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//
// Copyright 2013 Francisco Jerez
//
// Permission is hereby granted, free of charge, to any person obtaining a
// copy of this software and associated documentation files (the "Software"),
// to deal in the Software without restriction, including without limitation
// the rights to use, copy, modify, merge, publish, distribute, sublicense,
// and/or sell copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
// THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
// OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
// OTHER DEALINGS IN THE SOFTWARE.
//
#ifndef CLOVER_UTIL_FACTOR_HPP
#define CLOVER_UTIL_FACTOR_HPP
#include "util/range.hpp"
namespace clover {
namespace factor {
///
/// Calculate all prime integer factors of \p x.
///
/// If \p limit is non-zero, terminate early as soon as enough
/// factors have been collected to reach the product \p limit.
///
template<typename T>
std::vector<T>
find_integer_prime_factors(T x, T limit = 0)
{
const T max_d = (limit > 0 && limit < x ? limit : x);
const T min_x = x / max_d;
std::vector<T> factors;
for (T d = 2; d <= max_d && x > min_x; d++) {
if (x % d == 0) {
for (; x % d == 0; x /= d);
factors.push_back(d);
}
}
return factors;
}
namespace detail {
///
/// Walk the power set of prime factors of the n-dimensional
/// integer array \p grid subject to the constraints given by
/// \p limits.
///
template<typename T>
std::pair<T, std::vector<T>>
next_grid_factor(const std::pair<T, std::vector<T>> &limits,
const std::vector<T> &grid,
const std::vector<std::vector<T>> &factors,
std::pair<T, std::vector<T>> block,
unsigned d = 0, unsigned i = 0) {
if (d >= factors.size()) {
// We're done.
return {};
} else if (i >= factors[d].size()) {
// We're done with this grid dimension, try the next.
return next_grid_factor(limits, grid, factors,
std::move(block), d + 1, 0);
} else {
T f = factors[d][i];
// Try the next power of this factor.
block.first *= f;
block.second[d] *= f;
if (block.first <= limits.first &&
block.second[d] <= limits.second[d] &&
grid[d] % block.second[d] == 0) {
// We've found a valid grid divisor.
return block;
} else {
// Overflow, back off to the zeroth power,
while (block.second[d] % f == 0) {
block.second[d] /= f;
block.first /= f;
}
// ...and carry to the next factor.
return next_grid_factor(limits, grid, factors,
std::move(block), d, i + 1);
}
}
}
}
///
/// Find the divisor of the integer array \p grid that gives the
/// highest possible product not greater than \p product_limit
/// subject to the constraints given by \p coord_limit.
///
template<typename T>
std::vector<T>
find_grid_optimal_factor(T product_limit,
const std::vector<T> &coord_limit,
const std::vector<T> &grid) {
const std::vector<std::vector<T>> factors =
map(find_integer_prime_factors<T>, grid, coord_limit);
const auto limits = std::make_pair(product_limit, coord_limit);
auto best = std::make_pair(T(1), std::vector<T>(grid.size(), T(1)));
for (auto block = best;
block.first != 0 && best.first != product_limit;
block = detail::next_grid_factor(limits, grid, factors, block)) {
if (block.first > best.first)
best = block;
}
return best.second;
}
}
}
#endif
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