cover_instrument_mcdc.cpp

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/*******************************************************************\
 
Module: Coverage Instrumentation
 
Author: Daniel Kroening
 
\*******************************************************************/
 
 
#include "cover_instrument.h"
 
#include <util/expr_util.h>
 
#include <langapi/language_util.h>
 
#include <algorithm>
#include <iterator>
 
#include "cover_util.h"
 
void collect_mcdc_controlling_rec(
  const exprt &src,
  const std::vector<exprt> &conditions,
  std::set<exprt> &result)
{
  // src is conjunction (ID_and) or disjunction (ID_or)
  if(src.id() == ID_and || src.id() == ID_or)
  {
    std::vector<exprt> operands;
    collect_operands(src, operands);
 
    if(operands.size() == 1)
    {
      exprt e = *operands.begin();
      collect_mcdc_controlling_rec(e, conditions, result);
    }
    else if(!operands.empty())
    {
      for(std::size_t i = 0; i < operands.size(); i++)
      {
        const exprt op = operands[i];
 
        if(is_condition(op))
        {
          if(src.id() == ID_or)
          {
            std::vector<exprt> others1, others2;
            if(!conditions.empty())
            {
              others1.push_back(conjunction(conditions));
              others2.push_back(conjunction(conditions));
            }
 
            for(std::size_t j = 0; j < operands.size(); j++)
            {
              others1.push_back(not_exprt(operands[j]));
              if(i != j)
                others2.push_back(not_exprt(operands[j]));
              else
                others2.push_back((operands[j]));
            }
 
            result.insert(conjunction(others1));
            result.insert(conjunction(others2));
            continue;
          }
 
          std::vector<exprt> o = operands;
 
          // 'o[i]' needs to be true and false
          std::vector<exprt> new_conditions = conditions;
          new_conditions.push_back(conjunction(o));
          result.insert(conjunction(new_conditions));
 
          o[i] = boolean_negate(op);
          new_conditions.back() = conjunction(o);
          result.insert(conjunction(new_conditions));
        }
        else
        {
          std::vector<exprt> others;
          others.reserve(operands.size() - 1);
 
          for(std::size_t j = 0; j < operands.size(); j++)
            if(i != j)
            {
              if(src.id() == ID_or)
                others.push_back(not_exprt(operands[j]));
              else
                others.push_back(operands[j]);
            }
 
          exprt c = conjunction(others);
          std::vector<exprt> new_conditions = conditions;
          new_conditions.push_back(c);
 
          collect_mcdc_controlling_rec(op, new_conditions, result);
        }
      }
    }
  }
  else if(src.id() == ID_not)
  {
    exprt e = to_not_expr(src).op();
    if(!is_condition(e))
      collect_mcdc_controlling_rec(e, conditions, result);
    else
    {
      // to store a copy of ''src''
      std::vector<exprt> new_conditions1 = conditions;
      new_conditions1.push_back(src);
      result.insert(conjunction(new_conditions1));
 
      // to store a copy of its negation, i.e., ''e''
      std::vector<exprt> new_conditions2 = conditions;
      new_conditions2.push_back(e);
      result.insert(conjunction(new_conditions2));
    }
  }
  else
  {
    // It may happen that ''is_condition(src)'' is valid,
    // but we ignore this case here as it can be handled
    // by the routine decision/condition detection.
  }
}
 
std::set<exprt> collect_mcdc_controlling(const std::set<exprt> &decisions)
{
  std::set<exprt> result;
 
  for(const auto &d : decisions)
    collect_mcdc_controlling_rec(d, {}, result);
 
  return result;
}
 
std::set<exprt> replacement_conjunction(
  const std::set<exprt> &replacement_exprs,
  const std::vector<exprt> &operands,
  const std::size_t i)
{
  std::set<exprt> result;
  for(auto &y : replacement_exprs)
  {
    std::vector<exprt> others;
    for(std::size_t j = 0; j < operands.size(); j++)
      if(i != j)
        others.push_back(operands[j]);
 
    others.push_back(y);
    exprt c = conjunction(others);
    result.insert(c);
  }
  return result;
}
 
std::set<exprt>
collect_mcdc_controlling_nested(const std::set<exprt> &decisions)
{
  // To obtain the 1st-level controlling conditions
  std::set<exprt> controlling = collect_mcdc_controlling(decisions);
 
  std::set<exprt> result;
  // For each controlling condition, to check if it contains
  // non-atomic exprs
  for(auto &src : controlling)
  {
    std::set<exprt> s1, s2;
 
    // The final controlling conditions resulted from ''src''
    // will be stored in ''s1''; ''s2'' is usd to hold the
    // temporary expansion.
    s1.insert(src);
 
    // dual-loop structure to eliminate complex
    // non-atomic-conditional terms
    while(true)
    {
      bool changed = false;
      // the 2nd loop
      for(auto &x : s1)
      {
        // if ''x'' is atomic conditional term, there
        // is no expansion
        if(is_condition(x))
        {
          s2.insert(x);
          continue;
        }
        // otherwise, we apply the ''nested'' method to
        // each of its operands
        std::vector<exprt> operands;
        collect_operands(x, operands);
 
        for(std::size_t i = 0; i < operands.size(); i++)
        {
          std::set<exprt> res;
          // To expand an operand if it is not atomic,
          // and label the ''changed'' flag; the resulted
          // expansion of such an operand is stored in ''res''.
          if(operands[i].id() == ID_not)
          {
            exprt no = to_not_expr(operands[i]).op();
            if(!is_condition(no))
            {
              changed = true;
              std::set<exprt> ctrl_no;
              ctrl_no.insert(no);
              res = collect_mcdc_controlling(ctrl_no);
            }
          }
          else if(!is_condition(operands[i]))
          {
            changed = true;
            std::set<exprt> ctrl;
            ctrl.insert(operands[i]);
            res = collect_mcdc_controlling(ctrl);
          }
 
          // To replace a non-atomic expr with its expansion
          std::set<exprt> co = replacement_conjunction(res, operands, i);
          s2.insert(co.begin(), co.end());
          if(!res.empty())
            break;
        }
        // if there is no change x.r.t current operands of ''x'',
        // i.e., they are all atomic, we reserve ''x''
        if(!changed)
          s2.insert(x);
      }
      // update ''s1'' and check if change happens
      s1 = s2;
      if(!changed)
        break;
      s2.clear();
    }
 
    // The expansions of each ''src'' should be added into
    // the ''result''
    result.insert(s1.begin(), s1.end());
  }
 
  return result;
}
 
std::set<signed> sign_of_expr(const exprt &e, const exprt &E)
{
  std::set<signed> signs;
 
  // At fist, we pre-screen the case such that ''E''
  // is an atomic condition
  if(is_condition(E))
  {
    if(e == E)
      signs.insert(+1);
    return signs;
  }
 
  // or, ''E'' is the negation of ''e''?
  if(E.id() == ID_not)
  {
    if(e == to_not_expr(E).op())
    {
      signs.insert(-1);
      return signs;
    }
  }
 
  // In the general case, we analyze each operand of ''E''.
  std::vector<exprt> ops;
  collect_operands(E, ops);
  for(const auto &x : ops)
  {
    if(x == e)
      signs.insert(+1);
    else if(x.id() == ID_not)
    {
      const exprt &x_op = to_not_expr(x).op();
      if(x_op == e)
        signs.insert(-1);
      if(!is_condition(x_op))
      {
        std::set<signed> re = sign_of_expr(e, x_op);
        signs.insert(re.begin(), re.end());
      }
    }
    else if(!is_condition(x))
    {
      std::set<signed> re = sign_of_expr(e, x);
      signs.insert(re.begin(), re.end());
    }
  }
 
  return signs;
}
 
void remove_repetition(std::set<exprt> &exprs)
{
  // to obtain the set of atomic conditions
  std::set<exprt> conditions;
  for(auto &x : exprs)
  {
    std::set<exprt> new_conditions = collect_conditions(x);
    conditions.insert(new_conditions.begin(), new_conditions.end());
  }
  // exprt that contains multiple (inconsistent) signs should
  // be removed
  std::set<exprt> new_exprs;
  for(auto &x : exprs)
  {
    bool kept = true;
    for(auto &c : conditions)
    {
      std::set<signed> signs = sign_of_expr(c, x);
      if(signs.size() > 1)
      {
        kept = false;
        break;
      }
    }
    if(kept)
      new_exprs.insert(x);
  }
  exprs = new_exprs;
  new_exprs.clear();
 
  for(auto &x : exprs)
  {
    bool red = false;
    // To check if ''x'' is identical with some
    // expr in ''new_exprs''. Two exprs ''x''
    // and ''y'' are identical iff they have the
    // same sign for every atomic condition ''c''.
    for(auto &y : new_exprs)
    {
      bool iden = true;
      for(auto &c : conditions)
      {
        std::set<signed> signs1 = sign_of_expr(c, x);
        std::set<signed> signs2 = sign_of_expr(c, y);
        int s1 = signs1.size(), s2 = signs2.size();
        // it is easy to check non-equivalence;
        if(s1 != s2)
        {
          iden = false;
          break;
        }
        else
        {
          if(s1 == 0 && s2 == 0)
            continue;
          // it is easy to check non-equivalence
          if(*(signs1.begin()) != *(signs2.begin()))
          {
            iden = false;
            break;
          }
        }
      }
      // If ''x'' is found identical w.r.t some
      // expr in ''new_conditions, we label it
      // and break.
      if(iden)
      {
        red = true;
        break;
      }
    }
    // an expr is added into ''new_exprs''
    // if it is not found repetitive
    if(!red)
      new_exprs.insert(x);
  }
 
  // update the original ''exprs''
  exprs = new_exprs;
}
 
bool eval_expr(const std::map<exprt, signed> &atomic_exprs, const exprt &src)
{
  std::vector<exprt> operands;
  collect_operands(src, operands);
  // src is AND
  if(src.id() == ID_and)
  {
    for(auto &x : operands)
      if(!eval_expr(atomic_exprs, x))
        return false;
    return true;
  }
  // src is OR
  else if(src.id() == ID_or)
  {
    std::size_t fcount = 0;
 
    for(auto &x : operands)
      if(!eval_expr(atomic_exprs, x))
        fcount++;
 
    if(fcount < operands.size())
      return true;
    else
      return false;
  }
  // src is NOT
  else if(src.id() == ID_not)
  {
    return !eval_expr(atomic_exprs, to_not_expr(src).op());
  }
  else // if(is_condition(src))
  {
    // ''src'' should be guaranteed to be consistent
    // with ''atomic_exprs''
    if(atomic_exprs.find(src)->second == +1)
      return true;
    else // if(atomic_exprs.find(src)->second==-1)
      return false;
  }
}
 
std::map<exprt, signed>
values_of_atomic_exprs(const exprt &e, const std::set<exprt> &conditions)
{
  std::map<exprt, signed> atomic_exprs;
  for(auto &c : conditions)
  {
    std::set<signed> signs = sign_of_expr(c, e);
    if(signs.empty())
    {
      // ''c'' is not contained in ''e''
      atomic_exprs.insert(std::pair<exprt, signed>(c, 0));
      continue;
    }
    // we do not consider inconsistent expr ''e''
    if(signs.size() != 1)
      continue;
 
    atomic_exprs.insert(std::pair<exprt, signed>(c, *signs.begin()));
  }
  return atomic_exprs;
}
 
bool is_mcdc_pair(
  const exprt &e1,
  const exprt &e2,
  const exprt &c,
  const std::set<exprt> &conditions,
  const exprt &decision)
{
  // An controlling expr cannot be mcdc pair of itself
  if(e1 == e2)
    return false;
 
  // To obtain values of each atomic condition within ''e1''
  // and ''e2''
  std::map<exprt, signed> atomic_exprs_e1 =
    values_of_atomic_exprs(e1, conditions);
  std::map<exprt, signed> atomic_exprs_e2 =
    values_of_atomic_exprs(e2, conditions);
 
  // the sign of ''c'' inside ''e1'' and ''e2''
  signed cs1 = atomic_exprs_e1.find(c)->second;
  signed cs2 = atomic_exprs_e2.find(c)->second;
  // a mcdc pair should both contain ''c'', i.e., sign=+1 or -1
  if(cs1 == 0 || cs2 == 0)
    return false;
 
  // A mcdc pair regarding an atomic expr ''c''
  // should have different values of ''c''
  if(cs1 == cs2)
    return false;
 
  // A mcdc pair should result in different ''decision''
  if(
    eval_expr(atomic_exprs_e1, decision) ==
    eval_expr(atomic_exprs_e2, decision))
    return false;
 
  // A mcdc pair of controlling exprs regarding ''c''
  // can have different values for only one atomic
  // expr, i.e., ''c''. Otherwise, they are not
  // a mcdc pair.
  int diff_count = 0;
  auto e1_it = atomic_exprs_e1.begin();
  auto e2_it = atomic_exprs_e2.begin();
  while(e1_it != atomic_exprs_e1.end())
  {
    if(e1_it->second != e2_it->second)
      diff_count++;
    if(diff_count > 1)
      break;
    e1_it++;
    e2_it++;
  }
 
  if(diff_count == 1)
    return true;
  else
    return false;
}
 
bool has_mcdc_pair(
  const exprt &c,
  const std::set<exprt> &expr_set,
  const std::set<exprt> &conditions,
  const exprt &decision)
{
  for(auto y1 : expr_set)
  {
    for(auto y2 : expr_set)
    {
      if(is_mcdc_pair(y1, y2, c, conditions, decision))
      {
        return true;
      }
    }
  }
  return false;
}
 
void minimize_mcdc_controlling(
  std::set<exprt> &controlling,
  const exprt &decision)
{
  // to obtain the set of atomic conditions
  std::set<exprt> conditions;
  for(auto &x : controlling)
  {
    std::set<exprt> new_conditions = collect_conditions(x);
    conditions.insert(new_conditions.begin(), new_conditions.end());
  }
 
  while(true)
  {
    std::set<exprt> new_controlling;
    bool ctrl_update = false;
    // Iteratively, we test that after removing an item ''x''
    // from the ''controlling'', can a complete mcdc coverage
    // over ''decision'' still be reserved?
    //
    // If yes, we update ''controlling'' with the
    // ''new_controlling'' without ''x''; otherwise, we should
    // keep ''x'' within ''controlling''.
    //
    // If in the end all elements ''x'' in ''controlling'' are
    // reserved, this means that current ''controlling'' set is
    // minimum and the ''while'' loop should be broken out of.
    //
    // Note:  implementation here for the above procedure is
    //        not (meant to be) optimal.
    for(auto &x : controlling)
    {
      // To create a new ''controlling'' set without ''x''
      new_controlling.clear();
      for(auto &y : controlling)
        if(y != x)
          new_controlling.insert(y);
 
      bool removing_x = true;
      // For each atomic expr condition ''c'', to check if its is
      // covered by at least a mcdc pair.
      for(auto &c : conditions)
      {
        bool cOK = has_mcdc_pair(c, new_controlling, conditions, decision);
        // If there is no mcdc pair for an atomic condition ''c'',
        // then ''x'' should not be removed from the original
        // ''controlling'' set
        if(!cOK)
        {
          removing_x = false;
          break;
        }
      }
 
      // If ''removing_x'' is valid, it is safe to remove ''x''
      // from the original ''controlling''
      if(removing_x)
      {
        ctrl_update = true;
        break;
      }
    }
    // Update ''controlling'' or break the while loop
    if(ctrl_update)
    {
      controlling = new_controlling;
    }
    else
      break;
  }
}
 
void cover_mcdc_instrumentert::instrument(
  const irep_idt &function_id,
  goto_programt &goto_program,
  goto_programt::targett &i_it,
  const cover_blocks_baset &,
  const assertion_factoryt &make_assertion) const
{
  if(is_non_cover_assertion(i_it))
    i_it->turn_into_skip();
 
  // 1. Each entry and exit point is invoked
  // 2. Each decision takes every possible outcome
  // 3. Each condition in a decision takes every possible outcome
  // 4. Each condition in a decision is shown to independently
  //    affect the outcome of the decision.
  if(!i_it->source_location().is_built_in())
  {
    const std::set<exprt> conditions = collect_conditions(i_it);
    const std::set<exprt> decisions = collect_decisions(i_it);
 
    std::set<exprt> both;
    std::set_union(
      conditions.begin(),
      conditions.end(),
      decisions.begin(),
      decisions.end(),
      inserter(both, both.end()));
 
    const source_locationt source_location = i_it->source_location();
 
    for(const auto &p : both)
    {
      bool is_decision = decisions.find(p) != decisions.end();
      bool is_condition = conditions.find(p) != conditions.end();
 
      std::string description = (is_decision && is_condition)
                                  ? "decision/condition"
                                  : is_decision ? "decision" : "condition";
 
      std::string p_string = from_expr(ns, function_id, p);
 
      std::string comment_t = description + " '" + p_string + "' true";
      goto_program.insert_before_swap(i_it);
      *i_it = make_assertion(not_exprt(p), source_location);
      i_it->source_location_nonconst().set_comment(comment_t);
      i_it->source_location_nonconst().set(
        ID_coverage_criterion, coverage_criterion);
      i_it->source_location_nonconst().set_property_class(property_class);
      i_it->source_location_nonconst().set_function(function_id);
 
      std::string comment_f = description + " '" + p_string + "' false";
      goto_program.insert_before_swap(i_it);
      *i_it = make_assertion(p, source_location);
      i_it->source_location_nonconst().set_comment(comment_f);
      i_it->source_location_nonconst().set(
        ID_coverage_criterion, coverage_criterion);
      i_it->source_location_nonconst().set_property_class(property_class);
      i_it->source_location_nonconst().set_function(function_id);
    }
 
    std::set<exprt> controlling;
    controlling = collect_mcdc_controlling_nested(decisions);
    remove_repetition(controlling);
    // for now, we restrict to the case of a single ''decision'';
    // however, this is not true, e.g., ''? :'' operator.
    if(!decisions.empty())
    {
      minimize_mcdc_controlling(controlling, *decisions.begin());
    }
 
    for(const auto &p : controlling)
    {
      std::string p_string = from_expr(ns, function_id, p);
 
      std::string description =
        "MC/DC independence condition '" + p_string + "'";
 
      goto_program.insert_before_swap(i_it);
      *i_it = make_assertion(not_exprt(p), source_location);
      i_it->source_location_nonconst().set_comment(description);
      i_it->source_location_nonconst().set(
        ID_coverage_criterion, coverage_criterion);
      i_it->source_location_nonconst().set_property_class(property_class);
      i_it->source_location_nonconst().set_function(function_id);
    }
 
    for(std::size_t i = 0; i < both.size() * 2 + controlling.size(); i++)
      i_it++;
  }
}