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    1 //
    2 // Copyright 2013 Francisco Jerez
    3 //
    4 // Permission is hereby granted, free of charge, to any person obtaining a
    5 // copy of this software and associated documentation files (the "Software"),
    6 // to deal in the Software without restriction, including without limitation
    7 // the rights to use, copy, modify, merge, publish, distribute, sublicense,
    8 // and/or sell copies of the Software, and to permit persons to whom the
    9 // Software is furnished to do so, subject to the following conditions:
   10 //
   11 // The above copyright notice and this permission notice shall be included in
   12 // all copies or substantial portions of the Software.
   13 //
   14 // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
   15 // IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
   16 // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
   17 // THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
   18 // OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
   19 // ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
   20 // OTHER DEALINGS IN THE SOFTWARE.
   21 //
   22 
   23 #ifndef CLOVER_UTIL_FACTOR_HPP
   24 #define CLOVER_UTIL_FACTOR_HPP
   25 
   26 #include "util/range.hpp"
   27 
   28 namespace clover {
   29    namespace factor {
   30       ///
   31       /// Calculate all prime integer factors of \p x.
   32       ///
   33       /// If \p limit is non-zero, terminate early as soon as enough
   34       /// factors have been collected to reach the product \p limit.
   35       ///
   36       template<typename T>
   37       std::vector<T>
   38       find_integer_prime_factors(T x, T limit = 0)
   39       {
   40          const T max_d = (limit > 0 && limit < x ? limit : x);
   41          const T min_x = x / max_d;
   42          std::vector<T> factors;
   43 
   44          for (T d = 2; d <= max_d && x > min_x; d++) {
   45             if (x % d == 0) {
   46                for (; x % d == 0; x /= d);
   47                factors.push_back(d);
   48             }
   49          }
   50 
   51          return factors;
   52       }
   53 
   54       namespace detail {
   55          ///
   56          /// Walk the power set of prime factors of the n-dimensional
   57          /// integer array \p grid subject to the constraints given by
   58          /// \p limits.
   59          ///
   60          template<typename T>
   61          std::pair<T, std::vector<T>>
   62          next_grid_factor(const std::pair<T, std::vector<T>> &limits,
   63                           const std::vector<T> &grid,
   64                           const std::vector<std::vector<T>> &factors,
   65                           std::pair<T, std::vector<T>> block,
   66                           unsigned d = 0, unsigned i = 0) {
   67             if (d >= factors.size()) {
   68                // We're done.
   69                return {};
   70 
   71             } else if (i >= factors[d].size()) {
   72                // We're done with this grid dimension, try the next.
   73                return next_grid_factor(limits, grid, factors,
   74                                        std::move(block), d + 1, 0);
   75 
   76             } else {
   77                T f = factors[d][i];
   78 
   79                // Try the next power of this factor.
   80                block.first *= f;
   81                block.second[d] *= f;
   82 
   83                if (block.first <= limits.first &&
   84                    block.second[d] <= limits.second[d] &&
   85                    grid[d] % block.second[d] == 0) {
   86                   // We've found a valid grid divisor.
   87                   return block;
   88 
   89                } else {
   90                   // Overflow, back off to the zeroth power,
   91                   while (block.second[d] % f == 0) {
   92                      block.second[d] /= f;
   93                      block.first /= f;
   94                   }
   95 
   96                   // ...and carry to the next factor.
   97                   return next_grid_factor(limits, grid, factors,
   98                                           std::move(block), d, i + 1);
   99                }
  100             }
  101          }
  102       }
  103 
  104       ///
  105       /// Find the divisor of the integer array \p grid that gives the
  106       /// highest possible product not greater than \p product_limit
  107       /// subject to the constraints given by \p coord_limit.
  108       ///
  109       template<typename T>
  110       std::vector<T>
  111       find_grid_optimal_factor(T product_limit,
  112                                const std::vector<T> &coord_limit,
  113                                const std::vector<T> &grid) {
  114          const std::vector<std::vector<T>> factors =
  115             map(find_integer_prime_factors<T>, grid, coord_limit);
  116          const auto limits = std::make_pair(product_limit, coord_limit);
  117          auto best = std::make_pair(T(1), std::vector<T>(grid.size(), T(1)));
  118 
  119          for (auto block = best;
  120               block.first != 0 && best.first != product_limit;
  121               block = detail::next_grid_factor(limits, grid, factors, block)) {
  122             if (block.first > best.first)
  123                best = block;
  124          }
  125 
  126          return best.second;
  127       }
  128    }
  129 }
  130 
  131 #endif