  
-  virtual bool interpolate(const std::vector<ast> &frames, std::vector<ast> &itps, std::vector<int> parents) = 0;
-
-  FOCI2_EXPORT static foci2 *create(const std::string &);
-};
-
-#endif

src/interp/iz3foci.cpp

@@ -1,356 +0,0 @@
-/*++
-  Copyright (c) 2011 Microsoft Corporation
-
-  Module Name:
-
-  iz3foci.cpp
-
-  Abstract:
-
-  Implements a secondary solver using foci2.
-
-  Author:
-
-  Ken McMillan (kenmcmil)
-
-  Revision History:
-
-  --*/
-
-#include <sstream>
-#include <iostream>
-
-#include "iz3hash.h"
-#include "foci2.h"
-#include "iz3foci.h"
-
-using namespace stl_ext;
-
-class iz3foci_impl : public iz3secondary {
-
-    int frames;
-    int *parents;
-    foci2 *foci;
-    foci2::symb select_op;
-    foci2::symb store_op;
-    foci2::symb mod_op;
-
-public:
-    iz3foci_impl(iz3mgr *mgr, int _frames, int *_parents) : iz3secondary(*mgr) {
-        frames = _frames;
-        parents = _parents;
-        foci = 0;
-    }
-
-    typedef hash_map<ast,foci2::ast> AstToNode;
-    AstToNode ast_to_node;                    // maps Z3 ast's to foci expressions
-
-    typedef hash_map<foci2::ast,ast> NodeToAst;
-    NodeToAst node_to_ast;                    // maps Z3 ast's to foci expressions
-
-    // We only use this for FuncDeclToSymbol, which has no range destructor
-    struct symb_hash {
-        size_t operator()(const symb &s) const {
-            return (size_t) s;
-        }
-    };
-
-    typedef hash_map<symb,foci2::symb> FuncDeclToSymbol; 
-    FuncDeclToSymbol func_decl_to_symbol;     // maps Z3 func decls to symbols
-
-    typedef hash_map<foci2::symb,symb> SymbolToFuncDecl; 
-    SymbolToFuncDecl symbol_to_func_decl;     // maps symbols to Z3 func decls
-
-    int from_symb(symb func){
-        std::string name = string_of_symbol(func);
-        bool is_bool = is_bool_type(get_range_type(func));
-        foci2::symb f;
-        if(is_bool)
-            f = foci->mk_pred(name);
-        else
-            f = foci->mk_func(name);
-        symbol_to_func_decl[f] = func;
-        func_decl_to_symbol[func] = f;
-        return f;
-    }
-  
-    // create a symbol corresponding to a DeBruijn index of a particular type
-    // the type has to be encoded into the name because the same index can
-    // occur with different types
-    foci2::symb make_deBruijn_symbol(int index, type ty){
-        std::ostringstream s;
-        // s << "#" << index << "#" << type;
-        return foci->mk_func(s.str());
-    }
-
-    int from_Z3_ast(ast t){
-        std::pair<ast,foci2::ast> foo(t,0);
-        std::pair<AstToNode::iterator, bool> bar = ast_to_node.insert(foo);
-        int &res = bar.first->second;
-        if(!bar.second) return res;
-        int nargs = num_args(t);
-        std::vector<foci2::ast> args(nargs);
-        for(int i = 0; i < nargs; i++)
-            args[i] = from_Z3_ast(arg(t,i));
-    
-        switch(op(t)){
-        case True:
-            res = foci->mk_true(); break;
-        case False:
-            res = foci->mk_false(); break;
-        case And:
-            res = foci->mk_op(foci2::And,args); break;
-        case Or:
-            res = foci->mk_op(foci2::Or,args); break;
-        case Not:
-            res = foci->mk_op(foci2::Not,args[0]); break;
-        case Iff:
-            res = foci->mk_op(foci2::Iff,args); break;
-        case OP_OEQ: // bit of a mystery, this one...
-            if(args[0] == args[1]) res = foci->mk_true(); 
-            else res = foci->mk_op(foci2::Iff,args);
-            break;
-        case Ite:
-            if(is_bool_type(get_type(t)))
-                res = foci->mk_op(foci2::And,foci->mk_op(foci2::Or,foci->mk_op(foci2::Not,args[0]),args[1]),foci->mk_op(foci2::Or,args[0],args[2]));
-            else
-                res = foci->mk_op(foci2::Ite,args);
-            break;
-        case Equal:
-            res = foci->mk_op(foci2::Equal,args); break;
-        case Implies:
-            args[0] = foci->mk_op(foci2::Not,args[0]); res = foci->mk_op(foci2::Or,args); break;
-        case Xor:
-            res = foci->mk_op(foci2::Not,foci->mk_op(foci2::Iff,args)); break;
-        case Leq:
-            res = foci->mk_op(foci2::Leq,args); break;
-        case Geq:
-            std::swap(args[0],args[1]); res = foci->mk_op(foci2::Leq,args); break;
-        case Gt:
-            res = foci->mk_op(foci2::Not,foci->mk_op(foci2::Leq,args)); break;
-        case Lt:
-            std::swap(args[0],args[1]); res = foci->mk_op(foci2::Not,foci->mk_op(foci2::Leq,args)); break;
-        case Plus:
-            res = foci->mk_op(foci2::Plus,args); break;
-        case Sub:
-            args[1] = foci->mk_op(foci2::Times,foci->mk_int("-1"),args[1]); res = foci->mk_op(foci2::Plus,args); break;
-        case Uminus: 
-            res = foci->mk_op(foci2::Times,foci->mk_int("-1"),args[0]); break;
-        case Times:
-            res = foci->mk_op(foci2::Times,args); break;
-        case Idiv:
-            res = foci->mk_op(foci2::Div,args); break;
-        case Mod:
-            res = foci->mk_app(mod_op,args); break;
-        case Select:
-            res = foci->mk_app(select_op,args); break;
-        case Store:
-            res = foci->mk_app(store_op,args); break;
-        case Distinct:
-            res = foci->mk_op(foci2::Distinct,args); break;
-        case Uninterpreted: {
-            symb func = sym(t);
-            FuncDeclToSymbol::iterator it = func_decl_to_symbol.find(func);
-            foci2::symb f = (it == func_decl_to_symbol.end()) ? from_symb(func) : it->second;
-            if(foci->get_symb(f).substr(0,3) == "lbl" && args.size()==1) // HACK to handle Z3 labels
-                res = args[0];
-            else if(foci->get_symb(f).substr(0,3) == "lbl" && args.size()==0) // HACK to handle Z3 labels
-                res = foci->mk_true();
-            else res = foci->mk_app(f,args);
-            break;
-        }
-        case Numeral: {
-            std::string s = string_of_numeral(t);
-            res = foci->mk_int(s);
-            break;
-        }
-        case Forall: 
-        case Exists: {
-            bool is_forall = op(t) == Forall;
-            foci2::ops qop = is_forall ? foci2::Forall : foci2::Exists;
-            int bvs = get_quantifier_num_bound(t);
-            std::vector<int> foci_bvs(bvs);
-            for(int i = 0; i < bvs; i++){
-                std::string name = get_quantifier_bound_name(t,i);
-                //Z3_string name = Z3_get_symbol_string(ctx,sym);
-                // type ty = get_quantifier_bound_type(t,i);
-                foci2::symb f = foci->mk_func(name);
-                foci2::ast v = foci->mk_app(f,std::vector<foci2::ast>());
-                foci_bvs[i] = v;
-            }
-            foci2::ast body = from_Z3_ast(get_quantifier_body(t));
-            foci_bvs.push_back(body);
-            res = foci->mk_op(qop,foci_bvs);
-            node_to_ast[res] = t; // desperate
-            break;
-        }
-        case Variable: {  // a deBruijn index
-            int index = get_variable_index_value(t);
-            type ty = get_type(t);
-            foci2::symb symbol = make_deBruijn_symbol(index,ty);
-            res = foci->mk_app(symbol,std::vector<foci2::ast>());
-            break;
-        }
-        default:
-            {
-                std::cerr << "iZ3: unsupported Z3 operator in expression\n ";
-                print_expr(std::cerr,t);
-                std::cerr << "\n";
-                SASSERT(0 && "iZ3: unsupported Z3 operator");
-            }
-        }
-        return res;
-    }
-
-    // convert an expr to Z3 ast
-    ast to_Z3_ast(foci2::ast i){
-        std::pair<foci2::ast,ast> foo(i,ast());
-        std::pair<NodeToAst::iterator,bool> bar = node_to_ast.insert(foo);
-        if(!bar.second) return bar.first->second;
-        ast &res = bar.first->second;
-
-        if(i < 0){
-            res = mk_not(to_Z3_ast(-i));
-            return res;
-        }
-
-        // get the arguments
-        unsigned n = foci->get_num_args(i);
-        std::vector<ast> args(n);
-        for(unsigned j = 0; j < n; j++)
-            args[j] = to_Z3_ast(foci->get_arg(i,j));
-
-        // handle operators
-        foci2::ops o;
-        foci2::symb f;
-        std::string nval;
-        if(foci->get_true(i))
-            res = mk_true();
-        else if(foci->get_false(i))
-            res = mk_false();
-        else if(foci->get_op(i,o)){
-            switch(o){
-            case foci2::And:
-                res = make(And,args); break; 
-            case foci2::Or:
-                res = make(Or,args); break; 
-            case foci2::Not:
-                res = mk_not(args[0]); break; 
-            case foci2::Iff:
-                res = make(Iff,args[0],args[1]); break; 
-            case foci2::Ite:
-                res = make(Ite,args[0],args[1],args[2]); break;
-            case foci2::Equal:
-                res = make(Equal,args[0],args[1]); break; 
-            case foci2::Plus:
-                res = make(Plus,args); break; 
-            case foci2::Times:
-                res = make(Times,args); break; 
-            case foci2::Div:
-                res = make(Idiv,args[0],args[1]); break;
-            case foci2::Leq:
-                res = make(Leq,args[0],args[1]); break; 
-            case foci2::Distinct:
-                res = make(Distinct,args);
-                break;
-            case foci2::Tsym:
-                res = mk_true();
-                break;
-            case foci2::Fsym:
-                res = mk_false();
-                break;
-            case foci2::Forall:
-            case foci2::Exists:
-                {
-                    int nargs = n;
-                    std::vector<ast> bounds(nargs-1);
-                    for(int i = 0; i < nargs-1; i++)
-                        bounds[i] = args[i];
-                    opr oz = o == foci2::Forall ? Forall : Exists;
-                    res = make_quant(oz,bounds,args[nargs-1]);
-                }
-                break;
-            default:
-                SASSERT(false && "unknown built-in op");
-            }
-        }
-        else if(foci->get_int(i,nval)){
-            res = make_int(nval);
-        }
-        else if(foci->get_func(i,f)){
-            if(f == select_op){
-                SASSERT(n == 2);
-                res = make(Select,args[0],args[1]);
-            }
-            else if(f == store_op){
-                SASSERT(n == 3);
-                res = make(Store,args[0],args[1],args[2]);
-            }
-            else if(f == mod_op){
-                SASSERT(n == 2);
-                res = make(Mod,args[0],args[1]);
-            }
-            else {
-                std::pair<int,symb> foo(f,(symb)0);
-                std::pair<SymbolToFuncDecl::iterator,bool> bar = symbol_to_func_decl.insert(foo);
-                symb &func_decl = bar.first->second;
-                if(bar.second){
-                    std::cout << "unknown function symbol:\n";
-                    foci->show_ast(i);
-                    SASSERT(0);
-                }
-                res = make(func_decl,args);
-            }
-        }
-        else {
-            std::cerr << "iZ3: unknown FOCI expression kind\n";
-            SASSERT(0 && "iZ3: unknown FOCI expression kind");
-        }
-        return res;
-    }
-
-    int interpolate(const std::vector<ast> &cnsts, std::vector<ast> &itps){
-        SASSERT((int)cnsts.size() == frames);
-        std::string lia("lia");
-#ifdef _FOCI2
-        foci = foci2::create(lia);
-#else
-        foci = 0;
-#endif
-        if(!foci){
-            std::cerr << "iZ3: cannot find foci lia solver.\n";
-            SASSERT(0);
-        }
-        select_op = foci->mk_func("select");
-        store_op = foci->mk_func("store");
-        mod_op = foci->mk_func("mod");
-        std::vector<foci2::ast> foci_cnsts(frames), foci_itps(frames-1), foci_parents;
-        if(parents)
-            foci_parents.resize(frames);
-        for(int i = 0; i < frames; i++){
-            foci_cnsts[i] = from_Z3_ast(cnsts[i]);
-            if(parents)
-                foci_parents[i] = parents[i];
-        }
-        int res = foci->interpolate(foci_cnsts, foci_itps, foci_parents);
-        if(res == 0){
-            SASSERT((int)foci_itps.size() == frames-1);
-            itps.resize(frames-1);
-            for(int i = 0; i < frames-1; i++){
-                // foci->show_ast(foci_itps[i]);
-                itps[i] = to_Z3_ast(foci_itps[i]);
-            }
-        }
-        ast_to_node.clear();
-        node_to_ast.clear();
-        func_decl_to_symbol.clear();
-        symbol_to_func_decl.clear();
-        delete foci;
-        return res;
-    }
-
-};
-
-iz3secondary *iz3foci::create(iz3mgr *mgr, int num, int *parents){
-    return new iz3foci_impl(mgr,num,parents);
-}

src/interp/iz3foci.h

@@ -1,32 +0,0 @@
-/*++
-  Copyright (c) 2011 Microsoft Corporation
-
-  Module Name:
-
-  iz3foci.h
-
-  Abstract:
-
-  Implements a secondary solver using foci2.
-
-  Author:
-
-  Ken McMillan (kenmcmil)
-
-  Revision History:
-
-  --*/
-
-#ifndef IZ3FOCI_H
-#define IZ3FOCI_H
-
-#include "iz3secondary.h"
-
-/** Secondary prover based on Cadence FOCI. */
-
-class iz3foci {
- public:
-    static iz3secondary *create(iz3mgr *mgr, int num, int *parents);
-};
-
-#endif

src/interp/iz3interp.cpp

@@ -35,7 +35,6 @@
 
 #include "iz3profiling.h"
 #include "iz3translate.h"
-#include "iz3foci.h"
 #include "iz3proof.h"
 #include "iz3hash.h"
 #include "iz3interp.h"
@@ -167,22 +166,6 @@ struct frame_reducer {
 #endif  
 
 
-#if 0
-static lbool test_secondary(context ctx,
-                            int num, 
-                            ast *cnsts,
-                            ast *interps,
-                            int *parents = 0
-                            ){
-    iz3secondary *sp = iz3foci::create(ctx,num,parents);
-    std::vector<ast> frames(num), interpolants(num-1);
-    std::copy(cnsts,cnsts+num,frames.begin());
-    int res = sp->interpolate(frames,interpolants);
-    if(res == 0)
-        std::copy(interpolants.begin(),interpolants.end(),interps);
-    return res ? L_TRUE : L_FALSE;
-}                         
-#endif
     
 template<class T>
 struct killme {
@@ -213,11 +196,7 @@ public:
                         const std::vector<int> &parents,
                         std::vector<ast> &interps
                         ){
-        int num = cnsts.size();
-        iz3secondary *sp = iz3foci::create(this,num,(int *)(parents.empty()?0:&parents[0]));
-        int res = sp->interpolate(cnsts, interps);
-        if(res != 0)
-            throw iz3_exception("secondary failed");
+        throw iz3_exception("secondary interpolating prover not supported");
     }                         
 
     void proof_to_interpolant(z3pf proof,
@@ -248,10 +227,9 @@ public:
         if(is_linear(parents_vec))
             parents_vec.clear();
 
-        // create a secondary prover
-        iz3secondary *sp = iz3foci::create(this,num,parents_vec.empty()?0:&parents_vec[0]);
-        sp_killer.set(sp); // kill this on exit
-      
+        // secondary prover no longer supported
+        iz3secondary *sp = NULL;
+
 #define BINARY_INTERPOLATION
 #ifndef BINARY_INTERPOLATION    
         // create a translator

src/interp/iz3translate.h

@@ -53,12 +53,8 @@ class iz3translation : public iz3base {
      : iz3base(mgr,_cnsts,_parents,_theory)  {}
 };
 
-//#define IZ3_TRANSLATE_DIRECT2
-#ifdef _FOCI2
-#define IZ3_TRANSLATE_DIRECT
-#else
+// To use a secondary prover, define IZ3_TRANSLATE_DIRECT instead of this
 #define IZ3_TRANSLATE_FULL
-#endif
 
 #endif
 

src/interp/iz3translate_direct.cpp

@@ -332,7 +332,7 @@ public:
         }
     }
 
-    // get the lits of a Z3 clause as foci terms
+    // get the lits of a Z3 clause as secondary prover terms
     void get_Z3_lits(ast t, std::vector<ast> &lits){
         opr dk = op(t);
         if(dk == False)
@@ -666,9 +666,9 @@ public:
 #endif 
 
         // interpolate using secondary prover
-        profiling::timer_start("foci");
+        profiling::timer_start("secondary prover");
         int sat = secondary->interpolate(preds,itps);
-        profiling::timer_stop("foci");
+        profiling::timer_stop("secondary prover");
 
         std::cout << "lemma done" << std::endl;
 
@@ -1495,7 +1495,7 @@ public:
         return find_nll(new_proofs);
     }
 
-    // translate a Z3 proof term into a foci proof term
+    // translate a Z3 proof term into a secondary prover proof term
 
     Iproof::node translate_main(ast proof, non_local_lits *nll, bool expect_clause = true){
         non_local_lits *old_nll = nll;

src/opt/opt_solver.cpp

@@ -26,6 +26,7 @@ Notes:
 #include "theory_diff_logic.h"
 #include "theory_dense_diff_logic.h"
 #include "theory_pb.h"
+#include "theory_lra.h"
 #include "ast_pp.h"
 #include "ast_smt_pp.h"
 #include "pp_params.hpp"
@@ -143,6 +144,9 @@ namespace opt {
         else if (typeid(smt::theory_dense_si&) == typeid(*arith_theory)) {   
             return dynamic_cast<smt::theory_dense_si&>(*arith_theory); 
         }
+        else if (typeid(smt::theory_lra&) == typeid(*arith_theory)) {
+            return dynamic_cast<smt::theory_lra&>(*arith_theory); 
+        }
         else {
             UNREACHABLE();
             return dynamic_cast<smt::theory_mi_arith&>(*arith_theory); 
@@ -401,6 +405,14 @@ namespace opt {
             return th.mk_ge(m_fm, v, val);
         }
 
+
+        if (typeid(smt::theory_lra) == typeid(opt)) {
+            smt::theory_lra& th = dynamic_cast<smt::theory_lra&>(opt); 
+            SASSERT(val.is_finite());
+            return th.mk_ge(m_fm, v, val.get_numeral());            
+        }
+
+        // difference logic?
         if (typeid(smt::theory_dense_si) == typeid(opt) &&
             val.get_infinitesimal().is_zero()) {
             smt::theory_dense_si& th = dynamic_cast<smt::theory_dense_si&>(opt);

src/sat/card_extension.cpp

@@ -46,6 +46,8 @@ namespace sat {
         m_lit(lit),
         m_k(k),
         m_size(wlits.size()),
+        m_slack(0),
+        m_num_watch(0),
         m_max_sum(0) {
         for (unsigned i = 0; i < wlits.size(); ++i) {
             m_wlits[i] = wlits[i];
@@ -237,7 +239,6 @@ namespace sat {
             p.negate();
         }
         
-        TRACE("sat", display(tout << "init watch: ", p, true););
         SASSERT(p.lit() == null_literal || value(p.lit()) == l_true);
         unsigned sz = p.size(), bound = p.k();
 
@@ -249,7 +250,7 @@ namespace sat {
                     p.swap(i, j);
                 }
                 if (slack < bound) {
-                    slack += p[i].first;
+                    slack += p[j].first;
                     ++num_watch;
                 }
                 ++j;
@@ -266,7 +267,7 @@ namespace sat {
         if (slack < bound) {
             literal lit = p[j].second;
             SASSERT(value(p[j].second) == l_false);
-            for (unsigned i = j + 1; j < sz; ++i) {
+            for (unsigned i = j + 1; i < sz; ++i) {
                 if (lvl(lit) < lvl(p[i].second)) {
                     lit = p[i].second;
                 }
@@ -280,6 +281,7 @@ namespace sat {
             p.set_slack(slack);
             p.set_num_watch(num_watch);
         }
+        TRACE("sat", display(tout << "init watch: ", p, true););
     }
 
     /*
@@ -296,7 +298,7 @@ namespace sat {
           Lw = Lw u {l_s}
           Lu = Lu \ {l_s}
       }
-      if (Sw < bound) conflict
+      if (Sw < k) conflict
       while (Sw < k + a_max) {
           assign (l_max)
           a_max = max { ai | li in Lw, li = undef }
@@ -308,7 +310,19 @@ namespace sat {
       
         
     */
+    void card_extension::add_index(pb& p, unsigned index, literal lit) {
+        if (value(lit) == l_undef) {
+            m_pb_undef.push_back(index);
+            if (p[index].first > m_a_max) {
+                m_a_max = p[index].first;
+            }
+        }
+    }
+
     lbool card_extension::add_assign(pb& p, literal alit) {
+
+        TRACE("sat", display(tout << "assign: " << alit << "\n", p, true););
+        SASSERT(!s().inconsistent());
         unsigned sz = p.size();
         unsigned bound = p.k();
         unsigned num_watch = p.num_watch();
@@ -316,63 +330,43 @@ namespace sat {
         SASSERT(value(alit) == l_false);
         SASSERT(p.lit() == null_literal || value(p.lit()) == l_true);
         SASSERT(num_watch <= sz);
+        SASSERT(num_watch > 0);
         unsigned index = 0;
-        unsigned a_max = 0;
-        unsigned max_index = 0;
+        m_a_max = 0;
         m_pb_undef.reset();
         for (; index < num_watch; ++index) {
             literal lit = p[index].second;
             if (lit == alit) {
                 break;
             }
-            if (value(lit) == l_undef) {
-                m_pb_undef.push_back(index);
-                if (p[index].first > a_max) {
-                    a_max = p[index].first;
-                    max_index = index;
-                }
-            }
+            add_index(p, index, lit);
         }
-    
-        for (unsigned j = index + 1; a_max == 0 && j < num_watch; ++j) {
-            literal lit = p[j].second;
-            if (value(lit) == l_undef) {
-                m_pb_undef.push_back(j);
-                a_max = p[j].first;
-                max_index = j;
-            }
-        }
-        for (unsigned j = num_watch; a_max == 0 && j < sz; ++j) {
-            literal lit = p[j].second;
-            if (value(lit) == l_undef) {
-                p.swap(j, num_watch);
-                m_pb_undef.push_back(num_watch);
-                a_max = p[num_watch].first;
-                max_index = num_watch;
-            }
+        SASSERT(index < num_watch);
+
+        unsigned index1 = index + 1;
+        for (; m_a_max == 0 && index1 < num_watch; ++index1) {
+            add_index(p, index1, p[index1].second);
         }
 
         unsigned val = p[index].first;
-        SASSERT(num_watch > 0);
-        SASSERT(index < num_watch);
         SASSERT(value(p[index].second) == l_false);
         SASSERT(val <= slack);
         slack -= val;
         // find literals to swap with:            
-        for (unsigned j = num_watch; j < sz && slack < bound + a_max; ++j) {
-            if (value(p[j].second) != l_false) {
+        for (unsigned j = num_watch; j < sz && slack < bound + m_a_max; ++j) {
+            literal lit = p[j].second;
+            if (value(lit) != l_false) {
                 slack += p[j].first;
                 watch_literal(p, p[j]);
                 p.swap(num_watch, j);
-                if (value(p[num_watch].second) == l_undef && a_max < p[num_watch].first) {
-                    m_pb_undef.push_back(num_watch);
-                    a_max = p[num_watch].first;
-                    max_index = num_watch;
-                }
+                add_index(p, num_watch, lit);
                 ++num_watch;
             }
         }
 
+        SASSERT(!s().inconsistent());
+        DEBUG_CODE(for (auto idx : m_pb_undef) { SASSERT(value(p[idx].second) == l_undef); });
+
         if (slack < bound) {
             // maintain watching the literal
             slack += val;
@@ -385,34 +379,38 @@ namespace sat {
         }
 
         // swap out the watched literal.
-        p.set_slack(slack);
         --num_watch;
         SASSERT(num_watch > 0);
+        p.set_slack(slack);
         p.set_num_watch(num_watch);
         p.swap(num_watch, index);
-        if (num_watch == max_index) {
-            max_index = index;
-        }
 
-        SASSERT(max_index < sz);
-        while (slack < bound + a_max && !s().inconsistent()) {
-            // variable at max-index must be assigned to true.
-            assign(p, p[max_index].second);         
-
-            a_max = 0;
-            // find the next a_max among m_pb_undef
-            while (!m_pb_undef.empty() && l_undef != value(p[m_pb_undef.back()].second)) {
+        if (slack < bound + m_a_max) {
+            TRACE("sat", display(tout, p, false); for(auto j : m_pb_undef) tout << j << "\n";);
+            literal_vector to_assign;
+            while (!m_pb_undef.empty()) {
+                index1 = m_pb_undef.back();
+                literal lit = p[index1].second;
+                TRACE("sat", tout << index1 << " " << lit << "\n";);
+                if (slack >= bound + p[index1].first) {
+                    break;
+                }
                 m_pb_undef.pop_back();
+                to_assign.push_back(lit);
             }
-            if (m_pb_undef.empty()) {
-                break;
+
+            for (literal lit : to_assign) {
+                if (s().inconsistent()) break;
+                if (value(lit) == l_undef) {
+                    assign(p, lit);
+                }				
             }
-            max_index = m_pb_undef.back();
-            a_max = p[max_index].first;
-            m_pb_undef.pop_back();
         }
 
-        return s().inconsistent() ? l_false : l_true;  
+
+        TRACE("sat", display(tout << "assign: " << alit << "\n", p, true););
+
+        return l_undef;
     }
 
     void card_extension::watch_literal(pb& p, wliteral l) {
@@ -467,6 +465,7 @@ namespace sat {
             set_conflict(p, lit); 
             break;
         default:
+            SASSERT(validate_unit_propagation(p, lit));
             m_stats.m_num_pb_propagations++;
             m_num_propagations_since_pop++;
             if (s().m_config.m_drat) {
@@ -483,7 +482,8 @@ namespace sat {
     }
 
     void card_extension::display(std::ostream& out, pb const& p, bool values) const {
-        out << p.lit() << "[" << p.size() << "]";
+        if (p.lit() != null_literal) out << p.lit();
+        out << "[watch: " << p.num_watch() << ", slack: " << p.slack() << "]";
         if (p.lit() != null_literal && values) {
             out << "@(" << value(p.lit());
             if (value(p.lit()) != l_undef) {
@@ -514,7 +514,7 @@ namespace sat {
     }
 
     void card_extension::asserted_pb(literal l, ptr_vector<pb>* pbs, pb* p0) {
-        TRACE("sat", tout << l << " " << !is_tag_empty(pbs) << " " << (p0 != 0) << "\n";);
+        TRACE("sat", tout << "literal: " << l << " has pb: " << !is_tag_empty(pbs) << " p0 != 0: " << (p0 != 0) << "\n";);
         if (!is_tag_empty(pbs)) {
             ptr_vector<pb>::iterator begin = pbs->begin();
             ptr_vector<pb>::iterator it = begin, it2 = it, end = pbs->end();
@@ -524,20 +524,28 @@ namespace sat {
                     continue;
                 }
                 switch (add_assign(p, ~l)) {
-                case l_false: // conflict
-                    for (; it != end; ++it, ++it2) {
-                        *it2 = *it;
-                    }
-                    SASSERT(s().inconsistent());
-                    pbs->set_end(it2);
-                    return;
                 case l_true: // unit propagation, keep watching the literal
                     if (it2 != it) {
                         *it2 = *it;
                     }
                     ++it2;
                     break;
+                case l_false: // conflict.
+                    SASSERT(s().inconsistent());
+                    for (; it != end; ++it, ++it2) {
+                        *it2 = *it;
+                    }
+                    pbs->set_end(it2);
+                    return;                
                 case l_undef: // watch literal was swapped
+                    if (s().inconsistent()) {
+                        ++it;
+                        for (; it != end; ++it, ++it2) {
+                            *it2 = *it;
+                        }
+                        pbs->set_end(it2);
+                        return;
+                    }
                     break; 
                 }
             }
@@ -844,6 +852,7 @@ namespace sat {
         literal consequent = s().m_not_l;
         justification js = s().m_conflict;
         TRACE("sat", tout << consequent << " " << js << "\n";);
+        TRACE("sat", s().display(tout););
         m_conflict_lvl = s().get_max_lvl(consequent, js);
         if (consequent != null_literal) {
             consequent.neg();
@@ -942,7 +951,7 @@ namespace sat {
                     m_bound += offset;
                     inc_coeff(consequent, offset);
                     get_pb_antecedents(consequent, p, m_lemma);
-                    TRACE("sat", tout << m_lemma << "\n";);
+                    TRACE("sat", display(tout, p, true); tout << m_lemma << "\n";);
                     for (unsigned i = 0; i < m_lemma.size(); ++i) {
                         process_antecedent(~m_lemma[i], offset);
                     }
@@ -989,6 +998,7 @@ namespace sat {
             SASSERT(lvl(v) == m_conflict_lvl);
             s().reset_mark(v);
             --idx;
+            TRACE("sat", tout << "Unmark: v" << v << "\n";);
             --m_num_marks;
             js = s().m_justification[v];
             offset = get_abs_coeff(v);
@@ -1015,7 +1025,6 @@ namespace sat {
 
         m_lemma.reset();        
 
-#if 1
         m_lemma.push_back(null_literal);
         for (unsigned i = 0; 0 <= slack && i < m_active_vars.size(); ++i) { 
             bool_var v = m_active_vars[i];
@@ -1038,6 +1047,7 @@ namespace sat {
             }
         }
 
+#if 0
         if (jus.size() > 1) {
             std::cout << jus.size() << "\n";
             for (unsigned i = 0; i < jus.size(); ++i) {
@@ -1047,6 +1057,7 @@ namespace sat {
             active2pb(m_A);
             display(std::cout, m_A);
         }
+#endif
 
 
         if (slack >= 0) {
@@ -1057,7 +1068,7 @@ namespace sat {
         if (m_lemma[0] == null_literal) {
             m_lemma[0] = m_lemma.back();
             m_lemma.pop_back();
-            unsigned level = lvl(m_lemma[0]);
+            unsigned level = m_lemma.empty() ? 0 : lvl(m_lemma[0]);
             for (unsigned i = 1; i < m_lemma.size(); ++i) {
                 if (lvl(m_lemma[i]) > level) {
                     level = lvl(m_lemma[i]);
@@ -1066,37 +1077,6 @@ namespace sat {
             }
             IF_VERBOSE(2, verbose_stream() << "(sat.card set level to " << level << " < " << m_conflict_lvl << ")\n";);
         }        
-#else
-        ++idx;
-        while (0 <= slack) {            
-            literal lit = lits[idx];
-            bool_var v = lit.var();
-            if (m_active_var_set.contains(v)) {
-                int coeff = get_coeff(v);
-                if (coeff < 0 && !lit.sign()) {
-                    slack += coeff;
-                    m_lemma.push_back(~lit);
-                }
-                else if (coeff > 0 && lit.sign()) {
-                    slack -= coeff;
-                    m_lemma.push_back(~lit);
-                }
-            }
-            if (idx == 0 && slack >= 0) {
-                IF_VERBOSE(2, verbose_stream() << "(sat.card non-asserting)\n";);
-                goto bail_out;
-            }
-            SASSERT(idx > 0 || slack < 0);
-            --idx;
-        }
-        if (m_lemma.size() >= 2 && lvl(m_lemma[1]) == m_conflict_lvl) {
-            // TRACE("sat", tout << "Bail out on no progress " << lit << "\n";);
-            IF_VERBOSE(2, verbose_stream() << "(sat.card bail non-asserting resolvent)\n";);
-            goto bail_out;
-        }
-
-#endif
-
 
         SASSERT(slack < 0);
 
@@ -1108,7 +1088,7 @@ namespace sat {
             svector<drat::premise> ps; // TBD fill in
             s().m_drat.add(m_lemma, ps);
         }
-        
+
         s().m_lemma.reset();
         s().m_lemma.append(m_lemma);
         for (unsigned i = 1; i < m_lemma.size(); ++i) {
@@ -1153,6 +1133,7 @@ namespace sat {
 
         if (level > 0 && !s().is_marked(v) && level == m_conflict_lvl) {
             s().mark(v);
+            TRACE("sat", tout << "Mark: v" << v << "\n";);
             ++m_num_marks;
         }
         inc_coeff(l, offset);                
@@ -1347,20 +1328,30 @@ namespace sat {
     void card_extension::get_pb_antecedents(literal l, pb const& p, literal_vector& r) {
         if (p.lit() != null_literal) r.push_back(p.lit());
         SASSERT(p.lit() == null_literal || value(p.lit()) == l_true);
-        unsigned k = p.k();
-        unsigned max_sum = p.max_sum();
-        for (unsigned i = p.size(); i > 0 && max_sum >= k; ) {
-            --i;
-            literal lit = p[i].second;
-            if (lit == l) {
-                max_sum -= p[i].first;
-            }
-            else if (value(lit) == l_false) {
-                r.push_back(~p[i].second);
-                max_sum -= p[i].first;
+        TRACE("sat", display(tout, p, true););
+
+        // unsigned coeff = get_coeff(p, l);
+        unsigned coeff = 0;
+        for (unsigned j = 0; j < p.num_watch(); ++j) {
+            if (p[j].second == l) {
+                coeff = p[j].first;
+                break;
             }
         }
-        SASSERT(max_sum < k);
+        unsigned slack = p.slack() - coeff;
+        unsigned i = p.num_watch();
+
+        // skip entries that are not required for unit propagation.
+        // slack - coeff + w_head < k
+        unsigned h = 0;
+        for (; i < p.size() && p[i].first + h + slack < p.k(); ++i) { 
+            h += p[i].first;
+        }
+        for (; i < p.size(); ++i) {
+            literal lit = p[i].second;
+            SASSERT(l_false == value(lit));
+            r.push_back(~lit);
+        }
     }
 
     void card_extension::get_card_antecedents(literal l, card const& c, literal_vector& r) {
@@ -1720,7 +1711,9 @@ namespace sat {
     std::ostream& card_extension::display_justification(std::ostream& out, ext_justification_idx idx) const {
         if (is_card_index(idx)) {
             card& c = index2card(idx);
-            out << "bound " << c.lit() << ": ";
+            out << "bound ";
+            if (c.lit() != null_literal) out << c.lit();
+            out << ": ";
             for (unsigned i = 0; i < c.size(); ++i) {
                 out << c[i] << " ";
             }
@@ -1728,14 +1721,18 @@ namespace sat {
         }
         else if (is_xor_index(idx)) {
             xor& x = index2xor(idx);
-            out << "xor " << x.lit() << ": ";
+            out << "xor ";
+            if (x.lit() != null_literal) out << x.lit();
+            out << ": ";
             for (unsigned i = 0; i < x.size(); ++i) {
                 out << x[i] << " ";
             }            
         }
         else if (is_pb_index(idx)) {
             pb& p = index2pb(idx);
-            out << "pb " << p.lit() << ": ";
+            out << "pb ";
+            if (p.lit() != null_literal) out << p.lit();
+            out << ": ";
             for (unsigned i = 0; i < p.size(); ++i) {
                 out << p[i].first << "*" << p[i].second << " ";
             }
@@ -1776,6 +1773,21 @@ namespace sat {
         }
         return true;
     }
+    bool card_extension::validate_unit_propagation(pb const& p, literal alit) { 
+        if (p.lit() != null_literal && value(p.lit()) != l_true) return false;
+
+        unsigned sum = 0;
+        TRACE("sat", display(tout << "validate: " << alit << "\n", p, true););
+        for (unsigned i = 0; i < p.size(); ++i) {
+            literal lit = p[i].second;
+            lbool val = value(lit);
+            if (val != l_false && lit != alit) {
+                sum += p[i].first;
+            }
+        }
+        return sum < p.k();
+    }
+
     bool card_extension::validate_lemma() { 
         int val = -m_bound;
         normalize_active_coeffs();

src/sat/card_extension.h

@@ -232,10 +232,12 @@ namespace sat {
 
 
         // pb functionality
+        unsigned m_a_max;
         void copy_pb(card_extension& result);
         void asserted_pb(literal l, ptr_vector<pb>* pbs, pb* p);
         void init_watch(pb& p, bool is_true);
         lbool add_assign(pb& p, literal alit);
+        void add_index(pb& p, unsigned index, literal lit);
         void watch_literal(pb& p, wliteral lit);
         void clear_watch(pb& p);
         void set_conflict(pb& p, literal lit);
@@ -280,6 +282,7 @@ namespace sat {
         bool validate_assign(literal_vector const& lits, literal lit);
         bool validate_lemma();
         bool validate_unit_propagation(card const& c);
+        bool validate_unit_propagation(pb const& p, literal lit);
         bool validate_conflict(literal_vector const& lits, ineq& p);
 
         ineq m_A, m_B, m_C;

src/sat/sat_solver.cpp

@@ -1938,23 +1938,25 @@ namespace sat {
     void solver::learn_lemma_and_backjump() {
         TRACE("sat_lemma", tout << "new lemma size: " << m_lemma.size() << "\n" << m_lemma << "\n";);
 
-        if (m_config.m_minimize_lemmas) {
-            minimize_lemma();
-            reset_lemma_var_marks();
-            if (m_config.m_dyn_sub_res)
-                dyn_sub_res();
-            TRACE("sat_lemma", tout << "new lemma (after minimization) size: " << m_lemma.size() << "\n" << m_lemma << "\n";);
-        }
-        else
-            reset_lemma_var_marks();
-
-        literal_vector::iterator it  = m_lemma.begin();
-        literal_vector::iterator end = m_lemma.end();
         unsigned new_scope_lvl       = 0;
-        ++it;
-        for(; it != end; ++it) {
-            bool_var var = (*it).var();
-            new_scope_lvl = std::max(new_scope_lvl, lvl(var));
+        if (!m_lemma.empty()) {
+            if (m_config.m_minimize_lemmas) {
+                minimize_lemma();
+                reset_lemma_var_marks();
+                if (m_config.m_dyn_sub_res)
+                    dyn_sub_res();
+                TRACE("sat_lemma", tout << "new lemma (after minimization) size: " << m_lemma.size() << "\n" << m_lemma << "\n";);
+            }
+            else
+                reset_lemma_var_marks();
+
+            literal_vector::iterator it  = m_lemma.begin();
+            literal_vector::iterator end = m_lemma.end();
+            ++it;
+            for(; it != end; ++it) {
+                bool_var var = (*it).var();
+                new_scope_lvl = std::max(new_scope_lvl, lvl(var));
+            }
         }
 
         unsigned glue = num_diff_levels(m_lemma.size(), m_lemma.c_ptr());
@@ -2390,6 +2392,7 @@ namespace sat {
        assigned at level 0.
     */
     void solver::minimize_lemma() {
+        SASSERT(!m_lemma.empty());
         SASSERT(m_unmark.empty());
         //m_unmark.reset();
         updt_lemma_lvl_set();

src/shell/lp_frontend.cpp

@@ -0,0 +1,110 @@
+/*++
+Copyright (c) 2016 Microsoft Corporation
+
+Author: 
+
+    Lev Nachmanson 2016-10-27
+
+--*/
+
+#include "lp_params.hpp"
+#include "util/lp/lp_settings.h"
+#include "util/lp/mps_reader.h"
+#include "timeout.h"
+#include "cancel_eh.h"
+#include "scoped_timer.h"
+#include "rlimit.h"
+#include "gparams.h"
+#include <signal.h>
+
+static lean::lp_solver<double, double>* g_solver = 0;
+
+static void display_statistics() {
+    if (g_solver && g_solver->settings().print_statistics) {
+        // TBD display relevant information about statistics
+    }
+}
+
+static void STD_CALL on_ctrl_c(int) {
+    signal (SIGINT, SIG_DFL);
+    #pragma omp critical (g_display_stats)
+    {
+        display_statistics();
+    }
+    raise(SIGINT);
+}
+
+static void on_timeout() {
+    #pragma omp critical (g_display_stats)
+    {
+        display_statistics();
+        exit(0);
+    }
+}
+
+struct front_end_resource_limit : public lean::lp_resource_limit {
+    reslimit& m_reslim;
+
+    front_end_resource_limit(reslimit& lim):
+        m_reslim(lim)
+    {}
+
+    virtual bool get_cancel_flag() { return !m_reslim.inc(); }
+};
+
+void run_solver(lp_params & params, char const * mps_file_name) {
+
+    reslimit rlim;    
+    unsigned timeout = gparams::get().get_uint("timeout", 0);
+    unsigned rlimit  = gparams::get().get_uint("rlimit", 0);
+    front_end_resource_limit lp_limit(rlim);
+
+    scoped_rlimit _rlimit(rlim, rlimit);
+    cancel_eh<reslimit> eh(rlim);
+    scoped_timer timer(timeout, &eh);
+
+    std::string fn(mps_file_name);
+    lean::mps_reader<double, double> reader(fn);
+    reader.set_message_stream(&std::cout); // can be redirected
+    reader.read();
+    if (!reader.is_ok()) {
+        std::cerr << "cannot process " << mps_file_name << std::endl;
+        return;
+    }
+    lean::lp_solver<double, double> * solver =  reader.create_solver(false);  // false - to create the primal solver
+    solver->settings().set_resource_limit(lp_limit);
+    g_solver = solver;
+    if (params.min()) {
+        solver->flip_costs();
+    }
+    solver->settings().set_message_ostream(&std::cout);
+    solver->settings().report_frequency = params.rep_freq();
+    solver->settings().print_statistics = params.print_stats();
+    solver->find_maximal_solution();
+
+    *(solver->settings().get_message_ostream()) << "status is " << lp_status_to_string(solver->get_status()) << std::endl;
+    if (solver->get_status() == lean::OPTIMAL) {
+        if (params.min()) {
+            solver->flip_costs();
+        }
+        solver->print_model(std::cout);
+    }
+    
+//    #pragma omp critical (g_display_stats)
+    {    
+        display_statistics();
+        register_on_timeout_proc(0);
+        g_solver = 0;
+    }
+    delete solver;
+}
+
+unsigned read_mps_file(char const * mps_file_name) {
+    signal(SIGINT, on_ctrl_c);
+    register_on_timeout_proc(on_timeout);
+    lp_params p;
+    param_descrs r;
+    p.collect_param_descrs(r);
+    run_solver(p, mps_file_name);
+    return 0;
+}

src/shell/lp_frontend.h

@@ -0,0 +1,7 @@
+/*
+  Copyright (c) 2013 Microsoft Corporation. All rights reserved.
+
+  Author: Lev Nachmanson
+*/
+#pragma once
+unsigned read_mps_file(char const * mps_file_name);

src/shell/main.cpp

@@ -35,8 +35,9 @@ Revision History:
 #include"error_codes.h"
 #include"gparams.h"
 #include"env_params.h"
+#include "lp_frontend.h"
 
-typedef enum { IN_UNSPECIFIED, IN_SMTLIB, IN_SMTLIB_2, IN_DATALOG, IN_DIMACS, IN_WCNF, IN_OPB, IN_Z3_LOG } input_kind;
+typedef enum { IN_UNSPECIFIED, IN_SMTLIB, IN_SMTLIB_2, IN_DATALOG, IN_DIMACS, IN_WCNF, IN_OPB, IN_Z3_LOG, IN_MPS } input_kind;
 
 std::string         g_aux_input_file;
 char const *        g_input_file          = 0;
@@ -342,6 +343,10 @@ int STD_CALL main(int argc, char ** argv) {
                 else if (strcmp(ext, "smt") == 0) {
                     g_input_kind = IN_SMTLIB;
                 }
+                else if (strcmp(ext, "mps") == 0 || strcmp(ext, "sif") == 0 ||
+                         strcmp(ext, "MPS") == 0 || strcmp(ext, "SIF") == 0) {
+                    g_input_kind = IN_MPS;
+                }
             }
     }
         switch (g_input_kind) {
@@ -367,6 +372,9 @@ int STD_CALL main(int argc, char ** argv) {
         case IN_Z3_LOG:
             replay_z3_log(g_input_file);
             break;
+        case IN_MPS:
+            return_value = read_mps_file(g_input_file);
+            break;
         default:
             UNREACHABLE();
         }

src/smt/smt2_extra_cmds.cpp

@@ -44,4 +44,4 @@ public:
 
 void install_smt2_extra_cmds(cmd_context & ctx) {
     ctx.insert(alloc(include_cmd));
-}
+}

src/smt/smt_setup.cpp

@@ -20,6 +20,7 @@ Revision History:
 #include"smt_setup.h"
 #include"static_features.h"
 #include"theory_arith.h"
+#include"theory_lra.h"
 #include"theory_dense_diff_logic.h"
 #include"theory_diff_logic.h"
 #include"theory_utvpi.h"
@@ -442,7 +443,7 @@ namespace smt {
         m_params.m_arith_propagate_eqs = false;
         m_params.m_eliminate_term_ite  = true;
         m_params.m_nnf_cnf             = false;
-        setup_mi_arith();
+        setup_r_arith();
     }
 
     void setup::setup_QF_LRA(static_features const & st) {
@@ -467,6 +468,10 @@ namespace smt {
             m_params.m_restart_adaptive      = false;
         }
         m_params.m_arith_small_lemma_size = 32;
+        setup_r_arith();
+    }
+
+    void setup::setup_QF_LIRA(static_features const& st) {
         setup_mi_arith();
     }
 
@@ -475,7 +480,7 @@ namespace smt {
         m_params.m_relevancy_lvl       = 0;
         m_params.m_arith_expand_eqs    = true;
         m_params.m_arith_reflect       = false; 
-        m_params.m_arith_propagate_eqs = false;
+        m_params.m_arith_propagate_eqs = false; 
         m_params.m_nnf_cnf             = false;
         setup_i_arith();
     }
@@ -539,7 +544,7 @@ namespace smt {
         m_params.m_relevancy_lvl       = 0;
         m_params.m_arith_reflect       = false; 
         m_params.m_nnf_cnf             = false;
-        setup_mi_arith();
+        setup_r_arith();
     }
 
     void setup::setup_QF_BV() {
@@ -718,6 +723,12 @@ namespace smt {
         m_context.register_plugin(alloc(smt::theory_i_arith, m_manager, m_params));
     }
 
+    void setup::setup_r_arith() {
+        // to disable theory lra
+        // m_context.register_plugin(alloc(smt::theory_mi_arith, m_manager, m_params));        
+        m_context.register_plugin(alloc(smt::theory_lra, m_manager, m_params));
+    }
+
     void setup::setup_mi_arith() {
         if (m_params.m_arith_mode == AS_OPTINF) {
             m_context.register_plugin(alloc(smt::theory_inf_arith, m_manager, m_params));            
@@ -929,7 +940,9 @@ namespace smt {
         }
         
         if (st.num_theories() == 1 && is_arith(st)) {
-            if (st.m_has_real)
+            if ((st.m_has_int && st.m_has_real) || (st.m_num_non_linear != 0)) 
+                setup_QF_LIRA(st);
+            else if (st.m_has_real)
                 setup_QF_LRA(st);
             else
                 setup_QF_LIA(st);

src/smt/smt_setup.h

@@ -65,6 +65,7 @@ namespace smt {
         void setup_QF_LRA();
         void setup_QF_LRA(static_features const & st);
         void setup_QF_LIA();
+        void setup_QF_LIRA(static_features const& st);
         void setup_QF_LIA(static_features const & st);
         void setup_QF_UFLIA();
         void setup_QF_UFLIA(static_features & st);
@@ -99,6 +100,7 @@ namespace smt {
         void setup_card();
         void setup_i_arith();
         void setup_mi_arith();
+        void setup_r_arith();
         void setup_fpa();
         void setup_str();
 

src/smt/smt_theory.cpp

@@ -54,7 +54,7 @@ namespace smt {
         }
     }
 
-    void theory::display_app(std::ostream & out, app * n) const {
+    std::ostream& theory::display_app(std::ostream & out, app * n) const {
         func_decl * d = n->get_decl();
         if (n->get_num_args() == 0) {
             out << d->get_name();
@@ -73,9 +73,10 @@ namespace smt {
         else {
             out << "#" << n->get_id();
         }
+        return out;
     }
 
-    void theory::display_flat_app(std::ostream & out, app * n) const {
+    std::ostream& theory::display_flat_app(std::ostream & out, app * n) const {
         func_decl * d = n->get_decl();
         if (n->get_num_args() == 0) {
             out << d->get_name();
@@ -106,6 +107,7 @@ namespace smt {
         else {
             out << "#" << n->get_id();
         }
+        return out;
     }
     
     bool theory::is_relevant_and_shared(enode * n) const {

src/smt/smt_theory.h

@@ -337,14 +337,14 @@ namespace smt {
         
         virtual void collect_statistics(::statistics & st) const {
         }
-
-        void display_app(std::ostream & out, app * n) const;
-
-        void display_flat_app(std::ostream & out, app * n) const;
         
-        void display_var_def(std::ostream & out, theory_var v) const { return display_app(out, get_enode(v)->get_owner()); }
+        std::ostream& display_app(std::ostream & out, app * n) const;
         
-        void display_var_flat_def(std::ostream & out, theory_var v) const { return display_flat_app(out, get_enode(v)->get_owner()); }
+        std::ostream& display_flat_app(std::ostream & out, app * n) const;
+        
+        std::ostream& display_var_def(std::ostream & out, theory_var v) const { return display_app(out, get_enode(v)->get_owner()); }
+        
+        std::ostream& display_var_flat_def(std::ostream & out, theory_var v) const { return display_flat_app(out, get_enode(v)->get_owner());  }
 
         /**
            \brief Assume eqs between variable that are equal with respect to the given table.

src/smt/tactic/smt_tactic.cpp

@@ -21,6 +21,7 @@ Notes:
 #include"smt_kernel.h"
 #include"smt_params.h"
 #include"smt_params_helper.hpp"
+#include"lp_params.hpp"
 #include"rewriter_types.h"
 #include"filter_model_converter.h"
 #include"ast_util.h"
@@ -64,6 +65,10 @@ public:
         return m_params;
     }
 
+    params_ref & params() {
+        return m_params_ref;
+    }
+
     void updt_params_core(params_ref const & p) {
         m_candidate_models     = p.get_bool("candidate_models", false);
         m_fail_if_inconclusive = p.get_bool("fail_if_inconclusive", true);
@@ -73,6 +78,7 @@ public:
         TRACE("smt_tactic", tout << "updt_params: " << p << "\n";);
         updt_params_core(p);
         fparams().updt_params(p);
+        m_params_ref.copy(p);
         m_logic = p.get_sym(symbol("logic"), m_logic);
         if (m_logic != symbol::null && m_ctx) {
             m_ctx->set_logic(m_logic);
@@ -84,6 +90,7 @@ public:
         r.insert("candidate_models", CPK_BOOL, "(default: false) create candidate models even when quantifier or theory reasoning is incomplete.");
         r.insert("fail_if_inconclusive", CPK_BOOL, "(default: true) fail if found unsat (sat) for under (over) approximated goal.");
         smt_params_helper::collect_param_descrs(r);
+        lp_params::collect_param_descrs(r);
     }
 
 
@@ -112,10 +119,12 @@ public:
     struct scoped_init_ctx {
         smt_tactic & m_owner;
         smt_params   m_params; // smt-setup overwrites parameters depending on the current assertions.
+        params_ref   m_params_ref;
 
         scoped_init_ctx(smt_tactic & o, ast_manager & m):m_owner(o) {
             m_params = o.fparams();
-            smt::kernel * new_ctx = alloc(smt::kernel, m, m_params);
+            m_params_ref = o.params();
+            smt::kernel * new_ctx = alloc(smt::kernel, m, m_params, m_params_ref);
             TRACE("smt_tactic", tout << "logic: " << o.m_logic << "\n";);
             new_ctx->set_logic(o.m_logic);
             if (o.m_callback) {

src/smt/theory_lra.h

@@ -0,0 +1,97 @@
+/*++
+Copyright (c) 2016 Microsoft Corporation
+
+Module Name:
+
+    theory_lra.h
+
+Abstract:
+
+    <abstract>
+
+Author:
+
+    Lev Nachmanson (levnach) 2016-25-3
+    Nikolaj Bjorner (nbjorner)
+
+Revision History:
+
+
+--*/
+#pragma once
+
+#include "theory_opt.h"
+
+namespace smt {
+    class theory_lra : public theory, public theory_opt {
+        class imp;
+        imp* m_imp;
+
+    public:
+        theory_lra(ast_manager& m, theory_arith_params& ap);
+        virtual ~theory_lra();
+        virtual theory* mk_fresh(context* new_ctx);
+        virtual char const* get_name() const { return "lra"; }
+        
+        virtual void init(context * ctx);
+
+        virtual bool internalize_atom(app * atom, bool gate_ctx);
+                                                     
+        virtual bool internalize_term(app * term);
+
+        virtual void internalize_eq_eh(app * atom, bool_var v);
+
+        virtual void assign_eh(bool_var v, bool is_true);
+
+        virtual void new_eq_eh(theory_var v1, theory_var v2);
+
+        virtual bool use_diseqs() const;
+
+        virtual void new_diseq_eh(theory_var v1, theory_var v2);
+
+        virtual void push_scope_eh();
+
+        virtual void pop_scope_eh(unsigned num_scopes);
+
+        virtual void restart_eh();
+
+        virtual void relevant_eh(app* e);
+
+        virtual void init_search_eh();
+
+        virtual final_check_status final_check_eh();
+
+        virtual bool is_shared(theory_var v) const;
+    
+        virtual bool can_propagate();
+        
+        virtual void propagate();
+        
+        virtual justification * why_is_diseq(theory_var v1, theory_var v2);
+
+        // virtual void flush_eh();
+
+        virtual void reset_eh();
+
+        virtual void init_model(model_generator & m);
+        
+        virtual model_value_proc * mk_value(enode * n, model_generator & mg);
+
+        virtual bool get_value(enode* n, expr_ref& r);
+
+        virtual bool validate_eq_in_model(theory_var v1, theory_var v2, bool is_true) const;
+                
+        virtual void display(std::ostream & out) const;
+        
+        virtual void collect_statistics(::statistics & st) const;
+
+        // optimization
+        virtual inf_eps value(theory_var);
+        virtual inf_eps maximize(theory_var v, expr_ref& blocker, bool& has_shared); 
+        virtual theory_var add_objective(app* term);
+        virtual expr_ref mk_ge(filter_model_converter& fm, theory_var v, inf_rational const& val);
+
+
+    };
+
+}

src/smt/theory_seq.cpp

@@ -2176,6 +2176,8 @@ bool theory_seq::simplify_and_solve_eqs() {
     return m_new_propagation || ctx.inconsistent();
 }
 
+void theory_seq::internalize_eq_eh(app * atom, bool_var v) {}
+
 
 bool theory_seq::internalize_term(app* term) {
     context & ctx   = get_context();

src/smt/theory_seq.h

@@ -343,7 +343,7 @@ namespace smt {
         virtual final_check_status final_check_eh();
         virtual bool internalize_atom(app* atom, bool) { return internalize_term(atom); }
         virtual bool internalize_term(app*);
-        virtual void internalize_eq_eh(app * atom, bool_var v) {}
+        virtual void internalize_eq_eh(app * atom, bool_var v);
         virtual void new_eq_eh(theory_var, theory_var);
         virtual void new_diseq_eh(theory_var, theory_var);
         virtual void assign_eh(bool_var v, bool is_true);        

src/smt/theory_str.cpp

@@ -60,6 +60,7 @@ namespace smt {
         totalCacheAccessCount(0),
         cacheHitCount(0),
         cacheMissCount(0),
+        m_fresh_id(0),
         m_find(*this),
         m_trail_stack(*this)
     {
@@ -441,7 +442,12 @@ namespace smt {
     }
 
     app * theory_str::mk_fresh_const(char const* name, sort* s) {
-        return u.mk_skolem(symbol(name), 0, 0, s);
+        string_buffer<64> buffer;
+        buffer << name;
+        buffer << "!tmp";
+        buffer << m_fresh_id;
+        m_fresh_id++;
+        return u.mk_skolem(symbol(buffer.c_str()), 0, 0, s);
     }
 
 
@@ -5552,8 +5558,8 @@ namespace smt {
                     for (; arg1_grdItor != groundedMap[arg1DeAlias].end(); arg1_grdItor++) {
                         std::vector<expr*> ndVec;
                         ndVec.insert(ndVec.end(), arg0_grdItor->first.begin(), arg0_grdItor->first.end());
-                        int arg0VecSize = arg0_grdItor->first.size();
-                        int arg1VecSize = arg1_grdItor->first.size();
+                        size_t arg0VecSize = arg0_grdItor->first.size();
+                        size_t arg1VecSize = arg1_grdItor->first.size();
                         if (arg0VecSize > 0 && arg1VecSize > 0 && u.str.is_string(arg0_grdItor->first[arg0VecSize - 1]) && u.str.is_string(arg1_grdItor->first[0])) {
                             ndVec.pop_back();
                             ndVec.push_back(mk_concat(arg0_grdItor->first[arg0VecSize - 1], arg1_grdItor->first[0]));
@@ -5645,8 +5651,8 @@ namespace smt {
     }
 
     bool theory_str::is_partial_in_grounded_concat(const std::vector<expr*> & strVec, const std::vector<expr*> & subStrVec) {
-        int strCnt = strVec.size();
-        int subStrCnt = subStrVec.size();
+        size_t strCnt = strVec.size();
+        size_t subStrCnt = subStrVec.size();
 
         if (strCnt == 0 || subStrCnt == 0) {
             return false;
@@ -5717,7 +5723,7 @@ namespace smt {
                 }
 
                 // tail nodes
-                int tailIdx = i + subStrCnt - 1;
+                size_t tailIdx = i + subStrCnt - 1;
                 zstring subStrTailVal;
                 if (u.str.is_string(subStrVec[subStrCnt - 1], subStrTailVal)) {
                     zstring strTailVal;
@@ -5908,8 +5914,14 @@ namespace smt {
         app * n2_curr = to_app(n2);
 
         // case 0: n1_curr is const string, n2_curr is const string
-        if (u.str.is_string(n1_curr) && u.str.is_string(n2_curr)) {
-            if (n1_curr != n2_curr) {
+        zstring n1_curr_str, n2_curr_str;
+        if (u.str.is_string(n1_curr, n1_curr_str) && u.str.is_string(n2_curr, n2_curr_str)) {
+            TRACE("str", tout << "checking string constants: n1=" << n1_curr_str << ", n2=" << n2_curr_str << std::endl;);
+            if (n1_curr_str == n2_curr_str) {
+                // TODO(mtrberzi) potential correction: if n1_curr != n2_curr,
+                // assert that these two terms are in fact equal, because they ought to be
+                return true;
+            } else {
                 return false;
             }
         }
@@ -6864,7 +6876,7 @@ namespace smt {
                                 // easiest case. we will search within these bounds
                             } else if (upper_bound_exists && !lower_bound_exists) {
                                 // search between 0 and the upper bound
-                                v_lower_bound == rational::zero();
+                                v_lower_bound = rational::zero();
                             } else if (lower_bound_exists && !upper_bound_exists) {
                                 // check some finite portion of the search space
                                 v_upper_bound = v_lower_bound + rational(10);
@@ -8251,7 +8263,7 @@ namespace smt {
                         }
                     }
                     if (lId == -1)
-                        lId = mLMap.size();
+                        lId = static_cast<int>(mLMap.size());
                     for (std::set<expr*>::iterator itor2 = nSet.begin(); itor2 != nSet.end(); itor2++) {
                         bool itorHasEqcValue = false;
                         get_eqc_value(*itor2, itorHasEqcValue);
@@ -8290,7 +8302,7 @@ namespace smt {
                         }
                     }
                     if (rId == -1)
-                        rId = mRMap.size();
+                        rId = static_cast<int>(mRMap.size());
                     for (itor2 = nSet.begin(); itor2 != nSet.end(); itor2++) {
                         bool rHasEqcValue = false;
                         get_eqc_value(*itor2, rHasEqcValue);
@@ -9182,7 +9194,7 @@ namespace smt {
         // ----------------------------------------------------------------------------------------
         int len = atoi(lenStr.encode().c_str());
         bool coverAll = false;
-        svector<int_vector> options;
+        vector<int_vector, true, long long> options;
         int_vector base;
 
         TRACE("str", tout
@@ -9227,16 +9239,16 @@ namespace smt {
               );
 
         // ----------------------------------------------------------------------------------------
-
+        
         ptr_vector<expr> orList;
         ptr_vector<expr> andList;
 
         for (long long i = l; i < h; i++) {
             orList.push_back(m.mk_eq(val_indicator, mk_string(longlong_to_string(i).c_str()) ));
             if (m_params.m_AggressiveValueTesting) {
-                literal l = mk_eq(val_indicator, mk_string(longlong_to_string(i).c_str()), false);
-                ctx.mark_as_relevant(l);
-                ctx.force_phase(l);
+                literal lit = mk_eq(val_indicator, mk_string(longlong_to_string(i).c_str()), false);
+                ctx.mark_as_relevant(lit);
+                ctx.force_phase(lit);
             }
 
             zstring aStr = gen_val_string(len, options[i - l]);
@@ -10059,7 +10071,7 @@ namespace smt {
                 }
                 TRACE("str", tout << "last bounds are [" << lastBounds.lowerBound << " | " << lastBounds.midPoint << " | " << lastBounds.upperBound << "]!" << lastBounds.windowSize << std::endl;);
                 binary_search_info newBounds;
-                expr * newTester;
+                expr * newTester = 0;
                 if (lastTesterConstant == "more") {
                     // special case: if the midpoint, upper bound, and window size are all equal,
                     // we double the window size and adjust the bounds

src/smt/theory_str.h

@@ -350,6 +350,8 @@ protected:
     unsigned long cacheHitCount;
     unsigned long cacheMissCount;
 
+    unsigned m_fresh_id;
+
     // cache mapping each string S to Length(S)
     obj_map<expr, app*> length_ast_map;
 

src/tactic/portfolio/pb2bv_solver.cpp

@@ -20,6 +20,7 @@ Notes:
 #include "solver_na2as.h"
 #include "tactic.h"
 #include "pb2bv_rewriter.h"
+#include "th_rewriter.h"
 #include "filter_model_converter.h"
 #include "ast_pp.h"
 #include "model_smt2_pp.h"
@@ -29,6 +30,7 @@ class pb2bv_solver : public solver_na2as {
     params_ref       m_params;
     mutable expr_ref_vector  m_assertions;
     mutable ref<solver>      m_solver;
+    mutable th_rewriter      m_th_rewriter;
     mutable pb2bv_rewriter   m_rewriter;
 
 public:
@@ -39,6 +41,7 @@ public:
         m_params(p),
         m_assertions(m),
         m_solver(s),
+        m_th_rewriter(m, p),
         m_rewriter(m, p)
     {
     }
@@ -121,10 +124,11 @@ public:
 private:
     void flush_assertions() const {
         proof_ref proof(m);
-        expr_ref fml(m);
+        expr_ref fml1(m), fml(m);
         expr_ref_vector fmls(m);
         for (unsigned i = 0; i < m_assertions.size(); ++i) {
-            m_rewriter(m_assertions[i].get(), fml, proof);
+            m_th_rewriter(m_assertions[i].get(), fml1, proof);
+            m_rewriter(fml1, fml, proof);
             m_solver->assert_expr(fml);
         }
         m_rewriter.flush_side_constraints(fmls);

src/tactic/smtlogics/qflra_tactic.cpp

@@ -22,7 +22,6 @@ Notes:
 #include"solve_eqs_tactic.h"
 #include"elim_uncnstr_tactic.h"
 #include"smt_tactic.h"
-// include"mip_tactic.h"
 #include"recover_01_tactic.h"
 #include"ctx_simplify_tactic.h"
 #include"probe_arith.h"
@@ -72,5 +71,18 @@ tactic * mk_qflra_tactic(ast_manager & m, params_ref const & p) {
     //                            using_params(mk_smt_tactic(), pivot_p)),
     //                    p);
 
+#if 0
+
+    params_ref simplex_0, simplex_1, simplex_2;
+    simplex_0.set_uint("lp.simplex_strategy", 0);    
+    simplex_1.set_uint("lp.simplex_strategy", 1);    
+    simplex_2.set_uint("lp.simplex_strategy", 2);
+    
+    return par(using_params(mk_smt_tactic(), simplex_0), 
+               using_params(mk_smt_tactic(), simplex_1), 
+               using_params(mk_smt_tactic(), simplex_2));
+#else
     return using_params(using_params(mk_smt_tactic(), pivot_p), p);
+#endif
+
 }

src/test/argument_parser.h

@@ -0,0 +1,144 @@
+/*
+Copyright (c) 2013 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Author: Lev Nachmanson
+*/
+
+#include <unordered_map>
+#include <vector>
+#include <string>
+#include <set>
+#include <iostream>
+
+namespace lean {
+class argument_parser {
+    std::unordered_map<std::string, std::string> m_options;
+    std::unordered_map<std::string, std::string> m_options_with_after_string;
+    std::set<std::string> m_used_options;
+    std::unordered_map<std::string, std::string> m_used_options_with_after_string;
+    std::vector<std::string> m_free_args;
+    std::vector<std::string> m_args;
+
+public:
+    std::string m_error_message;
+    argument_parser(unsigned argn, char * const* args) {
+        for (unsigned i = 0; i < argn; i++) {
+            m_args.push_back(std::string(args[i]));
+        }
+    }
+
+    void add_option(std::string s) {
+        add_option_with_help_string(s, "");
+    }
+
+    void add_option_with_help_string(std::string s, std::string help_string) {
+        m_options[s]=help_string;
+    }
+
+    void add_option_with_after_string(std::string s) {
+        add_option_with_after_string_with_help(s, "");
+    }
+
+    void add_option_with_after_string_with_help(std::string s, std::string help_string) {
+        m_options_with_after_string[s]=help_string;
+    }
+
+
+    bool parse() {
+        bool status_is_ok = true;
+        for (unsigned i = 0; i < m_args.size(); i++) {
+            std::string ar = m_args[i];
+            if (m_options.find(ar) != m_options.end() )
+                m_used_options.insert(ar);
+            else if (m_options_with_after_string.find(ar) != m_options_with_after_string.end()) {
+                if (i == m_args.size() - 1) {
+                    m_error_message = "Argument is missing after "+ar;
+                    return false;
+                }
+                i++;
+                m_used_options_with_after_string[ar] = m_args[i];
+            } else {
+                 if (starts_with(ar, "-") || starts_with(ar, "//")) 
+                     status_is_ok = false;
+
+                m_free_args.push_back(ar);
+            }
+        }
+        return status_is_ok;
+    }
+
+    bool contains(std::unordered_map<std::string, std::string> & m, std::string s) {
+        return m.find(s) != m.end();
+    }
+
+    bool contains(std::set<std::string> & m, std::string s) {
+        return m.find(s) != m.end();
+    }
+
+    bool option_is_used(std::string option) {
+        return contains(m_used_options, option) || contains(m_used_options_with_after_string, option);
+    }
+
+    std::string get_option_value(std::string option) {
+        auto t = m_used_options_with_after_string.find(option);
+        if (t != m_used_options_with_after_string.end()){
+            return t->second;
+        }
+        return std::string();
+    }
+
+    bool starts_with(std::string s, char const * prefix) {
+        return starts_with(s, std::string(prefix));
+    }
+
+    bool starts_with(std::string s, std::string prefix) {
+        return s.substr(0, prefix.size()) == prefix;
+    }
+
+    std::string usage_string() {
+        std::string ret = "";
+        std::vector<std::string> unknown_options;
+        for (auto t : m_free_args) {
+            if (starts_with(t, "-") || starts_with(t, "\\")) {
+                unknown_options.push_back(t);
+            }
+        }
+        if (unknown_options.size()) {
+            ret = "Unknown options:";
+        }
+        for (auto unknownOption : unknown_options) {
+            ret += unknownOption;
+            ret += ",";
+        }
+        ret += "\n";
+        ret += "Usage:\n";
+        for (auto allowed_option : m_options)
+            ret += allowed_option.first + " " + (allowed_option.second.size() == 0 ? std::string("") : std::string("/") + allowed_option.second) + std::string("\n");
+        for (auto s : m_options_with_after_string) {
+            ret += s.first + " " + (s.second.size() == 0? " \"option value\"":("\""+ s.second+"\"")) + "\n";
+        }
+        return ret;
+    }
+
+    void print() {
+        if (m_used_options.size() == 0 && m_used_options_with_after_string.size() == 0 && m_free_args.size() == 0) {
+            std::cout << "no options are given" << std::endl;
+            return;
+        }
+        std::cout << "options are: " << std::endl;
+        for (std::string s : m_used_options) {
+            std::cout << s << std::endl;
+        }
+        for (auto & t : m_used_options_with_after_string) {
+            std::cout << t.first << " " << t.second << std::endl;
+        }
+        if (m_free_args.size() > 0) {
+            std::cout << "free arguments are: "  << std::endl;
+            for (auto & t : m_free_args) {
+                std::cout << t << " " <<  std::endl;
+            }
+        }
+    }
+};
+}

src/test/main.cpp

@@ -240,6 +240,7 @@ int main(int argc, char ** argv) {
     TST(pdr);
     TST_ARGV(ddnf);
     TST(model_evaluator);
+    TST_ARGV(lp);
     TST(get_consequences);
     TST(pb2bv);
     TST_ARGV(sat_lookahead);

src/test/smt_reader.h

@@ -0,0 +1,396 @@
+/*
+  Copyright (c) 2013 Microsoft Corporation. All rights reserved.
+  Released under Apache 2.0 license as described in the file LICENSE.
+
+  Author: Lev Nachmanson
+*/
+
+#pragma once
+
+// reads an MPS file reperesenting a Mixed Integer Program
+#include <string>
+#include <vector>
+#include <unordered_map>
+#include "util/lp/lp_primal_simplex.h"
+#include "util/lp/lp_dual_simplex.h"
+#include "util/lp/lar_solver.h"
+#include <iostream>
+#include <fstream>
+#include <functional>
+#include <algorithm>
+#include "util/lp/mps_reader.h"
+#include "util/lp/ul_pair.h"
+#include "util/lp/lar_constraints.h"
+#include <sstream>
+#include <cstdlib>
+namespace lean {
+
+    template<typename T>
+    T from_string(const std::string& str) {
+        std::istringstream ss(str);
+        T ret;
+        ss >> ret;
+        return ret;
+    }
+
+    class smt_reader {
+    public:
+        struct lisp_elem {
+            std::string m_head;
+            std::vector<lisp_elem> m_elems;
+            void print() {
+                if (m_elems.size()) {
+                    std::cout << '(';
+                    std::cout << m_head << ' ';
+                    for (auto & el : m_elems)
+                        el.print();
+
+                    std::cout << ')';
+                } else {
+                    std::cout << " " << m_head;
+                }
+            }
+            unsigned size() const { return static_cast<unsigned>(m_elems.size()); }
+            bool is_simple() const { return size() == 0; }
+        };
+        struct formula_constraint {
+            lconstraint_kind m_kind;
+            std::vector<std::pair<mpq, std::string>> m_coeffs;
+            mpq m_right_side;
+            void add_pair(mpq c, std::string name) {
+                m_coeffs.push_back(make_pair(c, name));
+            }
+            formula_constraint() : m_right_side(numeric_traits<mpq>::zero()) {}
+        };
+
+        lisp_elem m_formula_lisp_elem;
+
+        std::unordered_map<std::string, unsigned> m_name_to_var_index;
+        std::vector<formula_constraint>           m_constraints;
+        bool                                      m_is_OK;
+        unsigned                                  m_line_number;
+        std::string                               m_file_name;
+        std::ifstream                             m_file_stream;
+        std::string                               m_line;
+        smt_reader(std::string file_name):
+            m_is_OK(true),
+            m_line_number(0),
+            m_file_name(file_name), 
+            m_file_stream(file_name) {
+        }
+
+        void set_error() {
+            std::cout << "setting error" << std::endl;
+            m_is_OK = false;
+        }
+
+        bool is_ok() {
+            return m_is_OK;
+        }
+
+        bool prefix(const char * pr) {
+            return m_line.find(pr) == 0;
+        }
+
+        int first_separator() {
+            unsigned blank_pos = static_cast<unsigned>(m_line.find(' '));
+            unsigned br_pos = static_cast<unsigned>(m_line.find('('));
+            unsigned reverse_br_pos = static_cast<unsigned>(m_line.find(')'));
+            return std::min(blank_pos, std::min(br_pos, reverse_br_pos));
+        }
+
+        void fill_lisp_elem(lisp_elem & lm) {
+            if (m_line[0] == '(')
+                fill_nested_elem(lm);
+            else
+                fill_simple_elem(lm);
+        }
+
+        void fill_simple_elem(lisp_elem & lm) {
+            int separator = first_separator();
+            lean_assert(-1 != separator && separator != 0);
+            lm.m_head = m_line.substr(0, separator);
+            m_line = m_line.substr(separator);
+        }
+
+        void fill_nested_elem(lisp_elem & lm) {
+            lean_assert(m_line[0] == '(');
+            m_line = m_line.substr(1);
+            int separator = first_separator();
+            lm.m_head = m_line.substr(0, separator);
+            m_line = m_line.substr(lm.m_head.size());
+            eat_blanks();
+            while (m_line.size()) {
+                if (m_line[0] == '(') {
+                    lisp_elem el;
+                    fill_nested_elem(el);
+                    lm.m_elems.push_back(el);
+                } else {
+                    if (m_line[0] == ')') {
+                        m_line = m_line.substr(1);
+                        break;
+                    }
+                    lisp_elem el;
+                    fill_simple_elem(el);
+                    lm.m_elems.push_back(el);
+                }
+                eat_blanks();
+            }
+        }
+
+        void eat_blanks() {
+            while (m_line.size()) {
+                if (m_line[0] == ' ')
+                    m_line = m_line.substr(1);
+                else
+                    break;
+            }
+        }
+
+        void fill_formula_elem() {
+            fill_lisp_elem(m_formula_lisp_elem);
+        }
+
+        void parse_line() {
+            if (m_line.find(":formula") == 0) {
+                int first_br = static_cast<int>(m_line.find('('));
+                if (first_br == -1) {
+                    std::cout << "empty formula" << std::endl;
+                    return;
+                }
+                m_line = m_line.substr(first_br);
+                fill_formula_elem();
+            }
+        }
+
+        void set_constraint_kind(formula_constraint & c, lisp_elem & el) {
+            if (el.m_head == "=") {
+                c.m_kind = EQ;
+            } else if (el.m_head == ">=") {
+                c.m_kind = GE;
+            } else if (el.m_head == "<=") {
+                c.m_kind = LE;
+            } else if (el.m_head == ">") {
+                c.m_kind = GT;
+            } else if (el.m_head == "<") {
+                c.m_kind = LT;
+            } else {
+                std::cout << "kind " << el.m_head << " is not supported " << std::endl;
+                set_error();
+            }
+        }
+
+        void adjust_rigth_side(formula_constraint & /* c*/, lisp_elem & /*el*/) {
+            // lean_assert(el.m_head == "0"); // do nothing for the time being
+        }
+
+        void set_constraint_coeffs(formula_constraint & c, lisp_elem & el) {
+            lean_assert(el.m_elems.size() == 2);
+            set_constraint_coeffs_on_coeff_element(c, el.m_elems[0]);
+            adjust_rigth_side(c, el.m_elems[1]);
+        }
+
+
+        bool is_integer(std::string & s) {
+            if (s.size() == 0) return false;
+            return atoi(s.c_str()) != 0 || isdigit(s.c_str()[0]);
+        }
+
+        void add_complex_sum_elem(formula_constraint & c, lisp_elem & el) {
+            if (el.m_head == "*") {
+                add_mult_elem(c, el.m_elems);
+            } else if (el.m_head == "~") {
+                lisp_elem & minel = el.m_elems[0];
+                lean_assert(minel.is_simple());
+                c.m_right_side += mpq(str_to_int(minel.m_head));
+            } else {
+                std::cout << "unexpected input " << el.m_head << std::endl;
+                set_error();
+                return;
+            }
+        }
+
+        std::string get_name(lisp_elem & name) {
+            lean_assert(name.is_simple());
+            lean_assert(!is_integer(name.m_head));
+            return name.m_head;
+        }
+
+
+        void add_mult_elem(formula_constraint & c, std::vector<lisp_elem> & els) {
+            lean_assert(els.size() == 2);
+            mpq coeff = get_coeff(els[0]);
+            std::string col_name = get_name(els[1]);
+            c.add_pair(coeff, col_name);
+        }
+
+        mpq get_coeff(lisp_elem & le) {
+            if (le.is_simple()) {
+                return mpq(str_to_int(le.m_head));
+            } else {
+                lean_assert(le.m_head == "~");
+                lean_assert(le.size() == 1);
+                lisp_elem & el = le.m_elems[0];
+                lean_assert(el.is_simple());
+                return -mpq(str_to_int(el.m_head));
+            }
+        }
+
+        int str_to_int(std::string & s) {
+            lean_assert(is_integer(s));
+            return atoi(s.c_str());
+        }
+
+        void add_sum_elem(formula_constraint & c, lisp_elem & el) {
+            if (el.size()) {
+                add_complex_sum_elem(c, el);
+            } else {
+                lean_assert(is_integer(el.m_head));
+                int v = atoi(el.m_head.c_str());
+                mpq vr(v);
+                c.m_right_side -= vr;
+            }
+        }
+
+        void add_sum(formula_constraint & c, std::vector<lisp_elem> & sum_els) {
+            for (auto & el : sum_els)
+                add_sum_elem(c, el);
+        }
+
+        void set_constraint_coeffs_on_coeff_element(formula_constraint & c, lisp_elem & el) {
+            if (el.m_head == "*") {
+                add_mult_elem(c, el.m_elems);
+            } else if (el.m_head == "+") {
+                add_sum(c, el.m_elems);
+            } else {
+                lean_assert(false); // unexpected input
+            }
+        }
+
+        void create_constraint(lisp_elem & el) {
+            formula_constraint c;
+            set_constraint_kind(c, el);
+            set_constraint_coeffs(c, el);
+            m_constraints.push_back(c);
+        }
+
+        void fill_constraints() {
+            if (m_formula_lisp_elem.m_head != "and") {
+                std::cout << "unexpected top element " << m_formula_lisp_elem.m_head << std::endl;
+                set_error();
+                return;
+            }
+            for (auto & el : m_formula_lisp_elem.m_elems)
+                create_constraint(el);
+        }
+
+        void read() {
+            if (!m_file_stream.is_open()){
+                std::cout << "cannot open file " << m_file_name << std::endl;
+                set_error();
+                return;
+            }
+            while (m_is_OK && getline(m_file_stream, m_line)) {
+                parse_line();
+                m_line_number++;
+            }
+
+            m_file_stream.close();
+            fill_constraints();
+        }
+
+        /*
+        void fill_lar_solver_on_row(row * row, lar_solver *solver)  {
+            if (row->m_name != m_cost_row_name) {
+                lar_constraint c(get_lar_relation_from_row(row->m_type), row->m_right_side);
+                for (auto s : row->m_row_columns) {
+                    var_index i = solver->add_var(s.first);
+                    c.add_variable_to_constraint(i, s.second);
+                }
+                solver->add_constraint(&c);
+            } else {
+                // ignore the cost row
+            }
+        }
+
+
+        void fill_lar_solver_on_rows(lar_solver * solver) {
+            for (auto row_it : m_rows) {
+                fill_lar_solver_on_row(row_it.second, solver);
+            }
+        }
+
+        void create_low_constraint_for_var(column* col, bound * b, lar_solver *solver) {
+            lar_constraint c(GE, b->m_low);
+            var_index i = solver->add_var(col->m_name);
+            c.add_variable_to_constraint(i, numeric_traits<T>::one());
+            solver->add_constraint(&c);
+        }
+
+        void create_upper_constraint_for_var(column* col, bound * b, lar_solver *solver) {
+            lar_constraint c(LE, b->m_upper);
+            var_index i = solver->add_var(col->m_name);
+            c.add_variable_to_constraint(i, numeric_traits<T>::one());
+            solver->add_constraint(&c);
+        }
+
+        void create_equality_contraint_for_var(column* col, bound * b, lar_solver *solver) {
+            lar_constraint c(EQ, b->m_fixed_value);
+            var_index i = solver->add_var(col->m_name);
+            c.add_variable_to_constraint(i, numeric_traits<T>::one());
+            solver->add_constraint(&c);
+        }
+
+        void fill_lar_solver_on_columns(lar_solver * solver) {
+            for (auto s : m_columns) {
+                mps_reader::column * col = s.second;
+                solver->add_var(col->m_name);
+                auto b = col->m_bound;
+                if (b == nullptr) return;
+
+                if (b->m_free) continue;
+
+                if (b->m_low_is_set) {
+                    create_low_constraint_for_var(col, b, solver);
+                }
+                if (b->m_upper_is_set) {
+                    create_upper_constraint_for_var(col, b, solver);
+                }
+                if (b->m_value_is_fixed) {
+                    create_equality_contraint_for_var(col, b, solver);
+                }
+            }
+        }
+        */
+
+        unsigned register_name(std::string s) {
+            auto it = m_name_to_var_index.find(s);
+            if (it!= m_name_to_var_index.end())
+                return it->second;
+
+            unsigned ret = static_cast<unsigned>(m_name_to_var_index.size());
+            m_name_to_var_index[s] = ret;
+            return ret;
+        }
+        
+        void add_constraint_to_solver(lar_solver * solver, formula_constraint & fc) {
+            vector<std::pair<mpq, var_index>> ls;
+            for (auto & it : fc.m_coeffs) {
+                ls.push_back(std::make_pair(it.first, solver->add_var(register_name(it.second))));
+            }
+            solver->add_constraint(ls, fc.m_kind, fc.m_right_side);
+        }
+
+        void fill_lar_solver(lar_solver * solver) {
+            for (formula_constraint & fc : m_constraints)
+                add_constraint_to_solver(solver, fc);
+        }
+
+
+        lar_solver * create_lar_solver() {
+            lar_solver * ls = new lar_solver();
+            fill_lar_solver(ls);
+            return ls;
+        }
+    };
+}

src/test/test_file_reader.h

@@ -0,0 +1,73 @@
+/*
+Copyright (c) 2013 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Author: Lev Nachmanson
+*/
+#pragma once
+
+// reads a text file
+#include <string>
+#include <vector>
+#include <unordered_map>
+#include <iostream>
+#include <fstream>
+#include "util/lp/lp_utils.h"
+#include "util/lp/lp_solver.h"
+
+namespace lean {
+
+template <typename T>
+struct test_result {
+    lp_status m_status;
+    T m_cost;
+    std::unordered_map<std::string, T> column_values;
+};
+
+template <typename T>
+class test_file_reader {
+    struct raw_blob {
+        std::vector<std::string> m_unparsed_strings;
+        std::vector<raw_blob> m_blobs;
+    };
+
+    struct test_file_blob {
+        std::string m_name;
+        std::string m_content;
+        std::unordered_map<std::string, std::string> m_table;
+        std::unordered_map<std::string, test_file_blob> m_blobs;
+
+        test_result<T> * get_test_result() {
+            test_result<T> * tr = new test_result<T>();
+            throw "not impl";
+            return tr;
+        }
+    };
+    std::ifstream m_file_stream;
+public:
+    // constructor
+    test_file_reader(std::string file_name) :  m_file_stream(file_name) {
+        if (!m_file_stream.is_open()) {
+            std::cout << "cannot open file " << "\'" << file_name << "\'" << std::endl;
+        }
+    }
+
+    raw_blob scan_to_row_blob() {
+    }
+
+    test_file_blob scan_row_blob_to_test_file_blob(raw_blob /* rblob */) {
+    }
+
+    test_result<T> * get_test_result() {
+        if (!m_file_stream.is_open()) {
+            return nullptr;
+        }
+
+        raw_blob rblob = scan_to_row_blob();
+
+        test_file_blob tblob = scan_row_blob_to_test_file_blob(rblob);
+
+        return tblob.get_test_result();
+    }
+};
+}

src/util/hash.cpp

@@ -83,8 +83,8 @@ unsigned string_hash(const char * str, unsigned length, unsigned init_value) {
         Z3_fallthrough;
     case 1 : 
         a+=str[0];
-        Z3_fallthrough;
         /* case 0: nothing left to add */
+        break;
     }
     mix(a,b,c);
     /*-------------------------------------------- report the result */

src/util/lp/binary_heap_priority_queue.h

@@ -0,0 +1,70 @@
+
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#pragma once
+#include "util/vector.h"
+#include "util/debug.h"
+#include "util/lp/lp_utils.h"
+namespace lean {
+// the elements with the smallest priority are dequeued first
+template <typename T>
+class binary_heap_priority_queue {
+    vector<T> m_priorities;
+
+    // indexing for A starts from 1
+    vector<unsigned> m_heap; // keeps the elements of the queue
+    vector<int> m_heap_inverse; // o = m_heap[m_heap_inverse[o]]
+    unsigned m_heap_size;
+    // is is the child place in heap
+    void swap_with_parent(unsigned i);
+    void put_at(unsigned i, unsigned h);
+    void decrease_priority(unsigned o, T newPriority);
+public:
+#ifdef LEAN_DEBUG
+    bool is_consistent() const;
+#endif
+public:
+    void remove(unsigned o);
+    unsigned size() const { return m_heap_size; }
+    binary_heap_priority_queue(): m_heap(1), m_heap_size(0) {} // the empty constructror
+    // n is the initial queue capacity.
+    // The capacity will be enlarged two times automatically if needed
+    binary_heap_priority_queue(unsigned n);
+
+    void clear() {
+        for (unsigned i = 0; i < m_heap_size; i++) {
+            unsigned o = m_heap[i+1];
+            m_heap_inverse[o] = -1;
+        }
+        m_heap_size = 0;
+    }
+
+    void resize(unsigned n);
+    void put_to_heap(unsigned i, unsigned o);
+
+    void enqueue_new(unsigned o, const T& priority);
+
+    // This method can work with an element that is already in the queue.
+    // In this case the priority will be changed and the queue adjusted.
+    void enqueue(unsigned o, const T & priority);
+    void change_priority_for_existing(unsigned o, const T & priority);
+    T get_priority(unsigned o) const { return m_priorities[o]; }
+    bool is_empty() const { return m_heap_size == 0; }
+
+    /// return the first element of the queue and removes it from the queue
+    unsigned dequeue_and_get_priority(T & priority);
+    void fix_heap_under(unsigned i);
+    void put_the_last_at_the_top_and_fix_the_heap();
+    /// return the first element of the queue and removes it from the queue
+    unsigned dequeue();
+    unsigned peek() const {
+        lean_assert(m_heap_size > 0);
+        return m_heap[1];
+    }
+#ifdef LEAN_DEBUG
+    void print(std::ostream & out);
+#endif
+};
+}

src/util/lp/binary_heap_priority_queue.hpp

@@ -0,0 +1,194 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#include "util/vector.h"
+#include "util/lp/binary_heap_priority_queue.h"
+namespace lean {
+// is is the child place in heap
+template <typename T> void binary_heap_priority_queue<T>::swap_with_parent(unsigned i) {
+    unsigned parent = m_heap[i >> 1];
+    put_at(i >> 1, m_heap[i]);
+    put_at(i, parent);
+}
+
+template <typename T> void binary_heap_priority_queue<T>::put_at(unsigned i, unsigned h) {
+    m_heap[i] = h;
+    m_heap_inverse[h] = i;
+}
+
+template <typename T> void binary_heap_priority_queue<T>::decrease_priority(unsigned o, T newPriority) {
+    m_priorities[o] = newPriority;
+    int i = m_heap_inverse[o];
+    while (i > 1) {
+        if (m_priorities[m_heap[i]] < m_priorities[m_heap[i >> 1]])
+            swap_with_parent(i);
+        else
+            break;
+        i >>= 1;
+    }
+}
+
+#ifdef LEAN_DEBUG
+template <typename T> bool binary_heap_priority_queue<T>::is_consistent() const {
+    for (int i = 0; i < m_heap_inverse.size(); i++) {
+        int i_index = m_heap_inverse[i];
+        lean_assert(i_index <= static_cast<int>(m_heap_size));
+        lean_assert(i_index == -1 || m_heap[i_index] == i);
+    }
+    for (unsigned i = 1; i < m_heap_size; i++) {
+        unsigned ch = i << 1;
+        for (int k = 0; k < 2; k++) {
+            if (ch > m_heap_size) break;
+            if (!(m_priorities[m_heap[i]] <= m_priorities[m_heap[ch]])){
+                return false;
+            }
+            ch++;
+        }
+    }
+    return true;
+}
+#endif
+template <typename T> void binary_heap_priority_queue<T>::remove(unsigned o) {
+    T priority_of_o = m_priorities[o];
+    int o_in_heap = m_heap_inverse[o];
+    if (o_in_heap == -1)  {
+        return;  // nothing to do
+    }
+    lean_assert(static_cast<unsigned>(o_in_heap) <= m_heap_size);
+    if (static_cast<unsigned>(o_in_heap) < m_heap_size) {
+        put_at(o_in_heap, m_heap[m_heap_size--]);
+        if (m_priorities[m_heap[o_in_heap]] > priority_of_o) {
+            fix_heap_under(o_in_heap);
+        } else { // we need to propogate the m_heap[o_in_heap] up
+            unsigned i = o_in_heap;
+            while (i > 1) {
+                unsigned ip = i >> 1;
+                if (m_priorities[m_heap[i]] < m_priorities[m_heap[ip]])
+                    swap_with_parent(i);
+                else
+                    break;
+                i = ip;
+            }
+        }
+    } else {
+        lean_assert(static_cast<unsigned>(o_in_heap) == m_heap_size);
+        m_heap_size--;
+    }
+    m_heap_inverse[o] = -1;
+    // lean_assert(is_consistent());
+}
+// n is the initial queue capacity.
+// The capacity will be enlarged two times automatically if needed
+template <typename T> binary_heap_priority_queue<T>::binary_heap_priority_queue(unsigned n) :
+    m_priorities(n),
+    m_heap(n + 1), // because the indexing for A starts from 1
+    m_heap_inverse(n, -1),
+    m_heap_size(0)
+{ }
+
+
+template <typename T> void binary_heap_priority_queue<T>::resize(unsigned n) {
+    m_priorities.resize(n);
+    m_heap.resize(n + 1);
+    m_heap_inverse.resize(n, -1);
+}
+
+template <typename T> void binary_heap_priority_queue<T>::put_to_heap(unsigned i, unsigned o) {
+    m_heap[i] = o;
+    m_heap_inverse[o] = i;
+}
+
+template <typename T> void binary_heap_priority_queue<T>::enqueue_new(unsigned o, const T& priority) {
+    m_heap_size++;
+    int i = m_heap_size;
+    lean_assert(o < m_priorities.size());
+    m_priorities[o] = priority;
+    put_at(i, o);
+    while (i > 1 && m_priorities[m_heap[i >> 1]] > priority) {
+        swap_with_parent(i);
+        i >>= 1;
+    }
+}
+// This method can work with an element that is already in the queue.
+// In this case the priority will be changed and the queue adjusted.
+template <typename T> void binary_heap_priority_queue<T>::enqueue(unsigned o, const T & priority) {
+    if (o >= m_priorities.size()) {
+        resize(o << 1); // make the size twice larger
+    }
+    if (m_heap_inverse[o] == -1)
+        enqueue_new(o, priority);
+    else
+        change_priority_for_existing(o, priority);
+}
+
+template <typename T> void binary_heap_priority_queue<T>::change_priority_for_existing(unsigned o, const T & priority) {
+    if (m_priorities[o] > priority) {
+        decrease_priority(o, priority);
+    } else {
+        m_priorities[o] = priority;
+        fix_heap_under(m_heap_inverse[o]);
+    }
+}
+
+
+/// return the first element of the queue and removes it from the queue
+template <typename T> unsigned binary_heap_priority_queue<T>::dequeue_and_get_priority(T & priority) {
+    lean_assert(m_heap_size != 0);
+    int ret = m_heap[1];
+    priority = m_priorities[ret];
+    put_the_last_at_the_top_and_fix_the_heap();
+    return ret;
+}
+
+template <typename T> void binary_heap_priority_queue<T>::fix_heap_under(unsigned i) {
+    while (true) {
+        unsigned smallest = i;
+        unsigned l = i << 1;
+        if (l <= m_heap_size && m_priorities[m_heap[l]] < m_priorities[m_heap[i]])
+            smallest = l;
+        unsigned r = l + 1;
+        if (r <= m_heap_size && m_priorities[m_heap[r]] < m_priorities[m_heap[smallest]])
+            smallest = r;
+        if (smallest != i)
+            swap_with_parent(smallest);
+        else
+            break;
+        i = smallest;
+    }
+}
+
+template <typename T> void binary_heap_priority_queue<T>::put_the_last_at_the_top_and_fix_the_heap() {
+    if (m_heap_size > 1) {
+        put_at(1, m_heap[m_heap_size--]);
+        fix_heap_under(1);
+    } else {
+        m_heap_size--;
+    }
+}
+/// return the first element of the queue and removes it from the queue
+template <typename T> unsigned binary_heap_priority_queue<T>::dequeue() {
+    lean_assert(m_heap_size > 0);
+    int ret = m_heap[1];
+    put_the_last_at_the_top_and_fix_the_heap();
+    m_heap_inverse[ret] = -1;
+    return ret;
+}
+#ifdef LEAN_DEBUG
+template <typename T> void binary_heap_priority_queue<T>::print(std::ostream & out) {
+    vector<int> index;
+    vector<T> prs;
+    while (size()) {
+        T prior;
+        int j = dequeue_and_get_priority(prior);
+        index.push_back(j);
+        prs.push_back(prior);
+        out << "(" << j << ", " << prior << ")";
+    }
+    out << std::endl;
+    // restore the queue
+    for (int i = 0; i < index.size(); i++)
+        enqueue(index[i], prs[i]);
+}
+#endif
+}

src/util/lp/binary_heap_priority_queue_instances.cpp

@@ -0,0 +1,26 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#include "util/lp/numeric_pair.h"
+#include "util/lp/binary_heap_priority_queue.hpp"
+namespace lean {
+template binary_heap_priority_queue<int>::binary_heap_priority_queue(unsigned int);
+template unsigned binary_heap_priority_queue<int>::dequeue();
+template void binary_heap_priority_queue<int>::enqueue(unsigned int, int const&);
+template void binary_heap_priority_queue<double>::enqueue(unsigned int, double const&);
+template void binary_heap_priority_queue<mpq>::enqueue(unsigned int, mpq const&);
+template void binary_heap_priority_queue<int>::remove(unsigned int);
+template unsigned binary_heap_priority_queue<numeric_pair<mpq> >::dequeue();
+template unsigned binary_heap_priority_queue<double>::dequeue();
+template unsigned binary_heap_priority_queue<mpq>::dequeue();
+template void binary_heap_priority_queue<numeric_pair<mpq> >::enqueue(unsigned int, numeric_pair<mpq> const&);
+template void binary_heap_priority_queue<numeric_pair<mpq> >::resize(unsigned int);
+template void lean::binary_heap_priority_queue<double>::resize(unsigned int);
+template binary_heap_priority_queue<unsigned int>::binary_heap_priority_queue(unsigned int);
+template void binary_heap_priority_queue<unsigned>::resize(unsigned int);
+template unsigned binary_heap_priority_queue<unsigned int>::dequeue();
+template void binary_heap_priority_queue<unsigned int>::enqueue(unsigned int, unsigned int const&);
+template void binary_heap_priority_queue<unsigned int>::remove(unsigned int);
+template void lean::binary_heap_priority_queue<mpq>::resize(unsigned int);
+}

src/util/lp/binary_heap_upair_queue.h

@@ -0,0 +1,50 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+
+#pragma once
+#include <unordered_set>
+#include <unordered_map>
+#include <queue>
+#include "util/vector.h"
+#include <set>
+#include <utility>
+#include "util/lp/binary_heap_priority_queue.h"
+
+
+typedef std::pair<unsigned, unsigned> upair;
+
+namespace lean {
+template <typename  T>
+class binary_heap_upair_queue {
+    binary_heap_priority_queue<T> m_q;
+    std::unordered_map<upair, unsigned> m_pairs_to_index;
+    svector<upair> m_pairs; // inverse to index
+    svector<unsigned> m_available_spots;
+public:
+    binary_heap_upair_queue(unsigned size);
+
+    unsigned dequeue_available_spot();
+    bool is_empty() const { return m_q.is_empty(); }
+
+    unsigned size() const {return m_q.size(); }
+
+    bool contains(unsigned i, unsigned j) const { return m_pairs_to_index.find(std::make_pair(i, j)) != m_pairs_to_index.end();
+    }
+
+    void remove(unsigned i, unsigned j);
+    bool ij_index_is_new(unsigned ij_index) const;
+    void enqueue(unsigned i, unsigned j, const T & priority);
+    void dequeue(unsigned & i, unsigned &j);
+    T get_priority(unsigned i, unsigned j) const;
+#ifdef LEAN_DEBUG
+    bool pair_to_index_is_a_bijection() const;
+    bool available_spots_are_correct() const;
+    bool is_correct() const {
+        return m_q.is_consistent() && pair_to_index_is_a_bijection() && available_spots_are_correct();
+    }
+#endif
+    void resize(unsigned size) { m_q.resize(size); }
+};
+}

src/util/lp/binary_heap_upair_queue.hpp

@@ -0,0 +1,110 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+
+#include <set>
+#include "util/lp/lp_utils.h"
+#include "util/lp/binary_heap_upair_queue.h"
+namespace lean {
+template <typename T> binary_heap_upair_queue<T>::binary_heap_upair_queue(unsigned size) : m_q(size), m_pairs(size) {
+    for (unsigned i = 0; i < size; i++)
+        m_available_spots.push_back(i);
+}
+
+template <typename T> unsigned
+binary_heap_upair_queue<T>::dequeue_available_spot() {
+    lean_assert(m_available_spots.empty() == false);
+    unsigned ret = m_available_spots.back();
+    m_available_spots.pop_back();
+    return ret;
+}
+
+template <typename T> void binary_heap_upair_queue<T>::remove(unsigned i, unsigned j) {
+    upair p(i, j);
+    auto it = m_pairs_to_index.find(p);
+    if (it == m_pairs_to_index.end())
+        return; // nothing to do
+    m_q.remove(it->second);
+    m_available_spots.push_back(it->second);
+    m_pairs_to_index.erase(it);
+}
+
+
+template <typename T> bool binary_heap_upair_queue<T>::ij_index_is_new(unsigned ij_index) const {
+    for (auto it : m_pairs_to_index) {
+        if (it.second == ij_index)
+            return false;
+    }
+    return true;
+}
+
+template <typename T> void binary_heap_upair_queue<T>::enqueue(unsigned i, unsigned j, const T & priority) {
+    upair p(i, j);
+    auto it = m_pairs_to_index.find(p);
+    unsigned ij_index;
+    if (it == m_pairs_to_index.end()) {
+        // it is a new pair, let us find a spot for it
+        if (m_available_spots.empty()) {
+            // we ran out of empty spots
+            unsigned size_was = static_cast<unsigned>(m_pairs.size());
+            unsigned new_size = size_was << 1;
+            for (unsigned i = size_was; i < new_size; i++)
+                m_available_spots.push_back(i);
+            m_pairs.resize(new_size);
+        }
+        ij_index = dequeue_available_spot();
+        // lean_assert(ij_index<m_pairs.size() && ij_index_is_new(ij_index));
+        m_pairs[ij_index] = p;
+        m_pairs_to_index[p] = ij_index;
+    } else {
+        ij_index = it->second;
+    }
+    m_q.enqueue(ij_index, priority);
+}
+
+template <typename T> void binary_heap_upair_queue<T>::dequeue(unsigned & i, unsigned &j) {
+    lean_assert(!m_q.is_empty());
+    unsigned ij_index = m_q.dequeue();
+    upair & p = m_pairs[ij_index];
+    i = p.first;
+    j = p.second;
+    m_available_spots.push_back(ij_index);
+    m_pairs_to_index.erase(p);
+}
+
+
+template <typename T> T binary_heap_upair_queue<T>::get_priority(unsigned i, unsigned j) const {
+    auto it =  m_pairs_to_index.find(std::make_pair(i, j));
+    if (it == m_pairs_to_index.end())
+        return T(0xFFFFFF); // big number
+    return m_q.get_priority(it->second);
+}
+
+#ifdef LEAN_DEBUG
+template <typename T> bool binary_heap_upair_queue<T>::pair_to_index_is_a_bijection() const {
+    std::set<int> tmp;
+    for (auto p : m_pairs_to_index) {
+        unsigned j = p.second;
+        unsigned size = tmp.size();
+        tmp.insert(j);
+        if (tmp.size() == size)
+            return false;
+    }
+    return true;
+}
+
+template <typename T> bool binary_heap_upair_queue<T>::available_spots_are_correct() const {
+    std::set<int> tmp;
+    for (auto p : m_available_spots){
+        tmp.insert(p);
+    }
+    if (tmp.size() != m_available_spots.size())
+        return false;
+    for (auto it : m_pairs_to_index)
+        if (tmp.find(it.second) != tmp.end())
+            return false;
+    return true;
+}
+#endif
+}

src/util/lp/binary_heap_upair_queue_instances.cpp

@@ -0,0 +1,17 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#include "util/lp/binary_heap_upair_queue.hpp"
+namespace lean {
+template binary_heap_upair_queue<int>::binary_heap_upair_queue(unsigned int);
+template binary_heap_upair_queue<unsigned int>::binary_heap_upair_queue(unsigned int);
+template unsigned binary_heap_upair_queue<int>::dequeue_available_spot();
+template unsigned binary_heap_upair_queue<unsigned int>::dequeue_available_spot();
+template void binary_heap_upair_queue<int>::enqueue(unsigned int, unsigned int, int const&);
+template void binary_heap_upair_queue<int>::remove(unsigned int, unsigned int);
+template void binary_heap_upair_queue<unsigned int>::remove(unsigned int, unsigned int);
+template void binary_heap_upair_queue<int>::dequeue(unsigned int&, unsigned int&);
+template void binary_heap_upair_queue<unsigned int>::enqueue(unsigned int, unsigned int, unsigned int const&);
+template void binary_heap_upair_queue<unsigned int>::dequeue(unsigned int&, unsigned int&);
+}

src/util/lp/bound_analyzer_on_row.h

@@ -0,0 +1,335 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#pragma once
+#include "util/vector.h"
+#include "util/lp/linear_combination_iterator.h"
+#include "implied_bound.h"
+#include "test_bound_analyzer.h"
+#include <functional>
+#include "util/lp/bound_propagator.h"
+// We have an equality : sum by j of row[j]*x[j] = rs
+// We try to pin a var by pushing the total by using the variable bounds
+// In a loop we drive the partial sum down, denoting the variables of this process by _u.
+// In the same loop trying to pin variables by pushing the partial sum up, denoting the variable related to it by _l
+namespace lean {
+
+class bound_analyzer_on_row {
+    
+    linear_combination_iterator<mpq> & m_it;
+    bound_propagator &                 m_bp;
+    unsigned           m_row_or_term_index;
+    int                m_column_of_u; // index of an unlimited from above monoid
+                               // -1 means that such a value is not found, -2 means that at least two of such monoids were found
+    int                m_column_of_l; // index of an unlimited from below monoid
+    impq               m_rs;
+
+public :
+    // constructor
+    bound_analyzer_on_row(
+                          linear_combination_iterator<mpq> &it,
+                          const numeric_pair<mpq>& rs,
+                          unsigned row_or_term_index,
+                          bound_propagator & bp
+                          )
+        :
+        m_it(it),
+        m_bp(bp),
+        m_row_or_term_index(row_or_term_index),
+        m_column_of_u(-1),
+        m_column_of_l(-1),
+        m_rs(rs)
+    {}
+
+
+    unsigned j;
+    void analyze() {
+        
+        mpq a; unsigned j;
+        while (((m_column_of_l != -2) || (m_column_of_u != -2)) && m_it.next(a, j))
+            analyze_bound_on_var_on_coeff(j, a);
+
+        if (m_column_of_u >= 0)
+            limit_monoid_u_from_below();
+        else if (m_column_of_u == -1)
+            limit_all_monoids_from_below();
+
+        if (m_column_of_l >= 0)
+            limit_monoid_l_from_above();
+        else if (m_column_of_l == -1)
+            limit_all_monoids_from_above();
+    }
+
+    bool bound_is_available(unsigned j, bool low_bound) {
+        return (low_bound && low_bound_is_available(j)) ||
+            (!low_bound && upper_bound_is_available(j));
+    }
+
+    bool upper_bound_is_available(unsigned j) const {
+        switch (m_bp.get_column_type(j))
+        {
+        case column_type::fixed:
+        case column_type::boxed:
+        case column_type::upper_bound:
+            return true;
+        default:
+            return false;
+        }
+    }
+
+    bool low_bound_is_available(unsigned j) const {
+        switch (m_bp.get_column_type(j))
+        {
+        case column_type::fixed:
+        case column_type::boxed:
+        case column_type::low_bound:
+            return true;
+        default:
+            return false;
+        }
+    }
+
+    const impq & ub(unsigned j) const {
+        lean_assert(upper_bound_is_available(j));
+        return m_bp.get_upper_bound(j);
+    }
+    const impq & lb(unsigned j) const {
+        lean_assert(low_bound_is_available(j));
+        return m_bp.get_low_bound(j);
+    }
+
+
+    const mpq & monoid_max_no_mult(bool a_is_pos, unsigned j, bool & strict) const {
+        if (a_is_pos) {
+            strict = !is_zero(ub(j).y);
+            return ub(j).x;
+        }
+        strict = !is_zero(lb(j).y);
+        return lb(j).x;
+    }
+    mpq monoid_max(const mpq & a, unsigned j) const {
+        if (is_pos(a)) {
+            return a * ub(j).x;
+        }
+        return a * lb(j).x;
+    }
+	mpq monoid_max(const mpq & a, unsigned j, bool & strict) const {
+		if (is_pos(a)) {
+			strict = !is_zero(ub(j).y);
+			return a * ub(j).x;
+		}
+		strict = !is_zero(lb(j).y);
+		return a * lb(j).x;
+	}
+	const mpq & monoid_min_no_mult(bool a_is_pos, unsigned j, bool & strict) const {
+		if (!a_is_pos) {
+			strict = !is_zero(ub(j).y);
+			return ub(j).x;
+		}
+		strict = !is_zero(lb(j).y);
+		return lb(j).x;
+	}
+
+    mpq monoid_min(const mpq & a, unsigned j, bool& strict) const {
+        if (is_neg(a)) {
+            strict = !is_zero(ub(j).y);
+            return a * ub(j).x;
+        }
+        
+        strict = !is_zero(lb(j).y);
+        return a * lb(j).x;
+    }
+
+    mpq monoid_min(const mpq & a, unsigned j) const {
+        if (is_neg(a)) {
+            return a * ub(j).x;
+        }
+        
+        return a * lb(j).x;
+    }
+    
+
+    void limit_all_monoids_from_above() {
+        int strict = 0;
+        mpq total;
+        lean_assert(is_zero(total));
+        m_it.reset();
+        mpq a; unsigned j;
+        while (m_it.next(a, j)) {
+            bool str;
+            total -= monoid_min(a, j, str);
+            if (str)
+                strict++;
+        }
+
+        m_it.reset();
+        while (m_it.next(a, j)) {
+            bool str;
+			bool a_is_pos = is_pos(a);
+            mpq bound = total / a + monoid_min_no_mult(a_is_pos, j, str);
+            if (a_is_pos) {
+                limit_j(j, bound, true, false, strict - static_cast<int>(str) > 0);
+            }
+            else {
+                limit_j(j, bound, false, true, strict - static_cast<int>(str) > 0);
+            }
+        }
+    }
+
+    void limit_all_monoids_from_below() {
+        int strict = 0;
+        mpq total;
+        lean_assert(is_zero(total));
+        m_it.reset();
+        mpq a; unsigned j;
+        while (m_it.next(a, j)) {
+            bool str;
+            total -= monoid_max(a, j, str);
+            if (str)
+                strict++;
+        }
+        m_it.reset();
+        while (m_it.next(a, j)) {
+            bool str;
+			bool a_is_pos = is_pos(a);
+			mpq bound = total / a + monoid_max_no_mult(a_is_pos, j, str);
+            bool astrict = strict - static_cast<int>(str) > 0; 
+            if (a_is_pos) {
+                limit_j(j, bound, true, true, astrict);
+            }
+            else {
+                limit_j(j, bound, false, false, astrict);
+            }
+        }
+    }
+
+    
+    void limit_monoid_u_from_below() {
+        // we are going to limit from below the monoid m_column_of_u,
+        // every other monoid is impossible to limit from below
+        mpq u_coeff, a;
+        unsigned j;
+        mpq bound = -m_rs.x;
+        m_it.reset();
+        bool strict = false;
+        while (m_it.next(a, j)) {
+            if (j == static_cast<unsigned>(m_column_of_u)) {
+                u_coeff = a;
+                continue;
+            }
+            bool str;
+            bound -= monoid_max(a, j, str);
+            if (str)
+                strict = true;
+        }
+
+        bound /= u_coeff;
+        
+        if (numeric_traits<impq>::is_pos(u_coeff)) {
+            limit_j(m_column_of_u, bound, true, true, strict);
+        } else {
+            limit_j(m_column_of_u, bound, false, false, strict);
+        }
+    }
+
+
+    void limit_monoid_l_from_above() {
+        // we are going to limit from above the monoid m_column_of_l,
+        // every other monoid is impossible to limit from above
+        mpq l_coeff, a;
+        unsigned j;
+        mpq bound = -m_rs.x;
+        bool strict = false;
+        m_it.reset();
+        while (m_it.next(a, j)) {
+            if (j == static_cast<unsigned>(m_column_of_l)) {
+                l_coeff = a;
+                continue;
+            }
+
+            bool str;
+            bound -= monoid_min(a, j, str);
+            if (str)
+                strict = true;
+        }
+        bound /= l_coeff;
+        if (is_pos(l_coeff)) {
+            limit_j(m_column_of_l, bound, true, false, strict);
+        } else {
+            limit_j(m_column_of_l, bound, false, true, strict);
+        }
+    }
+    
+    // // it is the coefficent before the bounded column
+    // void provide_evidence(bool coeff_is_pos) {
+    //     /*
+    //     auto & be = m_ibounds.back();
+    //     bool low_bound = be.m_low_bound;
+    //     if (!coeff_is_pos)
+    //         low_bound = !low_bound;
+    //     auto it = m_it.clone();
+    //     mpq a; unsigned j;
+    //     while (it->next(a, j)) {
+    //         if (be.m_j == j) continue;
+    //         lean_assert(bound_is_available(j, is_neg(a) ? low_bound : !low_bound));
+    //         be.m_vector_of_bound_signatures.emplace_back(a, j, numeric_traits<impq>::
+    //                                                      is_neg(a)? low_bound: !low_bound);
+    //     }
+    //     delete it;
+    //     */
+    // }
+
+    void limit_j(unsigned j, const mpq& u, bool coeff_before_j_is_pos, bool is_low_bound, bool strict){
+        m_bp.try_add_bound(u, j, is_low_bound, coeff_before_j_is_pos, m_row_or_term_index, strict);
+    }
+
+    
+    void advance_u(unsigned j) {
+        if (m_column_of_u == -1)
+            m_column_of_u = j;
+        else
+            m_column_of_u = -2;
+    }
+    
+    void advance_l(unsigned j) {
+        if (m_column_of_l == -1)
+            m_column_of_l = j;
+        else
+            m_column_of_l = -2;
+    }
+    
+    void analyze_bound_on_var_on_coeff(int j, const mpq &a) {
+        switch (m_bp.get_column_type(j)) {
+        case column_type::low_bound:
+            if (numeric_traits<mpq>::is_pos(a))
+                advance_u(j);
+            else 
+                advance_l(j);
+            break;
+        case column_type::upper_bound:
+            if(numeric_traits<mpq>::is_neg(a))
+                advance_u(j);
+            else
+                advance_l(j);
+            break;
+        case column_type::free_column:
+            advance_u(j);
+            advance_l(j);
+            break;
+        default:
+            break;
+        }
+    }
+
+    static void analyze_row(linear_combination_iterator<mpq> &it,
+                            const numeric_pair<mpq>& rs,
+                            unsigned row_or_term_index,
+                            bound_propagator & bp
+                            ) {
+        bound_analyzer_on_row a(it, rs, row_or_term_index, bp);
+        a.analyze();
+    }
+
+};
+}

src/util/lp/bound_propagator.cpp

@@ -0,0 +1,47 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#include "util/lp/lar_solver.h"
+namespace lean {
+bound_propagator::bound_propagator(lar_solver & ls):
+    m_lar_solver(ls) {}
+column_type bound_propagator::get_column_type(unsigned j) const {
+    return m_lar_solver.m_mpq_lar_core_solver.m_column_types()[j];
+}
+const impq & bound_propagator::get_low_bound(unsigned j) const {
+    return m_lar_solver.m_mpq_lar_core_solver.m_r_low_bounds()[j];
+}
+const impq & bound_propagator::get_upper_bound(unsigned j) const {
+    return m_lar_solver.m_mpq_lar_core_solver.m_r_upper_bounds()[j];
+}
+void bound_propagator::try_add_bound(const mpq & v, unsigned j, bool is_low, bool coeff_before_j_is_pos, unsigned row_or_term_index, bool strict) {
+    j = m_lar_solver.adjust_column_index_to_term_index(j);
+    lconstraint_kind kind = is_low? GE : LE;
+    if (strict)
+        kind = static_cast<lconstraint_kind>(kind / 2);
+    
+    if (!bound_is_interesting(j, kind, v))
+        return;
+     unsigned k; // index to ibounds
+     if (is_low) {
+         if (try_get_val(m_improved_low_bounds, j, k)) {
+             auto & found_bound = m_ibounds[k];
+             if (v > found_bound.m_bound || (v == found_bound.m_bound && found_bound.m_strict == false && strict))
+                 found_bound = implied_bound(v, j, is_low, coeff_before_j_is_pos, row_or_term_index, strict);
+         } else {
+             m_improved_low_bounds[j] = m_ibounds.size();
+             m_ibounds.push_back(implied_bound(v, j, is_low, coeff_before_j_is_pos, row_or_term_index, strict));
+         }
+     } else { // the upper bound case
+         if (try_get_val(m_improved_upper_bounds, j, k)) {
+             auto & found_bound = m_ibounds[k];
+             if (v < found_bound.m_bound || (v == found_bound.m_bound && found_bound.m_strict == false && strict))
+                 found_bound = implied_bound(v, j, is_low, coeff_before_j_is_pos, row_or_term_index, strict);
+         } else {
+             m_improved_upper_bounds[j] = m_ibounds.size();
+             m_ibounds.push_back(implied_bound(v, j, is_low, coeff_before_j_is_pos, row_or_term_index, strict));
+        }
+     }
+}
+}

src/util/lp/bound_propagator.h

@@ -0,0 +1,27 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#pragma once
+#include "util/lp/lp_settings.h"
+namespace lean {
+class lar_solver;
+class bound_propagator {
+    std::unordered_map<unsigned, unsigned> m_improved_low_bounds; // these maps map a column index to the corresponding index in ibounds
+    std::unordered_map<unsigned, unsigned> m_improved_upper_bounds;
+    lar_solver & m_lar_solver;
+public:
+    vector<implied_bound> m_ibounds;
+public:
+    bound_propagator(lar_solver & ls);
+    column_type get_column_type(unsigned) const;
+    const impq & get_low_bound(unsigned) const;
+    const impq & get_upper_bound(unsigned) const;
+    void try_add_bound(const mpq & v, unsigned j, bool is_low, bool coeff_before_j_is_pos, unsigned row_or_term_index, bool strict);
+    virtual bool bound_is_interesting(unsigned vi,
+                                      lean::lconstraint_kind kind,
+                                      const rational & bval) {return true;}
+    unsigned number_of_found_bounds() const { return m_ibounds.size(); }
+    virtual void consume(mpq const& v, unsigned j) { std::cout << "doh\n"; }
+};
+}

src/util/lp/breakpoint.h

@@ -0,0 +1,20 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+
+#pragma once
+
+namespace lean {
+enum breakpoint_type {
+    low_break, upper_break, fixed_break
+};
+template <typename X>
+struct breakpoint {
+    unsigned m_j; // the basic column
+    breakpoint_type m_type;
+    X m_delta;
+    breakpoint(){}
+    breakpoint(unsigned j, X delta, breakpoint_type type):m_j(j), m_type(type), m_delta(delta) {}
+};
+}

src/util/lp/column_info.h

@@ -0,0 +1,250 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+
+#pragma once
+#include "util/vector.h"
+#include <unordered_map>
+#include <string>
+#include <algorithm>
+#include "util/lp/lp_settings.h"
+namespace lean {
+inline bool is_valid(unsigned j) { return static_cast<int>(j) >= 0;}
+
+template <typename T>
+class column_info {
+    std::string m_name;
+    bool        m_low_bound_is_set;
+    bool        m_low_bound_is_strict;
+    bool        m_upper_bound_is_set;
+    bool        m_upper_bound_is_strict;
+    T           m_low_bound;
+    T           m_upper_bound;
+    T           m_fixed_value;
+    bool        m_is_fixed;
+    T           m_cost;
+    unsigned    m_column_index;
+public:
+    bool operator==(const column_info & c) const {
+        return m_name == c.m_name &&
+            m_low_bound_is_set == c.m_low_bound_is_set &&
+            m_low_bound_is_strict == c.m_low_bound_is_strict &&
+            m_upper_bound_is_set == c.m_upper_bound_is_set&&
+            m_upper_bound_is_strict == c.m_upper_bound_is_strict&&
+            (!m_low_bound_is_set || m_low_bound == c.m_low_bound) &&
+            (!m_upper_bound_is_set || m_upper_bound == c.m_upper_bound) &&
+            m_cost == c.m_cost &&
+            m_is_fixed == c.m_is_fixed &&
+            (!m_is_fixed || m_fixed_value == c.m_fixed_value) &&
+            m_column_index == c.m_column_index;
+    }
+    bool operator!=(const column_info & c) const { return !((*this) == c); }
+    void set_column_index(unsigned j) {
+        m_column_index = j;
+    }
+    // the default constructor
+    column_info():
+        m_low_bound_is_set(false),
+        m_low_bound_is_strict(false),
+        m_upper_bound_is_set (false),
+        m_upper_bound_is_strict (false),
+        m_is_fixed(false),
+        m_cost(numeric_traits<T>::zero()),
+        m_column_index(static_cast<unsigned>(-1))
+    {}
+    
+    column_info(unsigned column_index) :
+        m_low_bound_is_set(false),
+        m_low_bound_is_strict(false),
+        m_upper_bound_is_set (false),
+        m_upper_bound_is_strict (false),
+        m_is_fixed(false),
+        m_cost(numeric_traits<T>::zero()),
+        m_column_index(column_index) {
+    }
+
+    column_info(const column_info & ci) {
+        m_name = ci.m_name;
+        m_low_bound_is_set = ci.m_low_bound_is_set;
+        m_low_bound_is_strict = ci.m_low_bound_is_strict;
+        m_upper_bound_is_set = ci.m_upper_bound_is_set;
+        m_upper_bound_is_strict = ci.m_upper_bound_is_strict;
+        m_low_bound = ci.m_low_bound;
+        m_upper_bound = ci.m_upper_bound;
+        m_cost = ci.m_cost;
+        m_fixed_value = ci.m_fixed_value;
+        m_is_fixed = ci.m_is_fixed;
+        m_column_index = ci.m_column_index;
+    }
+
+    unsigned get_column_index() const {
+        return m_column_index;
+    }
+
+    column_type get_column_type() const {
+        return m_is_fixed? column_type::fixed : (m_low_bound_is_set? (m_upper_bound_is_set? column_type::boxed : column_type::low_bound) : (m_upper_bound_is_set? column_type::upper_bound: column_type::free_column));
+    }
+
+    column_type get_column_type_no_flipping() const {
+        if (m_is_fixed) {
+            return column_type::fixed;
+        }
+
+        if (m_low_bound_is_set) {
+            return m_upper_bound_is_set? column_type::boxed: column_type::low_bound;
+        }
+        // we are flipping the bounds!
+        return m_upper_bound_is_set? column_type::upper_bound
+            : column_type::free_column;
+    }
+
+    T get_low_bound() const {
+        lean_assert(m_low_bound_is_set);
+        return m_low_bound;
+    }
+    T get_upper_bound() const {
+        lean_assert(m_upper_bound_is_set);
+        return m_upper_bound;
+    }
+
+    bool low_bound_is_set() const {
+        return m_low_bound_is_set;
+    }
+
+    bool upper_bound_is_set() const {
+        return m_upper_bound_is_set;
+    }
+
+    T get_shift() {
+        if (is_fixed()) {
+            return m_fixed_value;
+        }
+        if (is_flipped()){
+            return m_upper_bound;
+        }
+        return m_low_bound_is_set? m_low_bound : numeric_traits<T>::zero();
+    }
+
+    bool is_flipped() {
+        return m_upper_bound_is_set && !m_low_bound_is_set;
+    }
+
+    bool adjusted_low_bound_is_set() {
+        return !is_flipped()? low_bound_is_set(): upper_bound_is_set();
+    }
+
+    bool adjusted_upper_bound_is_set() {
+        return !is_flipped()? upper_bound_is_set(): low_bound_is_set();
+    }
+
+    T  get_adjusted_upper_bound() {
+        return get_upper_bound() - get_low_bound();
+    }
+
+    bool is_fixed() const {
+        return m_is_fixed;
+    }
+
+    bool is_free() {
+        return !m_low_bound_is_set && !m_upper_bound_is_set;
+    }
+
+    void set_fixed_value(T v) {
+        m_is_fixed = true;
+        m_fixed_value = v;
+    }
+
+    T get_fixed_value() const {
+        lean_assert(m_is_fixed);
+        return m_fixed_value;
+    }
+
+    T get_cost() const {
+        return m_cost;
+    }
+
+    void set_cost(T const & cost) {
+        m_cost = cost;
+    }
+
+    void set_name(std::string const & s) {
+        m_name = s;
+    }
+
+    std::string get_name() const {
+        return m_name;
+    }
+
+    void set_low_bound(T const & l) {
+        m_low_bound = l;
+        m_low_bound_is_set = true;
+    }
+
+    void set_upper_bound(T const & l) {
+        m_upper_bound = l;
+        m_upper_bound_is_set = true;
+    }
+
+    void unset_low_bound() {
+        m_low_bound_is_set = false;
+    }
+
+    void unset_upper_bound() {
+        m_upper_bound_is_set = false;
+    }
+
+    void unset_fixed() {
+        m_is_fixed = false;
+    }
+
+    bool low_bound_holds(T v) {
+        return !low_bound_is_set() || v >= m_low_bound -T(0.0000001);
+    }
+
+    bool upper_bound_holds(T v) {
+        return !upper_bound_is_set() || v <= m_upper_bound + T(0.000001);
+    }
+
+    bool bounds_hold(T v) {
+        return low_bound_holds(v) && upper_bound_holds(v);
+    }
+
+    bool adjusted_bounds_hold(T v) {
+        return adjusted_low_bound_holds(v) && adjusted_upper_bound_holds(v);
+    }
+
+    bool adjusted_low_bound_holds(T v) {
+        return !adjusted_low_bound_is_set() || v >= -T(0.0000001);
+    }
+
+    bool adjusted_upper_bound_holds(T v) {
+        return !adjusted_upper_bound_is_set() || v <= get_adjusted_upper_bound() + T(0.000001);
+    }
+    bool is_infeasible() {
+        if ((!upper_bound_is_set()) || (!low_bound_is_set()))
+            return false;
+        // ok, both bounds are set
+        bool at_least_one_is_strict = upper_bound_is_strict() || low_bound_is_strict();
+        if (!at_least_one_is_strict)
+            return get_upper_bound() < get_low_bound();
+        // at least on bound is strict
+        return get_upper_bound() <= get_low_bound(); // the equality is impossible
+    }
+    bool low_bound_is_strict() const {
+        return m_low_bound_is_strict;
+    }
+
+    void set_low_bound_strict(bool val) {
+        m_low_bound_is_strict = val;
+    }
+
+    bool upper_bound_is_strict() const {
+        return m_upper_bound_is_strict;
+    }
+
+    void set_upper_bound_strict(bool val) {
+        m_upper_bound_is_strict = val;
+    }
+};
+}

src/util/lp/column_namer.h

@@ -0,0 +1,82 @@
+#pragma once
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#include <string>
+#include "util/lp/linear_combination_iterator.h"
+namespace lean {
+class column_namer {
+public:
+    virtual std::string get_column_name(unsigned j) const = 0;
+    template <typename T>
+    void print_linear_iterator(linear_combination_iterator<T>* it, std::ostream & out) const {
+        vector<std::pair<T, unsigned>> coeff;
+        T a;
+        unsigned i;
+        while (it->next(a, i)) {
+            coeff.emplace_back(a, i);
+        }
+        print_linear_combination_of_column_indices(coeff, out);
+    }
+    template <typename T>
+    void print_linear_iterator_indices_only(linear_combination_iterator<T>* it, std::ostream & out) const {
+        vector<std::pair<T, unsigned>> coeff;
+        T a;
+        unsigned i;
+        while (it->next(a, i)) {
+            coeff.emplace_back(a, i);
+        }
+        print_linear_combination_of_column_indices_only(coeff, out);
+    }
+    
+    template <typename T>
+    void print_linear_combination_of_column_indices_only(const vector<std::pair<T, unsigned>> & coeffs, std::ostream & out) const {
+        bool first = true;
+        for (const auto & it : coeffs) {
+            auto val = it.first;
+            if (first) {
+                first = false;
+            } else {
+                if (numeric_traits<T>::is_pos(val)) {
+                    out << " + ";
+                } else {
+                    out << " - ";
+                    val = -val;
+                }
+            }
+            if (val == -numeric_traits<T>::one())
+                out << " - ";
+            else if (val != numeric_traits<T>::one())
+                out << T_to_string(val);
+        
+            out << "_" << it.second;
+        }
+    }
+    
+    template <typename T>
+    void print_linear_combination_of_column_indices(const vector<std::pair<T, unsigned>> & coeffs, std::ostream & out) const {
+        bool first = true;
+        for (const auto & it : coeffs) {
+            auto val = it.first;
+            if (first) {
+                first = false;
+            } else {
+                if (numeric_traits<T>::is_pos(val)) {
+                    out << " + ";
+                } else {
+                    out << " - ";
+                    val = -val;
+                }
+            }
+            if (val == -numeric_traits<T>::one())
+                out << " - ";
+            else if (val != numeric_traits<T>::one())
+                out << val;
+        
+            out << get_column_name(it.second);
+        }
+    }
+
+};
+}

src/util/lp/conversion_helper.h

@@ -0,0 +1,43 @@
+/*
+  Copyright (c) 2013 Microsoft Corporation. All rights reserved.
+
+  Author: Lev Nachmanson
+*/
+#pragma once
+namespace lean {
+template <typename V>
+struct conversion_helper {
+    static V get_low_bound(const column_info<mpq> & ci) {
+        return V(ci.get_low_bound(), ci.low_bound_is_strict()? 1 : 0);
+    }
+
+    static V get_upper_bound(const column_info<mpq> & ci) {
+        return V(ci.get_upper_bound(), ci.upper_bound_is_strict()? -1 : 0);
+    }
+};
+
+template<>
+struct conversion_helper <double> {
+    static double get_upper_bound(const column_info<mpq> & ci) {
+        if (!ci.upper_bound_is_strict())
+            return ci.get_upper_bound().get_double();
+        double eps = 0.00001;
+        if (!ci.low_bound_is_set())
+            return ci.get_upper_bound().get_double() - eps;
+        eps = std::min((ci.get_upper_bound() - ci.get_low_bound()).get_double() / 1000, eps);
+        return ci.get_upper_bound().get_double() - eps;
+    }
+
+    static double get_low_bound(const column_info<mpq> & ci) {
+        if (!ci.low_bound_is_strict())
+            return ci.get_low_bound().get_double();
+        double eps = 0.00001;
+        if (!ci.upper_bound_is_set())
+            return ci.get_low_bound().get_double() + eps;
+        eps = std::min((ci.get_upper_bound() - ci.get_low_bound()).get_double() / 1000, eps);
+        return ci.get_low_bound().get_double() + eps;
+    }
+
+};
+
+}

src/util/lp/core_solver_pretty_printer.h

@@ -0,0 +1,117 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#pragma once
+#include <limits>
+#include <string>
+#include <algorithm>
+#include "util/vector.h"
+#include <ostream>
+#include "util/lp/lp_settings.h"
+#include "util/lp/indexed_vector.h"
+namespace lean {
+template <typename T, typename X> class lp_core_solver_base; // forward definition
+
+template <typename T, typename X>
+class core_solver_pretty_printer {
+    std::ostream & m_out;
+    typedef std::string string;
+    lp_core_solver_base<T, X> & m_core_solver;
+    vector<unsigned> m_column_widths;
+    vector<vector<string>> m_A;
+    vector<vector<string>> m_signs;
+    vector<string> m_costs;
+    vector<string> m_cost_signs;
+    vector<string> m_lows; // low bounds
+    vector<string> m_upps; // upper bounds
+    vector<string> m_lows_signs;
+    vector<string> m_upps_signs;
+    unsigned m_rs_width;
+    vector<X> m_rs;
+    unsigned m_title_width;
+    std::string m_cost_title;
+    std::string m_basis_heading_title;
+    std::string m_x_title;
+    std::string m_low_bounds_title;
+    std::string m_upp_bounds_title;
+    std::string m_exact_norm_title;
+    std::string m_approx_norm_title;
+
+
+    unsigned ncols() { return m_core_solver.m_A.column_count(); }
+    unsigned nrows() { return m_core_solver.m_A.row_count(); }
+    unsigned m_artificial_start;
+    indexed_vector<T> m_w_buff;
+    indexed_vector<T> m_ed_buff;
+    vector<T> m_exact_column_norms;
+
+public:
+    core_solver_pretty_printer(lp_core_solver_base<T, X > & core_solver, std::ostream & out);
+
+    void init_costs();
+
+    ~core_solver_pretty_printer();
+    void init_rs_width();
+
+    T current_column_norm();
+
+    void init_m_A_and_signs();
+
+    void init_column_widths();
+
+    void adjust_width_with_low_bound(unsigned column, unsigned & w);
+    void adjust_width_with_upper_bound(unsigned column, unsigned & w);
+
+    void adjust_width_with_bounds(unsigned column, unsigned & w);
+
+    void adjust_width_with_basis_heading(unsigned column, unsigned & w) {
+        w = std::max(w, (unsigned)T_to_string(m_core_solver.m_basis_heading[column]).size());
+    }
+
+    unsigned get_column_width(unsigned column);
+
+    unsigned regular_cell_width(unsigned row, unsigned column, std::string name) {
+        return regular_cell_string(row, column, name).size();
+    }
+
+    std::string regular_cell_string(unsigned row, unsigned column, std::string name);
+
+
+    void set_coeff(vector<string>& row, vector<string> & row_signs, unsigned col, const T & t, string name);
+
+    void print_x();
+
+    std::string get_low_bound_string(unsigned j);
+
+    std::string get_upp_bound_string(unsigned j);
+
+
+    void print_lows();
+
+    void print_upps();
+
+    string get_exact_column_norm_string(unsigned col) {
+        return T_to_string(m_exact_column_norms[col]);
+    }
+
+    void print_exact_norms();
+
+    void print_approx_norms();
+
+    void print();
+
+    void print_basis_heading();
+
+    void print_bottom_line() {
+        m_out << "----------------------" << std::endl;
+    }
+
+    void print_cost();
+
+    void print_given_rows(vector<string> & row, vector<string> & signs, X rst);
+
+    void print_row(unsigned i);
+
+};
+}

src/util/lp/core_solver_pretty_printer.hpp

@@ -0,0 +1,383 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#include <limits>
+#include <string>
+#include <algorithm>
+#include "util/lp/lp_utils.h"
+#include "util/lp/lp_core_solver_base.h"
+#include "util/lp/core_solver_pretty_printer.h"
+#include "util/lp/numeric_pair.h"
+namespace lean {
+
+
+template <typename T, typename X>
+core_solver_pretty_printer<T, X>::core_solver_pretty_printer(lp_core_solver_base<T, X > & core_solver, std::ostream & out):
+    m_out(out),
+    m_core_solver(core_solver),
+    m_A(core_solver.m_A.row_count(), vector<string>(core_solver.m_A.column_count(), "")),
+    m_signs(core_solver.m_A.row_count(), vector<string>(core_solver.m_A.column_count(), " ")),
+    m_costs(ncols(), ""),
+    m_cost_signs(ncols(), " "),
+    m_rs(ncols(), zero_of_type<X>()),
+    m_w_buff(core_solver.m_w),
+    m_ed_buff(core_solver.m_ed) {
+    m_low_bounds_title = "low";
+    m_upp_bounds_title = "upp";
+    m_exact_norm_title = "exact cn";
+    m_approx_norm_title = "approx cn";
+    m_artificial_start = std::numeric_limits<unsigned>::max();
+
+    m_column_widths.resize(core_solver.m_A.column_count(), 0),
+    init_m_A_and_signs();
+    init_costs();
+    init_column_widths();
+    init_rs_width();
+    m_cost_title = "costs";
+    m_basis_heading_title = "heading";
+    m_x_title = "x*";
+    m_title_width = static_cast<unsigned>(std::max(std::max(m_cost_title.size(), std::max(m_basis_heading_title.size(), m_x_title.size())), m_approx_norm_title.size()));
+}
+
+template <typename T, typename X> void core_solver_pretty_printer<T, X>::init_costs() {
+    if (!m_core_solver.use_tableau()) {
+        vector<T> local_y(m_core_solver.m_m());
+        m_core_solver.solve_yB(local_y);
+        for (unsigned i = 0; i < ncols(); i++) {
+            if (m_core_solver.m_basis_heading[i] < 0) {
+                T t = m_core_solver.m_costs[i] - m_core_solver.m_A.dot_product_with_column(local_y, i);
+                set_coeff(m_costs, m_cost_signs, i, t, m_core_solver.column_name(i));
+            }
+        }
+    } else {
+        for (unsigned i = 0; i < ncols(); i++) {
+            if (m_core_solver.m_basis_heading[i] < 0) {
+                set_coeff(m_costs, m_cost_signs, i, m_core_solver.m_d[i], m_core_solver.column_name(i));
+            }
+        }
+    }
+}
+
+template <typename T, typename X> core_solver_pretty_printer<T, X>::~core_solver_pretty_printer() {
+    m_core_solver.m_w = m_w_buff;
+    m_core_solver.m_ed = m_ed_buff;
+}
+template <typename T, typename X> void core_solver_pretty_printer<T, X>::init_rs_width() {
+    m_rs_width = static_cast<unsigned>(T_to_string(m_core_solver.get_cost()).size());
+    for (unsigned i = 0; i < nrows(); i++) {
+        unsigned wt = static_cast<unsigned>(T_to_string(m_rs[i]).size());
+        if (wt > m_rs_width) {
+            m_rs_width = wt;
+        }
+    }
+}
+
+template <typename T, typename X> T core_solver_pretty_printer<T, X>::current_column_norm() {
+    T ret = zero_of_type<T>();
+    for (auto i : m_core_solver.m_ed.m_index)
+        ret += m_core_solver.m_ed[i] * m_core_solver.m_ed[i];
+    return ret;
+}
+
+template <typename T, typename X> void core_solver_pretty_printer<T, X>::init_m_A_and_signs() { 
+    if (numeric_traits<T>::precise() && m_core_solver.m_settings.use_tableau()) {
+        for (unsigned column = 0; column < ncols(); column++) {
+            vector<T> t(nrows(), zero_of_type<T>());
+            for (const auto & c : m_core_solver.m_A.m_columns[column]){
+                t[c.m_i] = m_core_solver.m_A.get_val(c);
+            }
+                
+            string name = m_core_solver.column_name(column);
+            for (unsigned row = 0; row < nrows(); row ++) {
+                set_coeff(
+                          m_A[row],
+                          m_signs[row],
+                          column,
+                          t[row],
+                          name);
+                m_rs[row] += t[row] * m_core_solver.m_x[column];
+            }
+        }
+    } else {
+        for (unsigned column = 0; column < ncols(); column++) {
+            m_core_solver.solve_Bd(column); // puts the result into m_core_solver.m_ed
+            string name = m_core_solver.column_name(column);
+            for (unsigned row = 0; row < nrows(); row ++) {
+                set_coeff(
+                          m_A[row],
+                          m_signs[row],
+                          column,
+                          m_core_solver.m_ed[row],
+                          name);
+                m_rs[row] += m_core_solver.m_ed[row] * m_core_solver.m_x[column];
+            }
+            if (!m_core_solver.use_tableau())
+                m_exact_column_norms.push_back(current_column_norm() + T(1)); // a conversion missing 1 -> T
+        }
+    }
+}
+
+template <typename T, typename X> void core_solver_pretty_printer<T, X>::init_column_widths() {
+    for (unsigned i = 0; i < ncols(); i++) {
+        m_column_widths[i] = get_column_width(i);
+    }
+}
+
+template <typename T, typename X> void core_solver_pretty_printer<T, X>::adjust_width_with_low_bound(unsigned column, unsigned & w) {
+    if (!m_core_solver.low_bounds_are_set()) return;
+    w = std::max(w, (unsigned)T_to_string(m_core_solver.low_bound_value(column)).size());
+}
+template <typename T, typename X> void core_solver_pretty_printer<T, X>::adjust_width_with_upper_bound(unsigned column, unsigned & w) {
+    w = std::max(w, (unsigned)T_to_string(m_core_solver.upper_bound_value(column)).size());
+}
+
+template <typename T, typename X> void core_solver_pretty_printer<T, X>::adjust_width_with_bounds(unsigned column, unsigned & w) {
+    switch (m_core_solver.get_column_type(column)) {
+    case column_type::fixed:
+    case column_type::boxed:
+        adjust_width_with_low_bound(column, w);
+        adjust_width_with_upper_bound(column, w);
+        break;
+    case column_type::low_bound:
+        adjust_width_with_low_bound(column, w);
+        break;
+    case column_type::upper_bound:
+        adjust_width_with_upper_bound(column, w);
+        break;
+    case column_type::free_column:
+        break;
+    default:
+        lean_assert(false);
+        break;
+    }
+}
+
+
+template <typename T, typename X> unsigned core_solver_pretty_printer<T, X>:: get_column_width(unsigned column) {
+    unsigned w = static_cast<unsigned>(std::max((size_t)m_costs[column].size(), T_to_string(m_core_solver.m_x[column]).size()));
+    adjust_width_with_bounds(column, w);
+    adjust_width_with_basis_heading(column, w);
+    for (unsigned i = 0; i < nrows(); i++) {
+        unsigned cellw = static_cast<unsigned>(m_A[i][column].size());
+        if (cellw > w) {
+            w = cellw;
+        }
+    }
+    if (!m_core_solver.use_tableau()) {
+        w = std::max(w, (unsigned)T_to_string(m_exact_column_norms[column]).size());
+        if (m_core_solver.m_column_norms.size() > 0)
+            w = std::max(w, (unsigned)T_to_string(m_core_solver.m_column_norms[column]).size());
+    }
+    return w;
+}
+
+template <typename T, typename X> std::string core_solver_pretty_printer<T, X>::regular_cell_string(unsigned row, unsigned /* column */, std::string name) {
+    T t = fabs(m_core_solver.m_ed[row]);
+    if ( t == 1) return name;
+    return T_to_string(t) + name;
+}
+
+
+template <typename T, typename X> void core_solver_pretty_printer<T, X>::set_coeff(vector<string>& row, vector<string> & row_signs, unsigned col, const T & t, string name) {
+    if (numeric_traits<T>::is_zero(t)) {
+        return;
+    }
+    if (col > 0) {
+        if (t > 0) {
+            row_signs[col] = "+";
+            row[col] = t != 1? T_to_string(t) + name : name;
+        } else {
+            row_signs[col] = "-";
+            row[col] = t != -1? T_to_string(-t) + name: name;
+        }
+    } else { // col == 0
+        if (t == -1) {
+            row[col] = "-" + name;
+        } else if (t == 1) {
+            row[col] = name;
+        } else {
+            row[col] = T_to_string(t) + name;
+        }
+    }
+}
+
+template <typename T, typename X> void core_solver_pretty_printer<T, X>::print_x() {
+    if (ncols() == 0) {
+        return;
+    }
+
+    int blanks = m_title_width + 1 - static_cast<int>(m_x_title.size());
+    m_out << m_x_title;
+    print_blanks(blanks, m_out);
+
+    auto bh = m_core_solver.m_x;
+    for (unsigned i = 0; i < ncols(); i++) {
+        string s = T_to_string(bh[i]);
+        int blanks = m_column_widths[i] - static_cast<int>(s.size());
+        print_blanks(blanks, m_out);
+        m_out << s << "   "; // the column interval
+    }
+    m_out << std::endl;
+}
+
+template <typename T, typename X> std::string core_solver_pretty_printer<T, X>::get_low_bound_string(unsigned j) {
+    switch (m_core_solver.get_column_type(j)){
+    case column_type::boxed:
+    case column_type::low_bound:
+    case column_type::fixed:
+        if (m_core_solver.low_bounds_are_set())
+            return T_to_string(m_core_solver.low_bound_value(j));
+        else
+            return std::string("0");
+        break;
+    default:
+        return std::string();
+    }
+}
+
+template <typename T, typename X> std::string core_solver_pretty_printer<T, X>::get_upp_bound_string(unsigned j) {
+    switch (m_core_solver.get_column_type(j)){
+    case column_type::boxed:
+    case column_type::upper_bound:
+    case column_type::fixed:
+        return T_to_string(m_core_solver.upper_bound_value(j));
+        break;
+    default:
+        return std::string();
+    }
+}
+
+
+template <typename T, typename X> void core_solver_pretty_printer<T, X>::print_lows() {
+    if (ncols() == 0) {
+        return;
+    }
+    int blanks = m_title_width + 1 - static_cast<unsigned>(m_low_bounds_title.size());
+    m_out << m_low_bounds_title;
+    print_blanks(blanks, m_out);
+
+    for (unsigned i = 0; i < ncols(); i++) {
+        string s = get_low_bound_string(i);
+        int blanks = m_column_widths[i] - static_cast<unsigned>(s.size());
+        print_blanks(blanks, m_out);
+        m_out << s << "   "; // the column interval
+    }
+    m_out << std::endl;
+}
+
+template <typename T, typename X> void core_solver_pretty_printer<T, X>::print_upps() {
+    if (ncols() == 0) {
+        return;
+    }
+    int blanks = m_title_width + 1 - static_cast<unsigned>(m_upp_bounds_title.size());
+    m_out << m_upp_bounds_title;
+    print_blanks(blanks, m_out);
+
+    for (unsigned i = 0; i < ncols(); i++) {
+        string s = get_upp_bound_string(i);
+        int blanks = m_column_widths[i] - static_cast<unsigned>(s.size());
+        print_blanks(blanks, m_out);
+        m_out << s << "   "; // the column interval
+    }
+    m_out << std::endl;
+}
+
+template <typename T, typename X> void core_solver_pretty_printer<T, X>::print_exact_norms() {
+    if (m_core_solver.use_tableau()) return;
+    int blanks = m_title_width + 1 - static_cast<int>(m_exact_norm_title.size());
+    m_out << m_exact_norm_title;
+    print_blanks(blanks, m_out);
+    for (unsigned i = 0; i < ncols(); i++) {
+        string s = get_exact_column_norm_string(i);
+        int blanks = m_column_widths[i] - static_cast<int>(s.size());
+        print_blanks(blanks, m_out);
+        m_out << s << "   ";
+    }
+    m_out << std::endl;
+}
+
+template <typename T, typename X> void core_solver_pretty_printer<T, X>::print_approx_norms() {
+    if (m_core_solver.use_tableau()) return;
+    int blanks = m_title_width + 1 - static_cast<int>(m_approx_norm_title.size());
+    m_out << m_approx_norm_title;
+    print_blanks(blanks, m_out);
+    for (unsigned i = 0; i < ncols(); i++) {
+        string s = T_to_string(m_core_solver.m_column_norms[i]);
+        int blanks = m_column_widths[i] - static_cast<int>(s.size());
+        print_blanks(blanks, m_out);
+        m_out << s << "   ";
+    }
+    m_out << std::endl;
+}
+
+template <typename T, typename X> void core_solver_pretty_printer<T, X>::print() {
+    for (unsigned i = 0; i < nrows(); i++) {
+        print_row(i);
+    }
+    print_bottom_line();
+    print_cost();
+    print_x();
+    print_basis_heading();
+    print_lows();
+    print_upps();
+    print_exact_norms();
+    if (m_core_solver.m_column_norms.size() > 0)
+        print_approx_norms();
+    m_out << std::endl;
+}
+
+template <typename T, typename X> void core_solver_pretty_printer<T, X>::print_basis_heading() {
+    int blanks = m_title_width + 1 - static_cast<int>(m_basis_heading_title.size());
+    m_out << m_basis_heading_title;
+    print_blanks(blanks, m_out);
+
+    if (ncols() == 0) {
+        return;
+    }
+    auto bh = m_core_solver.m_basis_heading;
+    for (unsigned i = 0; i < ncols(); i++) {
+        string s = T_to_string(bh[i]);
+        int blanks = m_column_widths[i] - static_cast<unsigned>(s.size());
+        print_blanks(blanks, m_out);
+        m_out << s << "   "; // the column interval
+    }
+    m_out << std::endl;
+}
+
+template <typename T, typename X> void core_solver_pretty_printer<T, X>::print_cost() {
+    int blanks = m_title_width + 1 - static_cast<int>(m_cost_title.size());
+    m_out << m_cost_title;
+    print_blanks(blanks, m_out);
+    print_given_rows(m_costs, m_cost_signs, m_core_solver.get_cost());
+}
+
+template <typename T, typename X> void core_solver_pretty_printer<T, X>::print_given_rows(vector<string> & row, vector<string> & signs, X rst) {
+    for (unsigned col = 0; col < row.size(); col++) {
+        unsigned width = m_column_widths[col];
+        string s = row[col];
+        int number_of_blanks = width - static_cast<unsigned>(s.size());
+        lean_assert(number_of_blanks >= 0);
+        print_blanks(number_of_blanks, m_out);
+        m_out << s << ' ';
+        if (col < row.size() - 1) {
+            m_out << signs[col + 1] << ' ';
+        }
+    }
+    m_out << '=';
+
+    string rs = T_to_string(rst);
+    int nb = m_rs_width - static_cast<int>(rs.size());
+    lean_assert(nb >= 0);
+    print_blanks(nb + 1, m_out);
+    m_out << rs << std::endl;
+}
+
+template <typename T, typename X> void core_solver_pretty_printer<T, X>::print_row(unsigned i){
+    print_blanks(m_title_width + 1, m_out);
+    auto row = m_A[i];
+    auto sign_row = m_signs[i];
+    auto rs = m_rs[i];
+    print_given_rows(row, sign_row, rs);
+}
+}

src/util/lp/core_solver_pretty_printer_instances.cpp

@@ -0,0 +1,15 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#include "util/lp/numeric_pair.h"
+#include "util/lp/core_solver_pretty_printer.hpp"
+template lean::core_solver_pretty_printer<double, double>::core_solver_pretty_printer(lean::lp_core_solver_base<double, double> &, std::ostream & out);
+template void lean::core_solver_pretty_printer<double, double>::print();
+template lean::core_solver_pretty_printer<double, double>::~core_solver_pretty_printer();
+template lean::core_solver_pretty_printer<lean::mpq, lean::mpq>::core_solver_pretty_printer(lean::lp_core_solver_base<lean::mpq, lean::mpq> &, std::ostream & out);
+template void lean::core_solver_pretty_printer<lean::mpq, lean::mpq>::print();
+template lean::core_solver_pretty_printer<lean::mpq, lean::mpq>::~core_solver_pretty_printer();
+template lean::core_solver_pretty_printer<lean::mpq, lean::numeric_pair<lean::mpq> >::core_solver_pretty_printer(lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> > &, std::ostream & out);
+template lean::core_solver_pretty_printer<lean::mpq, lean::numeric_pair<lean::mpq> >::~core_solver_pretty_printer();
+template void lean::core_solver_pretty_printer<lean::mpq, lean::numeric_pair<lean::mpq> >::print();

src/util/lp/dense_matrix.h

@@ -0,0 +1,92 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#pragma once
+#ifdef LEAN_DEBUG
+#include "util/vector.h"
+#include "util/lp/matrix.h"
+namespace lean {
+// used for debugging purposes only
+template <typename T, typename X>
+class dense_matrix: public matrix<T, X> {
+public:
+    struct ref {
+        unsigned m_i;
+        dense_matrix & m_s;
+        ref(unsigned i, dense_matrix & s) :m_i(i * s.m_n), m_s(s){}
+        T & operator[] (unsigned j) {
+            return m_s.m_values[m_i + j];
+        }
+        const T & operator[] (unsigned j) const {
+            return m_s.m_v[m_i + j];
+        }
+    };
+    ref operator[] (unsigned i) {
+        return ref(i, *this);
+    }
+    unsigned m_m; // number of rows
+    unsigned m_n; // number of const
+    vector<T> m_values;
+    dense_matrix(unsigned m, unsigned n);
+
+    dense_matrix operator*=(matrix<T, X> const & a) {
+        lean_assert(column_count() == a.row_count());
+        dense_matrix c(row_count(), a.column_count());
+        for (unsigned i = 0; i < row_count(); i++) {
+            for (unsigned j = 0; j < a.column_count(); j++) {
+                T v = numeric_traits<T>::zero();
+                for (unsigned k = 0; k < a.column_count(); k++) {
+                    v += get_elem(i, k) * a(k, j);
+                }
+                c.set_elem(i, j, v);
+            }
+        }
+        *this = c;
+        return *this;
+    }
+
+    dense_matrix & operator=(matrix<T, X> const & other);
+
+    dense_matrix & operator=(dense_matrix const & other);
+
+    dense_matrix(matrix<T, X> const * other);
+    void apply_from_right(T * w);
+
+    void apply_from_right(vector <T> & w);
+
+    T * apply_from_left_with_different_dims(vector<T> &  w);
+    void apply_from_left(vector<T> & w , lp_settings & ) { apply_from_left(w); }
+
+    void apply_from_left(vector<T> & w);
+
+    void apply_from_left(X * w, lp_settings & );
+
+    void apply_from_left_to_X(vector<X> & w, lp_settings & );
+
+    virtual void set_number_of_rows(unsigned /*m*/) {}
+    virtual void set_number_of_columns(unsigned /*n*/) { }
+
+    T get_elem(unsigned i, unsigned j) const { return m_values[i * m_n + j]; }
+
+    unsigned row_count() const { return m_m; }
+    unsigned column_count() const { return m_n; }
+
+    void set_elem(unsigned i, unsigned j, const T& val) {  m_values[i * m_n + j] = val;  }
+
+    // This method pivots row i to row i0 by muliplying row i by
+    //   alpha and adding it to row i0.
+    void pivot_row_to_row(unsigned i, const T& alpha, unsigned i0,
+                          const double & pivot_epsilon);
+
+    void swap_columns(unsigned a, unsigned b);
+
+    void swap_rows(unsigned a, unsigned b);
+
+    void multiply_row_by_constant(unsigned row, T & t);
+
+};
+template <typename T, typename X>
+dense_matrix<T, X> operator* (matrix<T, X> & a, matrix<T, X> & b);
+}
+#endif

src/util/lp/dense_matrix.hpp

@@ -0,0 +1,186 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#include "util/lp/lp_settings.h"
+#ifdef LEAN_DEBUG
+#include "util/vector.h"
+#include "util/lp/numeric_pair.h"
+#include "util/lp/dense_matrix.h"
+namespace lean {
+template <typename T> void print_vector(const vector<T> & t, std::ostream & out);
+template <typename T, typename X> dense_matrix<T, X>::dense_matrix(unsigned m, unsigned n) : m_m(m), m_n(n), m_values(m * n, numeric_traits<T>::zero()) {
+}
+
+template <typename T, typename X> dense_matrix<T, X>&
+dense_matrix<T, X>::operator=(matrix<T, X> const & other){
+    if ( this == & other)
+        return *this;
+    m_values = new T[m_m * m_n];
+    for (unsigned i = 0; i < m_m; i ++)
+        for (unsigned j = 0; j < m_n; j++)
+            m_values[i * m_n + j] = other.get_elem(i, j);
+    return *this;
+}
+
+template <typename T, typename X> dense_matrix<T, X>&
+dense_matrix<T, X>::operator=(dense_matrix const & other){
+    if ( this == & other)
+        return *this;
+    m_m = other.m_m;
+    m_n = other.m_n;
+    m_values.resize(m_m * m_n);
+    for (unsigned i = 0; i < m_m; i ++)
+        for (unsigned j = 0; j < m_n; j++)
+            m_values[i * m_n + j] = other.get_elem(i, j);
+    return *this;
+}
+
+template <typename T, typename X> dense_matrix<T, X>::dense_matrix(matrix<T, X> const * other) :
+    m_m(other->row_count()),
+    m_n(other->column_count()) {
+    m_values.resize(m_m*m_n);
+    for (unsigned i = 0; i < m_m; i++)
+        for (unsigned j = 0; j < m_n; j++)
+            m_values[i * m_n + j] = other->get_elem(i, j);
+}
+
+template <typename T, typename X> void dense_matrix<T, X>::apply_from_right(T * w) {
+    T * t = new T[m_m];
+    for (int i = 0; i < m_m; i ++) {
+        T v = numeric_traits<T>::zero();
+        for (int j = 0; j < m_m; j++) {
+            v += w[j]* get_elem(j, i);
+        }
+        t[i] = v;
+    }
+
+    for (int i = 0; i < m_m; i++) {
+        w[i] = t[i];
+    }
+    delete [] t;
+}
+
+template <typename T, typename X> void dense_matrix<T, X>::apply_from_right(vector <T> & w) {
+    vector<T> t(m_m, numeric_traits<T>::zero());
+    for (unsigned i = 0; i < m_m; i ++) {
+        auto & v = t[i];
+        for (unsigned j = 0; j < m_m; j++)
+            v += w[j]* get_elem(j, i);
+    }
+
+    for (unsigned i = 0; i < m_m; i++)
+        w[i] = t[i];
+}
+
+template <typename T, typename X> T* dense_matrix<T, X>::
+apply_from_left_with_different_dims(vector<T> &  w) {
+    T * t = new T[m_m];
+    for (int i = 0; i < m_m; i ++) {
+        T v = numeric_traits<T>::zero();
+        for (int j = 0; j < m_n; j++) {
+            v += w[j]* get_elem(i, j);
+        }
+        t[i] = v;
+    }
+
+    return t;
+}
+
+template <typename T, typename X> void dense_matrix<T, X>::apply_from_left(vector<T> & w) {
+    T * t = new T[m_m];
+    for (unsigned i = 0; i < m_m; i ++) {
+        T v = numeric_traits<T>::zero();
+        for (unsigned j = 0; j < m_m; j++) {
+            v += w[j]* get_elem(i, j);
+        }
+        t[i] = v;
+    }
+
+    for (unsigned i = 0; i < m_m; i ++) {
+        w[i] = t[i];
+    }
+    delete [] t;
+}
+
+template <typename T, typename X> void dense_matrix<T, X>::apply_from_left(X * w, lp_settings & ) {
+    T * t = new T[m_m];
+    for (int i = 0; i < m_m; i ++) {
+        T v = numeric_traits<T>::zero();
+        for (int j = 0; j < m_m; j++) {
+            v += w[j]* get_elem(i, j);
+        }
+        t[i] = v;
+    }
+
+    for (int i = 0; i < m_m; i ++) {
+        w[i] = t[i];
+    }
+    delete [] t;
+}
+
+template <typename T, typename X> void dense_matrix<T, X>::apply_from_left_to_X(vector<X> & w, lp_settings & ) {
+    vector<X> t(m_m);
+    for (int i = 0; i < m_m; i ++) {
+        X v = zero_of_type<X>();
+        for (int j = 0; j < m_m; j++) {
+            v += w[j]* get_elem(i, j);
+        }
+        t[i] = v;
+    }
+
+    for (int i = 0; i < m_m; i ++) {
+        w[i] = t[i];
+    }
+}
+
+// This method pivots row i to row i0 by muliplying row i by
+//   alpha and adding it to row i0.
+template <typename T, typename X> void dense_matrix<T, X>::pivot_row_to_row(unsigned i, const T& alpha, unsigned i0,
+                                                                            const double & pivot_epsilon) {
+    for (unsigned j = 0; j < m_n; j++) {
+        m_values[i0 * m_n + j] += m_values[i * m_n + j] * alpha;
+        if (fabs(m_values[i0 + m_n + j]) < pivot_epsilon) {
+            m_values[i0 + m_n + j] = numeric_traits<T>::zero();;
+        }
+    }
+}
+
+template <typename T, typename X> void dense_matrix<T, X>::swap_columns(unsigned a, unsigned b) {
+    for (unsigned i = 0; i < m_m; i++) {
+        T t = get_elem(i, a);
+        set_elem(i, a, get_elem(i, b));
+        set_elem(i, b, t);
+    }
+}
+
+template <typename T, typename X> void dense_matrix<T, X>::swap_rows(unsigned a, unsigned b) {
+    for (unsigned i = 0; i < m_n; i++) {
+        T t = get_elem(a, i);
+        set_elem(a, i, get_elem(b, i));
+        set_elem(b, i, t);
+    }
+}
+
+template <typename T, typename X> void dense_matrix<T, X>::multiply_row_by_constant(unsigned row, T & t) {
+    for (unsigned i = 0; i < m_n; i++) {
+        set_elem(row, i, t * get_elem(row, i));
+    }
+}
+
+template <typename T, typename X>
+dense_matrix<T, X> operator* (matrix<T, X> & a, matrix<T, X> & b){
+    lean_assert(a.column_count() == b.row_count());
+    dense_matrix<T, X> ret(a.row_count(), b.column_count());
+    for (unsigned i = 0; i < ret.m_m; i++)
+        for (unsigned j = 0; j< ret.m_n; j++) {
+            T v = numeric_traits<T>::zero();
+            for (unsigned k = 0; k < a.column_count(); k ++){
+                v += (a.get_elem(i, k) * b.get_elem(k, j));
+            }
+            ret.set_elem(i, j, v);
+        }
+    return  ret;
+}
+}
+#endif

src/util/lp/dense_matrix_instances.cpp

@@ -0,0 +1,24 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#include "util/lp/lp_settings.h"
+#include "util/lp/dense_matrix.hpp"
+#ifdef LEAN_DEBUG
+#include "util/vector.h"
+template lean::dense_matrix<double, double> lean::operator*<double, double>(lean::matrix<double, double>&, lean::matrix<double, double>&);
+template void lean::dense_matrix<double, double>::apply_from_left(vector<double> &);
+template lean::dense_matrix<double, double>::dense_matrix(lean::matrix<double, double> const*);
+template lean::dense_matrix<double, double>::dense_matrix(unsigned int, unsigned int);
+template lean::dense_matrix<double, double>& lean::dense_matrix<double, double>::operator=(lean::dense_matrix<double, double> const&);
+template lean::dense_matrix<lean::mpq, lean::numeric_pair<lean::mpq> >::dense_matrix(lean::matrix<lean::mpq, lean::numeric_pair<lean::mpq> > const*);
+template void lean::dense_matrix<lean::mpq, lean::numeric_pair<lean::mpq> >::apply_from_left(vector<lean::mpq>&);
+template lean::dense_matrix<lean::mpq, lean::mpq> lean::operator*<lean::mpq, lean::mpq>(lean::matrix<lean::mpq, lean::mpq>&, lean::matrix<lean::mpq, lean::mpq>&);
+template lean::dense_matrix<lean::mpq, lean::mpq> & lean::dense_matrix<lean::mpq, lean::mpq>::operator=(lean::dense_matrix<lean::mpq, lean::mpq> const&);
+template lean::dense_matrix<lean::mpq, lean::numeric_pair<lean::mpq> >::dense_matrix(unsigned int, unsigned int);
+template lean::dense_matrix<lean::mpq, lean::numeric_pair<lean::mpq> >& lean::dense_matrix<lean::mpq, lean::numeric_pair<lean::mpq> >::operator=(lean::dense_matrix<lean::mpq, lean::numeric_pair<lean::mpq> > const&);
+template lean::dense_matrix<lean::mpq, lean::numeric_pair<lean::mpq> > lean::operator*<lean::mpq, lean::numeric_pair<lean::mpq> >(lean::matrix<lean::mpq, lean::numeric_pair<lean::mpq> >&, lean::matrix<lean::mpq, lean::numeric_pair<lean::mpq> >&);
+template void lean::dense_matrix<lean::mpq, lean::numeric_pair< lean::mpq> >::apply_from_right( vector< lean::mpq> &);
+template void lean::dense_matrix<double,double>::apply_from_right(class vector<double> &);
+template void lean::dense_matrix<lean::mpq, lean::mpq>::apply_from_left(vector<lean::mpq>&);
+#endif

src/util/lp/eta_matrix.h

@@ -0,0 +1,83 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+
+#pragma once
+#include "util/vector.h"
+#include "util/lp/tail_matrix.h"
+#include "util/lp/permutation_matrix.h"
+namespace lean {
+
+// This is the sum of a unit matrix and a one-column matrix
+template <typename T, typename X>
+class eta_matrix
+    : public tail_matrix<T, X> {
+#ifdef LEAN_DEBUG
+    unsigned m_length;
+#endif
+    unsigned m_column_index;
+public:
+    sparse_vector<T> m_column_vector;
+    T m_diagonal_element;
+#ifdef LEAN_DEBUG
+    eta_matrix(unsigned column_index, unsigned length):
+#else
+        eta_matrix(unsigned column_index):
+#endif
+
+#ifdef LEAN_DEBUG
+        m_length(length),
+#endif
+        m_column_index(column_index) {}
+
+    bool is_dense() const { return false; }
+
+    void print(std::ostream & out) {
+        print_matrix(*this, out);
+    }
+
+    bool is_unit() {
+        return m_column_vector.size() == 0 && m_diagonal_element == 1;
+    }
+
+    bool set_diagonal_element(T const & diagonal_element) {
+        m_diagonal_element = diagonal_element;
+        return !lp_settings::is_eps_small_general(diagonal_element, 1e-12);
+    }
+
+    const T & get_diagonal_element() const {
+        return m_diagonal_element;
+    }
+
+    void apply_from_left(vector<X> & w, lp_settings & );
+
+    template <typename L>
+    void apply_from_left_local(indexed_vector<L> & w, lp_settings & settings);
+
+    void apply_from_left_to_T(indexed_vector<T> & w, lp_settings & settings) {
+        apply_from_left_local(w, settings);
+    }
+
+
+    void push_back(unsigned row_index, T val ) {
+        lean_assert(row_index != m_column_index);
+        m_column_vector.push_back(row_index, val);
+    }
+
+    void apply_from_right(vector<T> & w);
+    void apply_from_right(indexed_vector<T> & w);
+
+    T get_elem(unsigned i, unsigned j) const;
+#ifdef LEAN_DEBUG
+    unsigned row_count() const { return m_length; }
+    unsigned column_count() const { return m_length; }
+    void set_number_of_rows(unsigned m) { m_length = m; }
+    void set_number_of_columns(unsigned n) { m_length = n; }
+#endif
+    void divide_by_diagonal_element() {
+        m_column_vector.divide(m_diagonal_element);
+    }
+    void conjugate_by_permutation(permutation_matrix<T, X> & p);
+};
+}

src/util/lp/eta_matrix.hpp

@@ -0,0 +1,136 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+
+#pragma once
+#include "util/vector.h"
+#include "util/lp/eta_matrix.h"
+namespace lean {
+
+// This is the sum of a unit matrix and a one-column matrix
+template <typename T, typename X>
+void eta_matrix<T, X>::apply_from_left(vector<X> & w, lp_settings & ) {
+    auto & w_at_column_index = w[m_column_index];
+    for (auto & it : m_column_vector.m_data) {
+        w[it.first] += w_at_column_index * it.second;
+    }
+    w_at_column_index /= m_diagonal_element;
+}
+template <typename T, typename X>
+template <typename L>
+void eta_matrix<T, X>::
+apply_from_left_local(indexed_vector<L> & w, lp_settings & settings) {
+    const L w_at_column_index = w[m_column_index];
+    if (is_zero(w_at_column_index)) return;
+
+    if (settings.abs_val_is_smaller_than_drop_tolerance(w[m_column_index] /= m_diagonal_element)) {
+        w[m_column_index] = zero_of_type<L>();
+        w.erase_from_index(m_column_index);
+    }
+
+    for (auto & it : m_column_vector.m_data) {
+        unsigned i = it.first;
+        if (is_zero(w[i])) {
+            L v = w[i] = w_at_column_index * it.second;
+            if (settings.abs_val_is_smaller_than_drop_tolerance(v)) {
+                w[i] = zero_of_type<L>();
+                continue;
+            }
+            w.m_index.push_back(i);
+        } else  {
+            L v = w[i] += w_at_column_index * it.second;
+            if (settings.abs_val_is_smaller_than_drop_tolerance(v)) {
+                w[i] = zero_of_type<L>();
+                w.erase_from_index(i);
+            }
+        }
+    }
+}
+template <typename T, typename X>
+void eta_matrix<T, X>::apply_from_right(vector<T> & w) {
+#ifdef LEAN_DEBUG
+    // dense_matrix<T, X> deb(*this);
+    // auto clone_w = clone_vector<T>(w, get_number_of_rows());
+    // deb.apply_from_right(clone_w);
+#endif
+    T t = w[m_column_index] / m_diagonal_element;
+    for (auto & it : m_column_vector.m_data) {
+        t += w[it.first] * it.second;
+    }
+    w[m_column_index] = t;
+#ifdef LEAN_DEBUG
+    // lean_assert(vectors_are_equal<T>(clone_w, w, get_number_of_rows()));
+    // delete clone_w;
+#endif
+}
+template <typename T, typename X>
+void eta_matrix<T, X>::apply_from_right(indexed_vector<T> & w) {
+    if (w.m_index.size() == 0)
+        return;
+#ifdef LEAN_DEBUG
+    // vector<T> wcopy(w.m_data);
+    // apply_from_right(wcopy);
+#endif
+    T & t = w[m_column_index];
+    t /= m_diagonal_element;
+    bool was_in_index = (!numeric_traits<T>::is_zero(t));
+    
+    for (auto & it : m_column_vector.m_data) {
+        t += w[it.first] * it.second;
+    }
+
+    if (numeric_traits<T>::precise() ) {
+        if (!numeric_traits<T>::is_zero(t)) {
+            if (!was_in_index)
+                w.m_index.push_back(m_column_index);
+        } else {
+            if (was_in_index)
+                w.erase_from_index(m_column_index);
+        }
+    } else {
+        if (!lp_settings::is_eps_small_general(t, 1e-14)) {
+            if (!was_in_index)
+                w.m_index.push_back(m_column_index);
+        } else {
+            if (was_in_index)
+                w.erase_from_index(m_column_index);
+            t = zero_of_type<T>();
+        }
+    }
+    
+#ifdef LEAN_DEBUG
+    // lean_assert(w.is_OK());
+    // lean_assert(vectors_are_equal<T>(wcopy, w.m_data));
+#endif
+}
+#ifdef LEAN_DEBUG
+template <typename T, typename X>
+T eta_matrix<T, X>::get_elem(unsigned i, unsigned j) const {
+    if (j == m_column_index){
+        if (i == j) {
+            return 1 / m_diagonal_element;
+        }
+        return m_column_vector[i];
+    }
+
+    return i == j ? numeric_traits<T>::one() : numeric_traits<T>::zero();
+}
+#endif
+template <typename T, typename X>
+void eta_matrix<T, X>::conjugate_by_permutation(permutation_matrix<T, X> & p) {
+    // this = p * this * p(-1)
+#ifdef LEAN_DEBUG
+    // auto rev = p.get_reverse();
+    // auto deb = ((*this) * rev);
+    // deb = p * deb;
+#endif
+    m_column_index = p.get_rev(m_column_index);
+    for (auto & pair : m_column_vector.m_data) {
+        pair.first = p.get_rev(pair.first);
+    }
+#ifdef LEAN_DEBUG
+    // lean_assert(deb == *this);
+#endif
+}
+}

src/util/lp/eta_matrix_instances.cpp

@@ -0,0 +1,28 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#include <memory>
+#include "util/vector.h"
+#include "util/lp/numeric_pair.h"
+#include "util/lp/eta_matrix.hpp"
+#ifdef LEAN_DEBUG
+template double lean::eta_matrix<double, double>::get_elem(unsigned int, unsigned int) const;
+template lean::mpq lean::eta_matrix<lean::mpq, lean::mpq>::get_elem(unsigned int, unsigned int) const;
+template lean::mpq lean::eta_matrix<lean::mpq, lean::numeric_pair<lean::mpq> >::get_elem(unsigned int, unsigned int) const;
+#endif
+template void lean::eta_matrix<double, double>::apply_from_left(vector<double>&, lean::lp_settings&);
+template void lean::eta_matrix<double, double>::apply_from_right(vector<double>&);
+template void lean::eta_matrix<double, double>::conjugate_by_permutation(lean::permutation_matrix<double, double>&);
+template void lean::eta_matrix<lean::mpq, lean::mpq>::apply_from_left(vector<lean::mpq>&, lean::lp_settings&);
+template void lean::eta_matrix<lean::mpq, lean::mpq>::apply_from_right(vector<lean::mpq>&);
+template void lean::eta_matrix<lean::mpq, lean::mpq>::conjugate_by_permutation(lean::permutation_matrix<lean::mpq, lean::mpq>&);
+template void lean::eta_matrix<lean::mpq, lean::numeric_pair<lean::mpq> >::apply_from_left(vector<lean::numeric_pair<lean::mpq> >&, lean::lp_settings&);
+template void lean::eta_matrix<lean::mpq, lean::numeric_pair<lean::mpq> >::apply_from_right(vector<lean::mpq>&);
+template void lean::eta_matrix<lean::mpq, lean::numeric_pair<lean::mpq> >::conjugate_by_permutation(lean::permutation_matrix<lean::mpq, lean::numeric_pair<lean::mpq> >&);
+template void lean::eta_matrix<double, double>::apply_from_left_local<double>(lean::indexed_vector<double>&, lean::lp_settings&);
+template void lean::eta_matrix<lean::mpq, lean::mpq>::apply_from_left_local<lean::mpq>(lean::indexed_vector<lean::mpq>&, lean::lp_settings&);
+template void lean::eta_matrix<lean::mpq, lean::numeric_pair<lean::mpq> >::apply_from_left_local<lean::mpq>(lean::indexed_vector<lean::mpq>&, lean::lp_settings&);
+template void lean::eta_matrix<lean::mpq, lean::numeric_pair<lean::mpq> >::apply_from_right(lean::indexed_vector<lean::mpq>&);
+template void lean::eta_matrix<lean::mpq, lean::mpq>::apply_from_right(lean::indexed_vector<lean::mpq>&);
+template void lean::eta_matrix<double, double>::apply_from_right(lean::indexed_vector<double>&);

src/util/lp/hash_helper.h

@@ -0,0 +1,39 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#pragma once
+#include <utility>
+#include <functional>
+#include "util/numerics/mpq.h"
+#ifdef __CLANG__
+#pragma clang diagnostic push
+#pragma clang diagnostic ignored "-Wmismatched-tags"
+#endif
+namespace std {
+template<>
+struct hash<lean::mpq> {
+    inline size_t operator()(const lean::mpq & v) const {
+        return v.hash();
+    }
+};
+}
+
+template <class T>
+inline void hash_combine(std::size_t & seed, const T & v) {
+    seed ^= std::hash<T>()(v) + 0x9e3779b9 + (seed << 6) + (seed >> 2);
+}
+
+namespace std {
+template<typename S, typename T> struct hash<pair<S, T>> {
+    inline size_t operator()(const pair<S, T> & v) const {
+        size_t seed = 0;
+        hash_combine(seed, v.first);
+        hash_combine(seed, v.second);
+        return seed;
+    }
+};
+}
+#ifdef __CLANG__
+#pragma clang diagnostic pop
+#endif

src/util/lp/implied_bound.h

@@ -0,0 +1,42 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#pragma once
+#include "util/lp/lp_settings.h"
+#include "util/lp/lar_constraints.h"
+namespace lean {
+struct implied_bound {
+    mpq m_bound;
+    unsigned m_j; // the column for which the bound has been found
+    bool m_is_low_bound;
+    bool m_coeff_before_j_is_pos;
+    unsigned m_row_or_term_index;
+    bool m_strict;
+    
+    lconstraint_kind kind() const {
+        lconstraint_kind k = m_is_low_bound? GE : LE;
+        if (m_strict)
+            k = static_cast<lconstraint_kind>(k / 2);
+        return k;
+    }
+    bool operator==(const implied_bound & o) const {
+        return m_j == o.m_j && m_is_low_bound == o.m_is_low_bound && m_bound == o.m_bound &&
+            m_coeff_before_j_is_pos == o.m_coeff_before_j_is_pos &&
+            m_row_or_term_index == o.m_row_or_term_index && m_strict == o.m_strict;
+    }
+    implied_bound(){}
+    implied_bound(const mpq & a,
+                  unsigned j,
+                  bool low_bound,
+                  bool coeff_before_j_is_pos,
+                  unsigned row_or_term_index,
+                  bool strict):
+        m_bound(a),
+        m_j(j),
+        m_is_low_bound(low_bound),
+        m_coeff_before_j_is_pos(coeff_before_j_is_pos),
+        m_row_or_term_index(row_or_term_index),
+        m_strict(strict) {}
+};
+}

src/util/lp/indexed_value.h

@@ -0,0 +1,55 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#pragma once
+
+namespace lean {
+template <typename T>
+class indexed_value {
+public:
+    T m_value;
+    // the idea is that m_index for a row element gives its column, and for a column element its row
+    unsigned m_index;
+    // m_other point is the offset of the corresponding element in its vector : for a row element it point to the column element offset,
+    // for a column element it points to the row element offset
+    unsigned m_other;
+    indexed_value() {}
+    indexed_value(T v, unsigned i) : m_value(v), m_index(i) {}
+    indexed_value(T v, unsigned i, unsigned other) :
+        m_value(v), m_index(i), m_other(other) {
+    }
+
+    indexed_value(const indexed_value & iv) {
+        m_value = iv.m_value;
+        m_index = iv.m_index;
+        m_other = iv.m_other;
+    }
+
+    indexed_value & operator=(const indexed_value & right_side) {
+        m_value = right_side.m_value;
+        m_index = right_side.m_index;
+        m_other = right_side.m_other;
+        return *this;
+    }
+
+    const T & value() const {
+        return m_value;
+    }
+
+    void set_value(T val) {
+        m_value = val;
+    }
+};
+#ifdef LEAN_DEBUG
+template <typename X>
+bool check_vector_for_small_values(indexed_vector<X> & w, lp_settings & settings) {
+    for (unsigned i : w.m_index) {
+        const X & v = w[i];
+        if ((!is_zero(v)) && settings.abs_val_is_smaller_than_drop_tolerance(v))
+            return false;
+    }
+    return true;
+}
+#endif
+}

src/util/lp/indexed_vector.h

@@ -0,0 +1,169 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+
+#pragma once
+#include "util/vector.h"
+#include "util/debug.h"
+#include <string>
+#include <iomanip>
+#include "util/lp/lp_utils.h"
+#include "util/lp/lp_settings.h"
+#include <unordered_set>
+namespace lean {
+
+template <typename T> void print_vector(const vector<T> & t, std::ostream & out);
+template <typename T> void print_vector(const buffer<T> & t, std::ostream & out);
+template <typename T> void print_sparse_vector(const vector<T> & t, std::ostream & out);
+
+void print_vector(const vector<mpq> & t, std::ostream & out);
+template <typename T>
+class indexed_vector {
+public:
+    // m_index points to non-zero elements of m_data
+    vector<T> m_data;
+    vector<unsigned> m_index;
+    indexed_vector(unsigned data_size) {
+        m_data.resize(data_size, numeric_traits<T>::zero());
+    }
+
+    indexed_vector& operator=(const indexed_vector<T>& y) {
+        for (unsigned i: m_index)
+            m_data[i] = zero_of_type<T>();
+
+        m_index = y.m_index;
+
+        m_data.resize(y.data_size());
+        for (unsigned i : m_index)
+            m_data[i] = y[i];
+        return *this;
+    }
+
+    bool operator==(const indexed_vector<T>& y) const {
+        std::unordered_set<unsigned> y_index;
+        for (unsigned i : y.m_index)
+            y_index.insert(i);
+
+        std::unordered_set<unsigned> this_index;
+        for (unsigned i : m_index)
+            this_index.insert(i);
+
+        for (unsigned i : y.m_index) {
+            if (this_index.find(i) == this_index.end())
+                return false;
+        }
+           
+        for (unsigned i : m_index) {
+            if (y_index.find(i) == y_index.end())
+                return false;
+        }
+
+        return vectors_are_equal(m_data, m_data);
+
+    }
+
+    indexed_vector() {}
+
+    void resize(unsigned data_size);
+    unsigned data_size() const {
+        return m_data.size();
+    }
+
+    unsigned size() {
+        return m_index.size();
+    }
+
+    void set_value(const T& value, unsigned index);
+    void set_value_as_in_dictionary(unsigned index) {
+        lean_assert(index < m_data.size());
+        T & loc = m_data[index];
+        if (is_zero(loc)) {
+            m_index.push_back(index);
+            loc = one_of_type<T>(); // use as a characteristic function
+        } 
+    }
+    
+
+    void clear();
+    void clear_all();
+    const T& operator[] (unsigned i) const {
+        return m_data[i];
+    }
+
+    T& operator[] (unsigned i)  {
+        return m_data[i];
+    }
+
+    void clean_up() {
+#if 0==1
+        for (unsigned k = 0; k < m_index.size(); k++) {
+            unsigned i = m_index[k];
+            T & v = m_data[i];
+            if (lp_settings::is_eps_small_general(v, 1e-14)) {
+                v = zero_of_type<T>();
+                m_index.erase(m_index.begin() + k--);
+            }
+        }
+#endif
+       vector<unsigned> index_copy;
+       for (unsigned i : m_index) {
+           T & v = m_data[i];
+           if (!lp_settings::is_eps_small_general(v, 1e-14)) {
+               index_copy.push_back(i);
+           } else if (!numeric_traits<T>::is_zero(v)) {
+               v = zero_of_type<T>();
+           }
+       }
+       m_index = index_copy;
+    }
+
+    
+    void erase_from_index(unsigned j);
+
+    void add_value_at_index_with_drop_tolerance(unsigned j, const T& val_to_add) {
+        T & v = m_data[j];
+        bool was_zero = is_zero(v);
+        v += val_to_add;
+        if (lp_settings::is_eps_small_general(v, 1e-14)) {
+            v = zero_of_type<T>();
+            if (!was_zero) {
+                erase_from_index(j);
+            }
+        } else {
+            if (was_zero)
+                m_index.push_back(j);
+        }
+    }
+
+    void add_value_at_index(unsigned j, const T& val_to_add) {
+        T & v = m_data[j];
+        bool was_zero = is_zero(v);
+        v += val_to_add;
+        if (is_zero(v)) {
+            if (!was_zero)
+                erase_from_index(j);
+        } else {
+            if (was_zero)
+                m_index.push_back(j);
+        }
+    }
+
+    void restore_index_and_clean_from_data() {
+        m_index.resize(0);
+        for (unsigned i = 0; i < m_data.size(); i++) {
+            T & v = m_data[i];
+            if (lp_settings::is_eps_small_general(v, 1e-14)) {
+                v = zero_of_type<T>();
+            } else {
+                m_index.push_back(i);
+            }
+        }
+    }
+    
+#ifdef LEAN_DEBUG
+    bool is_OK() const;
+    void print(std::ostream & out);
+#endif
+};
+}

src/util/lp/indexed_vector.hpp

@@ -0,0 +1,110 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#include "util/vector.h"
+#include "util/lp/indexed_vector.h"
+#include "util/lp/lp_settings.h"
+namespace lean {
+
+template <typename T>
+void print_vector(const vector<T> & t, std::ostream & out) {
+    for (unsigned i = 0; i < t.size(); i++)
+        out << t[i] << " ";
+    out << std::endl;
+}
+
+
+template <typename T>
+void print_vector(const buffer<T> & t, std::ostream & out) {
+    for (unsigned i = 0; i < t.size(); i++)
+        out << t[i] << " ";
+    out << std::endl;
+}
+
+template <typename T>
+void print_sparse_vector(const vector<T> & t, std::ostream & out) {
+    for (unsigned i = 0; i < t.size(); i++) {
+        if (is_zero(t[i]))continue;
+        out << "[" << i << "] = " << t[i] << ", ";
+    }
+    out << std::endl;
+}
+
+void print_vector(const vector<mpq> & t, std::ostream & out) {
+    for (unsigned i = 0; i < t.size(); i++)
+        out << t[i].get_double() << std::setprecision(3) << " ";
+    out << std::endl;
+}
+
+template <typename T>
+void indexed_vector<T>::resize(unsigned data_size) {
+    clear();
+    m_data.resize(data_size, numeric_traits<T>::zero());
+    lean_assert(is_OK());
+}
+
+template <typename T>
+void indexed_vector<T>::set_value(const T& value, unsigned index) {
+    m_data[index] = value;
+    lean_assert(std::find(m_index.begin(), m_index.end(), index) == m_index.end());
+    m_index.push_back(index);
+}
+
+template <typename T>
+void indexed_vector<T>::clear() {
+    for (unsigned i : m_index)
+        m_data[i] = numeric_traits<T>::zero();
+    m_index.resize(0);
+}
+template <typename T>
+void indexed_vector<T>::clear_all() {
+    unsigned i = m_data.size();
+    while (i--)  m_data[i] = numeric_traits<T>::zero();
+    m_index.resize(0);
+}
+template <typename T>
+void indexed_vector<T>::erase_from_index(unsigned j) {
+    auto it = std::find(m_index.begin(), m_index.end(), j);
+    if (it != m_index.end())
+        m_index.erase(it);
+}
+
+#ifdef LEAN_DEBUG
+template <typename T>
+bool indexed_vector<T>::is_OK() const {
+    return true;
+    const double drop_eps = 1e-14;
+    for (unsigned i = 0; i < m_data.size(); i++) {
+        if (!is_zero(m_data[i]) && lp_settings::is_eps_small_general(m_data[i], drop_eps)) {
+            return false;
+        }
+        if (lp_settings::is_eps_small_general(m_data[i], drop_eps) != (std::find(m_index.begin(), m_index.end(), i) == m_index.end())) {
+            return false;
+        }
+    }
+
+    std::unordered_set<unsigned> s;
+    for (unsigned i : m_index) {
+        //no duplicates!!!
+        if (s.find(i) != s.end())
+            return false;
+        s.insert(i);
+        if (i >= m_data.size())
+            return false;
+    }
+
+    return true;
+}
+template <typename T>
+void indexed_vector<T>::print(std::ostream & out) {
+    out << "m_index " << std::endl;
+    for (unsigned i = 0; i < m_index.size(); i++) {
+        out << m_index[i] << " ";
+    }
+    out << std::endl;
+    print_vector(m_data, out);
+}
+#endif
+
+}

src/util/lp/indexed_vector_instances.cpp

@@ -0,0 +1,36 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#include "util/vector.h"
+#include "util/lp/indexed_vector.hpp"
+namespace lean {
+template void indexed_vector<double>::clear();
+template void indexed_vector<double>::clear_all();
+template void indexed_vector<double>::erase_from_index(unsigned int);
+template void indexed_vector<double>::set_value(const double&, unsigned int);
+template void indexed_vector<mpq>::clear();
+template void indexed_vector<unsigned>::clear();
+template void indexed_vector<mpq>::clear_all();
+template void indexed_vector<mpq>::erase_from_index(unsigned int);
+template void indexed_vector<mpq>::resize(unsigned int);
+template void indexed_vector<unsigned>::resize(unsigned int);
+template void indexed_vector<mpq>::set_value(const mpq&, unsigned int);
+template void indexed_vector<unsigned>::set_value(const unsigned&, unsigned int);
+#ifdef LEAN_DEBUG
+template bool indexed_vector<double>::is_OK() const;
+template bool indexed_vector<mpq>::is_OK() const;
+template bool indexed_vector<lean::numeric_pair<mpq> >::is_OK() const;
+template void lean::indexed_vector< lean::mpq>::print(std::basic_ostream<char,struct std::char_traits<char> > &);
+template void lean::indexed_vector<double>::print(std::basic_ostream<char,struct std::char_traits<char> > &);
+template void lean::indexed_vector<lean::numeric_pair<lean::mpq> >::print(std::ostream&);
+#endif
+}
+template void lean::print_vector<double>(vector<double> const&, std::ostream&);
+template void lean::print_vector<unsigned int>(vector<unsigned int> const&, std::ostream&);
+template void lean::print_vector<std::string>(vector<std::string> const&, std::ostream&);
+template void lean::print_vector<lean::numeric_pair<lean::mpq> >(vector<lean::numeric_pair<lean::mpq>> const&, std::ostream&);
+template void lean::indexed_vector<double>::resize(unsigned int);
+template void lean::print_vector< lean::mpq>(vector< lean::mpq> const &, std::basic_ostream<char, std::char_traits<char> > &);
+template void lean::print_vector<std::pair<lean::mpq, unsigned int> >(vector<std::pair<lean::mpq, unsigned int>> const&, std::ostream&);
+template void lean::indexed_vector<lean::numeric_pair<lean::mpq> >::erase_from_index(unsigned int);

src/util/lp/init_lar_solver.h

@@ -0,0 +1,576 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+
+// here we are inside lean::lar_solver class
+
+bool strategy_is_undecided() const {
+    return m_settings.simplex_strategy() == simplex_strategy_enum::undecided;
+}
+
+var_index add_var(unsigned ext_j) {
+    var_index i;
+    lean_assert (ext_j < m_terms_start_index); 
+
+    if (ext_j >= m_terms_start_index)
+        throw 0; // todo : what is the right way to exit?
+            
+    if (try_get_val(m_ext_vars_to_columns, ext_j, i)) {
+        return i;
+    }
+    lean_assert(m_vars_to_ul_pairs.size() == A_r().column_count());
+    i = A_r().column_count();
+    m_vars_to_ul_pairs.push_back (ul_pair(static_cast<unsigned>(-1)));
+    add_non_basic_var_to_core_fields(ext_j);
+    lean_assert(sizes_are_correct());
+    return i;
+}
+
+void register_new_ext_var_index(unsigned ext_v) {
+    lean_assert(!contains(m_ext_vars_to_columns, ext_v));
+    unsigned j = static_cast<unsigned>(m_ext_vars_to_columns.size());
+    m_ext_vars_to_columns[ext_v] = j;
+    lean_assert(m_columns_to_ext_vars_or_term_indices.size() == j);
+    m_columns_to_ext_vars_or_term_indices.push_back(ext_v);
+}
+
+void add_non_basic_var_to_core_fields(unsigned ext_j) {
+    register_new_ext_var_index(ext_j);
+    m_mpq_lar_core_solver.m_column_types.push_back(column_type::free_column);
+    m_columns_with_changed_bound.increase_size_by_one();
+    add_new_var_to_core_fields_for_mpq(false);
+    if (use_lu())
+        add_new_var_to_core_fields_for_doubles(false);
+}
+
+void add_new_var_to_core_fields_for_doubles(bool register_in_basis) {
+    unsigned j = A_d().column_count();
+    A_d().add_column();
+    lean_assert(m_mpq_lar_core_solver.m_d_x.size() == j);
+    //        lean_assert(m_mpq_lar_core_solver.m_d_low_bounds.size() == j && m_mpq_lar_core_solver.m_d_upper_bounds.size() == j);  // restore later
+    m_mpq_lar_core_solver.m_d_x.resize(j + 1 ); 
+    m_mpq_lar_core_solver.m_d_low_bounds.resize(j + 1);
+    m_mpq_lar_core_solver.m_d_upper_bounds.resize(j + 1);
+    lean_assert(m_mpq_lar_core_solver.m_d_heading.size() == j); // as A().column_count() on the entry to the method
+    if (register_in_basis) {
+        A_d().add_row();
+        m_mpq_lar_core_solver.m_d_heading.push_back(m_mpq_lar_core_solver.m_d_basis.size());
+        m_mpq_lar_core_solver.m_d_basis.push_back(j);
+    }else {
+        m_mpq_lar_core_solver.m_d_heading.push_back(- static_cast<int>(m_mpq_lar_core_solver.m_d_nbasis.size()) - 1);
+        m_mpq_lar_core_solver.m_d_nbasis.push_back(j);
+    }
+}
+
+void add_new_var_to_core_fields_for_mpq(bool register_in_basis) {
+    unsigned j = A_r().column_count();
+    A_r().add_column();
+    lean_assert(m_mpq_lar_core_solver.m_r_x.size() == j);
+    //        lean_assert(m_mpq_lar_core_solver.m_r_low_bounds.size() == j && m_mpq_lar_core_solver.m_r_upper_bounds.size() == j);  // restore later
+    m_mpq_lar_core_solver.m_r_x.resize(j + 1);
+    m_mpq_lar_core_solver.m_r_low_bounds.increase_size_by_one();
+    m_mpq_lar_core_solver.m_r_upper_bounds.increase_size_by_one();
+    m_mpq_lar_core_solver.m_r_solver.m_inf_set.increase_size_by_one();
+    m_mpq_lar_core_solver.m_r_solver.m_costs.resize(j + 1);
+    m_mpq_lar_core_solver.m_r_solver.m_d.resize(j + 1);
+    lean_assert(m_mpq_lar_core_solver.m_r_heading.size() == j); // as A().column_count() on the entry to the method
+    if (register_in_basis) {
+        A_r().add_row();
+        m_mpq_lar_core_solver.m_r_heading.push_back(m_mpq_lar_core_solver.m_r_basis.size());
+        m_mpq_lar_core_solver.m_r_basis.push_back(j);
+        if (m_settings.bound_propagation())
+            m_rows_with_changed_bounds.insert(A_r().row_count() - 1);
+    } else {
+        m_mpq_lar_core_solver.m_r_heading.push_back(- static_cast<int>(m_mpq_lar_core_solver.m_r_nbasis.size()) - 1);
+        m_mpq_lar_core_solver.m_r_nbasis.push_back(j);
+    }
+}
+
+
+var_index add_term_undecided(const vector<std::pair<mpq, var_index>> & coeffs,
+                             const mpq &m_v) {
+    m_terms.push_back(new lar_term(coeffs, m_v));
+    m_orig_terms.push_back(new lar_term(coeffs, m_v));
+    return m_terms_start_index +  m_terms.size() - 1;
+}
+
+// terms
+var_index add_term(const vector<std::pair<mpq, var_index>> & coeffs,
+                   const mpq &m_v) {
+    if (strategy_is_undecided())
+        return add_term_undecided(coeffs, m_v);
+
+    m_terms.push_back(new lar_term(coeffs, m_v));
+    m_orig_terms.push_back(new lar_term(coeffs, m_v));
+    unsigned adjusted_term_index = m_terms.size() - 1;
+    var_index ret = m_terms_start_index + adjusted_term_index;
+    if (use_tableau() && !coeffs.empty()) {
+        add_row_for_term(m_orig_terms.back(), ret);
+        if (m_settings.bound_propagation())
+            m_rows_with_changed_bounds.insert(A_r().row_count() - 1);
+    } 
+    lean_assert(m_ext_vars_to_columns.size() == A_r().column_count());
+    return ret;
+}
+
+void add_row_for_term(const lar_term * term, unsigned term_ext_index) {
+    lean_assert(sizes_are_correct());
+    add_row_from_term_no_constraint(term, term_ext_index);
+    lean_assert(sizes_are_correct());
+}
+
+void add_row_from_term_no_constraint(const lar_term * term, unsigned term_ext_index) {
+    register_new_ext_var_index(term_ext_index);
+    // j will be a new variable
+	unsigned j = A_r().column_count();
+    ul_pair ul(j);
+    m_vars_to_ul_pairs.push_back(ul);
+    add_basic_var_to_core_fields();
+    if (use_tableau()) {
+        auto it = iterator_on_term_with_basis_var(*term, j);
+        A_r().fill_last_row_with_pivoting(it,
+                                          m_mpq_lar_core_solver.m_r_solver.m_basis_heading);
+        m_mpq_lar_core_solver.m_r_solver.m_b.resize(A_r().column_count(), zero_of_type<mpq>());
+    } else {
+        fill_last_row_of_A_r(A_r(), term);
+    }
+    m_mpq_lar_core_solver.m_r_x[j] = get_basic_var_value_from_row_directly(A_r().row_count() - 1);
+    if (use_lu())
+        fill_last_row_of_A_d(A_d(), term);
+}
+
+void add_basic_var_to_core_fields() {
+    bool use_lu = m_mpq_lar_core_solver.need_to_presolve_with_double_solver();
+    lean_assert(!use_lu || A_r().column_count() == A_d().column_count());
+    m_mpq_lar_core_solver.m_column_types.push_back(column_type::free_column);
+    m_columns_with_changed_bound.increase_size_by_one();
+    m_rows_with_changed_bounds.increase_size_by_one();
+    add_new_var_to_core_fields_for_mpq(true);
+    if (use_lu)
+        add_new_var_to_core_fields_for_doubles(true);
+}
+
+constraint_index add_var_bound(var_index j, lconstraint_kind kind, const mpq & right_side)  {
+	constraint_index ci = m_constraints.size();
+    if (!is_term(j)) { // j is a var
+        auto vc = new lar_var_constraint(j, kind, right_side);
+        m_constraints.push_back(vc);
+        update_column_type_and_bound(j, kind, right_side, ci);
+    } else {
+        add_var_bound_on_constraint_for_term(j, kind, right_side, ci);
+    }
+    lean_assert(sizes_are_correct());
+    return ci;
+}
+
+void update_column_type_and_bound(var_index j, lconstraint_kind kind, const mpq & right_side, constraint_index constr_index) {
+    switch(m_mpq_lar_core_solver.m_column_types[j]) {
+    case column_type::free_column:
+        update_free_column_type_and_bound(j, kind, right_side, constr_index);
+        break;
+    case column_type::boxed:
+        update_boxed_column_type_and_bound(j, kind, right_side, constr_index);
+        break;
+    case column_type::low_bound:
+        update_low_bound_column_type_and_bound(j, kind, right_side, constr_index);
+        break;
+    case column_type::upper_bound:
+        update_upper_bound_column_type_and_bound(j, kind, right_side, constr_index);
+        break;
+    case column_type::fixed:
+        update_fixed_column_type_and_bound(j, kind, right_side, constr_index);
+        break;
+    default:
+        lean_assert(false); // cannot be here
+    }
+}
+
+void add_var_bound_on_constraint_for_term(var_index j, lconstraint_kind kind, const mpq & right_side, constraint_index ci) {
+    lean_assert(is_term(j));
+    unsigned adjusted_term_index = adjust_term_index(j);
+    unsigned term_j;
+    if (try_get_val(m_ext_vars_to_columns, j, term_j)) {
+        mpq rs = right_side - m_orig_terms[adjusted_term_index]->m_v;
+        m_constraints.push_back(new lar_term_constraint(m_orig_terms[adjusted_term_index], kind, right_side));
+        update_column_type_and_bound(term_j, kind, rs, ci);
+    }
+    else {
+        add_constraint_from_term_and_create_new_column_row(j, m_orig_terms[adjusted_term_index], kind, right_side);
+    }
+}
+
+
+void add_constraint_from_term_and_create_new_column_row(unsigned term_j, const lar_term* term,
+                                                        lconstraint_kind kind, const mpq & right_side) {
+
+    add_row_from_term_no_constraint(term, term_j);
+    unsigned j = A_r().column_count() - 1;
+    update_column_type_and_bound(j, kind, right_side - term->m_v, m_constraints.size());
+    m_constraints.push_back(new lar_term_constraint(term, kind, right_side));
+    lean_assert(A_r().column_count() == m_mpq_lar_core_solver.m_r_solver.m_costs.size());
+}
+
+void decide_on_strategy_and_adjust_initial_state() {
+	lean_assert(strategy_is_undecided());
+	if (m_vars_to_ul_pairs.size() > m_settings.column_number_threshold_for_using_lu_in_lar_solver) {
+        m_settings.simplex_strategy() = simplex_strategy_enum::lu;
+    } else {
+        m_settings.simplex_strategy() = simplex_strategy_enum::tableau_rows; // todo: when to switch to tableau_costs?
+    }
+    adjust_initial_state();
+}
+
+void adjust_initial_state() {
+    switch (m_settings.simplex_strategy()) {
+    case simplex_strategy_enum::lu:
+        adjust_initial_state_for_lu();
+        break;
+    case simplex_strategy_enum::tableau_rows:
+        adjust_initial_state_for_tableau_rows();
+        break;
+    case simplex_strategy_enum::tableau_costs:
+        lean_assert(false); // not implemented
+    case simplex_strategy_enum::undecided:
+        adjust_initial_state_for_tableau_rows();
+        break;
+    }
+}
+
+void adjust_initial_state_for_lu() {
+    copy_from_mpq_matrix(A_d());
+	unsigned n = A_d().column_count();
+	m_mpq_lar_core_solver.m_d_x.resize(n);
+	m_mpq_lar_core_solver.m_d_low_bounds.resize(n);
+	m_mpq_lar_core_solver.m_d_upper_bounds.resize(n);
+	m_mpq_lar_core_solver.m_d_heading = m_mpq_lar_core_solver.m_r_heading;
+	m_mpq_lar_core_solver.m_d_basis = m_mpq_lar_core_solver.m_r_basis;
+
+	/*
+    unsigned j = A_d().column_count();
+    A_d().add_column();
+    lean_assert(m_mpq_lar_core_solver.m_d_x.size() == j);
+    //        lean_assert(m_mpq_lar_core_solver.m_d_low_bounds.size() == j && m_mpq_lar_core_solver.m_d_upper_bounds.size() == j);  // restore later
+    m_mpq_lar_core_solver.m_d_x.resize(j + 1 ); 
+    m_mpq_lar_core_solver.m_d_low_bounds.resize(j + 1);
+    m_mpq_lar_core_solver.m_d_upper_bounds.resize(j + 1);
+    lean_assert(m_mpq_lar_core_solver.m_d_heading.size() == j); // as A().column_count() on the entry to the method
+    if (register_in_basis) {
+        A_d().add_row();
+        m_mpq_lar_core_solver.m_d_heading.push_back(m_mpq_lar_core_solver.m_d_basis.size());
+        m_mpq_lar_core_solver.m_d_basis.push_back(j);
+    }else {
+        m_mpq_lar_core_solver.m_d_heading.push_back(- static_cast<int>(m_mpq_lar_core_solver.m_d_nbasis.size()) - 1);
+        m_mpq_lar_core_solver.m_d_nbasis.push_back(j);
+        }*/
+}
+
+void adjust_initial_state_for_tableau_rows() {
+    for (unsigned j = 0; j < m_terms.size(); j++) {
+        if (contains(m_ext_vars_to_columns, j + m_terms_start_index))
+            continue;
+        add_row_from_term_no_constraint(m_terms[j], j + m_terms_start_index);
+    }
+}
+
+// this fills the last row of A_d and sets the basis column: -1 in the last column of the row
+void fill_last_row_of_A_d(static_matrix<double, double> & A, const lar_term* ls) {
+    lean_assert(A.row_count() > 0);
+    lean_assert(A.column_count() > 0);
+    unsigned last_row = A.row_count() - 1;
+    lean_assert(A.m_rows[last_row].empty());
+
+    for (auto & t : ls->m_coeffs) {
+        lean_assert(!is_zero(t.second));
+        var_index j = t.first;
+        A.set(last_row, j, - t.second.get_double());
+    }
+
+    unsigned basis_j = A.column_count() - 1;
+    A.set(last_row, basis_j, - 1 );
+}
+
+void update_free_column_type_and_bound(var_index j, lconstraint_kind kind, const mpq & right_side, constraint_index constr_ind) {
+    mpq y_of_bound(0);
+    switch (kind) {
+    case LT:
+        y_of_bound = -1;
+    case LE:
+        m_mpq_lar_core_solver.m_column_types[j] = column_type::upper_bound;
+        lean_assert(m_mpq_lar_core_solver.m_column_types()[j] == column_type::upper_bound);
+        lean_assert(m_mpq_lar_core_solver.m_r_upper_bounds.size() > j);
+        {
+            auto up = numeric_pair<mpq>(right_side, y_of_bound);
+            m_mpq_lar_core_solver.m_r_upper_bounds[j] = up;
+        }
+        set_upper_bound_witness(j, constr_ind);
+        break;
+    case GT:
+        y_of_bound = 1;
+    case GE:
+        m_mpq_lar_core_solver.m_column_types[j] = column_type::low_bound;
+        lean_assert(m_mpq_lar_core_solver.m_r_upper_bounds.size() > j);
+        {
+            auto low = numeric_pair<mpq>(right_side, y_of_bound);
+            m_mpq_lar_core_solver.m_r_low_bounds[j] = low;
+        }
+        set_low_bound_witness(j, constr_ind);
+        break;
+    case EQ:
+        m_mpq_lar_core_solver.m_column_types[j] = column_type::fixed;
+        m_mpq_lar_core_solver.m_r_low_bounds[j] = m_mpq_lar_core_solver.m_r_upper_bounds[j] = numeric_pair<mpq>(right_side, zero_of_type<mpq>());
+        set_upper_bound_witness(j, constr_ind);
+        set_low_bound_witness(j, constr_ind);
+        break;
+
+    default:
+        lean_unreachable();
+                
+    }
+    m_columns_with_changed_bound.insert(j);
+}
+
+void update_upper_bound_column_type_and_bound(var_index j, lconstraint_kind kind, const mpq & right_side, constraint_index ci) {
+    lean_assert(m_mpq_lar_core_solver.m_column_types()[j] == column_type::upper_bound);
+    mpq y_of_bound(0);
+    switch (kind) {
+    case LT:
+        y_of_bound = -1;
+    case LE:
+        {
+            auto up = numeric_pair<mpq>(right_side, y_of_bound);
+            if (up < m_mpq_lar_core_solver.m_r_upper_bounds()[j]) {
+                m_mpq_lar_core_solver.m_r_upper_bounds[j] = up;
+                set_upper_bound_witness(j, ci);
+                m_columns_with_changed_bound.insert(j);
+            }
+        }
+        break;
+    case GT:
+        y_of_bound = 1;
+    case GE:            
+        m_mpq_lar_core_solver.m_column_types[j] = column_type::boxed;
+        {
+            auto low = numeric_pair<mpq>(right_side, y_of_bound);
+            m_mpq_lar_core_solver.m_r_low_bounds[j] = low;
+            set_low_bound_witness(j, ci);
+            m_columns_with_changed_bound.insert(j);
+            if (low > m_mpq_lar_core_solver.m_r_upper_bounds[j]) {
+                m_status = INFEASIBLE;
+                m_infeasible_column_index = j;
+            } else {
+                m_mpq_lar_core_solver.m_column_types[j] = m_mpq_lar_core_solver.m_r_low_bounds()[j] < m_mpq_lar_core_solver.m_r_upper_bounds()[j]? column_type::boxed : column_type::fixed;
+            }                     
+        }
+        break;
+    case EQ:
+        {
+            auto v = numeric_pair<mpq>(right_side, zero_of_type<mpq>());
+            if (v > m_mpq_lar_core_solver.m_r_upper_bounds[j]) {
+                m_status = INFEASIBLE;
+                set_low_bound_witness(j, ci);
+                m_infeasible_column_index = j;
+            } else {
+                m_mpq_lar_core_solver.m_r_low_bounds[j] = m_mpq_lar_core_solver.m_r_upper_bounds[j] = v;
+                m_columns_with_changed_bound.insert(j);
+                set_low_bound_witness(j, ci);
+                set_upper_bound_witness(j, ci);
+                m_mpq_lar_core_solver.m_column_types[j] = column_type::fixed;
+            }
+            break;
+        }
+        break;
+
+    default:
+        lean_unreachable();
+                
+    }
+}
+    
+void update_boxed_column_type_and_bound(var_index j, lconstraint_kind kind, const mpq & right_side, constraint_index ci) {
+    lean_assert(m_status == INFEASIBLE || (m_mpq_lar_core_solver.m_column_types()[j] == column_type::boxed && m_mpq_lar_core_solver.m_r_low_bounds()[j] < m_mpq_lar_core_solver.m_r_upper_bounds()[j]));
+    mpq y_of_bound(0);
+    switch (kind) {
+    case LT:
+        y_of_bound = -1;
+    case LE:
+        {
+            auto up = numeric_pair<mpq>(right_side, y_of_bound);
+            if (up < m_mpq_lar_core_solver.m_r_upper_bounds[j]) {
+                m_mpq_lar_core_solver.m_r_upper_bounds[j] = up;
+                set_upper_bound_witness(j, ci);
+                m_columns_with_changed_bound.insert(j);
+            }
+
+            if (up < m_mpq_lar_core_solver.m_r_low_bounds[j]) {
+                m_status = INFEASIBLE;
+                lean_assert(false);
+                m_infeasible_column_index = j;
+            } else {
+                if (m_mpq_lar_core_solver.m_r_low_bounds()[j] == m_mpq_lar_core_solver.m_r_upper_bounds()[j])
+                    m_mpq_lar_core_solver.m_column_types[j] = column_type::fixed;
+            }                    
+        }
+        break;
+    case GT:
+        y_of_bound = 1;
+    case GE:            
+        {
+            auto low = numeric_pair<mpq>(right_side, y_of_bound);
+            if (low > m_mpq_lar_core_solver.m_r_low_bounds[j]) {
+                m_mpq_lar_core_solver.m_r_low_bounds[j] = low;
+                m_columns_with_changed_bound.insert(j);
+                set_low_bound_witness(j, ci);
+            }
+            if (low > m_mpq_lar_core_solver.m_r_upper_bounds[j]) {
+                m_status = INFEASIBLE;
+                m_infeasible_column_index = j;
+            } else if ( low == m_mpq_lar_core_solver.m_r_upper_bounds[j]) {
+                m_mpq_lar_core_solver.m_column_types[j] = column_type::fixed;
+            }
+        }
+        break;
+    case EQ:
+        {
+            auto v = numeric_pair<mpq>(right_side, zero_of_type<mpq>());
+            if (v < m_mpq_lar_core_solver.m_r_low_bounds[j]) {
+                m_status = INFEASIBLE;
+                m_infeasible_column_index = j;
+                set_upper_bound_witness(j, ci);                    
+            } else if (v > m_mpq_lar_core_solver.m_r_upper_bounds[j]) {
+                m_status = INFEASIBLE;
+                m_infeasible_column_index = j;
+                set_low_bound_witness(j, ci);                    
+            } else {
+                m_mpq_lar_core_solver.m_r_low_bounds[j] = m_mpq_lar_core_solver.m_r_upper_bounds[j] = v;
+                set_low_bound_witness(j, ci);
+                set_upper_bound_witness(j, ci);
+                m_mpq_lar_core_solver.m_column_types[j] = column_type::fixed;
+                m_columns_with_changed_bound.insert(j);
+            }
+                
+            break;
+        }
+
+    default:
+        lean_unreachable();
+                
+    }
+}
+void update_low_bound_column_type_and_bound(var_index j, lconstraint_kind kind, const mpq & right_side, constraint_index ci) {
+    lean_assert(m_mpq_lar_core_solver.m_column_types()[j] == column_type::low_bound);
+    mpq y_of_bound(0);
+    switch (kind) {
+    case LT:
+        y_of_bound = -1;
+    case LE:
+        {
+            auto up = numeric_pair<mpq>(right_side, y_of_bound);
+            m_mpq_lar_core_solver.m_r_upper_bounds[j] = up;
+            set_upper_bound_witness(j, ci);
+            m_columns_with_changed_bound.insert(j);
+
+            if (up < m_mpq_lar_core_solver.m_r_low_bounds[j]) {
+                m_status = INFEASIBLE;
+                m_infeasible_column_index = j;
+            } else {
+                m_mpq_lar_core_solver.m_column_types[j] = m_mpq_lar_core_solver.m_r_low_bounds()[j] < m_mpq_lar_core_solver.m_r_upper_bounds()[j]? column_type::boxed : column_type::fixed;
+            }                    
+        }
+        break;
+    case GT:
+        y_of_bound = 1;
+    case GE:            
+        {
+            auto low = numeric_pair<mpq>(right_side, y_of_bound);
+            if (low > m_mpq_lar_core_solver.m_r_low_bounds[j]) {
+                m_mpq_lar_core_solver.m_r_low_bounds[j] = low;
+                m_columns_with_changed_bound.insert(j);
+                set_low_bound_witness(j, ci);
+            }
+        }
+        break;
+    case EQ:
+        {
+            auto v = numeric_pair<mpq>(right_side, zero_of_type<mpq>());
+            if (v < m_mpq_lar_core_solver.m_r_low_bounds[j]) {
+                m_status = INFEASIBLE;
+                m_infeasible_column_index = j;
+                set_upper_bound_witness(j, ci);                    
+            } else {
+                m_mpq_lar_core_solver.m_r_low_bounds[j] = m_mpq_lar_core_solver.m_r_upper_bounds[j] = v;
+                set_low_bound_witness(j, ci);
+                set_upper_bound_witness(j, ci);
+                m_mpq_lar_core_solver.m_column_types[j] = column_type::fixed;
+            }
+            m_columns_with_changed_bound.insert(j);
+            break;
+        }
+
+    default:
+        lean_unreachable();
+                
+    }
+}
+
+void update_fixed_column_type_and_bound(var_index j, lconstraint_kind kind, const mpq & right_side, constraint_index ci) {
+    lean_assert(m_status == INFEASIBLE || (m_mpq_lar_core_solver.m_column_types()[j] == column_type::fixed && m_mpq_lar_core_solver.m_r_low_bounds()[j] == m_mpq_lar_core_solver.m_r_upper_bounds()[j]));
+    lean_assert(m_status == INFEASIBLE || (m_mpq_lar_core_solver.m_r_low_bounds()[j].y.is_zero() && m_mpq_lar_core_solver.m_r_upper_bounds()[j].y.is_zero()));
+    auto v = numeric_pair<mpq>(right_side, mpq(0));
+        
+    mpq y_of_bound(0);
+    switch (kind) {
+    case LT:
+        if (v <= m_mpq_lar_core_solver.m_r_low_bounds[j]) {
+            m_status = INFEASIBLE;
+            m_infeasible_column_index = j;
+            set_upper_bound_witness(j, ci);
+        }                   
+        break;
+    case LE:
+        {
+            if (v < m_mpq_lar_core_solver.m_r_low_bounds[j]) {
+                m_status = INFEASIBLE;
+                m_infeasible_column_index = j;
+                set_upper_bound_witness(j, ci);
+            }                   
+        }
+        break;
+    case GT:
+        {
+            if (v >= m_mpq_lar_core_solver.m_r_upper_bounds[j]) {
+                m_status = INFEASIBLE;
+                m_infeasible_column_index =j;
+                set_low_bound_witness(j, ci);
+            }
+        }
+        break;
+    case GE:            
+        {
+            if (v > m_mpq_lar_core_solver.m_r_upper_bounds[j]) {
+                m_status = INFEASIBLE;
+                m_infeasible_column_index = j;
+                set_low_bound_witness(j, ci);
+            }
+        }
+        break;
+    case EQ:
+        {
+            if (v < m_mpq_lar_core_solver.m_r_low_bounds[j]) {
+                m_status = INFEASIBLE;
+                m_infeasible_column_index = j;
+                set_upper_bound_witness(j, ci);                    
+            } else if (v > m_mpq_lar_core_solver.m_r_upper_bounds[j]) {
+                m_status = INFEASIBLE;
+                m_infeasible_column_index = j;
+                set_low_bound_witness(j, ci);                    
+            } 
+            break;
+        }
+
+    default:
+        lean_unreachable();
+                
+    }
+}
+    

src/util/lp/int_set.h

@@ -0,0 +1,66 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#pragma once
+#include "util/vector.h"
+#include "util/lp/indexed_vector.h"
+#include <ostream>
+namespace lean {
+// serves at a set of non-negative integers smaller than the set size
+class int_set {
+    vector<int> m_data;
+public:
+    vector<int> m_index;
+    int_set(unsigned size): m_data(size, -1) {}
+    int_set() {}
+    bool contains(unsigned j) const {
+        if (j >= m_data.size())
+            return false;
+        return m_data[j] >= 0;
+    }
+    void insert(unsigned j) {
+        lean_assert(j < m_data.size());
+        if (contains(j)) return;
+        m_data[j] = m_index.size();
+        m_index.push_back(j);
+    }
+    void erase(unsigned j) {
+        if (!contains(j)) return;
+        unsigned pos_j = m_data[j];
+        unsigned last_pos = m_index.size() - 1;
+        int last_j = m_index[last_pos];
+        if (last_pos != pos_j) {
+            // move last to j spot
+            m_data[last_j] = pos_j;
+            m_index[pos_j] = last_j;
+        }
+        m_index.pop_back();
+        m_data[j] = -1;
+    }
+
+    void resize(unsigned size) {
+        m_data.resize(size, -1);
+    }
+
+    void increase_size_by_one() {
+        resize(m_data.size() + 1);
+    }
+
+    unsigned data_size() const {  return m_data.size(); }
+    unsigned size() const { return m_index.size();}
+    bool is_empty() const { return size() == 0; }
+    void clear() {
+        for (unsigned j : m_index)
+            m_data[j] = -1;
+        m_index.resize(0);
+    }
+    void print(std::ostream & out ) const {
+        for (unsigned j : m_index) {
+            out << j << " ";
+        }
+        out << std::endl;
+    }
+    
+};
+}

src/util/lp/iterator_on_column.h

@@ -0,0 +1,50 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#pragma once
+#include "util/lp/linear_combination_iterator.h"
+#include "util/lp/static_matrix.h"
+#include "util/lp/lar_term.h"
+namespace lean {
+template <typename T, typename X>
+struct iterator_on_column:linear_combination_iterator<T> {
+    const vector<column_cell>& m_column; // the offset in term coeffs
+    const static_matrix<T, X> & m_A;
+    int m_i; // the initial offset in the column
+    unsigned size() const { return m_column.size(); }
+    iterator_on_column(const vector<column_cell>& column, const static_matrix<T,X> & A) // the offset in term coeffs
+        :
+        m_column(column),
+        m_A(A),
+        m_i(-1) {}
+    
+    bool next(mpq & a, unsigned & i) {
+        if (++m_i >= static_cast<int>(m_column.size()))
+            return false;
+
+        const column_cell& c = m_column[m_i];
+        a = m_A.get_val(c);
+        i = c.m_i;
+        return true;
+    }
+
+    bool next(unsigned & i) {
+        if (++m_i >= static_cast<int>(m_column.size()))
+            return false;
+
+        const column_cell& c = m_column[m_i];
+        i = c.m_i;
+        return true;
+    }
+    
+    void reset() {
+        m_i = -1;
+    }
+
+    linear_combination_iterator<mpq> * clone() {
+        iterator_on_column * r = new iterator_on_column(m_column, m_A);
+        return r;
+    }
+};
+}

src/util/lp/iterator_on_indexed_vector.h

@@ -0,0 +1,38 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#pragma once
+#include "util/lp/linear_combination_iterator.h"
+namespace lean {
+template <typename T>
+struct iterator_on_indexed_vector:linear_combination_iterator<T> {
+    const indexed_vector<T> & m_v;
+    unsigned m_offset;
+    iterator_on_indexed_vector(const indexed_vector<T> & v) :
+        m_v(v),
+        m_offset(0)
+    {}
+    unsigned size() const { return m_v.m_index.size(); }
+    bool next(T & a, unsigned & i) {
+        if (m_offset >= m_v.m_index.size())
+            return false;
+        i = m_v.m_index[m_offset++];
+        a = m_v.m_data[i];
+        return true;
+    }
+    
+    bool next(unsigned & i) {
+        if (m_offset >= m_v.m_index.size())
+            return false;
+        i = m_v.m_index[m_offset++];
+        return true;
+    }
+    void reset() {
+        m_offset = 0;
+    }
+    linear_combination_iterator<T>* clone() {
+        return new iterator_on_indexed_vector(m_v);
+    }
+};
+}

src/util/lp/iterator_on_pivot_row.h

@@ -0,0 +1,44 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#pragma once
+#include "util/lp/iterator_on_indexed_vector.h"
+namespace lean {
+template <typename T>
+struct iterator_on_pivot_row:linear_combination_iterator<T> {
+    bool m_basis_returned;
+    const indexed_vector<T> & m_v;
+    unsigned m_basis_j;
+    iterator_on_indexed_vector<T> m_it;
+    unsigned size() const { return m_it.size(); }
+    iterator_on_pivot_row(const indexed_vector<T> & v, unsigned basis_j) :
+        m_basis_returned(false),
+        m_v(v), m_basis_j(basis_j), m_it(v) {}
+    bool next(T & a, unsigned & i) {
+        if (m_basis_returned == false) {
+            m_basis_returned = true;
+            a = one_of_type<T>();
+            i = m_basis_j;
+            return true;
+        }
+        return m_it.next(a, i);
+    }
+    bool next(unsigned & i) {
+        if (m_basis_returned == false) {
+            m_basis_returned = true;
+            i = m_basis_j;
+            return true;
+        }
+        return m_it.next(i);
+    }
+    void reset() {
+        m_basis_returned = false;
+        m_it.reset();
+    }
+    linear_combination_iterator<T> * clone() {
+        iterator_on_pivot_row * r = new iterator_on_pivot_row(m_v, m_basis_j);
+        return r;
+    }
+};
+}

src/util/lp/iterator_on_row.h

@@ -0,0 +1,37 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#pragma once
+#include "util/lp/linear_combination_iterator.h"
+namespace lean {
+template <typename T>
+struct iterator_on_row:linear_combination_iterator<T> {
+    const vector<row_cell<T>> & m_row;
+    unsigned m_i; // offset
+    iterator_on_row(const vector<row_cell<T>> & row) : m_row(row), m_i(0)
+    {}
+    unsigned size() const { return m_row.size(); }
+    bool next(T & a, unsigned & i) {
+        if (m_i == m_row.size())
+            return false;
+        auto &c = m_row[m_i++];
+        i = c.m_j;
+        a = c.get_val();
+        return true;
+    }
+    bool next(unsigned & i) {
+        if (m_i == m_row.size())
+            return false;
+        auto &c = m_row[m_i++];
+        i = c.m_j;
+        return true;
+    }
+    void reset() {
+        m_i = 0;
+    }
+    linear_combination_iterator<T>* clone() {
+        return new iterator_on_row(m_row);
+    }
+};
+}

src/util/lp/iterator_on_term_with_basis_var.h

@@ -0,0 +1,57 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#pragma once
+#include "util/lp/linear_combination_iterator.h"
+#include "util/lp/numeric_pair.h"
+#include "util/lp/lar_term.h"
+namespace lean {
+struct iterator_on_term_with_basis_var:linear_combination_iterator<mpq> {
+    const lar_term & m_term;
+    std::unordered_map<unsigned, mpq>::const_iterator m_i; // the offset in term coeffs
+    bool             m_term_j_returned;
+    unsigned         m_term_j;
+    unsigned size() const {return static_cast<unsigned>(m_term.m_coeffs.size() + 1);}
+    iterator_on_term_with_basis_var(const lar_term & t, unsigned term_j) :
+        m_term(t),
+        m_i(t.m_coeffs.begin()),
+        m_term_j_returned(false),
+        m_term_j(term_j) {}
+
+    bool next(mpq & a, unsigned & i) {
+        if (m_term_j_returned == false) {
+            m_term_j_returned = true;
+            a = - one_of_type<mpq>();
+            i = m_term_j;
+            return true;
+        }
+        if (m_i == m_term.m_coeffs.end())
+            return false;
+        i = m_i->first;
+        a = m_i->second;
+        m_i++;
+        return true;
+    }
+    bool next(unsigned & i) {
+        if (m_term_j_returned == false) {
+            m_term_j_returned = true;
+            i = m_term_j;
+            return true;
+        }
+        if (m_i == m_term.m_coeffs.end())
+            return false;
+        i = m_i->first;
+        m_i++;
+        return true;
+    }
+    void reset() {
+        m_term_j_returned = false;
+        m_i = m_term.m_coeffs.begin();
+    }
+    linear_combination_iterator<mpq> * clone() {
+        iterator_on_term_with_basis_var * r = new iterator_on_term_with_basis_var(m_term, m_term_j);
+        return r;
+    }
+};
+}

src/util/lp/lar_constraints.h

@@ -0,0 +1,86 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+
+#pragma once
+#include "util/vector.h"
+#include <utility>
+#include <unordered_map>
+#include <string>
+#include <algorithm>
+#include "util/lp/lp_utils.h"
+#include "util/lp/ul_pair.h"
+#include "util/lp/lar_term.h"
+namespace lean {
+inline lconstraint_kind flip_kind(lconstraint_kind t) {
+    return static_cast<lconstraint_kind>( - static_cast<int>(t));
+}
+
+inline std::string lconstraint_kind_string(lconstraint_kind t) {
+    switch (t) {
+    case LE: return std::string("<=");
+    case LT: return std::string("<");
+    case GE: return std::string(">=");
+    case GT: return std::string(">");
+    case EQ: return std::string("=");
+    }
+    lean_unreachable();
+    return std::string(); // it is unreachable
+}
+
+class lar_base_constraint {
+public:
+    lconstraint_kind m_kind;
+    mpq m_right_side;
+    virtual vector<std::pair<mpq, var_index>> get_left_side_coefficients() const = 0;
+    lar_base_constraint() {}
+    lar_base_constraint(lconstraint_kind kind, const mpq& right_side) :m_kind(kind), m_right_side(right_side) {}
+
+    virtual unsigned size() const = 0;
+    virtual ~lar_base_constraint(){}
+    virtual mpq get_free_coeff_of_left_side() const { return zero_of_type<mpq>();}
+};
+
+struct lar_var_constraint: public lar_base_constraint {
+    unsigned m_j;
+    vector<std::pair<mpq, var_index>> get_left_side_coefficients() const {
+        vector<std::pair<mpq, var_index>> ret;
+        ret.push_back(std::make_pair(one_of_type<mpq>(), m_j));
+        return ret;
+    }
+    unsigned size() const { return 1;}
+    lar_var_constraint(unsigned j, lconstraint_kind kind, const mpq& right_side) : lar_base_constraint(kind, right_side), m_j(j) { }
+};
+
+
+struct lar_term_constraint: public lar_base_constraint {
+    const lar_term * m_term;
+    vector<std::pair<mpq, var_index>> get_left_side_coefficients() const {
+        return m_term->coeffs_as_vector();
+    }
+    unsigned size() const { return m_term->size();}
+    lar_term_constraint(const lar_term *t, lconstraint_kind kind, const mpq& right_side) : lar_base_constraint(kind, right_side), m_term(t) { }
+    virtual mpq get_free_coeff_of_left_side() const { return m_term->m_v;}
+
+};
+
+
+class lar_constraint : public lar_base_constraint {
+public:
+    vector<std::pair<mpq, var_index>> m_coeffs;
+    lar_constraint() {} 
+    lar_constraint(const vector<std::pair<mpq, var_index>> & left_side, lconstraint_kind kind, const mpq & right_side)
+        :  lar_base_constraint(kind, right_side), m_coeffs(left_side) {}
+    
+    lar_constraint(const lar_base_constraint & c) {
+        lean_assert(false); // should not be called : todo!
+    }
+
+    unsigned size() const {
+        return static_cast<unsigned>(m_coeffs.size());
+    }
+
+    vector<std::pair<mpq, var_index>> get_left_side_coefficients() const { return m_coeffs; }
+};
+}

src/util/lp/lar_core_solver.h

@@ -0,0 +1,801 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#pragma once
+#include "util/vector.h"
+#include <string>
+#include <utility>
+#include "util/lp/lp_core_solver_base.h"
+#include <algorithm>
+#include "util/lp/indexed_vector.h"
+#include "util/lp/binary_heap_priority_queue.h"
+#include "util/lp/breakpoint.h"
+#include "util/lp/stacked_unordered_set.h"
+#include "util/lp/lp_primal_core_solver.h"
+#include "util/lp/stacked_vector.h"
+#include "util/lp/lar_solution_signature.h"
+#include "util/lp/iterator_on_column.h"
+#include "util/lp/iterator_on_indexed_vector.h"
+#include "util/lp/stacked_value.h"
+namespace lean {
+
+class lar_core_solver  {
+    // m_sign_of_entering is set to 1 if the entering variable needs
+    // to grow and is set to -1  otherwise
+    int m_sign_of_entering_delta;
+    vector<std::pair<mpq, unsigned>> m_infeasible_linear_combination;
+    int m_infeasible_sum_sign; // todo: get rid of this field
+    vector<numeric_pair<mpq>> m_right_sides_dummy;
+    vector<mpq> m_costs_dummy;
+    vector<double> m_d_right_sides_dummy;
+    vector<double> m_d_costs_dummy;
+public:
+    stacked_value<simplex_strategy_enum> m_stacked_simplex_strategy;
+    stacked_vector<column_type> m_column_types;
+    // r - solver fields, for rational numbers
+    vector<numeric_pair<mpq>> m_r_x; // the solution
+    stacked_vector<numeric_pair<mpq>> m_r_low_bounds;
+    stacked_vector<numeric_pair<mpq>> m_r_upper_bounds;
+    static_matrix<mpq, numeric_pair<mpq>> m_r_A;
+    stacked_vector<unsigned> m_r_pushed_basis;
+    vector<unsigned> m_r_basis;
+    vector<unsigned> m_r_nbasis;
+    vector<int> m_r_heading;
+    stacked_vector<unsigned> m_r_columns_nz;
+    stacked_vector<unsigned> m_r_rows_nz;
+    
+    // d - solver fields, for doubles
+    vector<double> m_d_x; // the solution in doubles
+    vector<double> m_d_low_bounds;
+    vector<double> m_d_upper_bounds;
+    static_matrix<double, double> m_d_A;
+    stacked_vector<unsigned> m_d_pushed_basis;
+    vector<unsigned> m_d_basis;
+    vector<unsigned> m_d_nbasis;
+    vector<int> m_d_heading;
+
+
+    lp_primal_core_solver<mpq, numeric_pair<mpq>> m_r_solver; // solver in rational numbers
+
+    lp_primal_core_solver<double, double> m_d_solver; // solver in doubles
+    
+    lar_core_solver(
+                    lp_settings & settings,
+                    const column_namer & column_names
+                    );
+
+    lp_settings & settings() { return m_r_solver.m_settings;}
+    const lp_settings & settings() const { return m_r_solver.m_settings;}
+    
+    int get_infeasible_sum_sign() const { return m_infeasible_sum_sign;   }
+
+    const vector<std::pair<mpq, unsigned>> & get_infeasibility_info(int & inf_sign) const {
+        inf_sign = m_infeasible_sum_sign;
+        return m_infeasible_linear_combination;
+    }
+
+    void fill_not_improvable_zero_sum_from_inf_row();
+    
+    column_type get_column_type(unsigned j) { return m_column_types[j];}
+    
+    void init_costs(bool first_time);
+
+    void init_cost_for_column(unsigned j);
+
+    // returns m_sign_of_alpha_r
+    int column_is_out_of_bounds(unsigned j);
+
+    void calculate_pivot_row(unsigned i);
+
+    void print_pivot_row(std::ostream & out, unsigned row_index) const  { // remove later debug !!!!
+        for (unsigned j : m_r_solver.m_pivot_row.m_index) {
+            if (numeric_traits<mpq>::is_pos(m_r_solver.m_pivot_row.m_data[j]))
+                out << "+";
+            out << m_r_solver.m_pivot_row.m_data[j] << m_r_solver.column_name(j) << " ";
+        }
+        
+        out << " +" << m_r_solver.column_name(m_r_solver.m_basis[row_index]) << std::endl;
+        
+        for (unsigned j : m_r_solver.m_pivot_row.m_index) {
+            m_r_solver.print_column_bound_info(j, out);
+        }
+        m_r_solver.print_column_bound_info(m_r_solver.m_basis[row_index], out);
+        
+    }
+    
+
+    void advance_on_sorted_breakpoints(unsigned entering);
+
+    void change_slope_on_breakpoint(unsigned entering, breakpoint<numeric_pair<mpq>> * b, mpq & slope_at_entering);
+
+    bool row_is_infeasible(unsigned row);
+
+    bool row_is_evidence(unsigned row);
+
+    bool find_evidence_row();
+
+    void prefix_r();
+
+    void prefix_d();
+
+    unsigned m_m() const {
+        return m_r_A.row_count();
+    }
+
+    unsigned m_n() const {
+        return m_r_A.column_count();
+    }
+    
+    bool is_tiny() const { return this->m_m() < 10 && this->m_n() < 20; }
+
+    bool is_empty() const { return this->m_m() == 0 && this->m_n() == 0; }
+
+    template <typename L>
+    int get_sign(const L & v) {
+        return v > zero_of_type<L>() ? 1 : (v < zero_of_type<L>() ? -1 : 0);
+    }
+
+
+
+    void fill_evidence(unsigned row);
+
+
+
+    void solve();
+
+    bool low_bounds_are_set() const { return true; }
+
+    const indexed_vector<mpq> & get_pivot_row() const {
+        return m_r_solver.m_pivot_row;
+    }
+    
+    void fill_not_improvable_zero_sum();
+
+    void pop_basis(unsigned k) {
+        if (!settings().use_tableau()) {
+            m_r_pushed_basis.pop(k);        
+            m_r_basis = m_r_pushed_basis();
+            m_r_solver.init_basis_heading_and_non_basic_columns_vector();
+            m_d_pushed_basis.pop(k);
+            m_d_basis = m_d_pushed_basis();
+            m_d_solver.init_basis_heading_and_non_basic_columns_vector();
+        } else {
+            m_d_basis = m_r_basis;
+            m_d_nbasis = m_r_nbasis;
+            m_d_heading = m_r_heading;
+        }
+    }
+
+    void push() {
+        lean_assert(m_r_solver.basis_heading_is_correct());
+        lean_assert(!need_to_presolve_with_double_solver() || m_d_solver.basis_heading_is_correct());
+        lean_assert(m_column_types.size() == m_r_A.column_count());
+        m_stacked_simplex_strategy = settings().simplex_strategy();
+        m_stacked_simplex_strategy.push();
+        m_column_types.push();
+        // rational
+        if (!settings().use_tableau()) 
+            m_r_A.push();
+        m_r_low_bounds.push();
+        m_r_upper_bounds.push();
+        if (!settings().use_tableau()) {
+            push_vector(m_r_pushed_basis, m_r_basis);
+            push_vector(m_r_columns_nz, m_r_solver.m_columns_nz);
+            push_vector(m_r_rows_nz, m_r_solver.m_rows_nz);
+        }
+        
+        m_d_A.push();
+        if (!settings().use_tableau())
+            push_vector(m_d_pushed_basis, m_d_basis);
+    }
+
+    template <typename K> 
+    void push_vector(stacked_vector<K> & pushed_vector, const vector<K> & vector) {
+        lean_assert(pushed_vector.size() <= vector.size());
+        for (unsigned i = 0; i < vector.size();i++) {
+            if (i == pushed_vector.size()) {
+                pushed_vector.push_back(vector[i]);
+            } else {
+                pushed_vector[i] = vector[i];
+            }
+        }
+        pushed_vector.push();
+    }
+
+    void pop_markowitz_counts(unsigned k) {
+        m_r_columns_nz.pop(k);
+        m_r_rows_nz.pop(k);
+        m_r_solver.m_columns_nz.resize(m_r_columns_nz.size());
+        m_r_solver.m_rows_nz.resize(m_r_rows_nz.size());
+        for (unsigned i = 0; i < m_r_columns_nz.size(); i++)
+            m_r_solver.m_columns_nz[i] = m_r_columns_nz[i];
+        for (unsigned i = 0; i < m_r_rows_nz.size(); i++)
+            m_r_solver.m_rows_nz[i] = m_r_rows_nz[i];
+    }
+
+    
+    void pop(unsigned k) {
+        // rationals
+        if (!settings().use_tableau()) 
+            m_r_A.pop(k);
+        m_r_low_bounds.pop(k);
+        m_r_upper_bounds.pop(k);
+        m_column_types.pop(k);
+        
+        if (m_r_solver.m_factorization != nullptr) {
+            delete m_r_solver.m_factorization;
+            m_r_solver.m_factorization = nullptr;
+        }
+        m_r_x.resize(m_r_A.column_count());
+        m_r_solver.m_costs.resize(m_r_A.column_count());
+        m_r_solver.m_d.resize(m_r_A.column_count());
+        if(!settings().use_tableau())
+            pop_markowitz_counts(k);
+        m_d_A.pop(k);
+        if (m_d_solver.m_factorization != nullptr) {
+            delete m_d_solver.m_factorization;
+            m_d_solver.m_factorization = nullptr;
+        }
+        
+        m_d_x.resize(m_d_A.column_count());
+        pop_basis(k);
+        m_stacked_simplex_strategy.pop(k);
+        settings().simplex_strategy() = m_stacked_simplex_strategy;
+        lean_assert(m_r_solver.basis_heading_is_correct());
+        lean_assert(!need_to_presolve_with_double_solver() || m_d_solver.basis_heading_is_correct());
+    }
+
+    bool need_to_presolve_with_double_solver() const {
+        return settings().simplex_strategy() == simplex_strategy_enum::lu;
+    }
+
+    template <typename L>
+    bool is_zero_vector(const vector<L> & b) {
+        for (const L & m: b)
+            if (!is_zero(m)) return false;
+        return true;
+    }
+
+
+    bool update_xj_and_get_delta(unsigned j, non_basic_column_value_position pos_type, numeric_pair<mpq> & delta) {
+        auto & x = m_r_x[j];
+        switch (pos_type) {
+        case at_low_bound:
+            if (x == m_r_solver.m_low_bounds[j])
+                return false;
+            delta = m_r_solver.m_low_bounds[j] - x;
+            m_r_solver.m_x[j] = m_r_solver.m_low_bounds[j];
+            break;
+        case at_fixed:
+        case at_upper_bound:
+            if (x == m_r_solver.m_upper_bounds[j])
+                return false;
+            delta = m_r_solver.m_upper_bounds[j] - x;
+            x = m_r_solver.m_upper_bounds[j];
+            break;
+        case free_of_bounds: {
+            return false;
+        }
+        case not_at_bound:
+            switch (m_column_types[j]) {
+            case column_type::free_column:
+                return false;
+            case column_type::upper_bound:
+                delta = m_r_solver.m_upper_bounds[j] - x;
+                x = m_r_solver.m_upper_bounds[j];
+                break;
+            case column_type::low_bound:
+                delta = m_r_solver.m_low_bounds[j] - x;
+                x = m_r_solver.m_low_bounds[j];
+                break;
+            case column_type::boxed:
+                if (x > m_r_solver.m_upper_bounds[j]) {
+                    delta = m_r_solver.m_upper_bounds[j] - x;
+                    x += m_r_solver.m_upper_bounds[j];
+                } else {
+                    delta = m_r_solver.m_low_bounds[j] - x;
+                    x = m_r_solver.m_low_bounds[j];
+                }
+                break;
+            case column_type::fixed:
+                delta = m_r_solver.m_low_bounds[j] - x;
+                x = m_r_solver.m_low_bounds[j];
+                break;
+
+            default:
+                lean_assert(false);
+            }
+            break;
+        default:
+            lean_unreachable();
+        }
+        m_r_solver.remove_column_from_inf_set(j);
+        return true;
+    }
+
+    
+    
+    void prepare_solver_x_with_signature_tableau(const lar_solution_signature & signature) {
+        lean_assert(m_r_solver.inf_set_is_correct());
+        for (auto &t : signature) {
+            unsigned j = t.first;
+            if (m_r_heading[j] >= 0)
+                continue;
+            auto pos_type = t.second;
+            numeric_pair<mpq> delta;
+            if (!update_xj_and_get_delta(j, pos_type, delta))
+                continue;
+            for (const auto & cc : m_r_solver.m_A.m_columns[j]){
+                unsigned i = cc.m_i;
+                unsigned jb = m_r_solver.m_basis[i];
+                m_r_solver.m_x[jb] -= delta * m_r_solver.m_A.get_val(cc);
+                m_r_solver.update_column_in_inf_set(jb);
+            }
+            lean_assert(m_r_solver.A_mult_x_is_off() == false);
+        }
+        lean_assert(m_r_solver.inf_set_is_correct());
+    }
+
+    
+    template <typename L, typename K>
+    void prepare_solver_x_with_signature(const lar_solution_signature & signature, lp_primal_core_solver<L,K> & s) {
+        for (auto &t : signature) {
+            unsigned j = t.first;
+            lean_assert(m_r_heading[j] < 0);
+            auto pos_type = t.second;
+            switch (pos_type) {
+            case at_low_bound:
+                s.m_x[j] = s.m_low_bounds[j];
+                break;
+            case at_fixed:
+            case at_upper_bound:
+                s.m_x[j] = s.m_upper_bounds[j];
+                break;
+            case free_of_bounds: {
+                s.m_x[j] = zero_of_type<K>();
+                continue;
+            }
+            case not_at_bound:
+                  switch (m_column_types[j]) {
+                  case column_type::free_column:
+                      lean_assert(false); // unreachable
+                  case column_type::upper_bound:
+                      s.m_x[j] = s.m_upper_bounds[j];
+                      break;
+                  case column_type::low_bound:
+                      s.m_x[j] = s.m_low_bounds[j];
+                      break;
+                  case column_type::boxed:
+                      if (settings().random_next() % 2) {
+                          s.m_x[j] = s.m_low_bounds[j];
+                      } else {
+                          s.m_x[j] = s.m_upper_bounds[j];
+                      }
+                      break;
+                  case column_type::fixed:
+                      s.m_x[j] = s.m_low_bounds[j];
+                      break;
+                  default:
+                      lean_assert(false);
+                  }
+                  break;
+            default:
+                lean_unreachable();
+            }
+        }
+
+        lean_assert(is_zero_vector(s.m_b));
+        s.solve_Ax_eq_b();
+    }
+
+    template <typename L, typename K> 
+    void catch_up_in_lu_in_reverse(const vector<unsigned> & trace_of_basis_change, lp_primal_core_solver<L,K> & cs) {
+        // recover the previous working basis
+        for (unsigned i = trace_of_basis_change.size(); i > 0;  i-= 2) {
+            unsigned entering = trace_of_basis_change[i-1];
+            unsigned leaving = trace_of_basis_change[i-2];
+            cs.change_basis_unconditionally(entering, leaving);
+        }
+        cs.init_lu();
+    }
+
+    //basis_heading is the basis heading of the solver owning trace_of_basis_change
+    // here we compact the trace as we go to avoid unnecessary column changes
+    template <typename L, typename K> 
+    void catch_up_in_lu(const vector<unsigned> & trace_of_basis_change, const vector<int> & basis_heading, lp_primal_core_solver<L,K> & cs) {
+        if (cs.m_factorization == nullptr || cs.m_factorization->m_refactor_counter + trace_of_basis_change.size()/2 >= 200) {
+            for (unsigned i = 0; i < trace_of_basis_change.size(); i+= 2) {
+                unsigned entering = trace_of_basis_change[i];
+                unsigned leaving = trace_of_basis_change[i+1];
+                cs.change_basis_unconditionally(entering, leaving);
+            }
+            if (cs.m_factorization != nullptr)
+                delete cs.m_factorization;
+            cs.m_factorization = nullptr;
+        } else {
+            indexed_vector<L> w(cs.m_A.row_count());
+            // the queues of delayed indices
+            std::queue<unsigned> entr_q, leav_q;
+            auto * l = cs.m_factorization;
+            lean_assert(l->get_status() == LU_status::OK);
+            for (unsigned i = 0; i < trace_of_basis_change.size(); i+= 2) {
+                unsigned entering = trace_of_basis_change[i];
+                unsigned leaving = trace_of_basis_change[i+1];
+                bool good_e = basis_heading[entering] >= 0 && cs.m_basis_heading[entering] < 0;
+                bool good_l = basis_heading[leaving] < 0 && cs.m_basis_heading[leaving] >= 0;
+                if (!good_e && !good_l) continue;
+                if (good_e && !good_l) {
+                    while (!leav_q.empty() && cs.m_basis_heading[leav_q.front()] < 0)
+                        leav_q.pop();
+                    if (!leav_q.empty()) {
+                        leaving = leav_q.front();
+                        leav_q.pop();
+                    } else {
+                        entr_q.push(entering);
+                        continue;
+                    }
+                } else if (!good_e && good_l) {
+                    while (!entr_q.empty() && cs.m_basis_heading[entr_q.front()] >= 0)
+                        entr_q.pop();
+                    if (!entr_q.empty()) {
+                        entering = entr_q.front();
+                        entr_q.pop();
+                    } else {
+                        leav_q.push(leaving);
+                        continue;
+                    }
+                }
+                lean_assert(cs.m_basis_heading[entering] < 0);
+                lean_assert(cs.m_basis_heading[leaving] >= 0);
+                if (l->get_status() == LU_status::OK) {
+                    l->prepare_entering(entering, w); // to init vector w
+                    l->replace_column(zero_of_type<L>(), w, cs.m_basis_heading[leaving]);
+                }
+                cs.change_basis_unconditionally(entering, leaving);
+            }
+            if (l->get_status() != LU_status::OK) {
+                delete l;
+                cs.m_factorization = nullptr;
+            }
+        }
+        if (cs.m_factorization == nullptr) {
+            if (numeric_traits<L>::precise())
+                init_factorization(cs.m_factorization, cs.m_A, cs.m_basis, settings());
+        }
+    }
+
+    bool no_r_lu() const {
+        return m_r_solver.m_factorization == nullptr || m_r_solver.m_factorization->get_status() == LU_status::Degenerated; 
+    }
+
+    void solve_on_signature_tableau(const lar_solution_signature & signature, const vector<unsigned> & changes_of_basis) {
+        r_basis_is_OK();
+        lean_assert(settings().use_tableau());
+        bool r = catch_up_in_lu_tableau(changes_of_basis, m_d_solver.m_basis_heading);
+
+        if (!r) { // it is the case where m_d_solver gives a degenerated basis
+            prepare_solver_x_with_signature_tableau(signature); // still are going to use the signature partially
+            m_r_solver.find_feasible_solution();
+            m_d_basis = m_r_basis;
+            m_d_heading = m_r_heading;
+            m_d_nbasis = m_r_nbasis;
+            delete m_d_solver.m_factorization;
+            m_d_solver.m_factorization = nullptr;
+        } else {
+            prepare_solver_x_with_signature_tableau(signature);
+            m_r_solver.start_tracing_basis_changes();
+            m_r_solver.find_feasible_solution();
+            if (settings().get_cancel_flag())
+                return;
+            m_r_solver.stop_tracing_basis_changes();
+            // and now catch up in the double solver
+            lean_assert(m_r_solver.total_iterations() >= m_r_solver.m_trace_of_basis_change_vector.size() /2);
+            catch_up_in_lu(m_r_solver.m_trace_of_basis_change_vector, m_r_solver.m_basis_heading, m_d_solver);
+        }
+        lean_assert(r_basis_is_OK());
+    }
+
+    bool adjust_x_of_column(unsigned j) {
+        /*
+        if (m_r_solver.m_basis_heading[j] >= 0) {
+            return false;
+        }
+
+        if (m_r_solver.column_is_feasible(j)) {
+            return false;
+        }
+
+        m_r_solver.snap_column_to_bound_tableau(j);
+        lean_assert(m_r_solver.column_is_feasible(j));
+        m_r_solver.m_inf_set.erase(j);
+        */
+        lean_assert(false);
+        return true;
+    }
+
+    
+    bool catch_up_in_lu_tableau(const vector<unsigned> & trace_of_basis_change, const vector<int> & basis_heading) {
+        lean_assert(r_basis_is_OK());
+        // the queues of delayed indices
+        std::queue<unsigned> entr_q, leav_q;
+        for (unsigned i = 0; i < trace_of_basis_change.size(); i+= 2) {
+            unsigned entering = trace_of_basis_change[i];
+            unsigned leaving = trace_of_basis_change[i+1];
+            bool good_e = basis_heading[entering] >= 0 && m_r_solver.m_basis_heading[entering] < 0;
+            bool good_l = basis_heading[leaving] < 0 && m_r_solver.m_basis_heading[leaving] >= 0;
+            if (!good_e && !good_l) continue;
+            if (good_e && !good_l) {
+                while (!leav_q.empty() && m_r_solver.m_basis_heading[leav_q.front()] < 0)
+                    leav_q.pop();
+                if (!leav_q.empty()) {
+                    leaving = leav_q.front();
+                    leav_q.pop();
+                } else {
+                    entr_q.push(entering);
+                    continue;
+                }
+            } else if (!good_e && good_l) {
+                while (!entr_q.empty() && m_r_solver.m_basis_heading[entr_q.front()] >= 0)
+                    entr_q.pop();
+                if (!entr_q.empty()) {
+                    entering = entr_q.front();
+                    entr_q.pop();
+                } else {
+                    leav_q.push(leaving);
+                    continue;
+                }
+            }
+            lean_assert(m_r_solver.m_basis_heading[entering] < 0);
+            lean_assert(m_r_solver.m_basis_heading[leaving] >= 0);
+            m_r_solver.change_basis_unconditionally(entering, leaving);
+            if(!m_r_solver.pivot_column_tableau(entering, m_r_solver.m_basis_heading[entering])) {
+				// unroll the last step
+                m_r_solver.change_basis_unconditionally(leaving, entering);
+#ifdef LEAN_DEBUG
+                bool t =
+#endif
+                    m_r_solver.pivot_column_tableau(leaving, m_r_solver.m_basis_heading[leaving]);
+#ifdef LEAN_DEBUG
+                lean_assert(t);
+#endif 
+                return false;
+            }
+        }
+        lean_assert(r_basis_is_OK());
+        return true;
+    }
+
+
+    bool r_basis_is_OK() const {
+#ifdef LEAN_DEBUG
+        if (!m_r_solver.m_settings.use_tableau())
+            return true;
+        for (unsigned j : m_r_solver.m_basis) {
+            lean_assert(m_r_solver.m_A.m_columns[j].size() == 1);
+            lean_assert(m_r_solver.m_A.get_val(m_r_solver.m_A.m_columns[j][0]) == one_of_type<mpq>());
+        }
+        for (unsigned j =0; j < m_r_solver.m_basis_heading.size(); j++) {
+            if (m_r_solver.m_basis_heading[j] >= 0) continue;
+            if (m_r_solver.m_column_types[j] == column_type::fixed) continue;
+            lean_assert(static_cast<unsigned>(- m_r_solver.m_basis_heading[j] - 1) < m_r_solver.m_column_types.size());
+            lean_assert( m_r_solver.m_basis_heading[j] <= -1);
+        }
+#endif
+        return true;
+    }
+    
+    void solve_on_signature(const lar_solution_signature & signature, const vector<unsigned> & changes_of_basis) {
+        lean_assert(!settings().use_tableau());
+        if (m_r_solver.m_factorization == nullptr) {
+            for (unsigned j = 0; j < changes_of_basis.size(); j+=2) {
+                unsigned entering = changes_of_basis[j];
+                unsigned leaving = changes_of_basis[j + 1];
+                m_r_solver.change_basis_unconditionally(entering, leaving);
+            }
+            init_factorization(m_r_solver.m_factorization, m_r_A, m_r_basis, settings());
+        } else {
+            catch_up_in_lu(changes_of_basis, m_d_solver.m_basis_heading, m_r_solver);
+        }
+
+        if (no_r_lu()) { // it is the case where m_d_solver gives a degenerated basis, we need to roll back
+            //            std::cout << "no_r_lu" << std::endl;
+            catch_up_in_lu_in_reverse(changes_of_basis, m_r_solver);
+            m_r_solver.find_feasible_solution();
+            m_d_basis = m_r_basis;
+            m_d_heading = m_r_heading;
+            m_d_nbasis = m_r_nbasis;
+            delete m_d_solver.m_factorization;
+            m_d_solver.m_factorization = nullptr;
+        } else {
+            prepare_solver_x_with_signature(signature, m_r_solver);
+            m_r_solver.start_tracing_basis_changes();
+            m_r_solver.find_feasible_solution();
+            if (settings().get_cancel_flag())
+                return;
+            m_r_solver.stop_tracing_basis_changes();
+            // and now catch up in the double solver
+            lean_assert(m_r_solver.total_iterations() >= m_r_solver.m_trace_of_basis_change_vector.size() /2);
+            catch_up_in_lu(m_r_solver.m_trace_of_basis_change_vector, m_r_solver.m_basis_heading, m_d_solver);
+        }
+    }
+
+    void create_double_matrix(static_matrix<double, double> & A) {
+        for (unsigned i = 0; i < m_r_A.row_count(); i++) {
+            auto & row = m_r_A.m_rows[i];
+            for (row_cell<mpq> & c : row) {
+                A.set(i, c.m_j, c.get_val().get_double());
+            }
+        }
+    }
+
+    void fill_basis_d(
+                      vector<unsigned>& basis_d,
+                      vector<int>& heading_d,
+                      vector<unsigned>& nbasis_d){
+        basis_d = m_r_basis;
+        heading_d = m_r_heading;
+        nbasis_d = m_r_nbasis;
+    }
+
+    template <typename L, typename K>
+    void extract_signature_from_lp_core_solver(const lp_primal_core_solver<L, K> & solver, lar_solution_signature & signature) {
+        signature.clear();
+        lean_assert(signature.size() == 0);
+        for (unsigned j = 0; j < solver.m_basis_heading.size(); j++) {
+            if (solver.m_basis_heading[j] < 0) {
+                signature[j] = solver.get_non_basic_column_value_position(j);
+            }
+        }
+    }
+
+    void get_bounds_for_double_solver() {
+        unsigned n = m_n();
+        m_d_low_bounds.resize(n);
+        m_d_upper_bounds.resize(n);
+        double delta = find_delta_for_strict_boxed_bounds().get_double();
+        if (delta > 0.000001)
+            delta = 0.000001;
+        for (unsigned j = 0; j < n; j++) {
+            if (low_bound_is_set(j)) {
+                const auto & lb = m_r_solver.m_low_bounds[j];
+                m_d_low_bounds[j] = lb.x.get_double() + delta * lb.y.get_double();
+            }
+            if (upper_bound_is_set(j)) {
+                const auto & ub = m_r_solver.m_upper_bounds[j];
+                m_d_upper_bounds[j] = ub.x.get_double() + delta * ub.y.get_double();
+                lean_assert(!low_bound_is_set(j) || (m_d_upper_bounds[j] >= m_d_low_bounds[j]));
+            }
+        }
+    }
+
+    void scale_problem_for_doubles(
+                        static_matrix<double, double>& A,        
+                        vector<double> & low_bounds,
+                        vector<double> & upper_bounds) {
+        vector<double> column_scale_vector;
+        vector<double> right_side_vector(A.column_count());
+        settings().reps_in_scaler = 5;
+        scaler<double, double > scaler(right_side_vector,
+                                       A,
+                                       settings().scaling_minimum,
+                                       settings().scaling_maximum,
+                                       column_scale_vector,
+                                       settings());
+        if (! scaler.scale()) {
+            // the scale did not succeed, unscaling
+            A.clear();
+            create_double_matrix(A);
+        } else {
+            for (unsigned j = 0; j < A.column_count(); j++) {
+                if (m_r_solver.column_has_upper_bound(j)) {
+                    upper_bounds[j] /= column_scale_vector[j];
+                }
+                if (m_r_solver.column_has_low_bound(j)) {
+                    low_bounds[j] /= column_scale_vector[j];
+                }
+            }
+        }
+        
+    }
+    // returns the trace of basis changes
+    vector<unsigned> find_solution_signature_with_doubles(lar_solution_signature & signature) {
+        if (m_d_solver.m_factorization == nullptr || m_d_solver.m_factorization->get_status() != LU_status::OK) {
+            vector<unsigned> ret;
+            return ret;
+        }
+        get_bounds_for_double_solver();
+
+        extract_signature_from_lp_core_solver(m_r_solver, signature);
+        prepare_solver_x_with_signature(signature, m_d_solver);
+        m_d_solver.start_tracing_basis_changes();
+        m_d_solver.find_feasible_solution();
+        if (settings().get_cancel_flag())
+            return vector<unsigned>();
+            
+        m_d_solver.stop_tracing_basis_changes();
+        extract_signature_from_lp_core_solver(m_d_solver, signature);
+        return m_d_solver.m_trace_of_basis_change_vector;
+    }
+
+
+    bool low_bound_is_set(unsigned j) const {
+        switch (m_column_types[j]) {
+        case column_type::free_column:
+        case column_type::upper_bound:
+            return false;
+        case column_type::low_bound:
+        case column_type::boxed:
+        case column_type::fixed:
+            return true;
+        default:
+            lean_assert(false);
+        }
+        return false;
+    }
+    
+    bool upper_bound_is_set(unsigned j) const {
+        switch (m_column_types[j]) {
+        case column_type::free_column:
+        case column_type::low_bound:
+            return false;
+        case column_type::upper_bound:
+        case column_type::boxed:
+        case column_type::fixed:
+            return true;
+        default:
+            lean_assert(false);
+        }
+        return false;
+    }
+
+    void update_delta(mpq& delta, numeric_pair<mpq> const& l, numeric_pair<mpq> const& u) const {
+        lean_assert(l <= u);
+        if (l.x < u.x && l.y > u.y) {
+            mpq delta1 = (u.x - l.x) / (l.y - u.y);
+            if (delta1 < delta) {
+                delta = delta1;
+            }
+        }
+        lean_assert(l.x + delta * l.y <= u.x + delta * u.y);
+    }
+
+
+    mpq find_delta_for_strict_boxed_bounds() const{
+        mpq delta = numeric_traits<mpq>::one();
+        for (unsigned j = 0; j < m_r_A.column_count(); j++ ) {
+            if (m_column_types()[j] != column_type::boxed)
+                continue;
+            update_delta(delta, m_r_low_bounds[j], m_r_upper_bounds[j]);
+
+        }
+        return delta;
+    }
+
+    
+    mpq find_delta_for_strict_bounds(const mpq & initial_delta) const{
+        mpq delta = initial_delta;
+        for (unsigned j = 0; j < m_r_A.column_count(); j++ ) {
+            if (low_bound_is_set(j))
+                update_delta(delta, m_r_low_bounds[j], m_r_x[j]);
+            if (upper_bound_is_set(j))
+                update_delta(delta, m_r_x[j], m_r_upper_bounds[j]);
+        }
+        return delta;
+    }
+
+    void init_column_row_nz_for_r_solver() {
+        m_r_solver.init_column_row_non_zeroes();
+    }
+
+    linear_combination_iterator<mpq> * get_column_iterator(unsigned j) {
+        if (settings().use_tableau()) {
+            return new iterator_on_column<mpq, numeric_pair<mpq>>(m_r_solver.m_A.m_columns[j], m_r_solver.m_A);
+        } else {
+            m_r_solver.solve_Bd(j);
+            return new iterator_on_indexed_vector<mpq>(m_r_solver.m_ed);
+        }
+    }
+    
+};
+}

src/util/lp/lar_core_solver.hpp

@@ -0,0 +1,293 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#include <string>
+#include "util/vector.h"
+#include "util/lp/lar_core_solver.h"
+#include "util/lp/lar_solution_signature.h"
+namespace lean {
+lar_core_solver::lar_core_solver(
+                                 lp_settings & settings,
+                                 const column_namer & column_names
+                                 ):
+    m_infeasible_sum_sign(0),
+    m_r_solver(m_r_A,
+                    m_right_sides_dummy,
+                    m_r_x,
+                    m_r_basis,
+                    m_r_nbasis,
+                    m_r_heading,
+                    m_costs_dummy,
+                    m_column_types(),
+                    m_r_low_bounds(),
+                    m_r_upper_bounds(),
+                    settings,
+               column_names),
+    m_d_solver(m_d_A,
+                    m_d_right_sides_dummy,
+                    m_d_x,
+                    m_d_basis,
+                    m_d_nbasis,
+                    m_d_heading,
+                    m_d_costs_dummy,
+                    m_column_types(),
+                    m_d_low_bounds,
+                    m_d_upper_bounds,
+                    settings,
+                    column_names){}
+
+void lar_core_solver::init_costs(bool first_time) {
+    lean_assert(false); // should not be called
+    // lean_assert(this->m_x.size() >= this->m_n());
+    // lean_assert(this->m_column_types.size() >= this->m_n());
+    // if (first_time)
+    //     this->m_costs.resize(this->m_n());
+    // X inf = this->m_infeasibility;
+    // this->m_infeasibility = zero_of_type<X>();
+    // for (unsigned j = this->m_n(); j--;)
+    //     init_cost_for_column(j);
+    // if (!(first_time || inf >= this->m_infeasibility)) {
+    //     LP_OUT(this->m_settings, "iter = " << this->total_iterations() << std::endl);
+    //     LP_OUT(this->m_settings, "inf was " << T_to_string(inf) << " and now " << T_to_string(this->m_infeasibility) << std::endl);
+    //     lean_assert(false);
+    // }
+    // if (inf == this->m_infeasibility)
+    //     this->m_iters_with_no_cost_growing++;
+}
+
+
+void lar_core_solver::init_cost_for_column(unsigned j) {
+    /*
+    // If j is a breakpoint column, then we set the cost zero.
+    // When anylyzing an entering column candidate we update the cost of the breakpoints columns to get the left or the right derivative if the infeasibility function
+    const numeric_pair<mpq> & x = this->m_x[j];
+    // set zero cost for each non-basis column
+    if (this->m_basis_heading[j] < 0) {
+        this->m_costs[j] = numeric_traits<T>::zero();
+        return;
+    }
+    // j is a basis column
+    switch (this->m_column_types[j]) {
+    case fixed:
+    case column_type::boxed:
+        if (x > this->m_upper_bounds[j]) {
+            this->m_costs[j] = 1;
+            this->m_infeasibility += x - this->m_upper_bounds[j];
+        } else if (x < this->m_low_bounds[j]) {
+            this->m_infeasibility += this->m_low_bounds[j] - x;
+            this->m_costs[j] = -1;
+        } else {
+            this->m_costs[j] = numeric_traits<T>::zero();
+        }
+        break;
+    case low_bound:
+        if (x < this->m_low_bounds[j]) {
+            this->m_costs[j] = -1;
+            this->m_infeasibility += this->m_low_bounds[j] - x;
+        } else {
+            this->m_costs[j] = numeric_traits<T>::zero();
+        }
+        break;
+    case upper_bound:
+        if (x > this->m_upper_bounds[j]) {
+            this->m_costs[j] = 1;
+            this->m_infeasibility += x - this->m_upper_bounds[j];
+        } else {
+            this->m_costs[j] = numeric_traits<T>::zero();
+        }
+        break;
+    case free_column:
+        this->m_costs[j] = numeric_traits<T>::zero();
+        break;
+    default:
+        lean_assert(false);
+        break;
+        }*/
+}
+
+
+// returns m_sign_of_alpha_r
+int lar_core_solver::column_is_out_of_bounds(unsigned j) {
+    /*
+    switch (this->m_column_type[j]) {
+    case fixed:
+    case column_type::boxed:
+        if (this->x_below_low_bound(j)) {
+            return -1;
+        }
+        if (this->x_above_upper_bound(j)) {
+            return 1;
+        }
+        return 0;
+    case low_bound:
+        if (this->x_below_low_bound(j)) {
+            return -1;
+        }
+        return 0;
+    case upper_bound:
+        if (this->x_above_upper_bound(j)) {
+            return 1;
+        }
+        return 0;
+    default:
+        return 0;
+        break;
+        }*/
+    lean_assert(false);
+    return true;
+}
+
+
+
+void lar_core_solver::calculate_pivot_row(unsigned i) {
+    lean_assert(!m_r_solver.use_tableau());
+    lean_assert(m_r_solver.m_pivot_row.is_OK());
+    m_r_solver.m_pivot_row_of_B_1.clear();
+    m_r_solver.m_pivot_row_of_B_1.resize(m_r_solver.m_m());
+    m_r_solver.m_pivot_row.clear();
+    m_r_solver.m_pivot_row.resize(m_r_solver.m_n());
+    if (m_r_solver.m_settings.use_tableau()) {
+        unsigned basis_j = m_r_solver.m_basis[i];
+        for (auto & c : m_r_solver.m_A.m_rows[i]) {
+            if (c.m_j != basis_j)
+                m_r_solver.m_pivot_row.set_value(c.get_val(), c.m_j);
+        }
+        return;
+    }
+
+    m_r_solver.calculate_pivot_row_of_B_1(i);
+    m_r_solver.calculate_pivot_row_when_pivot_row_of_B1_is_ready(i);
+}
+
+
+
+ void lar_core_solver::prefix_r() {
+     if (!m_r_solver.m_settings.use_tableau()) {
+        m_r_solver.m_copy_of_xB.resize(m_r_solver.m_n());
+        m_r_solver.m_ed.resize(m_r_solver.m_m());
+        m_r_solver.m_pivot_row.resize(m_r_solver.m_n()); 
+        m_r_solver.m_pivot_row_of_B_1.resize(m_r_solver.m_m());
+        m_r_solver.m_w.resize(m_r_solver.m_m());
+        m_r_solver.m_y.resize(m_r_solver.m_m());
+        m_r_solver.m_rows_nz.resize(m_r_solver.m_m(), 0);
+        m_r_solver.m_columns_nz.resize(m_r_solver.m_n(), 0); 
+        init_column_row_nz_for_r_solver();
+    }
+
+    m_r_solver.m_b.resize(m_r_solver.m_m());
+    if (m_r_solver.m_settings.simplex_strategy() != simplex_strategy_enum::tableau_rows) {
+        if(m_r_solver.m_settings.use_breakpoints_in_feasibility_search)
+            m_r_solver.m_breakpoint_indices_queue.resize(m_r_solver.m_n());
+        m_r_solver.m_costs.resize(m_r_solver.m_n());
+        m_r_solver.m_d.resize(m_r_solver.m_n());
+        m_r_solver.m_using_infeas_costs = true;
+    }
+}
+
+ void lar_core_solver::prefix_d() {
+    m_d_solver.m_b.resize(m_d_solver.m_m());
+    m_d_solver.m_breakpoint_indices_queue.resize(m_d_solver.m_n());
+    m_d_solver.m_copy_of_xB.resize(m_d_solver.m_n());
+    m_d_solver.m_costs.resize(m_d_solver.m_n());
+    m_d_solver.m_d.resize(m_d_solver.m_n());
+    m_d_solver.m_ed.resize(m_d_solver.m_m());
+    m_d_solver.m_pivot_row.resize(m_d_solver.m_n());
+    m_d_solver.m_pivot_row_of_B_1.resize(m_d_solver.m_m());
+    m_d_solver.m_w.resize(m_d_solver.m_m());
+    m_d_solver.m_y.resize(m_d_solver.m_m());
+    m_d_solver.m_steepest_edge_coefficients.resize(m_d_solver.m_n());
+    m_d_solver.m_column_norms.clear();
+    m_d_solver.m_column_norms.resize(m_d_solver.m_n(), 2);
+    m_d_solver.m_inf_set.clear();
+    m_d_solver.m_inf_set.resize(m_d_solver.m_n());
+}
+
+void lar_core_solver::fill_not_improvable_zero_sum_from_inf_row() {
+    lean_assert(m_r_solver.A_mult_x_is_off() == false);
+    unsigned bj = m_r_basis[m_r_solver.m_inf_row_index_for_tableau];
+    m_infeasible_sum_sign =  m_r_solver.inf_sign_of_column(bj);
+    m_infeasible_linear_combination.clear();
+    for (auto & rc : m_r_solver.m_A.m_rows[m_r_solver.m_inf_row_index_for_tableau]) {
+        m_infeasible_linear_combination.push_back(std::make_pair( rc.get_val(), rc.m_j));
+    }
+}
+
+void lar_core_solver::fill_not_improvable_zero_sum() {
+    if (m_r_solver.m_settings.simplex_strategy() == simplex_strategy_enum::tableau_rows) {
+        fill_not_improvable_zero_sum_from_inf_row();
+        return;
+    }
+    //  reusing the existing mechanism for row_feasibility_loop
+    m_infeasible_sum_sign = m_r_solver.m_settings.use_breakpoints_in_feasibility_search? -1 : 1;
+    m_infeasible_linear_combination.clear();
+    for (auto j : m_r_solver.m_basis) {
+        const mpq & cost_j = m_r_solver.m_costs[j];
+        if (!numeric_traits<mpq>::is_zero(cost_j)) {
+            m_infeasible_linear_combination.push_back(std::make_pair(cost_j, j));
+        }
+    }
+    // m_costs are expressed by m_d ( additional costs), substructing the latter gives 0
+    for (unsigned j = 0; j < m_r_solver.m_n(); j++) {
+        if (m_r_solver.m_basis_heading[j] >= 0) continue;
+        const mpq & d_j = m_r_solver.m_d[j];
+        if (!numeric_traits<mpq>::is_zero(d_j)) {
+            m_infeasible_linear_combination.push_back(std::make_pair(-d_j, j));
+        }
+    }
+}
+
+
+void lar_core_solver::solve() {
+    lean_assert(m_r_solver.non_basic_columns_are_set_correctly());
+    lean_assert(m_r_solver.inf_set_is_correct());
+    if (m_r_solver.current_x_is_feasible() && m_r_solver.m_look_for_feasible_solution_only) {
+        m_r_solver.set_status(OPTIMAL);
+        return;
+    }
+    ++settings().st().m_need_to_solve_inf;
+    lean_assert(!m_r_solver.A_mult_x_is_off());
+    lean_assert((!settings().use_tableau()) || r_basis_is_OK());
+    if (need_to_presolve_with_double_solver()) {
+        prefix_d();
+        lar_solution_signature solution_signature;
+        vector<unsigned> changes_of_basis = find_solution_signature_with_doubles(solution_signature);
+        if (m_d_solver.get_status() == TIME_EXHAUSTED) {
+            m_r_solver.set_status(TIME_EXHAUSTED);
+            return;
+        }
+        if (settings().use_tableau())
+            solve_on_signature_tableau(solution_signature, changes_of_basis);
+        else 
+            solve_on_signature(solution_signature, changes_of_basis);
+        lean_assert(!settings().use_tableau() || r_basis_is_OK());
+    } else {
+        if (!settings().use_tableau()) {
+            bool snapped = m_r_solver.snap_non_basic_x_to_bound();   
+            lean_assert(m_r_solver.non_basic_columns_are_set_correctly());
+            if (snapped)
+                m_r_solver.solve_Ax_eq_b();
+        }
+        if (m_r_solver.m_look_for_feasible_solution_only)
+            m_r_solver.find_feasible_solution();
+        else
+            m_r_solver.solve();
+        lean_assert(!settings().use_tableau() || r_basis_is_OK());
+    }
+    if (m_r_solver.get_status() == INFEASIBLE) {
+        fill_not_improvable_zero_sum();
+    } else if (m_r_solver.get_status() != UNBOUNDED) {
+        m_r_solver.set_status(OPTIMAL);
+    }
+    lean_assert(r_basis_is_OK());
+    lean_assert(m_r_solver.non_basic_columns_are_set_correctly());
+    lean_assert(m_r_solver.inf_set_is_correct());
+}
+
+
+}
+

src/util/lp/lar_core_solver_instances.cpp

@@ -0,0 +1,10 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#include <utility>
+#include <memory>
+#include <string>
+#include "util/vector.h"
+#include <functional>
+#include "util/lp/lar_core_solver.hpp"

src/util/lp/lar_solution_signature.h

@@ -0,0 +1,13 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+
+#pragma once
+#include "util/vector.h"
+#include "util/debug.h"
+#include "util/lp/lp_settings.h"
+#include <unordered_map>
+namespace lean {
+typedef std::unordered_map<unsigned, non_basic_column_value_position> lar_solution_signature;
+}

src/util/lp/lar_term.h

@@ -0,0 +1,64 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#pragma once
+#include "util/lp/indexed_vector.h"
+namespace lean {
+struct lar_term {
+    // the term evaluates to sum of m_coeffs + m_v
+    std::unordered_map<unsigned, mpq> m_coeffs;
+    mpq m_v;
+    lar_term() {}
+    void add_to_map(unsigned j, const mpq& c) {
+        auto it = m_coeffs.find(j);
+        if (it == m_coeffs.end()) {
+            m_coeffs.emplace(j, c);
+        } else {
+            it->second += c;
+            if (is_zero(it->second))
+                m_coeffs.erase(it);
+        }
+    }
+
+    unsigned size() const { return static_cast<unsigned>(m_coeffs.size()); }
+    
+    const std::unordered_map<unsigned, mpq> & coeffs() const {
+        return m_coeffs;
+    }
+    
+    lar_term(const vector<std::pair<mpq, unsigned>>& coeffs,
+             const mpq & v) : m_v(v) {
+        for (const auto & p : coeffs) {
+            add_to_map(p.second, p.first);
+        }
+    }
+    bool operator==(const lar_term & a) const {  return false; } // take care not to create identical terms
+    bool operator!=(const lar_term & a) const {  return ! (*this == a);}
+    // some terms get used in add constraint
+    // it is the same as the offset in the m_constraints
+
+    vector<std::pair<mpq, unsigned>> coeffs_as_vector() const {
+        vector<std::pair<mpq, unsigned>> ret;
+        for (const auto & p :  m_coeffs) {
+            ret.push_back(std::make_pair(p.second, p.first));
+        }
+        return ret;
+    }
+
+    // j is the basic variable to substitute
+    void subst(unsigned j, indexed_vector<mpq> & li) {
+        auto it = m_coeffs.find(j);
+        if (it == m_coeffs.end()) return;
+        const mpq & b = it->second;
+        for (unsigned it_j :li.m_index) {
+            add_to_map(it_j, - b * li.m_data[it_j]);
+        }
+        m_coeffs.erase(it);
+    }
+    
+    bool contains(unsigned j) const {
+        return m_coeffs.find(j) != m_coeffs.end();
+    }
+};
+}

src/util/lp/linear_combination_iterator.h

@@ -0,0 +1,50 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#pragma once
+namespace lean {
+template <typename T>
+struct linear_combination_iterator {
+    virtual bool next(T & a, unsigned & i) = 0;
+    virtual bool next(unsigned & i) = 0;
+    virtual void reset() = 0;
+    virtual linear_combination_iterator * clone() = 0;
+    virtual ~linear_combination_iterator(){}
+    virtual unsigned size() const = 0;
+};
+template <typename T>
+struct linear_combination_iterator_on_vector : linear_combination_iterator<T> {
+    vector<std::pair<T, unsigned>> & m_vector;
+    int m_offset;
+    bool next(T & a, unsigned & i) {
+        if(m_offset >= m_vector.size())
+            return false;
+        auto & p = m_vector[m_offset];
+        a = p.first;
+        i = p.second;
+        m_offset++;
+        return true;
+    }
+
+    bool next(unsigned & i) {
+        if(m_offset >= m_vector.size())
+            return false;
+        auto & p = m_vector[m_offset];
+        i = p.second;
+        m_offset++;
+        return true;
+    }
+    
+    void reset() {m_offset = 0;}
+    linear_combination_iterator<T> * clone() {
+        return new linear_combination_iterator_on_vector(m_vector);
+    }
+    linear_combination_iterator_on_vector(vector<std::pair<T, unsigned>> & vec):
+        m_vector(vec),
+        m_offset(0)
+    {}
+    unsigned size() const { return m_vector.size(); }
+};
+
+}

src/util/lp/lp_core_solver_base.h

@@ -0,0 +1,690 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#pragma once
+#include <set>
+#include "util/vector.h"
+#include <string>
+#include "util/lp/lp_utils.h"
+#include "util/lp/core_solver_pretty_printer.h"
+#include "util/lp/numeric_pair.h"
+#include "util/lp/static_matrix.h"
+#include "util/lp/lu.h"
+#include "util/lp/permutation_matrix.h"
+#include "util/lp/column_namer.h"
+namespace lean {
+
+template <typename T, typename X> // X represents the type of the x variable and the bounds
+class lp_core_solver_base {    
+    unsigned m_total_iterations;
+    unsigned m_iters_with_no_cost_growing;
+    unsigned inc_total_iterations() { ++m_settings.st().m_total_iterations; return m_total_iterations++; }
+private:
+    lp_status m_status;
+public:
+    bool current_x_is_feasible() const { return m_inf_set.size() == 0; }
+    bool current_x_is_infeasible() const { return m_inf_set.size() != 0; }
+    int_set m_inf_set;
+    bool m_using_infeas_costs;
+
+
+    vector<unsigned>      m_columns_nz; // m_columns_nz[i] keeps an approximate value of non zeroes the i-th column
+    vector<unsigned>      m_rows_nz; // m_rows_nz[i] keeps an approximate value of non zeroes in the i-th row
+    indexed_vector<T>     m_pivot_row_of_B_1;  // the pivot row of the reverse of B
+    indexed_vector<T>     m_pivot_row; // this is the real pivot row of the simplex tableu
+    static_matrix<T, X> & m_A; // the matrix A
+    vector<X> &           m_b; // the right side
+    vector<unsigned> &    m_basis;
+    vector<unsigned>&     m_nbasis;
+    vector<int>&          m_basis_heading;
+    vector<X> &           m_x; // a feasible solution, the fist time set in the constructor
+    vector<T> &           m_costs;
+    lp_settings &         m_settings;
+    vector<T>             m_y; // the buffer for yB = cb
+    // a device that is able to solve Bx=c, xB=d, and change the basis
+    lu<T, X> *            m_factorization;
+    const column_namer &  m_column_names;
+    indexed_vector<T>     m_w; // the vector featuring in 24.3 of the Chvatal book
+    vector<T>             m_d; // the vector of reduced costs
+    indexed_vector<T>     m_ed; // the solution of B*m_ed = a
+    const vector<column_type> & m_column_types;
+    const vector<X> &     m_low_bounds;
+    const vector<X> &     m_upper_bounds;
+    vector<T>             m_column_norms; // the approximate squares of column norms that help choosing a profitable column
+    vector<X>             m_copy_of_xB;
+    unsigned              m_basis_sort_counter;
+    vector<T>             m_steepest_edge_coefficients;
+    vector<unsigned>      m_trace_of_basis_change_vector; // the even positions are entering, the odd positions are leaving
+    bool                  m_tracing_basis_changes;
+    int_set*              m_pivoted_rows;
+    bool                  m_look_for_feasible_solution_only;
+    void start_tracing_basis_changes() {
+        m_trace_of_basis_change_vector.resize(0);
+        m_tracing_basis_changes = true;
+    }
+        
+    void stop_tracing_basis_changes() {
+        m_tracing_basis_changes = false;
+    }
+
+    void trace_basis_change(unsigned entering, unsigned leaving) {
+        unsigned size = m_trace_of_basis_change_vector.size();
+        if (size >= 2 && m_trace_of_basis_change_vector[size-2] == leaving
+                &&  m_trace_of_basis_change_vector[size -1] == entering) {
+            m_trace_of_basis_change_vector.pop_back();
+            m_trace_of_basis_change_vector.pop_back();
+        } else {
+            m_trace_of_basis_change_vector.push_back(entering);
+            m_trace_of_basis_change_vector.push_back(leaving);
+        }
+    }
+    
+    unsigned m_m() const { return m_A.row_count(); } // it is the length of basis. The matrix m_A has m_m rows and the dimension of the matrix A is m_m
+    unsigned m_n() const { return m_A.column_count(); } // the number of columns in the matrix m_A
+
+    lp_core_solver_base(static_matrix<T, X> & A,
+                        vector<X> & b, // the right side vector
+                        vector<unsigned> & basis,
+                        vector<unsigned> & nbasis,
+                        vector<int> & heading,
+                        vector<X> & x,
+                        vector<T> & costs,
+                        lp_settings & settings,
+                        const column_namer& column_names,
+                        const vector<column_type> & column_types,
+                        const vector<X> & low_bound_values,
+                        const vector<X> & upper_bound_values);
+
+    void allocate_basis_heading();
+    void init();
+
+    virtual ~lp_core_solver_base() {
+        if (m_factorization != nullptr)
+            delete m_factorization;
+     }
+
+    vector<unsigned> & non_basis() {
+        return m_nbasis;
+    }
+
+    const vector<unsigned> & non_basis() const { return m_nbasis; }
+
+
+    
+    void set_status(lp_status status) {
+        m_status = status;
+    }
+    lp_status get_status() const{
+        return m_status;
+    }
+
+    void fill_cb(T * y);
+
+    void fill_cb(vector<T> & y);
+
+    void solve_yB(vector<T> & y);
+
+    void solve_Bd(unsigned entering);
+
+    void solve_Bd(unsigned entering, indexed_vector<T> & column);
+
+    void pretty_print(std::ostream & out);
+
+    void save_state(T * w_buffer, T * d_buffer);
+
+    void restore_state(T * w_buffer, T * d_buffer);
+
+    X get_cost() {
+        return dot_product(m_costs, m_x);
+    }
+
+    void copy_m_w(T * buffer);
+
+    void restore_m_w(T * buffer);
+
+    // needed for debugging
+    void copy_m_ed(T * buffer);
+
+    void restore_m_ed(T * buffer);
+
+    bool A_mult_x_is_off() const;
+
+    bool A_mult_x_is_off_on_index(const vector<unsigned> & index) const;
+    // from page 182 of Istvan Maros's book
+    void calculate_pivot_row_of_B_1(unsigned pivot_row);
+
+    void calculate_pivot_row_when_pivot_row_of_B1_is_ready(unsigned pivot_row);
+
+    void update_x(unsigned entering, const X & delta);
+
+    const T & get_var_value(unsigned j) const {
+        return m_x[j];
+    }
+
+    void print_statistics(char const* str, X cost, std::ostream & message_stream);
+
+    bool print_statistics_with_iterations_and_check_that_the_time_is_over(std::ostream & message_stream);
+
+    bool print_statistics_with_iterations_and_nonzeroes_and_cost_and_check_that_the_time_is_over(char const* str, std::ostream & message_stream);
+
+    bool print_statistics_with_cost_and_check_that_the_time_is_over(X cost, std::ostream & message_stream);
+
+    unsigned total_iterations() const { return m_total_iterations; }
+
+    void set_total_iterations(unsigned s) { m_total_iterations = s; }
+
+    void set_non_basic_x_to_correct_bounds();
+
+    bool at_bound(const X &x, const X & bound) const {
+        return !below_bound(x, bound) && !above_bound(x, bound);
+    }
+
+
+    bool need_to_pivot_to_basis_tableau() const {
+        lean_assert(m_A.is_correct());
+        unsigned m = m_A.row_count();
+        for (unsigned i = 0; i < m; i++) {
+            unsigned bj = m_basis[i];
+            lean_assert(m_A.m_columns[bj].size() > 0);
+            if (m_A.m_columns[bj].size() > 1 || m_A.get_val(m_A.m_columns[bj][0]) != one_of_type<mpq>()) return true;
+        }
+        return false;
+    }
+    
+    bool reduced_costs_are_correct_tableau() const {
+        if (m_settings.simplex_strategy() == simplex_strategy_enum::tableau_rows)
+            return true;
+        lean_assert(m_A.is_correct());
+        if (m_using_infeas_costs) {
+            if (infeasibility_costs_are_correct() == false) {
+                std::cout << "infeasibility_costs_are_correct() does not hold" << std::endl;
+                return false;
+            }
+        }
+            
+        unsigned n = m_A.column_count();
+        for (unsigned j = 0; j < n; j++) {
+            if (m_basis_heading[j] >= 0) {
+                if (!is_zero(m_d[j])) {
+                    
+                    std::cout << "case a\n";
+                    print_column_info(j, std::cout);
+                    return false;
+                }
+            } else {
+                auto d = m_costs[j];
+                for (auto & cc : this->m_A.m_columns[j]) {
+                    d -= this->m_costs[this->m_basis[cc.m_i]] * this->m_A.get_val(cc);
+                }
+                if (m_d[j] != d) {
+                    std::cout << "case b\n";
+                    print_column_info(j, std::cout);
+                    return false;
+                }
+            }
+        }
+        return true;
+    }
+    
+    bool below_bound(const X & x, const X & bound) const {
+        if (precise()) return x < bound;
+        return below_bound_numeric<X>(x, bound, m_settings.primal_feasibility_tolerance);
+    }
+
+    bool above_bound(const X & x, const X & bound) const {
+        if (precise()) return x > bound;
+        return above_bound_numeric<X>(x, bound, m_settings.primal_feasibility_tolerance);
+    }
+
+    bool x_below_low_bound(unsigned p) const {
+        return below_bound(m_x[p], m_low_bounds[p]);
+    }
+
+    bool infeasibility_costs_are_correct() const;
+    bool infeasibility_cost_is_correct_for_column(unsigned j) const;
+    
+    bool x_above_low_bound(unsigned p) const {
+        return above_bound(m_x[p], m_low_bounds[p]);
+    }
+
+    bool x_below_upper_bound(unsigned p) const {
+        return below_bound(m_x[p], m_upper_bounds[p]);
+    }
+
+
+    bool x_above_upper_bound(unsigned p) const {
+        return above_bound(m_x[p], m_upper_bounds[p]);
+    }
+    bool x_is_at_low_bound(unsigned j) const {
+        return at_bound(m_x[j], m_low_bounds[j]);
+    }
+    bool x_is_at_upper_bound(unsigned j) const {
+        return at_bound(m_x[j], m_upper_bounds[j]);
+    }
+
+    bool x_is_at_bound(unsigned j) const {
+        return x_is_at_low_bound(j) || x_is_at_upper_bound(j);
+    }
+    bool column_is_feasible(unsigned j) const;
+
+    bool calc_current_x_is_feasible_include_non_basis() const;
+
+    bool inf_set_is_correct() const;
+    
+    bool column_is_dual_feasible(unsigned j) const;
+
+    bool d_is_not_negative(unsigned j) const;
+
+    bool d_is_not_positive(unsigned j) const;
+
+
+    bool time_is_over();
+
+    void rs_minus_Anx(vector<X> & rs);
+
+    bool find_x_by_solving();
+
+    bool update_basis_and_x(int entering, int leaving, X const & tt);
+
+    bool basis_has_no_doubles() const;
+
+    bool non_basis_has_no_doubles() const;
+
+    bool basis_is_correctly_represented_in_heading() const ;
+    bool non_basis_is_correctly_represented_in_heading() const ;
+
+    bool basis_heading_is_correct() const;
+
+    void restore_x_and_refactor(int entering, int leaving, X const & t);
+
+    void restore_x(unsigned entering, X const & t);
+
+    void fill_reduced_costs_from_m_y_by_rows();
+
+    void copy_rs_to_xB(vector<X> & rs);
+    virtual bool low_bounds_are_set() const { return false; }
+    X low_bound_value(unsigned j) const { return m_low_bounds[j]; }
+    X upper_bound_value(unsigned j) const { return m_upper_bounds[j]; }
+
+    column_type get_column_type(unsigned j) const {return m_column_types[j]; }
+
+    bool pivot_row_element_is_too_small_for_ratio_test(unsigned j) {
+        return m_settings.abs_val_is_smaller_than_pivot_tolerance(m_pivot_row[j]);
+    }
+
+    X bound_span(unsigned j) const {
+        return m_upper_bounds[j] - m_low_bounds[j];
+    }
+
+    std::string column_name(unsigned column) const;
+
+    void copy_right_side(vector<X> & rs);
+
+    void add_delta_to_xB(vector<X> & del);
+
+    void find_error_in_BxB(vector<X>& rs);
+
+    // recalculates the projection of x to B, such that Ax = b, whereab is the right side
+    void solve_Ax_eq_b();
+
+    bool snap_non_basic_x_to_bound() {
+        bool ret = false;
+        for (unsigned j : non_basis())
+            ret = snap_column_to_bound(j) || ret;
+        return ret;
+    }
+
+    
+    
+    bool snap_column_to_bound(unsigned j) {
+        switch (m_column_types[j]) {
+        case column_type::fixed:
+            if (x_is_at_bound(j))
+                break;
+            m_x[j] = m_low_bounds[j];
+            return true;
+        case column_type::boxed:
+            if (x_is_at_bound(j))
+                break; // we should preserve x if possible
+            // snap randomly
+            if (m_settings.random_next() % 2 == 1) 
+                m_x[j] = m_low_bounds[j];
+            else
+                m_x[j] = m_upper_bounds[j];
+            return true;
+        case column_type::low_bound:
+            if (x_is_at_low_bound(j))
+                break;
+            m_x[j] = m_low_bounds[j];
+            return true;
+        case column_type::upper_bound:
+            if (x_is_at_upper_bound(j))
+                break;
+            m_x[j] = m_upper_bounds[j];
+            return true;
+        default:
+            break;
+        }
+        return false;
+    }
+
+    bool make_column_feasible(unsigned j, numeric_pair<mpq> & delta) {
+        lean_assert(m_basis_heading[j] < 0);
+        auto & x = m_x[j];
+        switch (m_column_types[j]) {
+        case column_type::fixed:
+            lean_assert(m_low_bounds[j] == m_upper_bounds[j]);
+            if (x != m_low_bounds[j]) {
+                delta = m_low_bounds[j] - x;
+                x = m_low_bounds[j];
+                return true;
+            }
+            break;
+        case column_type::boxed:
+            if (x < m_low_bounds[j]) {
+                delta = m_low_bounds[j] - x;
+                x = m_low_bounds[j];
+                return true;
+            }
+            if (x > m_upper_bounds[j]) {
+                delta = m_upper_bounds[j] - x;
+                x = m_upper_bounds[j];
+                return true;
+            }
+            break;
+        case column_type::low_bound:
+            if (x < m_low_bounds[j]) {
+                delta = m_low_bounds[j] - x;
+                x = m_low_bounds[j];
+                return true;
+            }
+            break;
+        case column_type::upper_bound:
+            if (x > m_upper_bounds[j]) {
+                delta = m_upper_bounds[j] - x;
+                x = m_upper_bounds[j];
+                return true;
+            }
+            break;
+        case column_type::free_column:
+            break;
+        default:
+            lean_assert(false);
+            break;
+        }
+        return false;
+    }
+
+    
+    void snap_non_basic_x_to_bound_and_free_to_zeroes();
+    void snap_xN_to_bounds_and_fill_xB();
+
+    void snap_xN_to_bounds_and_free_columns_to_zeroes();
+
+    void init_reduced_costs_for_one_iteration();
+
+    non_basic_column_value_position get_non_basic_column_value_position(unsigned j) const;
+
+    void init_lu();
+    int pivots_in_column_and_row_are_different(int entering, int leaving) const;
+    void pivot_fixed_vars_from_basis();
+    bool pivot_for_tableau_on_basis();
+    bool pivot_row_for_tableau_on_basis(unsigned row);
+    void init_basic_part_of_basis_heading() {
+        unsigned m = m_basis.size();
+        for (unsigned i = 0; i < m; i++) {
+            unsigned column = m_basis[i];
+            m_basis_heading[column] = i;
+        }
+    }
+
+    void init_non_basic_part_of_basis_heading() {
+        this->m_nbasis.clear();
+        for (int j = m_basis_heading.size(); j--;){
+            if (m_basis_heading[j] < 0) {
+                m_nbasis.push_back(j);
+                // the index of column j in m_nbasis is (- basis_heading[j] - 1)
+                m_basis_heading[j] = - static_cast<int>(m_nbasis.size());
+            }
+        }
+    }
+    
+    void init_basis_heading_and_non_basic_columns_vector() {
+        m_basis_heading.resize(0);
+        m_basis_heading.resize(m_n(), -1);
+        init_basic_part_of_basis_heading();
+        init_non_basic_part_of_basis_heading();
+    }
+
+    void change_basis_unconditionally(unsigned entering, unsigned leaving) {
+        lean_assert(m_basis_heading[entering] < 0);
+        int place_in_non_basis = -1 - m_basis_heading[entering];
+        if (static_cast<unsigned>(place_in_non_basis) >= m_nbasis.size()) {
+              // entering variable in not in m_nbasis, we need to put it back;
+            m_basis_heading[entering] = place_in_non_basis = m_nbasis.size();
+            m_nbasis.push_back(entering);
+        }
+        
+        int place_in_basis =  m_basis_heading[leaving];
+        m_basis_heading[entering] = place_in_basis;
+        m_basis[place_in_basis] = entering;
+        m_basis_heading[leaving] = -place_in_non_basis - 1;
+        m_nbasis[place_in_non_basis] = leaving;
+        if (m_tracing_basis_changes)
+            trace_basis_change(entering, leaving);
+        
+    }
+    
+    void change_basis(unsigned entering, unsigned leaving) {
+        lean_assert(m_basis_heading[entering] < 0);
+        
+        int place_in_basis =  m_basis_heading[leaving];
+        int place_in_non_basis = - m_basis_heading[entering] - 1;
+        m_basis_heading[entering] = place_in_basis;
+        m_basis[place_in_basis] = entering;
+
+        m_basis_heading[leaving] = -place_in_non_basis - 1;
+        m_nbasis[place_in_non_basis] = leaving;
+        
+        if (m_tracing_basis_changes)
+            trace_basis_change(entering, leaving);
+    }
+
+    void restore_basis_change(unsigned entering, unsigned leaving) {
+        if (m_basis_heading[entering] < 0) {
+            return; // the basis has not been changed
+        }
+        change_basis_unconditionally(leaving, entering);
+    }
+
+    bool non_basic_column_is_set_correctly(unsigned j) const {
+        if (j >= this->m_n())
+            return false;
+        switch (this->m_column_types[j]) {
+        case column_type::fixed:
+        case column_type::boxed:
+            if (!this->x_is_at_bound(j))
+                return false;
+            break;
+        case column_type::low_bound:
+            if (!this->x_is_at_low_bound(j))
+                return false;
+            break;
+        case column_type::upper_bound:
+            if (!this->x_is_at_upper_bound(j))
+                return false;
+            break;
+        case column_type::free_column:
+            break;
+        default:
+            lean_assert(false);
+            break;
+        }
+        return true;
+    }
+    bool non_basic_columns_are_set_correctly() const {
+        for (unsigned j : this->m_nbasis)
+            if (!column_is_feasible(j)) {
+                print_column_info(j, std::cout);
+                return false;
+            }
+        return true;
+    }
+
+    void print_column_bound_info(unsigned j, std::ostream & out) const {
+        out << column_name(j) << " type = " << column_type_to_string(m_column_types[j]) << std::endl;
+        switch (m_column_types[j]) {
+        case column_type::fixed:
+        case column_type::boxed:
+            out << "(" << m_low_bounds[j] << ", " << m_upper_bounds[j] << ")" << std::endl;
+            break;
+        case column_type::low_bound:
+            out << m_low_bounds[j] << std::endl;
+            break;
+        case column_type::upper_bound:
+            out << m_upper_bounds[j] << std::endl;
+            break;
+        default:
+            break;
+        }
+    }
+
+    void print_column_info(unsigned j, std::ostream & out) const {
+        out << "column_index = " << j << ", name = "<< column_name(j) << " type = " << column_type_to_string(m_column_types[j]) << std::endl;
+        switch (m_column_types[j]) {
+        case column_type::fixed:
+        case column_type::boxed:
+            out << "(" << m_low_bounds[j] << ", " << m_upper_bounds[j] << ")" << std::endl;
+            break;
+        case column_type::low_bound:
+            out << m_low_bounds[j] << std::endl;
+            break;
+        case column_type::upper_bound:
+            out << m_upper_bounds[j] << std::endl;
+            break;
+        case column_type::free_column:
+            break;
+        default:
+            lean_assert(false);
+        }
+        std::cout << "basis heading = " << m_basis_heading[j] << std::endl;
+        std::cout << "x = " << m_x[j] << std::endl;
+        /*
+        std::cout << "cost = " << m_costs[j] << std::endl;
+        std:: cout << "m_d = " << m_d[j] << std::endl;*/
+    }
+
+    bool column_is_free(unsigned j) { return this->m_column_type[j] == free; }
+
+    bool column_has_upper_bound(unsigned j) {
+        switch(m_column_types[j]) {
+        case column_type::free_column:
+        case column_type::low_bound:
+            return false;
+        default:
+            return true;
+        }
+    }
+
+    bool bounds_for_boxed_are_set_correctly() const {
+        for (unsigned j = 0; j < m_column_types.size(); j++) {
+            if (m_column_types[j] != column_type::boxed) continue;
+            if (m_low_bounds[j] > m_upper_bounds[j])
+                return false;
+        }
+        return true;
+    }
+    
+    bool column_has_low_bound(unsigned j) {
+        switch(m_column_types[j]) {
+        case column_type::free_column:
+        case column_type::upper_bound:
+            return false;
+        default:
+            return true;
+        }
+    }
+
+    // only check for basic columns
+    bool calc_current_x_is_feasible() const {
+        unsigned i = this->m_m();
+        while (i--) {
+            if (!column_is_feasible(m_basis[i]))
+                return false;
+        }
+        return true;
+    }
+
+    int find_pivot_index_in_row(unsigned i, const vector<column_cell> & col) const {
+        for (const auto & c: col) {
+            if (c.m_i == i)
+                return c.m_offset;
+        }
+        return -1;
+    }
+
+    void transpose_rows_tableau(unsigned i, unsigned ii);
+    
+    void pivot_to_reduced_costs_tableau(unsigned i, unsigned j);
+
+    bool pivot_column_tableau(unsigned j, unsigned row_index);
+    bool divide_row_by_pivot(unsigned pivot_row, unsigned pivot_col);
+    
+    bool precise() const { return numeric_traits<T>::precise(); }
+
+    simplex_strategy_enum simplex_strategy() const { return
+            m_settings.simplex_strategy();
+    }
+
+    bool use_tableau() const { return m_settings.use_tableau(); }
+    
+    template <typename K>
+    static void swap(vector<K> &v, unsigned i, unsigned j) {
+        auto t = v[i];
+        v[i] = v[j];
+        v[j] = t;
+    }
+        
+    // called when transposing row i and ii
+    void transpose_basis(unsigned i, unsigned ii) {
+        swap(m_basis, i, ii);
+        swap(m_basis_heading, m_basis[i], m_basis[ii]);
+    }
+
+    bool column_is_in_inf_set(unsigned j) const {
+        return m_inf_set.contains(j);
+    }
+
+    void update_column_in_inf_set(unsigned j) {
+        if (column_is_feasible(j)) {
+            m_inf_set.erase(j);
+        } else {
+            m_inf_set.insert(j);
+        }
+    }
+    void insert_column_into_inf_set(unsigned j) {
+        m_inf_set.insert(j);
+        lean_assert(!column_is_feasible(j));
+    }
+    void remove_column_from_inf_set(unsigned j) {
+        m_inf_set.erase(j);
+        lean_assert(column_is_feasible(j));
+    }
+    bool costs_on_nbasis_are_zeros() const {
+        lean_assert(this->basis_heading_is_correct());
+        for (unsigned j = 0; j < this->m_n(); j++) {
+            if (this->m_basis_heading[j] < 0)
+                lean_assert(is_zero(this->m_costs[j]));
+        }
+        return true;
+    }
+    unsigned & iters_with_no_cost_growing() {
+        return m_iters_with_no_cost_growing;
+    }
+
+    const unsigned & iters_with_no_cost_growing() const {
+        return m_iters_with_no_cost_growing;
+    }
+};
+}

src/util/lp/lp_core_solver_base_instances.cpp

@@ -0,0 +1,131 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#include <utility>
+#include <memory>
+#include <string>
+#include "util/vector.h"
+#include <functional>
+#include "util/lp/lp_core_solver_base.hpp"
+template bool lean::lp_core_solver_base<double, double>::A_mult_x_is_off() const;
+template bool lean::lp_core_solver_base<double, double>::A_mult_x_is_off_on_index(const vector<unsigned> &) const;
+template bool lean::lp_core_solver_base<double, double>::basis_heading_is_correct() const;
+template void lean::lp_core_solver_base<double, double>::calculate_pivot_row_of_B_1(unsigned int);
+template void lean::lp_core_solver_base<double, double>::calculate_pivot_row_when_pivot_row_of_B1_is_ready(unsigned);
+template bool lean::lp_core_solver_base<double, double>::column_is_dual_feasible(unsigned int) const;
+template void lean::lp_core_solver_base<double, double>::fill_reduced_costs_from_m_y_by_rows();
+template bool lean::lp_core_solver_base<double, double>::find_x_by_solving();
+template lean::non_basic_column_value_position lean::lp_core_solver_base<double, double>::get_non_basic_column_value_position(unsigned int) const;
+template lean::non_basic_column_value_position lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::get_non_basic_column_value_position(unsigned int) const;
+template lean::non_basic_column_value_position lean::lp_core_solver_base<lean::mpq, lean::mpq>::get_non_basic_column_value_position(unsigned int) const;
+template void lean::lp_core_solver_base<double, double>::init_reduced_costs_for_one_iteration();
+template lean::lp_core_solver_base<double, double>::lp_core_solver_base(
+    lean::static_matrix<double, double>&, vector<double>&, 
+    vector<unsigned int >&,
+    vector<unsigned> &, vector<int> &,
+    vector<double >&, 
+    vector<double >&, 
+    lean::lp_settings&, const column_namer&, const vector<lean::column_type >&,
+    const vector<double >&,
+    const vector<double >&);
+
+template bool lean::lp_core_solver_base<double, double>::print_statistics_with_iterations_and_nonzeroes_and_cost_and_check_that_the_time_is_over(char const*, std::ostream &);
+template bool lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::print_statistics_with_iterations_and_nonzeroes_and_cost_and_check_that_the_time_is_over(char const*, std::ostream &);
+template void lean::lp_core_solver_base<double, double>::restore_x(unsigned int, double const&);
+template void lean::lp_core_solver_base<double, double>::set_non_basic_x_to_correct_bounds();
+template void lean::lp_core_solver_base<double, double>::snap_xN_to_bounds_and_free_columns_to_zeroes();
+template void lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::snap_xN_to_bounds_and_free_columns_to_zeroes();
+template void lean::lp_core_solver_base<double, double>::solve_Ax_eq_b();
+template void lean::lp_core_solver_base<double, double>::solve_Bd(unsigned int);
+template void lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq>>::solve_Bd(unsigned int, indexed_vector<lean::mpq>&);
+template void lean::lp_core_solver_base<double, double>::solve_yB(vector<double >&);
+template bool lean::lp_core_solver_base<double, double>::update_basis_and_x(int, int, double const&);
+template void lean::lp_core_solver_base<double, double>::update_x(unsigned int, const double&);
+template bool lean::lp_core_solver_base<lean::mpq, lean::mpq>::A_mult_x_is_off() const;
+template bool lean::lp_core_solver_base<lean::mpq, lean::mpq>::A_mult_x_is_off_on_index(const vector<unsigned> &) const;
+template bool lean::lp_core_solver_base<lean::mpq, lean::mpq>::basis_heading_is_correct() const ;
+template void lean::lp_core_solver_base<lean::mpq, lean::mpq>::calculate_pivot_row_of_B_1(unsigned int);
+template void lean::lp_core_solver_base<lean::mpq, lean::mpq>::calculate_pivot_row_when_pivot_row_of_B1_is_ready(unsigned);
+template bool lean::lp_core_solver_base<lean::mpq, lean::mpq>::column_is_dual_feasible(unsigned int) const;
+template void lean::lp_core_solver_base<lean::mpq, lean::mpq>::fill_reduced_costs_from_m_y_by_rows();
+template bool lean::lp_core_solver_base<lean::mpq, lean::mpq>::find_x_by_solving();
+template void lean::lp_core_solver_base<lean::mpq, lean::mpq>::init_reduced_costs_for_one_iteration();
+template bool lean::lp_core_solver_base<lean::mpq, lean::mpq>::print_statistics_with_iterations_and_nonzeroes_and_cost_and_check_that_the_time_is_over(char const*, std::ostream &);
+template void lean::lp_core_solver_base<lean::mpq, lean::mpq>::restore_x(unsigned int, lean::mpq const&);
+template void lean::lp_core_solver_base<lean::mpq, lean::mpq>::set_non_basic_x_to_correct_bounds();
+template void lean::lp_core_solver_base<lean::mpq, lean::mpq>::solve_Ax_eq_b();
+template void lean::lp_core_solver_base<lean::mpq, lean::mpq>::solve_Bd(unsigned int);
+template void lean::lp_core_solver_base<lean::mpq, lean::mpq>::solve_yB(vector<lean::mpq>&);
+template bool lean::lp_core_solver_base<lean::mpq, lean::mpq>::update_basis_and_x(int, int, lean::mpq const&);
+template void lean::lp_core_solver_base<lean::mpq, lean::mpq>::update_x(unsigned int, const lean::mpq&);
+template void lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::calculate_pivot_row_of_B_1(unsigned int);
+template void lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::calculate_pivot_row_when_pivot_row_of_B1_is_ready(unsigned);
+template void lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::init();
+template void lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::init_basis_heading_and_non_basic_columns_vector();
+template void lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::init_reduced_costs_for_one_iteration();
+template lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::lp_core_solver_base(lean::static_matrix<lean::mpq, lean::numeric_pair<lean::mpq> >&, vector<lean::numeric_pair<lean::mpq> >&, vector<unsigned int >&, vector<unsigned> &, vector<int> &, vector<lean::numeric_pair<lean::mpq> >&, vector<lean::mpq>&, lean::lp_settings&, const column_namer&, const vector<lean::column_type >&,
+                                                                                                   const vector<lean::numeric_pair<lean::mpq> >&,
+                                                                                                   const vector<lean::numeric_pair<lean::mpq> >&);
+template bool lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::print_statistics_with_cost_and_check_that_the_time_is_over(lean::numeric_pair<lean::mpq>, std::ostream&);
+template void lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::snap_xN_to_bounds_and_fill_xB();
+template void lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::solve_Bd(unsigned int);
+template bool lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::update_basis_and_x(int, int, lean::numeric_pair<lean::mpq> const&);
+template void lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::update_x(unsigned int, const lean::numeric_pair<lean::mpq>&);
+template lean::lp_core_solver_base<lean::mpq, lean::mpq>::lp_core_solver_base(
+                                                                              lean::static_matrix<lean::mpq, lean::mpq>&,
+                                                                              vector<lean::mpq>&,
+                                                                              vector<unsigned int >&,
+                                                                              vector<unsigned> &, vector<int> &,
+                                                                              vector<lean::mpq>&,
+                                                                              vector<lean::mpq>&,
+                                                                              lean::lp_settings&,
+                                                                              const column_namer&,
+                                                                              const vector<lean::column_type >&,
+                                                                              const vector<lean::mpq>&,
+                                                                              const vector<lean::mpq>&);
+template bool lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::print_statistics_with_iterations_and_check_that_the_time_is_over(std::ostream &);
+template std::string lean::lp_core_solver_base<double, double>::column_name(unsigned int) const;
+template void lean::lp_core_solver_base<double, double>::pretty_print(std::ostream & out);
+template void lean::lp_core_solver_base<double, double>::restore_state(double*, double*);
+template void lean::lp_core_solver_base<double, double>::save_state(double*, double*);
+template std::string lean::lp_core_solver_base<lean::mpq, lean::mpq>::column_name(unsigned int) const;
+template void lean::lp_core_solver_base<lean::mpq, lean::mpq>::pretty_print(std::ostream & out);
+template void lean::lp_core_solver_base<lean::mpq, lean::mpq>::restore_state(lean::mpq*, lean::mpq*);
+template void lean::lp_core_solver_base<lean::mpq, lean::mpq>::save_state(lean::mpq*, lean::mpq*);
+template std::string lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::column_name(unsigned int) const;
+template void lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::pretty_print(std::ostream & out);
+template void lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::restore_state(lean::mpq*, lean::mpq*);
+template void lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::save_state(lean::mpq*, lean::mpq*);
+template void lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::solve_yB(vector<lean::mpq>&);
+template void lean::lp_core_solver_base<double, double>::init_lu();
+template void lean::lp_core_solver_base<lean::mpq, lean::mpq>::init_lu();
+template int lean::lp_core_solver_base<double, double>::pivots_in_column_and_row_are_different(int, int) const;
+template int lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::pivots_in_column_and_row_are_different(int, int) const;
+template int lean::lp_core_solver_base<lean::mpq, lean::mpq>::pivots_in_column_and_row_are_different(int, int) const;
+template bool lean::lp_core_solver_base<double, double>::calc_current_x_is_feasible_include_non_basis(void)const;
+template bool lean::lp_core_solver_base<lean::mpq, lean::mpq>::calc_current_x_is_feasible_include_non_basis(void)const;
+template bool lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::calc_current_x_is_feasible_include_non_basis() const;
+template void  lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::pivot_fixed_vars_from_basis();
+template bool lean::lp_core_solver_base<double, double>::column_is_feasible(unsigned int) const;
+template bool lean::lp_core_solver_base<lean::mpq, lean::mpq>::column_is_feasible(unsigned int) const;
+// template void lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::print_linear_combination_of_column_indices(vector<std::pair<lean::mpq, unsigned int>, std::allocator<std::pair<lean::mpq, unsigned int> > > const&, std::ostream&) const;
+template bool lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::column_is_feasible(unsigned int) const;
+template bool lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::snap_non_basic_x_to_bound();
+template void lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::init_lu();
+template bool lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::A_mult_x_is_off_on_index(vector<unsigned int> const&) const;
+template bool lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::find_x_by_solving();
+template void lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::restore_x(unsigned int, lean::numeric_pair<lean::mpq> const&);
+template bool lean::lp_core_solver_base<double, double>::pivot_for_tableau_on_basis();
+template bool lean::lp_core_solver_base<lean::mpq, lean::mpq>::pivot_for_tableau_on_basis();
+template bool lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq>>::pivot_for_tableau_on_basis();
+template bool lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq>>::pivot_column_tableau(unsigned int, unsigned int);
+template bool lean::lp_core_solver_base<double, double>::pivot_column_tableau(unsigned int, unsigned int);
+template bool lean::lp_core_solver_base<lean::mpq, lean::mpq>::pivot_column_tableau(unsigned int, unsigned int);
+template void lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::transpose_rows_tableau(unsigned int, unsigned int);
+template bool lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::inf_set_is_correct() const;
+template bool lean::lp_core_solver_base<double, double>::inf_set_is_correct() const;
+template bool lean::lp_core_solver_base<lean::mpq, lean::mpq>::inf_set_is_correct() const;
+template bool lean::lp_core_solver_base<lean::mpq, lean::numeric_pair<lean::mpq> >::infeasibility_costs_are_correct() const;
+template bool lean::lp_core_solver_base<lean::mpq, lean::mpq >::infeasibility_costs_are_correct() const;
+template bool lean::lp_core_solver_base<double, double >::infeasibility_costs_are_correct() const;

src/util/lp/lp_dual_core_solver.h

@@ -0,0 +1,197 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#pragma once
+#include "util/lp/static_matrix.h"
+#include "util/lp/lp_core_solver_base.h"
+#include <string>
+#include <limits>
+#include <set>
+#include <algorithm>
+#include "util/vector.h"
+
+namespace lean {
+template <typename T, typename X>
+class lp_dual_core_solver:public lp_core_solver_base<T, X> {
+public:
+    vector<bool> & m_can_enter_basis;
+    int m_r; // the row of the leaving column
+    int m_p; // leaving column; that is m_p = m_basis[m_r]
+    T m_delta; // the offset of the leaving basis variable
+    int m_sign_of_alpha_r; // see page 27
+    T m_theta_D;
+    T m_theta_P;
+    int m_q;
+    // todo : replace by a vector later
+    std::set<unsigned> m_breakpoint_set; // it is F in "Progress in the dual simplex method ..."
+    std::set<unsigned> m_flipped_boxed;
+    std::set<unsigned> m_tight_set; // it is the set of all breakpoints that become tight when m_q becomes tight
+    vector<T> m_a_wave;
+    vector<T> m_betas; // m_betas[i] is approximately a square of the norm of the i-th row of the reverse of B
+    T m_harris_tolerance;
+    std::set<unsigned> m_forbidden_rows;
+
+    lp_dual_core_solver(static_matrix<T, X> & A,
+                        vector<bool> & can_enter_basis,
+                        vector<X> & b, // the right side vector
+                        vector<X> & x, // the number of elements in x needs to be at least as large as the number of columns in A
+                        vector<unsigned> & basis,
+                        vector<unsigned> & nbasis,
+                        vector<int> & heading,
+                        vector<T> & costs,
+                        vector<column_type> & column_type_array,
+                        vector<X> & low_bound_values,
+                        vector<X> & upper_bound_values,
+                        lp_settings & settings,
+                        const column_namer & column_names):
+        lp_core_solver_base<T, X>(A,
+                                  b,
+                                  basis,
+                                  nbasis,
+                                  heading,
+                                  x,
+                                  costs,
+                                  settings,
+                                  column_names,
+                                  column_type_array,
+                                  low_bound_values,
+                                  upper_bound_values),
+        m_can_enter_basis(can_enter_basis),
+        m_a_wave(this->m_m()),
+        m_betas(this->m_m()) {
+        m_harris_tolerance = numeric_traits<T>::precise()? numeric_traits<T>::zero() : T(this->m_settings.harris_feasibility_tolerance);
+        this->solve_yB(this->m_y);
+        this->init_basic_part_of_basis_heading();
+        fill_non_basis_with_only_able_to_enter_columns();
+    }
+
+    void init_a_wave_by_zeros();
+
+    void fill_non_basis_with_only_able_to_enter_columns() {
+        auto & nb = this->m_nbasis;
+        nb.reset();
+        unsigned j = this->m_n();
+        while (j--) {
+            if (this->m_basis_heading[j] >= 0 || !m_can_enter_basis[j]) continue;
+            nb.push_back(j);
+            this->m_basis_heading[j] = - static_cast<int>(nb.size());
+        }
+    }
+
+    void restore_non_basis();
+
+    bool update_basis(int entering, int leaving);
+
+    void recalculate_xB_and_d();
+
+    void recalculate_d();
+
+    void init_betas();
+
+    void adjust_xb_for_changed_xn_and_init_betas();
+
+    void start_with_initial_basis_and_make_it_dual_feasible();
+
+    bool done();
+
+    T get_edge_steepness_for_low_bound(unsigned p);
+
+    T get_edge_steepness_for_upper_bound(unsigned p);
+
+    T pricing_for_row(unsigned i);
+
+    void pricing_loop(unsigned number_of_rows_to_try, unsigned offset_in_rows);
+
+    bool advance_on_known_p();
+
+    int define_sign_of_alpha_r();
+
+    bool can_be_breakpoint(unsigned j);
+
+    void fill_breakpoint_set();
+
+    void DSE_FTran();
+    T get_delta();
+
+    void restore_d();
+
+    bool d_is_correct();
+
+    void xb_minus_delta_p_pivot_column();
+
+    void update_betas();
+
+    void apply_flips();
+
+    void snap_xN_column_to_bounds(unsigned j);
+
+    void snap_xN_to_bounds();
+
+    void init_beta_precisely(unsigned i);
+
+    void init_betas_precisely();
+
+    // step 7 of the algorithm from Progress
+    bool basis_change_and_update();
+
+    void revert_to_previous_basis();
+
+    non_basic_column_value_position m_entering_boundary_position;
+    bool update_basis_and_x_local(int entering, int leaving, X const & tt);
+    void recover_leaving();
+
+    bool problem_is_dual_feasible() const;
+
+    bool snap_runaway_nonbasic_column(unsigned);
+
+    bool snap_runaway_nonbasic_columns();
+
+    unsigned get_number_of_rows_to_try_for_leaving();
+
+    void update_a_wave(const T & del, unsigned j) {
+        this->m_A.add_column_to_vector(del, j, & m_a_wave[0]);
+    }
+
+    bool delta_keeps_the_sign(int initial_delta_sign, const T & delta);
+
+    void set_status_to_tentative_dual_unbounded_or_dual_unbounded();
+
+    // it is positive if going from low bound to upper bound and negative if going from upper bound to low bound
+    T signed_span_of_boxed(unsigned j) {
+        return this->x_is_at_low_bound(j)? this->bound_span(j): - this->bound_span(j);
+    }
+
+    void add_tight_breakpoints_and_q_to_flipped_set();
+
+    T delta_lost_on_flips_of_tight_breakpoints();
+
+    bool tight_breakpoinst_are_all_boxed();
+
+    T calculate_harris_delta_on_breakpoint_set();
+
+    void fill_tight_set_on_harris_delta(const T & harris_delta );
+
+    void find_q_on_tight_set();
+
+    void find_q_and_tight_set();
+
+    void erase_tight_breakpoints_and_q_from_breakpoint_set();
+
+    bool ratio_test();
+
+    void process_flipped();
+    void update_d_and_xB();
+
+    void calculate_beta_r_precisely();
+    // see "Progress in the dual simplex method for large scale LP problems: practical dual phase 1 algorithms"
+
+    void update_xb_after_bound_flips();
+
+    void one_iteration();
+
+    void solve();
+
+    bool low_bounds_are_set() const { return true; }
+};
+}

src/util/lp/lp_dual_core_solver.hpp

@@ -0,0 +1,743 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#include <algorithm>
+#include <string>
+#include "util/vector.h"
+#include "util/lp/lp_dual_core_solver.h"
+
+namespace lean {
+
+template <typename T, typename X> void lp_dual_core_solver<T, X>::init_a_wave_by_zeros() {
+    unsigned j = this->m_m();
+    while (j--) {
+        m_a_wave[j] = numeric_traits<T>::zero();
+    }
+}
+
+template <typename T, typename X> void lp_dual_core_solver<T, X>::restore_non_basis() {
+    auto & nb = this->m_nbasis;
+    nb.reset();
+    unsigned j = this->m_n();
+    while (j--) {
+        if (this->m_basis_heading[j] >= 0 ) continue;
+        if (m_can_enter_basis[j]) {
+            lean_assert(std::find(nb.begin(), nb.end(), j) == nb.end());
+            nb.push_back(j);
+            this->m_basis_heading[j] = - static_cast<int>(nb.size());
+        }
+    }
+}
+
+template <typename T, typename X> bool lp_dual_core_solver<T, X>::update_basis(int entering, int leaving) {
+    // the second argument is the element of the entering column from the pivot row - its value should be equal to the low diagonal element of the bump after all pivoting is done
+    if (this->m_refactor_counter++ < 200) {
+        this->m_factorization->replace_column(this->m_ed[this->m_factorization->basis_heading(leaving)], this->m_w);
+        if (this->m_factorization->get_status() == LU_status::OK) {
+            this->m_factorization->change_basis(entering, leaving);
+            return true;
+        }
+    }
+    // need to refactor
+    this->m_factorization->change_basis(entering, leaving);
+    init_factorization(this->m_factorization, this->m_A, this->m_basis, this->m_basis_heading, this->m_settings);
+    this->m_refactor_counter = 0;
+    if (this->m_factorization->get_status() != LU_status::OK) {
+        LP_OUT(this->m_settings, "failing refactor for entering = " << entering << ", leaving = " << leaving << " total_iterations = " << this->total_iterations() << std::endl);
+        this->m_iters_with_no_cost_growing++;
+        return false;
+    }
+    return true;
+}
+
+template <typename T, typename X> void lp_dual_core_solver<T, X>::recalculate_xB_and_d() {
+    this->solve_Ax_eq_b();
+    recalculate_d();
+}
+
+template <typename T, typename X> void lp_dual_core_solver<T, X>::recalculate_d() {
+    this->solve_yB(this->m_y);
+    this->fill_reduced_costs_from_m_y_by_rows();
+}
+
+template <typename T, typename X> void lp_dual_core_solver<T, X>::init_betas() {
+    // todo : look at page 194 of Progress in the dual simplex algorithm for solving large scale LP problems : techniques for a fast and stable implementation
+    // the current implementation is not good enough: todo
+    unsigned i = this->m_m();
+    while (i--) {
+        m_betas[i] = 1;
+    }
+}
+
+template <typename T, typename X> void lp_dual_core_solver<T, X>::adjust_xb_for_changed_xn_and_init_betas() {
+    this->solve_Ax_eq_b();
+    init_betas();
+}
+
+template <typename T, typename X> void lp_dual_core_solver<T, X>::start_with_initial_basis_and_make_it_dual_feasible() {
+    this->set_non_basic_x_to_correct_bounds(); // It is not an efficient version, see 3.29,
+    // however this version does not require that m_x is the solution of Ax = 0 beforehand
+    adjust_xb_for_changed_xn_and_init_betas();
+}
+
+template <typename T, typename X> bool lp_dual_core_solver<T, X>::done() {
+    if (this->get_status() == OPTIMAL) {
+        return true;
+    }
+    if (this->total_iterations() > this->m_settings.max_total_number_of_iterations) { // debug !!!!
+        this->set_status(ITERATIONS_EXHAUSTED);
+        return true;
+    }
+    return false; // todo, need to be more cases
+}
+
+template <typename T, typename X> T lp_dual_core_solver<T, X>::get_edge_steepness_for_low_bound(unsigned p) {
+    lean_assert(this->m_basis_heading[p] >= 0 && static_cast<unsigned>(this->m_basis_heading[p]) < this->m_m());
+    T del = this->m_x[p] - this->m_low_bounds[p];
+    del *= del;
+    return del / this->m_betas[this->m_basis_heading[p]];
+}
+
+template <typename T, typename X> T lp_dual_core_solver<T, X>::get_edge_steepness_for_upper_bound(unsigned p) {
+    lean_assert(this->m_basis_heading[p] >= 0 && static_cast<unsigned>(this->m_basis_heading[p]) < this->m_m());
+    T del = this->m_x[p] - this->m_upper_bounds[p];
+    del *= del;
+    return del / this->m_betas[this->m_basis_heading[p]];
+}
+
+template <typename T, typename X> T lp_dual_core_solver<T, X>::pricing_for_row(unsigned i) {
+    unsigned p = this->m_basis[i];
+    switch (this->m_column_types[p]) {
+    case column_type::fixed:
+    case column_type::boxed:
+        if (this->x_below_low_bound(p)) {
+            T del =  get_edge_steepness_for_low_bound(p);
+            return del;
+        }
+        if (this->x_above_upper_bound(p)) {
+            T del =  get_edge_steepness_for_upper_bound(p);
+            return del;
+        }
+        return numeric_traits<T>::zero();
+    case column_type::low_bound:
+        if (this->x_below_low_bound(p)) {
+            T del =  get_edge_steepness_for_low_bound(p);
+            return del;
+        }
+        return numeric_traits<T>::zero();
+        break;
+    case column_type::upper_bound:
+        if (this->x_above_upper_bound(p)) {
+            T del =  get_edge_steepness_for_upper_bound(p);
+            return del;
+        }
+        return numeric_traits<T>::zero();
+        break;
+    case column_type::free_column:
+        lean_assert(numeric_traits<T>::is_zero(this->m_d[p]));
+        return numeric_traits<T>::zero();
+    default:
+        lean_unreachable();
+    }
+    lean_unreachable();
+    return numeric_traits<T>::zero();
+}
+
+template <typename T, typename X> void lp_dual_core_solver<T, X>::pricing_loop(unsigned number_of_rows_to_try, unsigned offset_in_rows) {
+    m_r = -1;
+    T steepest_edge_max = numeric_traits<T>::zero();
+    unsigned initial_offset_in_rows = offset_in_rows;
+    unsigned i = offset_in_rows;
+    unsigned rows_left = number_of_rows_to_try;
+    do  {
+        if (m_forbidden_rows.find(i) != m_forbidden_rows.end()) {
+            if (++i == this->m_m()) {
+                i = 0;
+            }
+            continue;
+        }
+        T se = pricing_for_row(i);
+        if (se > steepest_edge_max) {
+            steepest_edge_max = se;
+            m_r = i;
+            if (rows_left > 0) {
+                rows_left--;
+            }
+        }
+        if (++i == this->m_m()) {
+            i = 0;
+        }
+    } while (i != initial_offset_in_rows && rows_left);
+    if (m_r == -1) {
+        if (this->get_status() != UNSTABLE) {
+            this->set_status(OPTIMAL);
+        }
+    } else {
+        m_p = this->m_basis[m_r];
+        m_delta = get_delta();
+        if (advance_on_known_p()){
+            m_forbidden_rows.clear();
+            return;
+        }
+        // failure in advance_on_known_p
+        if (this->get_status() == FLOATING_POINT_ERROR) {
+            return;
+        }
+        this->set_status(UNSTABLE);
+        m_forbidden_rows.insert(m_r);
+    }
+}
+
+    // this calculation is needed for the steepest edge update,
+    // it hijackes m_pivot_row_of_B_1 for this purpose since we will need it anymore to the end of the cycle
+template <typename T, typename X> void lp_dual_core_solver<T, X>::DSE_FTran() { // todo, see algorithm 7 from page 35
+    this->m_factorization->solve_By_for_T_indexed_only(this->m_pivot_row_of_B_1, this->m_settings);
+}
+
+template <typename T, typename X> bool lp_dual_core_solver<T, X>::advance_on_known_p() {
+    if (done()) {
+        return true;
+    }
+    this->calculate_pivot_row_of_B_1(m_r);
+    this->calculate_pivot_row_when_pivot_row_of_B1_is_ready(m_r);
+    if (!ratio_test()) {
+        return true;
+    }
+    calculate_beta_r_precisely();
+    this->solve_Bd(m_q); // FTRAN
+    int pivot_compare_result = this->pivots_in_column_and_row_are_different(m_q, m_p);
+    if (!pivot_compare_result){;}
+    else if (pivot_compare_result == 2) { // the sign is changed, cannot continue
+        lean_unreachable(); // not implemented yet
+    } else {
+        lean_assert(pivot_compare_result == 1);
+        this->init_lu();
+    }
+    DSE_FTran();
+    return basis_change_and_update();
+}
+
+template <typename T, typename X> int lp_dual_core_solver<T, X>::define_sign_of_alpha_r() {
+    switch (this->m_column_types[m_p]) {
+    case column_type::boxed:
+    case column_type::fixed:
+        if (this->x_below_low_bound(m_p)) {
+            return -1;
+        }
+        if (this->x_above_upper_bound(m_p)) {
+            return 1;
+        }
+        lean_unreachable();
+    case column_type::low_bound:
+        if (this->x_below_low_bound(m_p)) {
+            return -1;
+        }
+        lean_unreachable();
+    case column_type::upper_bound:
+        if (this->x_above_upper_bound(m_p)) {
+            return 1;
+        }
+        lean_unreachable();
+    default:
+        lean_unreachable();
+    }
+    lean_unreachable();
+    return 0;
+}
+
+template <typename T, typename X> bool lp_dual_core_solver<T, X>::can_be_breakpoint(unsigned j) {
+    if (this->pivot_row_element_is_too_small_for_ratio_test(j)) return false;
+    switch (this->m_column_types[j]) {
+    case column_type::low_bound:
+        lean_assert(this->m_settings.abs_val_is_smaller_than_harris_tolerance(this->m_x[j] - this->m_low_bounds[j]));
+        return m_sign_of_alpha_r * this->m_pivot_row[j]  > 0;
+    case column_type::upper_bound:
+        lean_assert(this->m_settings.abs_val_is_smaller_than_harris_tolerance(this->m_x[j] - this->m_upper_bounds[j]));
+        return m_sign_of_alpha_r * this->m_pivot_row[j] < 0;
+    case column_type::boxed:
+        {
+            bool low_bound = this->x_is_at_low_bound(j);
+            bool grawing = m_sign_of_alpha_r * this->m_pivot_row[j] > 0;
+            return low_bound == grawing;
+        }
+    case column_type::fixed: // is always dual feasible so we ingore it
+        return false;
+    case column_type::free_column:
+        return true;
+    default:
+        return false;
+    }
+}
+
+template <typename T, typename X> void lp_dual_core_solver<T, X>::fill_breakpoint_set() {
+    m_breakpoint_set.clear();
+    for (unsigned j : this->non_basis()) {
+        if (can_be_breakpoint(j)) {
+            m_breakpoint_set.insert(j);
+        }
+    }
+}
+
+// template <typename T, typename X> void lp_dual_core_solver<T, X>::FTran() {
+//     this->solve_Bd(m_q);
+// }
+
+template <typename T, typename X> T lp_dual_core_solver<T, X>::get_delta() {
+    switch (this->m_column_types[m_p]) {
+    case column_type::boxed:
+        if (this->x_below_low_bound(m_p)) {
+            return this->m_x[m_p] - this->m_low_bounds[m_p];
+        }
+        if (this->x_above_upper_bound(m_p)) {
+            return this->m_x[m_p] - this->m_upper_bounds[m_p];
+        }
+        lean_unreachable();
+    case column_type::low_bound:
+        if (this->x_below_low_bound(m_p)) {
+            return this->m_x[m_p] - this->m_low_bounds[m_p];
+        }
+        lean_unreachable();
+    case column_type::upper_bound:
+        if (this->x_above_upper_bound(m_p)) {
+            return get_edge_steepness_for_upper_bound(m_p);
+        }
+        lean_unreachable();
+    case column_type::fixed:
+        return this->m_x[m_p] - this->m_upper_bounds[m_p];
+    default:
+        lean_unreachable();
+    }
+    lean_unreachable();
+    return zero_of_type<T>();
+}
+
+template <typename T, typename X> void lp_dual_core_solver<T, X>::restore_d() {
+    this->m_d[m_p] = numeric_traits<T>::zero();
+    for (auto j : this->non_basis()) {
+        this->m_d[j] += m_theta_D * this->m_pivot_row[j];
+    }
+}
+
+template <typename T, typename X> bool lp_dual_core_solver<T, X>::d_is_correct() {
+    this->solve_yB(this->m_y);
+    for  (auto j : this->non_basis()) {
+        T d = this->m_costs[j] -  this->m_A.dot_product_with_column(this->m_y, j);
+        if (numeric_traits<T>::get_double(abs(d - this->m_d[j])) >= 0.001) {
+            LP_OUT(this->m_settings, "total_iterations = " << this->total_iterations() << std::endl
+                << "d[" << j << "] = " << this->m_d[j] << " but should be " << d << std::endl);
+            return false;
+        }
+    }
+    return true;
+}
+
+template <typename T, typename X> void lp_dual_core_solver<T, X>::xb_minus_delta_p_pivot_column() {
+    unsigned i = this->m_m();
+    while (i--) {
+        this->m_x[this->m_basis[i]] -= m_theta_P * this->m_ed[i];
+    }
+}
+
+template <typename T, typename X> void lp_dual_core_solver<T, X>::update_betas() { // page 194 of Progress ... todo - once in a while betas have to be reinitialized
+    T one_over_arq = numeric_traits<T>::one() / this->m_pivot_row[m_q];
+    T beta_r = this->m_betas[m_r] = std::max(T(0.0001), (m_betas[m_r] * one_over_arq) *  one_over_arq);
+    T k = -2 * one_over_arq;
+    unsigned i = this->m_m();
+    while (i--) {
+        if (static_cast<int>(i) == m_r) continue;
+        T a = this->m_ed[i];
+        m_betas[i] += a * (a * beta_r + k * this->m_pivot_row_of_B_1[i]);
+        if (m_betas[i] < T(0.0001))
+            m_betas[i] = T(0.0001);
+    }
+}
+
+template <typename T, typename X> void lp_dual_core_solver<T, X>::apply_flips() {
+    for (unsigned j : m_flipped_boxed) {
+        lean_assert(this->x_is_at_bound(j));
+        if (this->x_is_at_low_bound(j)) {
+            this->m_x[j] = this->m_upper_bounds[j];
+        } else {
+            this->m_x[j] = this->m_low_bounds[j];
+        }
+    }
+}
+
+template <typename T, typename X> void lp_dual_core_solver<T, X>::snap_xN_column_to_bounds(unsigned j) {
+    switch (this->m_column_type[j]) {
+    case column_type::fixed:
+        this->m_x[j] = this->m_low_bounds[j];
+        break;
+    case column_type::boxed:
+        if (this->x_is_at_low_bound(j)) {
+            this->m_x[j] = this->m_low_bounds[j];
+        } else {
+            this->m_x[j] = this->m_upper_bounds[j];
+        }
+        break;
+    case column_type::low_bound:
+        this->m_x[j] = this->m_low_bounds[j];
+        break;
+    case column_type::upper_bound:
+        this->m_x[j] = this->m_upper_bounds[j];
+        break;
+    case column_type::free_column:
+        break;
+    default:
+        lean_unreachable();
+    }
+}
+
+template <typename T, typename X> void lp_dual_core_solver<T, X>::snap_xN_to_bounds() {
+    for (auto j : this->non_basis()) {
+        snap_xN_column_to_bounds(j);
+    }
+}
+
+template <typename T, typename X> void lp_dual_core_solver<T, X>::init_beta_precisely(unsigned i) {
+    vector<T> vec(this->m_m(), numeric_traits<T>::zero());
+    vec[i] = numeric_traits<T>::one();
+    this->m_factorization->solve_yB_with_error_check(vec, this->m_basis);
+    T beta = numeric_traits<T>::zero();
+    for (T & v : vec) {
+        beta += v * v;
+    }
+    this->m_betas[i] =beta;
+}
+
+template <typename T, typename X> void lp_dual_core_solver<T, X>::init_betas_precisely() {
+    unsigned i = this->m_m();
+    while (i--) {
+        init_beta_precisely(i);
+    }
+}
+
+// step 7 of the algorithm from Progress
+template <typename T, typename X> bool lp_dual_core_solver<T, X>::basis_change_and_update() {
+    update_betas();
+    update_d_and_xB();
+    //    m_theta_P = m_delta / this->m_ed[m_r];
+    m_theta_P = m_delta / this->m_pivot_row[m_q];
+    //    xb_minus_delta_p_pivot_column();
+    apply_flips();
+    if (!this->update_basis_and_x(m_q, m_p, m_theta_P)) {
+          init_betas_precisely();
+          return false;
+    }
+
+    if (snap_runaway_nonbasic_column(m_p)) {
+        if (!this->find_x_by_solving()) {
+            revert_to_previous_basis();
+            this->iters_with_no_cost_growing()++;
+            return false;
+        }
+    }
+
+    if (!problem_is_dual_feasible()) {
+        // todo : shift the costs!!!!
+        revert_to_previous_basis();
+        this->iters_with_no_cost_growing()++;
+        return false;
+    }
+
+    lean_assert(d_is_correct());
+    return true;
+}
+
+template <typename T, typename X> void lp_dual_core_solver<T, X>::recover_leaving() {
+    switch (m_entering_boundary_position) {
+    case at_low_bound:
+    case at_fixed:
+        this->m_x[m_q] = this->m_low_bounds[m_q];
+        break;
+    case at_upper_bound:
+        this->m_x[m_q] = this->m_upper_bounds[m_q];
+        break;
+    case free_of_bounds:
+        this->m_x[m_q] = zero_of_type<X>();
+    default:
+        lean_unreachable();
+    }
+}
+
+template <typename T, typename X> void lp_dual_core_solver<T, X>::revert_to_previous_basis() {
+    LP_OUT(this->m_settings, "revert to previous basis on ( " << m_p << ", " << m_q << ")" << std::endl);
+    this->change_basis_unconditionally(m_p, m_q);
+    init_factorization(this->m_factorization, this->m_A, this->m_basis, this->m_settings);
+    if (this->m_factorization->get_status() != LU_status::OK) {
+        this->set_status(FLOATING_POINT_ERROR); // complete failure
+        return;
+    }
+    recover_leaving();
+    if (!this->find_x_by_solving()) {
+        this->set_status(FLOATING_POINT_ERROR);
+        return;
+    }
+    recalculate_xB_and_d();
+    init_betas_precisely();
+}
+
+// returns true if the column has been snapped
+template <typename T, typename X> bool lp_dual_core_solver<T, X>::snap_runaway_nonbasic_column(unsigned j) {
+    switch (this->m_column_types[j]) {
+    case column_type::fixed:
+    case column_type::low_bound:
+        if (!this->x_is_at_low_bound(j)) {
+            this->m_x[j] = this->m_low_bounds[j];
+            return true;
+        }
+        break;
+    case column_type::boxed:
+        {
+            bool closer_to_low_bound = abs(this->m_low_bounds[j] - this->m_x[j]) < abs(this->m_upper_bounds[j] - this->m_x[j]);
+            if (closer_to_low_bound) {
+                if (!this->x_is_at_low_bound(j)) {
+                    this->m_x[j] = this->m_low_bounds[j];
+                    return true;
+                }
+            } else {
+                if (!this->x_is_at_upper_bound(j)) {
+                    this->m_x[j] = this->m_low_bounds[j];
+                    return true;
+                }
+            }
+        }
+        break;
+    case column_type::upper_bound:
+        if (!this->x_is_at_upper_bound(j)) {
+            this->m_x[j] = this->m_upper_bounds[j];
+            return true;
+        }
+        break;
+    default:
+        break;
+    }
+    return false;
+}
+
+
+template <typename T, typename X> bool lp_dual_core_solver<T, X>::problem_is_dual_feasible() const {
+    for (unsigned j : this->non_basis()){
+        if (!this->column_is_dual_feasible(j)) {
+            // std::cout << "column " << j << " is not dual feasible" << std::endl;
+            // std::cout << "m_d[" << j << "] = " << this->m_d[j] << std::endl;
+            // std::cout << "x[" << j << "] = " << this->m_x[j] << std::endl;
+            // std::cout << "type = " << column_type_to_string(this->m_column_type[j]) << std::endl;
+            // std::cout << "bounds = " << this->m_low_bounds[j] << "," << this->m_upper_bounds[j] << std::endl;
+            // std::cout << "total_iterations = " << this->total_iterations() << std::endl;
+            return false;
+        }
+    }
+    return true;
+}
+
+template <typename T, typename X> unsigned lp_dual_core_solver<T, X>::get_number_of_rows_to_try_for_leaving() {
+    unsigned s = this->m_m();
+    if (this->m_m() > 300) {
+        s = (unsigned)((s / 100.0) * this->m_settings.percent_of_entering_to_check);
+    }
+    return this->m_settings.random_next() % s + 1;
+}
+
+template <typename T, typename X> bool lp_dual_core_solver<T, X>::delta_keeps_the_sign(int initial_delta_sign, const T & delta) {
+    if (numeric_traits<T>::precise())
+        return ((delta > numeric_traits<T>::zero()) && (initial_delta_sign == 1)) ||
+            ((delta < numeric_traits<T>::zero()) && (initial_delta_sign == -1));
+
+    double del = numeric_traits<T>::get_double(delta);
+    return ( (del > this->m_settings.zero_tolerance) && (initial_delta_sign == 1)) ||
+        ((del < - this->m_settings.zero_tolerance) && (initial_delta_sign == -1));
+}
+
+template <typename T, typename X> void lp_dual_core_solver<T, X>::set_status_to_tentative_dual_unbounded_or_dual_unbounded() {
+    if (this->get_status() == TENTATIVE_DUAL_UNBOUNDED) {
+        this->set_status(DUAL_UNBOUNDED);
+    } else {
+        this->set_status(TENTATIVE_DUAL_UNBOUNDED);
+    }
+}
+
+template <typename T, typename X> void lp_dual_core_solver<T, X>::add_tight_breakpoints_and_q_to_flipped_set() {
+    m_flipped_boxed.insert(m_q);
+    for (auto j : m_tight_set) {
+        m_flipped_boxed.insert(j);
+    }
+}
+
+template <typename T, typename X> T lp_dual_core_solver<T, X>::delta_lost_on_flips_of_tight_breakpoints() {
+    T ret = abs(this->bound_span(m_q) * this->m_pivot_row[m_q]);
+    for (auto j : m_tight_set) {
+        ret += abs(this->bound_span(j) * this->m_pivot_row[j]);
+    }
+    return ret;
+}
+
+template <typename T, typename X> bool lp_dual_core_solver<T, X>::tight_breakpoinst_are_all_boxed() {
+    if (this->m_column_types[m_q] != column_type::boxed) return false;
+    for (auto j : m_tight_set) {
+        if (this->m_column_types[j] != column_type::boxed) return false;
+    }
+    return true;
+}
+
+template <typename T, typename X> T lp_dual_core_solver<T, X>::calculate_harris_delta_on_breakpoint_set() {
+    bool first_time = true;
+    T ret = zero_of_type<T>();
+    lean_assert(m_breakpoint_set.size() > 0);
+    for (auto j : m_breakpoint_set) {
+        T t;
+        if (this->x_is_at_low_bound(j)) {
+            t = abs((std::max(this->m_d[j], numeric_traits<T>::zero()) + m_harris_tolerance) / this->m_pivot_row[j]);
+        } else {
+            t = abs((std::min(this->m_d[j], numeric_traits<T>::zero()) - m_harris_tolerance) / this->m_pivot_row[j]);
+        }
+        if (first_time) {
+            ret = t;
+            first_time = false;
+        } else if (t < ret) {
+            ret = t;
+        }
+    }
+    return ret;
+}
+
+template <typename T, typename X> void lp_dual_core_solver<T, X>::fill_tight_set_on_harris_delta(const T & harris_delta ){
+    m_tight_set.clear();
+    for (auto j : m_breakpoint_set) {
+        if (this->x_is_at_low_bound(j)) {
+            if (abs(std::max(this->m_d[j], numeric_traits<T>::zero()) / this->m_pivot_row[j]) <= harris_delta){
+                m_tight_set.insert(j);
+            }
+        } else {
+            if (abs(std::min(this->m_d[j], numeric_traits<T>::zero() ) / this->m_pivot_row[j]) <= harris_delta){
+                m_tight_set.insert(j);
+            }
+        }
+    }
+}
+
+template <typename T, typename X> void lp_dual_core_solver<T, X>::find_q_on_tight_set() {
+    m_q = -1;
+    T max_pivot;
+    for (auto j : m_tight_set) {
+        T r = abs(this->m_pivot_row[j]);
+        if (m_q != -1) {
+            if (r > max_pivot) {
+                max_pivot = r;
+                m_q = j;
+            }
+        } else {
+            max_pivot = r;
+            m_q = j;
+        }
+    }
+    m_tight_set.erase(m_q);
+    lean_assert(m_q != -1);
+}
+
+template <typename T, typename X> void lp_dual_core_solver<T, X>::find_q_and_tight_set() {
+    T harris_del = calculate_harris_delta_on_breakpoint_set();
+    fill_tight_set_on_harris_delta(harris_del);
+    find_q_on_tight_set();
+    m_entering_boundary_position = this->get_non_basic_column_value_position(m_q);
+}
+
+template <typename T, typename X> void lp_dual_core_solver<T, X>::erase_tight_breakpoints_and_q_from_breakpoint_set() {
+    m_breakpoint_set.erase(m_q);
+    for (auto j : m_tight_set) {
+        m_breakpoint_set.erase(j);
+    }
+}
+
+template <typename T, typename X> bool lp_dual_core_solver<T, X>::ratio_test() {
+    m_sign_of_alpha_r = define_sign_of_alpha_r();
+    fill_breakpoint_set();
+    m_flipped_boxed.clear();
+    int initial_delta_sign = m_delta >= numeric_traits<T>::zero()? 1: -1;
+    do {
+        if (m_breakpoint_set.size() == 0) {
+            set_status_to_tentative_dual_unbounded_or_dual_unbounded();
+            return false;
+        }
+        this->set_status(FEASIBLE);
+        find_q_and_tight_set();
+        if (!tight_breakpoinst_are_all_boxed())  break;
+        T del = m_delta - delta_lost_on_flips_of_tight_breakpoints() * initial_delta_sign;
+        if (!delta_keeps_the_sign(initial_delta_sign, del)) break;
+        if (m_tight_set.size() + 1 == m_breakpoint_set.size()) {
+            break; // deciding not to flip since we might get stuck without finding m_q, the column entering the basis
+        }
+        // we can flip m_q together with the tight set and look for another breakpoint candidate for m_q and another tight set
+        add_tight_breakpoints_and_q_to_flipped_set();
+        m_delta = del;
+        erase_tight_breakpoints_and_q_from_breakpoint_set();
+    } while (true);
+    m_theta_D = this->m_d[m_q] / this->m_pivot_row[m_q];
+    return true;
+}
+
+template <typename T, typename X> void lp_dual_core_solver<T, X>::process_flipped() {
+    init_a_wave_by_zeros();
+    for (auto j : m_flipped_boxed) {
+        update_a_wave(signed_span_of_boxed(j), j);
+    }
+}
+template <typename T, typename X> void lp_dual_core_solver<T, X>::update_d_and_xB() {
+    for (auto j : this->non_basis()) {
+        this->m_d[j] -= m_theta_D * this->m_pivot_row[j];
+    }
+    this->m_d[m_p] = - m_theta_D;
+    if (m_flipped_boxed.size() > 0) {
+        process_flipped();
+        update_xb_after_bound_flips();
+    }
+}
+
+template <typename T, typename X> void lp_dual_core_solver<T, X>::calculate_beta_r_precisely() {
+    T t = numeric_traits<T>::zero();
+    unsigned i = this->m_m();
+    while (i--) {
+        T b = this->m_pivot_row_of_B_1[i];
+        t += b * b;
+    }
+    m_betas[m_r] = t;
+}
+// see "Progress in the dual simplex method for large scale LP problems: practical dual phase 1 algorithms"
+
+template <typename T, typename X> void lp_dual_core_solver<T, X>::update_xb_after_bound_flips() {
+    this->m_factorization->solve_By(m_a_wave);
+    unsigned i = this->m_m();
+    while (i--) {
+        this->m_x[this->m_basis[i]] -= m_a_wave[i];
+    }
+}
+
+template <typename T, typename X> void lp_dual_core_solver<T, X>::one_iteration() {
+    unsigned number_of_rows_to_try = get_number_of_rows_to_try_for_leaving();
+    unsigned offset_in_rows = this->m_settings.random_next() % this->m_m();
+    if (this->get_status() == TENTATIVE_DUAL_UNBOUNDED) {
+        number_of_rows_to_try = this->m_m();
+    } else {
+        this->set_status(FEASIBLE);
+    }
+    pricing_loop(number_of_rows_to_try, offset_in_rows);
+    lean_assert(problem_is_dual_feasible());
+}
+
+template <typename T, typename X> void lp_dual_core_solver<T, X>::solve() { // see the page 35
+    lean_assert(d_is_correct());
+    lean_assert(problem_is_dual_feasible());
+    lean_assert(this->basis_heading_is_correct());
+    this->set_total_iterations(0);
+    this->iters_with_no_cost_growing() = 0;
+    do {
+        if (this->print_statistics_with_iterations_and_nonzeroes_and_cost_and_check_that_the_time_is_over("", *this->m_settings.get_message_ostream())){
+            return;
+        }
+        one_iteration();
+    } while (this->get_status() != FLOATING_POINT_ERROR && this->get_status() != DUAL_UNBOUNDED && this->get_status() != OPTIMAL &&
+             this->iters_with_no_cost_growing() <= this->m_settings.max_number_of_iterations_with_no_improvements
+             && this->total_iterations() <= this->m_settings.max_total_number_of_iterations);
+}
+}

src/util/lp/lp_dual_core_solver_instances.cpp

@@ -0,0 +1,29 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#include <utility>
+#include <memory>
+#include <string>
+#include "util/vector.h"
+#include <functional>
+#include "util/lp/lp_dual_core_solver.hpp"
+template void lean::lp_dual_core_solver<lean::mpq, lean::mpq>::start_with_initial_basis_and_make_it_dual_feasible();
+template void lean::lp_dual_core_solver<lean::mpq, lean::mpq>::solve();
+template lean::lp_dual_core_solver<double, double>::lp_dual_core_solver(lean::static_matrix<double, double>&, vector<bool>&,
+                                                                        vector<double>&,
+                                                                        vector<double>&,
+                                                                        vector<unsigned int>&,
+                                                                        vector<unsigned> &,
+                                                                        vector<int> &,
+                                                                        vector<double>&,
+                                                                        vector<lean::column_type>&,
+                                                                        vector<double>&,
+                                                                        vector<double>&,
+                                                                        lean::lp_settings&, const lean::column_namer&);
+template void lean::lp_dual_core_solver<double, double>::start_with_initial_basis_and_make_it_dual_feasible();
+template void lean::lp_dual_core_solver<double, double>::solve();
+template void lean::lp_dual_core_solver<lean::mpq, lean::mpq>::restore_non_basis();
+template void lean::lp_dual_core_solver<double, double>::restore_non_basis();
+template void lean::lp_dual_core_solver<double, double>::revert_to_previous_basis();
+template void lean::lp_dual_core_solver<lean::mpq, lean::mpq>::revert_to_previous_basis();

src/util/lp/lp_dual_simplex.h

@@ -0,0 +1,80 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#pragma once
+#include "util/vector.h"
+#include "util/lp/lp_utils.h"
+#include "util/lp/lp_solver.h"
+#include "util/lp/lp_dual_core_solver.h"
+namespace lean {
+
+template <typename T, typename X>
+class lp_dual_simplex: public lp_solver<T, X> {
+    lp_dual_core_solver<T, X> * m_core_solver;
+    vector<T> m_b_copy;
+    vector<T> m_low_bounds; // We don't have a convention here that all low bounds are zeros. At least it does not hold for the first stage solver
+    vector<column_type> m_column_types_of_core_solver;
+    vector<column_type> m_column_types_of_logicals;
+    vector<bool>  m_can_enter_basis;
+public:
+    ~lp_dual_simplex() {
+        if (m_core_solver != nullptr) {
+            delete m_core_solver;
+        }
+    }
+
+    lp_dual_simplex() : m_core_solver(nullptr) {}
+
+
+    void decide_on_status_after_stage1();
+
+    void fix_logical_for_stage2(unsigned j);
+
+    void fix_structural_for_stage2(unsigned j);
+
+    void unmark_boxed_and_fixed_columns_and_fix_structural_costs();
+
+    void restore_right_sides();
+
+    void solve_for_stage2();
+
+    void fill_x_with_zeros();
+
+    void stage1();
+
+    void stage2();
+
+    void fill_first_stage_solver_fields();
+
+    column_type get_column_type(unsigned j);
+
+    void fill_costs_bounds_types_and_can_enter_basis_for_the_first_stage_solver_structural_column(unsigned j);
+
+    void fill_costs_bounds_types_and_can_enter_basis_for_the_first_stage_solver_logical_column(unsigned j);
+
+    void fill_costs_and_bounds_and_column_types_for_the_first_stage_solver();
+
+    void set_type_for_logical(unsigned j, column_type col_type) {
+        this->m_column_types_of_logicals[j - this->number_of_core_structurals()] = col_type;
+    }
+
+    void fill_first_stage_solver_fields_for_row_slack_and_artificial(unsigned row,
+                                                              unsigned & slack_var,
+                                                                     unsigned & artificial);
+
+    void augment_matrix_A_and_fill_x_and_allocate_some_fields();
+
+
+
+    void copy_m_b_aside_and_set_it_to_zeros();
+
+    void find_maximal_solution();
+
+    virtual T get_column_value(unsigned column) const {
+        return this->get_column_value_with_core_solver(column, m_core_solver);
+    }
+
+    T get_current_cost() const;
+};
+}

src/util/lp/lp_dual_simplex.hpp

@@ -0,0 +1,362 @@
+/*
+  Copyright (c) 2017 Microsoft Corporation
+  Author: Lev Nachmanson
+*/
+#include "util/lp/lp_dual_simplex.h"
+namespace lean{
+
+template <typename T, typename X> void lp_dual_simplex<T, X>::decide_on_status_after_stage1() {
+    switch (m_core_solver->get_status()) {
+    case OPTIMAL:
+        if (this->m_settings.abs_val_is_smaller_than_artificial_tolerance(m_core_solver->get_cost())) {
+            this->m_status = FEASIBLE;
+        } else {
+            this->m_status = UNBOUNDED;
+        }
+        break;
+    case DUAL_UNBOUNDED:
+        lean_unreachable();
+    case ITERATIONS_EXHAUSTED:
+        this->m_status = ITERATIONS_EXHAUSTED;
+        break;
+    case TIME_EXHAUSTED:
+        this->m_status = TIME_EXHAUSTED;
+        break;
+    case FLOATING_POINT_ERROR:
+        this->m_status = FLOATING_POINT_ERROR;
+        break;
+    default:
+        lean_unreachable();
+    }
+}
+
+template <typename T, typename X> void lp_dual_simplex<T, X>::fix_logical_for_stage2(unsigned j) {
+    lean_assert(j >= this->number_of_core_structurals());
+    switch (m_column_types_of_logicals[j - this->number_of_core_structurals()]) {
+    case column_type::low_bound:
+        m_low_bounds[j] = numeric_traits<T>::zero();
+        m_column_types_of_core_solver[j] = column_type::low_bound;
+        m_can_enter_basis[j] = true;
+        break;
+    case column_type::fixed:
+        this->m_upper_bounds[j] = m_low_bounds[j] = numeric_traits<T>::zero();
+        m_column_types_of_core_solver[j] = column_type::fixed;
+        m_can_enter_basis[j] = false;
+        break;
+    default:
+        lean_unreachable();
+    }
+}
+
+template <typename T, typename X> void lp_dual_simplex<T, X>::fix_structural_for_stage2(unsigned j) {
+    column_info<T> * ci = this->m_map_from_var_index_to_column_info[this->m_core_solver_columns_to_external_columns[j]];
+    switch (ci->get_column_type()) {
+    case column_type::low_bound:
+        m_low_bounds[j] = numeric_traits<T>::zero();
+        m_column_types_of_core_solver[j] = column_type::low_bound;
+        m_can_enter_basis[j] = true;
+        break;
+    case column_type::fixed:
+    case column_type::upper_bound:
+        lean_unreachable();
+    case column_type::boxed:
+        this->m_upper_bounds[j] = ci->get_adjusted_upper_bound() / this->m_column_scale[j];
+        m_low_bounds[j] = numeric_traits<T>::zero();
+        m_column_types_of_core_solver[j] = column_type::boxed;
+        m_can_enter_basis[j] = true;
+        break;
+    case column_type::free_column:
+        m_can_enter_basis[j] = true;
+        m_column_types_of_core_solver[j] = column_type::free_column;
+        break;
+    default:
+        lean_unreachable();
+    }
+    //    T cost_was = this->m_costs[j];
+    this->set_scaled_cost(j);
+}
+
+template <typename T, typename X> void lp_dual_simplex<T, X>::unmark_boxed_and_fixed_columns_and_fix_structural_costs() {
+    unsigned j = this->m_A->column_count();
+    while (j-- > this->number_of_core_structurals()) {
+        fix_logical_for_stage2(j);
+    }
+    j = this->number_of_core_structurals();
+    while (j--) {
+        fix_structural_for_stage2(j);
+    }
+}
+
+template <typename T, typename X> void lp_dual_simplex<T, X>::restore_right_sides() {
+    unsigned i = this->m_A->row_count();
+    while (i--) {
+        this->m_b[i] = m_b_copy[i];
+    }
+}
+
+template <typename T, typename X> void lp_dual_simplex<T, X>::solve_for_stage2() {
+    m_core_solver->restore_non_basis();
+    m_core_solver->solve_yB(m_core_solver->m_y);
+    m_core_solver->fill_reduced_costs_from_m_y_by_rows();
+    m_core_solver->start_with_initial_basis_and_make_it_dual_feasible();
+    m_core_solver->set_status(FEASIBLE);
+    m_core_solver->solve();
+    switch (m_core_solver->get_status()) {
+    case OPTIMAL:
+        this->m_status = OPTIMAL;
+        break;
+    case DUAL_UNBOUNDED:
+        this->m_status = INFEASIBLE;
+        break;
+    case TIME_EXHAUSTED:
+        this->m_status = TIME_EXHAUSTED;
+        break;
+    case FLOATING_POINT_ERROR:
+        this->m_status = FLOATING_POINT_ERROR;
+        break;
+    default:
+        lean_unreachable();
+    }
+    this->m_second_stage_iterations = m_core_solver->total_iterations();
+    this->m_total_iterations = (this->m_first_stage_iterations + this->m_second_stage_iterations);
+}
+
+template <typename T, typename X> void lp_dual_simplex<T, X>::fill_x_with_zeros() {
+    unsigned j = this->m_A->column_count();
+    while (j--) {
+        this->m_x[j] = numeric_traits<T>::zero();
+    }
+}
+
+template <typename T, typename X> void lp_dual_simplex<T, X>::stage1() {
+    lean_assert(m_core_solver == nullptr);
+    this->m_x.resize(this->m_A->column_count(), numeric_traits<T>::zero());
+    if (this->m_settings.get_message_ostream() != nullptr)
+        this->print_statistics_on_A(*this->m_settings.get_message_ostream());
+    m_core_solver = new lp_dual_core_solver<T, X>(
+                                                  *this->m_A,
+                                                  m_can_enter_basis,
+                                                  this->m_b, // the right side vector
+                                                  this->m_x,
+                                                  this->m_basis,
+                                                  this->m_nbasis,
+                                                  this->m_heading,
+                                                  this->m_costs,
+                                                  this->m_column_types_of_core_solver,
+                                                  this->m_low_bounds,
+                                                  this->m_upper_bounds,
+                                                  this->m_settings,
+                                                  *this);
+    m_core_solver->fill_reduced_costs_from_m_y_by_rows();
+    m_core_solver->start_with_initial_basis_and_make_it_dual_feasible();
+    if (this->m_settings.abs_val_is_smaller_than_artificial_tolerance(m_core_solver->get_cost())) {
+        // skipping stage 1
+        m_core_solver->set_status(OPTIMAL);
+        m_core_solver->set_total_iterations(0);
+    } else {
+        m_core_solver->solve();
+    }
+    decide_on_status_after_stage1();
+    this->m_first_stage_iterations = m_core_solver->total_iterations();
+}
+
+template <typename T, typename X> void lp_dual_simplex<T, X>::stage2() {
+    unmark_boxed_and_fixed_columns_and_fix_structural_costs();
+    restore_right_sides();
+    solve_for_stage2();
+}
+
+template <typename T, typename X> void lp_dual_simplex<T, X>::fill_first_stage_solver_fields() {
+    unsigned slack_var = this->number_of_core_structurals();
+    unsigned artificial = this->number_of_core_structurals() + this->m_slacks;
+
+    for (unsigned row = 0; row < this->row_count(); row++) {
+        fill_first_stage_solver_fields_for_row_slack_and_artificial(row, slack_var, artificial);
+    }
+    fill_costs_and_bounds_and_column_types_for_the_first_stage_solver();
+}
+
+template <typename T, typename X> column_type lp_dual_simplex<T, X>::get_column_type(unsigned j) {
+    lean_assert(j < this->m_A->column_count());
+    if (j >= this->number_of_core_structurals()) {
+        return m_column_types_of_logicals[j - this->number_of_core_structurals()];
+    }
+    return this->m_map_from_var_index_to_column_info[this->m_core_solver_columns_to_external_columns[j]]->get_column_type();
+}
+
+template <typename T, typename X> void lp_dual_simplex<T, X>::fill_costs_bounds_types_and_can_enter_basis_for_the_first_stage_solver_structural_column(unsigned j) {
+    // see 4.7 in the dissertation of Achim Koberstein
+    lean_assert(this->m_core_solver_columns_to_external_columns.find(j) !=
+                this->m_core_solver_columns_to_external_columns.end());
+
+    T free_bound = T(1e4); // see 4.8
+    unsigned jj = this->m_core_solver_columns_to_external_columns[j];
+    lean_assert(this->m_map_from_var_index_to_column_info.find(jj) != this->m_map_from_var_index_to_column_info.end());
+    column_info<T> * ci = this->m_map_from_var_index_to_column_info[jj];
+    switch (ci->get_column_type()) {
+    case column_type::upper_bound: {
+        std::stringstream s;
+        s << "unexpected bound type " << j << " "
+          << column_type_to_string(get_column_type(j));
+        throw_exception(s.str());
+        break;
+    }
+    case column_type::low_bound: {
+        m_can_enter_basis[j] = true;
+        this->set_scaled_cost(j);
+        this->m_low_bounds[j] = numeric_traits<T>::zero();
+        this->m_upper_bounds[j] =numeric_traits<T>::one();
+        break;
+    }
+    case column_type::free_column: {
+        m_can_enter_basis[j] = true;
+        this->set_scaled_cost(j);
+        this->m_upper_bounds[j] = free_bound;
+        this->m_low_bounds[j] =  -free_bound;
+        break;
+    }
+    case column_type::boxed:
+        m_can_enter_basis[j] = false;
+        this->m_costs[j] = numeric_traits<T>::zero();
+        this->m_upper_bounds[j] = this->m_low_bounds[j] =  numeric_traits<T>::zero(); // is it needed?
+        break;
+    default:
+        lean_unreachable();
+    }
+    m_column_types_of_core_solver[j] = column_type::boxed;
+}
+
+template <typename T, typename X> void lp_dual_simplex<T, X>::fill_costs_bounds_types_and_can_enter_basis_for_the_first_stage_solver_logical_column(unsigned j) {
+    this->m_costs[j] = 0;
+    lean_assert(get_column_type(j) != column_type::upper_bound);
+    if ((m_can_enter_basis[j] = (get_column_type(j) == column_type::low_bound))) {
+        m_column_types_of_core_solver[j] = column_type::boxed;
+        this->m_low_bounds[j] = numeric_traits<T>::zero();
+        this->m_upper_bounds[j] = numeric_traits<T>::one();
+    } else {
+        m_column_types_of_core_solver[j] = column_type::fixed;
+        this->m_low_bounds[j] = numeric_traits<T>::zero();
+        this->m_upper_bounds[j] = numeric_traits<T>::zero();
+    }
+}
+
+template <typename T, typename X> void lp_dual_simplex<T, X>::fill_costs_and_bounds_and_column_types_for_the_first_stage_solver() {
+    unsigned j = this->m_A->column_count();
+    while (j-- > this->number_of_core_structurals()) { // go over logicals here
+        fill_costs_bounds_types_and_can_enter_basis_for_the_first_stage_solver_logical_column(j);
+    }
+    j = this->number_of_core_structurals();
+    while (j--) {
+        fill_costs_bounds_types_and_can_enter_basis_for_the_first_stage_solver_structural_column(j);
+    }
+}
+
+template <typename T, typename X> void lp_dual_simplex<T, X>::fill_first_stage_solver_fields_for_row_slack_and_artificial(unsigned row,
+                                                                                                                          unsigned & slack_var,
+                                                                                                                          unsigned & artificial) {
+    lean_assert(row < this->row_count());
+    auto & constraint = this->m_constraints[this->m_core_solver_rows_to_external_rows[row]];
+    // we need to bring the program to the form Ax = b
+    T rs = this->m_b[row];
+    switch (constraint.m_relation) {
+    case Equal: // no slack variable here
+        set_type_for_logical(artificial, column_type::fixed);
+        this->m_basis[row] = artificial;
+        this->m_costs[artificial] = numeric_traits<T>::zero();
+        (*this->m_A)(row, artificial) = numeric_traits<T>::one();
+        artificial++;
+        break;
+
+    case Greater_or_equal:
+        set_type_for_logical(slack_var, column_type::low_bound);
+        (*this->m_A)(row, slack_var) = - numeric_traits<T>::one();
+        if (rs > 0) {
+            // adding one artificial
+            set_type_for_logical(artificial, column_type::fixed);
+            (*this->m_A)(row, artificial) = numeric_traits<T>::one();
+            this->m_basis[row] = artificial;
+            this->m_costs[artificial] = numeric_traits<T>::zero();
+            artificial++;
+        } else {
+            // we can put a slack_var into the basis, and avoid adding an artificial variable
+            this->m_basis[row] = slack_var;
+            this->m_costs[slack_var] = numeric_traits<T>::zero();
+        }
+        slack_var++;
+        break;
+    case Less_or_equal:
+        // introduce a non-negative slack variable
+        set_type_for_logical(slack_var, column_type::low_bound);
+        (*this->m_A)(row, slack_var) = numeric_traits<T>::one();
+        if (rs < 0) {
+            // adding one artificial
+            set_type_for_logical(artificial, column_type::fixed);
+            (*this->m_A)(row, artificial) = - numeric_traits<T>::one();
+            this->m_basis[row] = artificial;
+            this->m_costs[artificial] = numeric_traits<T>::zero();
+            artificial++;
+        } else {
+            // we can put slack_var into the basis, and avoid adding an artificial variable
+            this->m_basis[row] = slack_var;
+            this->m_costs[slack_var] = numeric_traits<T>::zero();
+        }
+        slack_var++;
+        break;
+    }
+}
+
+template <typename T, typename X> void lp_dual_simplex<T, X>::augment_matrix_A_and_fill_x_and_allocate_some_fields() {
+    this->count_slacks_and_artificials();
+    this->m_A->add_columns_at_the_end(this->m_slacks + this->m_artificials);
+    unsigned n = this->m_A->column_count();
+    this->m_column_types_of_core_solver.resize(n);
+    m_column_types_of_logicals.resize(this->m_slacks + this->m_artificials);
+    this->m_costs.resize(n);
+    this->m_upper_bounds.resize(n);
+    this->m_low_bounds.resize(n);
+    m_can_enter_basis.resize(n);
+    this->m_basis.resize(this->m_A->row_count());
+}
+
+
+
+template <typename T, typename X> void lp_dual_simplex<T, X>::copy_m_b_aside_and_set_it_to_zeros() {
+    for (unsigned i = 0; i < this->m_b.size(); i++) {
+        m_b_copy.push_back(this->m_b[i]);
+        this->m_b[i] = numeric_traits<T>::zero(); // preparing for the first stage
+    }
+}
+
+template <typename T, typename X> void lp_dual_simplex<T, X>::find_maximal_solution(){
+    if (this->problem_is_empty()) {
+        this->m_status = lp_status::EMPTY;
+        return;
+    }
+
+    this->flip_costs(); // do it for now, todo ( remove the flipping)
+
+    this->cleanup();
+    if (this->m_status == INFEASIBLE) {
+        return;
+    }
+    this->fill_matrix_A_and_init_right_side();
+    this->fill_m_b();
+    this->scale();
+    augment_matrix_A_and_fill_x_and_allocate_some_fields();
+    fill_first_stage_solver_fields();
+    copy_m_b_aside_and_set_it_to_zeros();
+    stage1();
+    if (this->m_status == FEASIBLE) {
+        stage2();
+    }
+}
+
+
+template <typename T, typename X> T lp_dual_simplex<T, X>::get_current_cost() const {
+    T ret = numeric_traits<T>::zero();
+    for (auto it : this->m_map_from_var_index_to_column_info) {
+        ret += this->get_column_cost_value(it.first, it.second);
+    }
+    return -ret; // we flip costs for now
+}
+}