subset.cpp

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/**
 * @file subset.cpp
 * @brief Valid-world enumeration for aggregate HAVING predicates.
 *
 * Implements @c enumerate_valid_worlds() declared in @c subset.hpp.
 *
 * For a list of @f$n@f$ tuples with individual values, the function
 * iterates over all @f$2^n@f$ possible worlds (bitmasks), computes the
 * aggregate of the present tuples' values using the requested
 * @c AggregationOperator, and tests the comparison predicate.  All
 * valid worlds are collected and returned.
 *
 * The @c upset output flag is set to @c true when the set of valid
 * worlds is upward-closed (every superset of a valid world is also
 * valid), which is the case for monotone aggregation predicates (e.g.
 * SUM ≥ k).  This information is used to optimise the evaluation of
 * monotone HAVING clauses.
 *
 * Internal helpers in an anonymous namespace:
 * - @c increment(): advance a bitmask to the next possible world.
 * - @c compute_agg(): compute the aggregate value for one bitmask.
 */
#include "subset.hpp"
#include <algorithm>
#include <cstddef>
#include <cstdint>
#include <limits>
#include <vector>
#include <stdexcept>
#include <cassert>
 
namespace {
static bool increment(mask_t &v)
{
  for(size_t i=0; i<v.size(); ++i)
  {
    v[i]=!v[i];
    if(v[i])
      return true;
  }
  return false;
}
 
static std::vector<mask_t> all_worlds(const std::vector<long> &values)
{
  std::vector<mask_t> worlds;
  mask_t mask(values.size());
  // Skip empty world
  while(increment(mask))
    worlds.push_back(mask);
  return worlds;
}
 
static void append_range(std::vector<mask_t> &out,
                         const std::vector<std::vector<mask_t> > &dp,
                         int lo,
                         int hi)
{
  if (dp.empty()) return;
  const int J = static_cast<int>(dp.size())-1;
  lo = std::max(lo, 0);
  hi = std::min(hi, J);
  if (lo>hi) return;
 
  for (int j = lo; j <= hi; ++j) {
    out.insert(out.end(), dp[j].begin(), dp[j].end());
  }
}
 
class DPException : public std::exception {};
 
/** @brief Return the minimum of two values. */
#define MIN(x,y) ((x)<(y)?(x):(y))
 
static std::vector<mask_t> sum_dp(const std::vector<long> &values, int C, ComparisonOperator op, bool absorptive, bool &upset)
{
  const std::size_t n = values.size();
 
  std::vector<mask_t> R;
 
  // We first deal with NEQ by combining LT and GT
  if(op == ComparisonOperator::NE) {
    std::vector<mask_t> lt= sum_dp(values, C, ComparisonOperator::LT, absorptive, upset);
    std::vector<mask_t> gt= sum_dp(values, C, ComparisonOperator::GT, absorptive, upset);
    R.reserve(lt.size()+gt.size());
    R.insert(R.end(),lt.begin(),lt.end());
    R.insert(R.end(),gt.begin(),gt.end());
    return R;
  }
 
  long long T=0;
  for (int w: values) {
    if (w < 0)
      throw DPException();
    T+=w;
  }
 
  //no valid worlds case
  if (op == ComparisonOperator::GT && C>=T) return {};
  if (op == ComparisonOperator::GE && C>T) return {};
  if (op == ComparisonOperator::LT && C<=0) return {};
  if (op == ComparisonOperator::LE && C<0) return {};
  if (op == ComparisonOperator::EQ && (C>T || C<0)) return {};
 
  //tautology cases
  if (op == ComparisonOperator::GT && C<0) return all_worlds(values);
  if (op == ComparisonOperator::GE && C<=0) return all_worlds(values);
  if (op == ComparisonOperator::LT && C>T) return all_worlds(values);
  if (op == ComparisonOperator::LE && C>=T) return all_worlds(values);
 
  long long J=0;
  if (op == ComparisonOperator::GT || op == ComparisonOperator::GE)
    J=T;
  else if (op==ComparisonOperator::LT)
    J=MIN(C-1,T);
  else
    J=MIN(C,T);
 
  assert(J>=0);
 
  std::vector<std::vector<mask_t> > dp(static_cast<std::size_t>(J) + 1);
  dp[0].push_back(mask_t(n)); // dp[0] <- {emptyset}
 
  int pref_sum=0;
 
  for (std::size_t i=0; i<n; ++i)
  {
    const int w=values[i];
    pref_sum+=w;
    const int j_max=MIN(J,pref_sum);
 
    for (int j = j_max; j >= w; --j) {
      const int p = j - w;
      if(absorptive && ((op==ComparisonOperator::GT && p>C) ||
                        (op==ComparisonOperator::GE && p>=C))) {
        upset=true;
        continue;
      }
      size_t s=dp[p].size();
      for(size_t k=0; k<s; ++k) {
        mask_t m = dp[p][k];
        m[i] = true;
        dp[j].push_back(m);
      }
    }
  }
 
  switch(op){
  case ComparisonOperator::EQ:
    append_range(R,dp,C,C);
    break;
 
  case ComparisonOperator::GT:
    append_range(R,dp,C+1,J);
    break;
 
 
  case ComparisonOperator::LT:
    append_range(R,dp,1,C-1);
    break;
 
  case ComparisonOperator::GE:
    append_range(R,dp,C,J);
    break;
 
  case ComparisonOperator::LE:
    append_range(R,dp,1,C);
    break;
 
  case ComparisonOperator::NE: // case already processed
    assert(false);
  }
 
  return R;
}
 
//generate k-subsets form an n-set
static void combinations(std::size_t start,
                         int k_left,
                         mask_t mask,
                         std::vector<mask_t> &out)
{
  const size_t n = mask.size();
 
  if (k_left == 0) {
    out.push_back(mask);
    return;
  }
 
  if (start >= n) return;
 
  const std::size_t remaining = n - start;
  if (remaining < static_cast<std::size_t>(k_left)) return;
 
  combinations(start + 1, k_left, mask, out);
 
  mask[start]=true;
  combinations(start + 1, k_left - 1, mask, out);
}
 
static std::vector<mask_t> count_enum(const std::vector<long> &values, int m, ComparisonOperator op, bool absorptive, bool &upset)
{
  const int n = static_cast<int>(values.size());
  std::vector<mask_t> out;
 
  auto add_exact_k = [&](int k) {
                       if (k < 0 || k > n) return;
                       combinations(0, k, mask_t(n), out);
                     };
 
  switch (op)
  {
  case ComparisonOperator::EQ:
    if(m!=0) add_exact_k(m);
    break;
 
  case ComparisonOperator::GT:
    ++m;
    [[fallthrough]];
  case ComparisonOperator::GE:
    /* Skip the empty subset, mirroring the // Skip empty world rule
     * in @c all_worlds and @c enumerate_exhaustive: a HAVING
     * predicate on an empty group is undefined in SQL semantics
     * (the group does not exist, so HAVING is not evaluated), so
     * the @c count >= 0 / @c count > -K family must collapse to
     * "group is non-empty" rather than to a universal tautology
     * (probability 1 in every world).  Equivalently, m is clamped
     * to at least 1 here. */
    if (m < 1) m = 1;
    if(absorptive) {
      upset=true;
      add_exact_k(m);
    } else
      for (int k = m; k <= n; ++k) add_exact_k(k);
    break;
 
  case ComparisonOperator::LT:
    --m;
    [[fallthrough]];
  case ComparisonOperator::LE:
    for (int k = 1; k <= m; ++k) add_exact_k(k);
    break;
 
  case ComparisonOperator::NE:
    for (int k = 1; k <= n; ++k)
    {
      if (k != m) add_exact_k(k);
    }
    break;
  }
 
  return out;
}
 
}
 
/**
 * @brief Apply a comparison operator to two values.
 * @tparam I  Type of the left operand.
 * @tparam J  Type of the right operand.
 * @param a   Left operand.
 * @param op  Comparison operator.
 * @param b   Right operand.
 * @return    Result of the comparison.
 */
template<typename I, typename J>
static bool compare(I a, ComparisonOperator op, J b) {
  switch (op) {
  case ComparisonOperator::EQ:  return a == b;
  case ComparisonOperator::NE:  return a != b;
  case ComparisonOperator::GT:  return a >  b;
  case ComparisonOperator::LT:  return a <  b;
  case ComparisonOperator::GE:  return a >= b;
  case ComparisonOperator::LE:  return a <= b;
  }
  return false;
}
 
/**
 * @brief Evaluate whether the aggregation of @p values masked by @p mask satisfies @p op @p constant.
 * @param values      Input values to aggregate.
 * @param mask        Boolean mask selecting which values to include.
 * @param constant    Right-hand side constant of the comparison.
 * @param op          Comparison operator.
 * @param aggregator  Aggregator to apply to the selected values.
 * @return            @c true if the aggregate result satisfies the comparison.
 */
bool evaluate(const std::vector<long>& values,
              const std::vector<bool>& mask,
              int constant, ComparisonOperator op,
              std::unique_ptr<Aggregator> aggregator)
{
  for (std::size_t i = 0; i < values.size(); ++i) {
    if (mask[i]) aggregator->add(AggValue {values[i]});
  }
  auto res = aggregator->finalize();
  switch(aggregator->resultType()) {
  case ValueType::INT:
    return compare(std::get<long>(res.v), op, constant);
  case ValueType::BOOLEAN:
    return compare(std::get<bool>(res.v), op, constant);
  case ValueType::FLOAT:
    return compare(std::get<double>(res.v), op, constant);
  default:
    throw std::runtime_error("Cannot compare this kind of value");
  }
}
 
/**
 * @brief Enumerate all subsets satisfying a HAVING predicate by exhaustive search.
 * @param values      Input values.
 * @param constant    Constant for the comparison.
 * @param op          Comparison operator.
 * @param agg_kind    Aggregation function to apply.
 * @param absorptive  Whether the semiring is absorptive.
 * @param upset       Set to @c true if the result set forms an upset (monotone).
 * @return            Vector of satisfying subset masks.
 */
std::vector<mask_t> enumerate_exhaustive(
  const std::vector<long> &values,
  int constant,
  ComparisonOperator op,
  AggregationOperator agg_kind,
  bool absorptive,
  bool &upset)
{
  const size_t n = values.size();
 
  std::vector<mask_t> worlds;
  mask_t mask(n);
 
  bool all_worlds = true;
 
  while(increment(mask)) { // Skipping empty world
    auto aggregator = makeAggregator(agg_kind, ValueType::INT);
 
    if(evaluate(values, mask, constant, op, std::move(aggregator)))
      worlds.push_back(mask);
    else
      all_worlds=false;
  }
 
  if(all_worlds && absorptive)
  {
    worlds.clear();
 
    // In that case, the result is equivalent to the upset generated by
    // the single-tuple possible worlds
    combinations(0, 1, mask_t(n), worlds);
    upset=true;
  }
 
  return worlds;
}
 
std::vector<mask_t> enumerate_valid_worlds(
  const std::vector<long> &values,
  int constant,
  ComparisonOperator op,
  AggregationOperator agg_kind,
  bool absorptive,
  bool &upset
  )
{
  if (agg_kind == AggregationOperator::COUNT)
    return count_enum(values,constant,op, absorptive, upset);
 
  if(agg_kind == AggregationOperator::SUM)
    try {
      return sum_dp(values, constant, op, absorptive, upset);
    } catch(DPException &e) {
      // We will use the default implementation of the enumeration
    }
 
  return enumerate_exhaustive(values, constant, op, agg_kind, absorptive, upset);
}