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hybridsort.h
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1349 lines (1206 loc) · 72.4 KB
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#ifndef HYBRIDSORT_H
#define HYBRIDSORT_H
#include <algorithm>
#include <cmath>
#include <cstddef>
#include <functional>
#include <omp.h>
#include <type_traits>
#include <utility>
namespace parallel_stable_sorting {
constexpr int INSERTION_SORT_MAXLEN = 32; // at what length swap to insertion sort
constexpr int K_THREADS_TASK = 64; // how many tasks per thread
constexpr int IN_PLACE_INSERTION_SORT_MAXLEN = 32; // at what length swap to insertion sort for in place merge
constexpr int INPLACE_K_THREADS_TASK = 8; // how many tasks per thread for in place merge
constexpr int EXCHANGE_BLOCK_SWAP_BLOCK_LENGTH_MIN = 512; // at what length swap to rotation block swap method
namespace util_funcs {
inline int upper_power_of_two(int i) {
--i; // in case i == 2^k
i |= i >> 1; // fill with 1s starting from the highest 1 position
i |= i >> 2;
i |= i >> 4;
i |= i >> 8;
i |= i >> 16;
return i + 1;
}
inline int lower_power_of_two(int i) {
i |= i >> 1; // again fill with 1s from the highest 1 position
i |= i >> 2;
i |= i >> 4;
i |= i >> 8;
i |= i >> 16;
return (i + 1) >> 1;
}
// splits sorted array into 2 pairs of blocks such that both pairs can be sorted independently while maintaining stability
// both pairs have same total length +/-1
template <class RandomAccessIteratorA, class RandomAccessIteratorB, class Comparator>
inline void SplitEvenly(Comparator compare, RandomAccessIteratorA left_begin, std::size_t left_length, RandomAccessIteratorB right_begin, std::size_t right_length, RandomAccessIteratorA& left_middle, RandomAccessIteratorB& right_middle) {
if (left_length < right_length) {
right_begin += (right_length - left_length) / 2;
}
else {
left_begin += (left_length - right_length) / 2;
left_length = right_length;
}
while (left_length) {
if (compare(right_begin[left_length / 2], left_begin[(left_length - 1) / 2])) {
right_begin += (left_length + 2) / 2;
left_length = (left_length - 1) / 2;
}
else {
left_begin += (left_length + 1) / 2;
left_length /= 2;
}
}
left_middle = left_begin;
right_middle = right_begin;
}
} // namespace util_funcs
using namespace util_funcs;
namespace block_operations {
template <class RandomAccessIteratorA, class RandomAccessIteratorB>
inline void MoveBlock(RandomAccessIteratorA src, RandomAccessIteratorB dest, std::size_t length) {
for (std::size_t i = 0; i < length; ++i) dest[i] = std::move(src[i]);
}
template <class RandomAccessIteratorA, class RandomAccessIteratorB>
inline void SwapBlocks(RandomAccessIteratorA left_begin, RandomAccessIteratorB right_begin, std::size_t length) {
for (std::size_t i = 0; i < length; ++i) std::swap(left_begin[i], right_begin[i]);
}
template <class RandomAccessIteratorA, class RandomAccessIteratorB>
inline void ReverseSwapBlocks(RandomAccessIteratorA left_begin, RandomAccessIteratorB right_end, std::size_t length) {
for (std::size_t i = 0; i < length; ++i) std::swap(left_begin[i], *--right_end);
}
template <class RandomAccessIteratorA, class RandomAccessIteratorB>
inline void Reverse(RandomAccessIteratorA begin, RandomAccessIteratorB end) {
while (begin < --end) std::swap(*begin++, *end);
}
// rotates block simply by reversing both individual blocks and then reversing them as one whole block
template <class RandomAccessIteratorA, class RandomAccessIteratorB>
inline void ReversingRotateBlocks(RandomAccessIteratorA left_begin, RandomAccessIteratorA left_end, RandomAccessIteratorB right_begin, RandomAccessIteratorB right_end) {
if (left_begin != left_end && right_begin != right_end) {
Reverse(left_begin, left_end);
Reverse(right_begin, right_end);
Reverse(left_begin, right_end);
}
}
// the rotation algorithm using block swaps
template <class RandomAccessIteratorA, class RandomAccessIteratorB>
inline void ExchangeRotateBlocks(RandomAccessIteratorA left_begin, std::size_t left_length, RandomAccessIteratorB right_begin, std::size_t right_length) {
while (left_length > EXCHANGE_BLOCK_SWAP_BLOCK_LENGTH_MIN && right_length > EXCHANGE_BLOCK_SWAP_BLOCK_LENGTH_MIN) {
if (left_length < right_length) {
SwapBlocks(left_begin, right_begin + right_length - left_length, left_length);
right_length -= left_length;
}
else {
SwapBlocks(left_begin, right_begin, right_length);
left_length -= right_length;
left_begin += right_length;
}
}
ReversingRotateBlocks(left_begin, left_begin + left_length, right_begin, right_begin + right_length);
}
// used for cross swapping blocks, leaving one of the blocks ordered normally and the other one reversed
template <class RandomAccessIteratorA, class RandomAccessIteratorB>
inline void HalfReverseSwapBlocks(RandomAccessIteratorA keep_begin, RandomAccessIteratorB reverse_begin, std::size_t length) {
typename std::remove_reference<decltype(*reverse_begin)>::type tmp;
RandomAccessIteratorA keep_last = keep_begin + length - 1, reverse_last = reverse_begin + length - 1;
while (keep_begin < keep_last) {
tmp = std::move(*reverse_begin);
*reverse_begin = std::move(*keep_begin);
*keep_begin = std::move(*reverse_last);
*reverse_last = std::move(*keep_last);
*keep_last = std::move(tmp);
++keep_begin, ++reverse_begin;
--keep_last, --reverse_last;
}
if (keep_begin == keep_last) std::swap(*keep_begin, *reverse_begin);
}
// the better hybrid algorithm, that reverses one of the blocks while swapping
template <class RandomAccessIteratorA, class RandomAccessIteratorB>
inline void ReversingExchangeRotateBlocks(RandomAccessIteratorA left_begin, std::size_t left_length, RandomAccessIteratorB right_begin, std::size_t right_length) {
if (left_length > EXCHANGE_BLOCK_SWAP_BLOCK_LENGTH_MIN && right_length > EXCHANGE_BLOCK_SWAP_BLOCK_LENGTH_MIN) for (;;) {
if (left_length < right_length) {
right_length -= left_length;
if (right_length > EXCHANGE_BLOCK_SWAP_BLOCK_LENGTH_MIN) {
SwapBlocks(left_begin, right_begin + right_length, left_length);
}
else {
HalfReverseSwapBlocks(left_begin, right_begin + right_length, left_length);
Reverse(right_begin, right_begin + right_length);
Reverse(left_begin, right_begin + right_length);
return;
}
}
else {
left_length -= right_length;
if (left_length > EXCHANGE_BLOCK_SWAP_BLOCK_LENGTH_MIN) {
SwapBlocks(left_begin, right_begin, right_length);
}
else if (left_length == 0) {
SwapBlocks(left_begin, right_begin, right_length);
return;
}
else {
HalfReverseSwapBlocks(right_begin, left_begin, right_length);
left_begin += right_length;
Reverse(left_begin, left_begin + left_length);
Reverse(left_begin, right_begin + right_length);
return;
}
left_begin += right_length;
}
}
else {
ReversingRotateBlocks(left_begin, left_begin + left_length, right_begin, right_begin + right_length);
}
}
// used as a simple interface to choose block rotating algorithm
template <class RandomAccessIteratorA, class RandomAccessIteratorB>
inline void RotateBlocks(RandomAccessIteratorA left_begin, RandomAccessIteratorA left_end, RandomAccessIteratorB right_begin, RandomAccessIteratorB right_end) {
//ReversingRotateBlocks(left_begin, left_end, right_begin, right_end);
//ExchangeRotateBlocks(left_begin, left_end - left_begin, right_begin, right_end - left_end);
ReversingExchangeRotateBlocks(left_begin, left_end - left_begin, right_begin, right_end - left_end);
}
template <class RandomAccessIteratorA, class RandomAccessIteratorB>
inline void ParallelReverse(RandomAccessIteratorA begin, RandomAccessIteratorB end, int tasks) {
std::size_t length = (end - begin) / 2;
if (length < tasks) std::reverse(begin, end);
else {
std::size_t tasklength = length / tasks;
for (int i = 1; i < tasks; ++i) {
#pragma omp task
ReverseSwapBlocks(begin, end, tasklength);
begin += tasklength;
end -= tasklength;
}
std::reverse(begin, end);
#pragma omp taskwait
}
}
// was used to test parallel reverse during parallel in place merge, it was awfully slow, probably could be better implemented but still kind of limited by the core task dividing
template <class RandomAccessIteratorA, class RandomAccessIteratorB>
inline void ParallelReversingRotateBlocks(RandomAccessIteratorA left_begin, RandomAccessIteratorA left_end, RandomAccessIteratorB right_begin, RandomAccessIteratorB right_end, int tasks) {
#pragma omp task
ParallelReverse(left_begin, left_end, tasks / 2);
ParallelReverse(right_begin, right_end, tasks / 2);
#pragma omp taskwait
ParallelReverse(left_begin, right_end, tasks);
}
// interface for parallel block rotating, lost its meaning after being found really slow, still exists since then
template <class RandomAccessIteratorA, class RandomAccessIteratorB>
inline void ParallelRotateBlocks(RandomAccessIteratorA left_begin, RandomAccessIteratorA left_end, RandomAccessIteratorB right_begin, RandomAccessIteratorB right_end, int tasks) {
ParallelReversingRotateBlocks(left_begin, left_end, right_begin, right_end, tasks);
}
} // namespace block_operations
using namespace block_operations;
namespace insertion_sort {
// simple insertion sort using a floating hole technique to minimize moves
template <class RandomAccessIterator, class Comparator>
inline void InsertionSort(Comparator compare, RandomAccessIterator begin, RandomAccessIterator end) {
typename std::remove_reference<decltype(*begin)>::type tmp;
RandomAccessIterator to_insert = begin + 1;
while (to_insert < end) {
RandomAccessIterator to_compare = to_insert - 1;
if (compare(*to_insert, *to_compare)) {
tmp = std::move(*to_insert);
*to_insert = std::move(*to_compare);
while (--to_compare >= begin && compare(tmp, *to_compare)) {
to_compare[1] = std::move(*to_compare);
}
to_compare[1] = std::move(tmp);
}
++to_insert;
}
}
// to be used when we know, that the beginning part of what is to be sorted is already sorted
template <class RandomAccessIterator, class Comparator>
inline void InsertionSort(Comparator compare, RandomAccessIterator begin, RandomAccessIterator end, RandomAccessIterator to_insert) {
typename std::remove_reference<decltype(*begin)>::type tmp;
while (to_insert < end) {
RandomAccessIterator to_compare = to_insert - 1;
if (compare(*to_insert, *to_compare)) {
tmp = std::move(*to_insert);
*to_insert = std::move(*to_compare);
while (--to_compare >= begin && compare(tmp, *to_compare)) {
to_compare[1] = std::move(*to_compare);
}
to_compare[1] = std::move(tmp);
}
++to_insert;
}
}
} // namespace insertion_sort
using namespace insertion_sort;
namespace buffer_extraction {
// used to extract buffer from sorted array from the right
template <class RandomAccessIterator, class Comparator>
inline std::size_t ExtractBufferBack(Comparator compare, RandomAccessIterator begin, RandomAccessIterator end, std::size_t buffer_length) {
if (end - begin == 0) return 0;
std::swap(begin, end);
--begin; --end;
std::size_t max_length = 1;
RandomAccessIterator next = begin - 1, buffer_begin = begin;
while (max_length < buffer_length) {
if (end < next && !(compare(*next, next[1]))) {
do --next; while (end < next && !(compare(*next, next[1])));
if (next == end) break;
RotateBlocks(next + 1, buffer_begin, buffer_begin, buffer_begin + max_length);
}
if (next == end) break;
++max_length;
buffer_begin = next;
--next;
}
RotateBlocks(buffer_begin, buffer_begin + max_length, buffer_begin + max_length, begin + 1);
return max_length;
}
// used to extract buffer from sorted array from the left
template <class RandomAccessIterator, class Comparator>
inline std::size_t ExtractBuffer(Comparator compare, RandomAccessIterator begin, RandomAccessIterator end, std::size_t buffer_length) {
if (end - begin == 0) return 0;
std::size_t max_length = 1;
RandomAccessIterator next = begin + 1, buffer_begin = begin;
while (max_length < buffer_length) {
if (next < end && !(compare(next[-1], *next))) {
do ++next; while (next < end && !(compare(next[-1], *next)));
if (next == end) break;
RotateBlocks(buffer_begin, buffer_begin + max_length, buffer_begin + max_length, next);
buffer_begin = next - max_length;
}
if (next == end) break;
++max_length;
++next;
}
RotateBlocks(begin, buffer_begin, buffer_begin, buffer_begin + max_length);
return max_length;
}
// used to extract buffer from a not yet sorted block
template <class RandomAccessIterator, class Comparator>
inline std::size_t ExtractBufferAssorted(Comparator compare, RandomAccessIterator begin, RandomAccessIterator end, std::size_t buffer_length) {
if (end - begin == 0) return 0;
std::size_t max_length = 1;
RandomAccessIterator next = begin + 1, buffer_begin = begin;
while (max_length < buffer_length) {
while (next < end && std::binary_search(buffer_begin, buffer_begin + max_length, *next, compare)) ++next;
if (next == end) break;
RotateBlocks(buffer_begin, buffer_begin + max_length, buffer_begin + max_length, next);
buffer_begin = next - max_length;
++max_length;
InsertionSort(compare, buffer_begin, buffer_begin + max_length, next);
++next;
}
RotateBlocks(begin, buffer_begin, buffer_begin, buffer_begin + max_length);
return max_length;
}
} // namespace buffer_extraction
using namespace buffer_extraction;
namespace inplace_merge {
// simple merge using an internal buffer
template <class RandomAccessIterator, class SortedTypePointer, class Comparator>
inline void InternalBufferMerge(Comparator compare, SortedTypePointer left_begin, SortedTypePointer left_end, RandomAccessIterator right_begin, RandomAccessIterator right_end, RandomAccessIterator buffer) {
if (left_begin < left_end) {
typename std::remove_reference<decltype(*buffer)>::type tmp = std::move(*buffer);
if (right_begin < right_end) for (;;) {
if (compare(*right_begin, *left_begin)) {
*buffer = std::move(*right_begin);
++buffer;
*right_begin = std::move(*buffer);
++right_begin;
if (right_begin == right_end) break;
}
else {
*buffer = std::move(*left_begin);
++buffer;
*left_begin = std::move(*buffer);
++left_begin;
if (left_begin == left_end) {
*buffer = std::move(left_begin[-1]);
break;
}
}
}
if (left_begin < left_end) for (;;) {
*buffer = std::move(*left_begin);
++left_begin;
++buffer;
if (left_begin == left_end) break;
left_begin[-1] = std::move(*buffer);
}
left_begin[-1] = std::move(tmp);
}
}
template <class RandomAccessIterator, class Comparator>
inline void RotationMerge(Comparator compare, RandomAccessIterator left_begin, std::size_t left_length, RandomAccessIterator right_begin, std::size_t right_length) {
while (left_length && right_length) {
RandomAccessIterator breakpoint = std::lower_bound(right_begin, right_begin + right_length, *left_begin, compare);
std::size_t length = breakpoint - right_begin;
if (length) {
RotateBlocks(left_begin, left_begin + left_length, right_begin, breakpoint);
left_begin += length;
right_begin = breakpoint;
right_length -= length;
}
++left_begin;
--left_length;
}
}
// rotation merge utilizing a small internal buffer
template <class RandomAccessIterator, class Comparator>
inline void SmallBufferRotationMerge(Comparator compare, RandomAccessIterator left_begin, std::size_t left_length, RandomAccessIterator right_begin, std::size_t right_length, RandomAccessIterator buffer_begin, std::size_t buffer_length) {
while (buffer_length < left_length) {
RandomAccessIterator breakpoint = std::lower_bound(right_begin, right_begin + right_length, left_begin[buffer_length - 1], compare);
std::size_t length = breakpoint - right_begin;
if (length) {
RotateBlocks(left_begin + buffer_length, left_begin + left_length, right_begin, breakpoint);
SwapBlocks(left_begin, buffer_begin, buffer_length);
InternalBufferMerge(compare, buffer_begin, buffer_begin + buffer_length, left_begin + buffer_length, left_begin + buffer_length + length, left_begin);
left_begin += length;
right_begin = breakpoint;
right_length -= length;
}
left_begin += buffer_length;
left_length -= buffer_length;
}
if (right_length) {
SwapBlocks(left_begin, buffer_begin, left_length);
InternalBufferMerge(compare, buffer_begin, buffer_begin + left_length, right_begin, right_begin + right_length, left_begin);
}
}
// finds the position of the lowest member of the buffer
template <class RandomAccessIterator, class Comparator>
inline std::size_t FindMin(Comparator compare, RandomAccessIterator begin, std::size_t length) {
std::size_t min = 0;
for (std::size_t i = 1; i < length; ++i) if (compare(begin[i], begin[min])) min = i;
return min;
}
// rearranges w and v blocks using the internal buffer to keep track of w blocks order
template <class RandomAccessIterator, class Comparator>
inline std::size_t RearrangeBlocks(Comparator compare, RandomAccessIterator s1_begin, RandomAccessIterator s2_begin, RandomAccessIterator w_begin, std::size_t w_num, RandomAccessIterator v_begin, std::size_t v_num, RandomAccessIterator mi_begin, std::size_t block_length) {
typename std::remove_reference<decltype(*mi_begin)>::type tmp;
std::size_t w = 0, bds_id = 0;
while (w_num) {
if (v_num && compare(v_begin[block_length - 1], w_begin[w * block_length])) {
SwapBlocks(w_begin, v_begin, block_length);
tmp = std::move(mi_begin[0]);
for (std::size_t i = 1; i < w_num; ++i) mi_begin[i - 1] = std::move(mi_begin[i]);
mi_begin[w_num - 1] = std::move(tmp);
if (w == 0) w = w_num - 1;
else --w;
--v_num;
v_begin += block_length;
}
else {
if (w != 0) {
SwapBlocks(w_begin, w_begin + w * block_length, block_length);
std::swap(mi_begin[0], mi_begin[w]);
}
--w_num;
++mi_begin;
w = FindMin(compare, mi_begin, w_num);
std::swap(s1_begin[bds_id], s2_begin[bds_id]);
}
w_begin += block_length;
++bds_id;
}
return bds_id;
}
// merges w blocks with their corresponding v blocks
template <class RandomAccessIterator, class Comparator>
inline RandomAccessIterator MergeBlocks(Comparator compare, RandomAccessIterator s1_begin, RandomAccessIterator s2_begin, RandomAccessIterator left_begin, RandomAccessIterator right_end, RandomAccessIterator buffer_begin, std::size_t buffer_length, std::size_t bds_id, std::size_t block_length, bool enough_buffer) {
RandomAccessIterator right_begin = left_begin + bds_id * block_length;
while (bds_id--) {
if (compare(s1_begin[bds_id], s2_begin[bds_id])) {
right_begin = left_begin + bds_id * block_length;
}
else {
std::swap(s1_begin[bds_id], s2_begin[bds_id]);
RandomAccessIterator w_begin = left_begin + bds_id * block_length;
if (right_begin < right_end) {
RandomAccessIterator q1_begin = right_begin;
right_begin = std::lower_bound(right_begin, right_end, *w_begin, compare);
std::size_t q1_length = right_begin - q1_begin;
if (enough_buffer) {
SwapBlocks(buffer_begin, w_begin, block_length);
SwapBlocks(w_begin, q1_begin, q1_length);
right_begin = w_begin;
w_begin += q1_length;
InternalBufferMerge(compare, buffer_begin, buffer_begin + block_length, q1_begin + q1_length, right_end, w_begin);
}
else {
RotateBlocks(w_begin, w_begin + block_length, q1_begin, q1_begin + q1_length);
right_begin = w_begin;
w_begin += q1_length;
SmallBufferRotationMerge(compare, w_begin, block_length, q1_begin + q1_length, right_end - (q1_begin + q1_length), buffer_begin, buffer_length);
}
}
right_end = w_begin;
}
}
return right_end;
}
// used with pre extracted internal buffer
template <class RandomAccessIterator, class Comparator>
inline void InPlaceMerge(Comparator compare, RandomAccessIterator left_begin, std::size_t left_length, RandomAccessIterator right_begin, std::size_t right_length, RandomAccessIterator buffer_begin, std::size_t buffer_length) {
std::size_t max_block_length = (std::size_t)sqrt(left_length);
std::size_t block_length = buffer_length;
bool enough_buffer = (buffer_length >= max_block_length);
if (!enough_buffer) block_length = left_length / buffer_length;
std::size_t bds_length = left_length / block_length + right_length / block_length;
RandomAccessIterator s1_begin = left_begin, s2_begin = left_begin + bds_length, left_end = left_begin + left_length, right_end = right_begin + right_length, array_end = right_end;
while (s2_begin < left_end && !(compare(s2_begin[-1], *s2_begin))) ++s2_begin;
if (s2_begin + bds_length >= left_end) {
SmallBufferRotationMerge(compare, left_begin, left_length, right_begin, right_length, buffer_begin, buffer_length);
return;
}
left_begin = s2_begin + bds_length;
left_length = left_end - left_begin;
InsertionSort(compare, buffer_begin, buffer_begin + left_length / block_length);
RandomAccessIterator w1_begin = left_begin;
std::size_t w1_length = left_length % block_length;
left_begin += w1_length;
left_length -= w1_length;
std::size_t bds_id = RearrangeBlocks(compare, s1_begin, s2_begin, left_begin, left_length / block_length, right_begin, right_length / block_length, buffer_begin, block_length);
right_end = MergeBlocks(compare, s1_begin, s2_begin, left_begin, right_end, buffer_begin, buffer_length, bds_id, block_length, enough_buffer);
right_begin = left_begin;
if (right_begin < right_end) {
RandomAccessIterator v1_begin = right_begin;
right_begin = std::lower_bound(right_begin, right_end, s2_begin[bds_length - 1], compare);
std::size_t v1_length = right_begin - v1_begin;
RotateBlocks(w1_begin, w1_begin + w1_length, v1_begin, right_begin);
v1_begin = w1_begin;
w1_begin += v1_length;
if (right_begin < right_end) {
if (w1_length < buffer_length) {
SwapBlocks(buffer_begin, w1_begin, w1_length);
InternalBufferMerge(compare, buffer_begin, buffer_begin + w1_length, right_begin, right_end, w1_begin);
}
else {
SmallBufferRotationMerge(compare, w1_begin, w1_length, right_begin, right_end - right_begin, buffer_begin, buffer_length);
}
}
right_begin = v1_begin;
right_end = right_begin + v1_length;
if (right_begin < right_end) {
RandomAccessIterator v1_begin = right_begin;
right_begin = std::lower_bound(right_begin, right_end, s1_begin[bds_length - 1], compare);
std::size_t v1_length = right_begin - v1_begin;
RotateBlocks(s1_begin + bds_length, v1_begin, v1_begin, right_begin);
s2_begin += v1_length;
SmallBufferRotationMerge(compare, s1_begin, bds_length, s1_begin + bds_length, v1_length, buffer_begin, buffer_length);
SmallBufferRotationMerge(compare, s2_begin, right_begin - s2_begin, right_begin, right_end - right_begin, buffer_begin, buffer_length);
}
}
}
template <class RandomAccessIterator, class Comparator>
inline void BlockRotationMerge(Comparator compare, RandomAccessIterator left_begin, std::size_t left_length, RandomAccessIterator right_begin, std::size_t right_length, std::size_t block_length) {
while (block_length < left_length) {
RandomAccessIterator breakpoint = std::lower_bound(right_begin, right_begin + right_length, left_begin[block_length - 1], compare);
std::size_t length = breakpoint - right_begin;
if (length) {
RotateBlocks(left_begin + block_length, left_begin + left_length, right_begin, breakpoint);
RotationMerge(compare, left_begin, block_length, left_begin + block_length, length);
left_begin += length;
right_begin = breakpoint;
right_length -= length;
}
left_begin += block_length;
left_length -= block_length;
}
RotationMerge(compare, left_begin, left_length, right_begin, right_length);
}
template <class RandomAccessIterator, class Comparator>
inline void InPlaceMerge(Comparator compare, RandomAccessIterator left_begin, std::size_t left_length, RandomAccessIterator right_begin, std::size_t right_length) {
std::size_t max_block_length = (std::size_t)sqrt(left_length);
std::size_t bds_length = left_length / max_block_length + right_length / max_block_length;
RandomAccessIterator s1_begin = left_begin, s2_begin = left_begin + bds_length, left_end = left_begin + left_length, right_end = right_begin + right_length, array_end = right_end;
while (s2_begin < left_end && !(compare(s2_begin[-1], *s2_begin))) ++s2_begin;
if (s2_begin + bds_length >= left_end) {
BlockRotationMerge(compare, left_begin, left_length, right_begin, right_length, max_block_length);
return;
}
left_begin = s2_begin + bds_length;
std::size_t buffer_length = ExtractBuffer(compare, left_begin, left_end, max_block_length), block_length = buffer_length;
bool enough_buffer = (buffer_length >= max_block_length);
if (!enough_buffer) block_length = left_length / buffer_length;
RandomAccessIterator buffer_begin = left_begin;
left_begin += buffer_length;
left_length = left_end - left_begin;
RandomAccessIterator w1_begin = left_begin;
std::size_t w1_length = left_length % block_length;
left_begin += w1_length;
left_length -= w1_length;
std::size_t bds_id = RearrangeBlocks(compare, s1_begin, s2_begin, left_begin, left_length / block_length, right_begin, right_length / block_length, buffer_begin, block_length);
right_end = MergeBlocks(compare, s1_begin, s2_begin, left_begin, right_end, buffer_begin, buffer_length, bds_id, block_length, enough_buffer);
right_begin = left_begin;
if (right_begin < right_end) {
RandomAccessIterator v1_begin = right_begin;
right_begin = std::lower_bound(right_begin, right_end, s2_begin[bds_length - 1], compare);
std::size_t v1_length = right_begin - v1_begin;
RotateBlocks(buffer_begin, w1_begin + w1_length, v1_begin, right_begin);
w1_begin += v1_length;
v1_begin = buffer_begin;
buffer_begin += v1_length;
if (right_begin < right_end) {
if (w1_length < buffer_length) {
SwapBlocks(buffer_begin, w1_begin, w1_length);
InternalBufferMerge(compare, buffer_begin, buffer_begin + w1_length, right_begin, right_end, w1_begin);
}
else {
SmallBufferRotationMerge(compare, w1_begin, w1_length, right_begin, right_end - right_begin, buffer_begin, buffer_length);
}
}
right_begin = v1_begin;
right_end = right_begin + v1_length;
if (right_begin < right_end) {
RandomAccessIterator v1_begin = right_begin;
right_begin = std::lower_bound(right_begin, right_end, s1_begin[bds_length - 1], compare);
std::size_t v1_length = right_begin - v1_begin;
RotateBlocks(s1_begin + bds_length, v1_begin, v1_begin, right_begin);
s2_begin += v1_length;
SmallBufferRotationMerge(compare, s1_begin, bds_length, s1_begin + bds_length, v1_length, buffer_begin, buffer_length);
SmallBufferRotationMerge(compare, s2_begin, right_begin - s2_begin, right_begin, right_end - right_begin, buffer_begin, buffer_length);
}
}
InsertionSort(compare, buffer_begin, buffer_begin + buffer_length);
RotationMerge(compare, buffer_begin, buffer_length, w1_begin, array_end - w1_begin);
}
// used to distribute internal buffer from right
template <class RandomAccessIterator, class Comparator>
inline void RotationMergeBack(Comparator compare, RandomAccessIterator left_begin, std::size_t left_length, RandomAccessIterator right_begin, std::size_t right_length) {
while (left_length && right_length) {
RandomAccessIterator breakpoint = std::upper_bound(left_begin, left_begin + left_length, right_begin[right_length - 1], compare);
std::size_t length = (left_begin + left_length) - breakpoint;
if (length) {
RotateBlocks(breakpoint, right_begin, right_begin, right_begin + right_length);
left_length -= length;
right_begin = breakpoint;
}
--right_length;
}
}
// used when the right part is longer, extracts buffer from right part, otherwise does the same
template <class RandomAccessIterator, class Comparator>
inline void InPlaceMergeRight(Comparator compare, RandomAccessIterator left_begin, std::size_t left_length, RandomAccessIterator right_begin, std::size_t right_length) {
RandomAccessIterator array_begin = left_begin;
std::size_t max_block_length = (std::size_t)sqrt(right_length);
std::size_t bds_length = left_length / max_block_length + right_length / max_block_length;
RandomAccessIterator s1_begin = left_begin, s2_begin = left_begin + bds_length, left_end = left_begin + left_length, right_end = right_begin + right_length;
while (s2_begin < left_end && !(compare(s2_begin[-1], *s2_begin))) ++s2_begin;
if (s2_begin + bds_length >= left_end) {
BlockRotationMerge(compare, left_begin, left_length, right_begin, right_length, max_block_length);
return;
}
left_begin = s2_begin + bds_length;
left_length = left_end - left_begin;
std::size_t buffer_length = ExtractBufferBack(compare, right_begin, right_end, max_block_length), block_length = buffer_length;
bool enough_buffer = (buffer_length >= max_block_length);
if (!enough_buffer) block_length = right_length / buffer_length;
RandomAccessIterator buffer_begin = right_end - buffer_length;
right_end -= buffer_length;
right_length -= buffer_length;
RandomAccessIterator w1_begin = left_begin;
std::size_t w1_length = left_length % block_length;
left_begin += w1_length;
left_length -= w1_length;
std::size_t bds_id = RearrangeBlocks(compare, s1_begin, s2_begin, left_begin, left_length / block_length, right_begin, right_length / block_length, buffer_begin, block_length);
right_end = MergeBlocks(compare, s1_begin, s2_begin, left_begin, right_end, buffer_begin, buffer_length, bds_id, block_length, enough_buffer);
right_begin = left_begin;
if (right_begin < right_end) {
RandomAccessIterator v1_begin = right_begin;
right_begin = std::lower_bound(right_begin, right_end, s2_begin[bds_length - 1], compare);
std::size_t v1_length = right_begin - v1_begin;
RotateBlocks(w1_begin, w1_begin + w1_length, v1_begin, right_begin);
v1_begin = w1_begin;
w1_begin += v1_length;
if (right_begin < right_end) {
if (w1_length < buffer_length) {
SwapBlocks(buffer_begin, w1_begin, w1_length);
InternalBufferMerge(compare, buffer_begin, buffer_begin + w1_length, right_begin, right_end, w1_begin);
}
else {
SmallBufferRotationMerge(compare, w1_begin, w1_length, right_begin, right_end - right_begin, buffer_begin, buffer_length);
}
}
right_begin = v1_begin;
right_end = right_begin + v1_length;
if (right_begin < right_end) {
RandomAccessIterator v1_begin = right_begin;
right_begin = std::lower_bound(right_begin, right_end, s1_begin[bds_length - 1], compare);
std::size_t v1_length = right_begin - v1_begin;
RotateBlocks(s1_begin + bds_length, v1_begin, v1_begin, right_begin);
s2_begin += v1_length;
SmallBufferRotationMerge(compare, s1_begin, bds_length, s1_begin + bds_length, v1_length, buffer_begin, buffer_length);
SmallBufferRotationMerge(compare, s2_begin, right_begin - s2_begin, right_begin, right_end - right_begin, buffer_begin, buffer_length);
}
}
InsertionSort(compare, buffer_begin, buffer_begin + buffer_length);
RotationMergeBack(compare, array_begin, buffer_begin - array_begin, buffer_begin, buffer_length);
}
// distributes merging between threads
template <class RandomAccessIterator, class Comparator>
inline void ParallelInPlaceMerge(Comparator compare, RandomAccessIterator left_begin, std::size_t left_length, RandomAccessIterator right_begin, std::size_t right_length, int tasks) {
if (tasks == 1 || left_length < 2 || right_length < 2) {
if (right_length > left_length) {
InPlaceMergeRight(compare, left_begin, left_length, right_begin, right_length);
}
else {
InPlaceMerge(compare, left_begin, left_length, right_begin, right_length);
}
}
else {
RandomAccessIterator left_middle, right_middle;
SplitEvenly(compare, left_begin, left_length, right_begin, right_length, left_middle, right_middle);
RotateBlocks(left_middle, left_begin + left_length, right_begin, right_middle);
#pragma omp task
ParallelInPlaceMerge(compare, left_begin, left_middle - left_begin, left_middle, right_middle - right_begin, tasks / 2);
ParallelInPlaceMerge(compare, left_middle + (right_middle - right_begin), left_length - (left_middle - left_begin), right_middle, right_length - (right_middle - right_begin), tasks / 2);
#pragma omp taskwait
}
}
} // namespace inplace_merge
using namespace inplace_merge;
namespace merge {
template <class RandomAccessIteratorA, class RandomAccessIteratorB, class RandomAccessIteratorC, class Comparator>
inline void OutPlaceMerge(Comparator compare, RandomAccessIteratorA left_begin, RandomAccessIteratorA left_end, RandomAccessIteratorB right_begin, RandomAccessIteratorB right_end, RandomAccessIteratorC buffer) {
while (left_begin < left_end && right_begin < right_end) {
if (compare(*right_begin, *left_begin)) *buffer++ = std::move(*right_begin++);
else *buffer++ = std::move(*left_begin++);
}
if (&*left_begin != &*buffer) while (left_begin < left_end) *buffer++ = std::move(*left_begin++);
if (&*right_begin != &*buffer) while (right_begin < right_end) *buffer++ = std::move(*right_begin++);
}
// merges from the end
template <class RandomAccessIteratorA, class RandomAccessIteratorB, class RandomAccessIteratorC, class Comparator>
inline void OutPlaceMergeBack(Comparator compare, RandomAccessIteratorA left_begin, RandomAccessIteratorA left_end, RandomAccessIteratorB right_begin, RandomAccessIteratorB right_end, RandomAccessIteratorC buffer) {
while (left_begin < left_end && right_begin < right_end) {
if (compare(*right_end, *left_end)) *buffer-- = std::move(*left_end--);
else *buffer-- = std::move(*right_end--);
}
if (&*left_end != &*buffer) while (left_begin < left_end) *buffer-- = std::move(*left_end--);
if (&*right_end != &*buffer) while (right_begin < right_end) *buffer-- = std::move(*right_end--);
}
// distributes merging into different tasks, evenly divides the longer one of provided parts
template <class RandomAccessIteratorA, class RandomAccessIteratorB, class RandomAccessIteratorC, class Comparator>
inline void ParallelOutPlaceMerge(Comparator compare, RandomAccessIteratorA left_begin, RandomAccessIteratorA left_end, RandomAccessIteratorB right_begin, RandomAccessIteratorB right_end, RandomAccessIteratorC buffer, int tasks) {
if (tasks == 1) {
OutPlaceMerge(compare, left_begin, left_end, right_begin, right_end, buffer);
}
else {
std::size_t left_length = left_end - left_begin, right_length = right_end - right_begin;
RandomAccessIteratorA left_middle;
RandomAccessIteratorB right_middle;
SplitEvenly(compare, left_begin, left_length, right_begin, right_length, left_middle, right_middle);
#pragma omp task
ParallelOutPlaceMerge(compare, left_begin, left_middle, right_begin, right_middle, buffer, tasks / 2);
ParallelOutPlaceMerge(compare, left_middle, left_end, right_middle, right_end, buffer + (left_middle - left_begin) + (right_middle - right_begin), tasks / 2);
#pragma omp taskwait
}
}
} // namespace merge
using namespace merge;
namespace hybrid_merge {
// changed to use external buffer
template <class RandomAccessIterator, class SortedTypePointer, class Comparator>
inline void ExternalSmallBufferRotationMerge(Comparator compare, RandomAccessIterator left_begin, std::size_t left_length, RandomAccessIterator right_begin, std::size_t right_length, SortedTypePointer buffer_begin, std::size_t buffer_length) {
while (buffer_length < left_length) {
RandomAccessIterator breakpoint = std::lower_bound(right_begin, right_begin + right_length, left_begin[buffer_length - 1], compare);
std::size_t length = breakpoint - right_begin;
if (length) {
RotateBlocks(left_begin + buffer_length, left_begin + left_length, right_begin, breakpoint);
MoveBlock(left_begin, buffer_begin, buffer_length);
OutPlaceMerge(compare, buffer_begin, buffer_begin + buffer_length, left_begin + buffer_length, left_begin + buffer_length + length, left_begin);
left_begin += length;
right_begin = breakpoint;
right_length -= length;
}
left_begin += buffer_length;
left_length -= buffer_length;
}
if (right_length) {
MoveBlock(left_begin, buffer_begin, left_length);
OutPlaceMerge(compare, buffer_begin, buffer_begin + left_length, right_begin, right_begin + right_length, left_begin);
}
}
// changed to use external buffer
template <class RandomAccessIterator, class SortedTypePointer, class Comparator>
inline RandomAccessIterator ExternalMergeBlocks(Comparator compare, RandomAccessIterator s1_begin, RandomAccessIterator s2_begin, RandomAccessIterator left_begin, RandomAccessIterator right_end, SortedTypePointer buffer_begin, std::size_t buffer_length, std::size_t bds_id, std::size_t block_length, bool enough_buffer) {
RandomAccessIterator right_begin = left_begin + bds_id * block_length;
while (bds_id--) {
if (compare(s1_begin[bds_id], s2_begin[bds_id])) {
right_begin = left_begin + bds_id * block_length;
}
else {
std::swap(s1_begin[bds_id], s2_begin[bds_id]);
RandomAccessIterator w_begin = left_begin + bds_id * block_length;
if (right_begin < right_end) {
RandomAccessIterator q1_begin = right_begin;
right_begin = std::lower_bound(right_begin, right_end, *w_begin, compare);
std::size_t q1_length = right_begin - q1_begin;
if (enough_buffer) {
MoveBlock(w_begin, buffer_begin, block_length);
MoveBlock(q1_begin, w_begin, q1_length);
right_begin = w_begin;
w_begin += q1_length;
OutPlaceMerge(compare, buffer_begin, buffer_begin + block_length, q1_begin + q1_length, right_end, w_begin);
}
else {
RotateBlocks(w_begin, w_begin + block_length, q1_begin, q1_begin + q1_length);
right_begin = w_begin;
w_begin += q1_length;
ExternalSmallBufferRotationMerge(compare, w_begin, block_length, q1_begin + q1_length, right_end - (q1_begin + q1_length), buffer_begin, buffer_length);
}
}
right_end = w_begin;
}
}
return right_end;
}
// changed to use external buffer, not sort the internal buffer etc.
template <class RandomAccessIterator, class SortedTypePointer, class Comparator>
inline void HybridMerge(Comparator compare, RandomAccessIterator left_begin, std::size_t left_length, RandomAccessIterator right_begin, std::size_t right_length, RandomAccessIterator internal_buffer_begin, std::size_t internal_buffer_length, SortedTypePointer external_buffer_begin, std::size_t external_buffer_length) {
std::size_t block_length = external_buffer_length;
bool enough_buffer = (internal_buffer_length >= left_length / block_length);
if (!enough_buffer) block_length = left_length / internal_buffer_length;
std::size_t bds_length = left_length / block_length + right_length / block_length;
RandomAccessIterator s1_begin = left_begin, s2_begin = left_begin + bds_length, left_end = left_begin + left_length, right_end = right_begin + right_length, array_end = right_end;
while (s2_begin < left_end && !(compare(s2_begin[-1], *s2_begin))) ++s2_begin;
if (s2_begin + bds_length >= left_end) {
ExternalSmallBufferRotationMerge(compare, left_begin, left_length, right_begin, right_length, external_buffer_begin, external_buffer_length);
return;
}
left_begin = s2_begin + bds_length;
left_length = left_end - left_begin;
RandomAccessIterator w1_begin = left_begin;
std::size_t w1_length = left_length % block_length;
left_begin += w1_length;
left_length -= w1_length;
std::size_t bds_id = RearrangeBlocks(compare, s1_begin, s2_begin, left_begin, left_length / block_length, right_begin, right_length / block_length, internal_buffer_begin, block_length);
right_end = ExternalMergeBlocks(compare, s1_begin, s2_begin, left_begin, right_end, external_buffer_begin, external_buffer_length, bds_id, block_length, enough_buffer);
right_begin = left_begin;
if (right_begin < right_end) {
RandomAccessIterator v1_begin = right_begin;
right_begin = std::lower_bound(right_begin, right_end, s2_begin[bds_length - 1], compare);
std::size_t v1_length = right_begin - v1_begin;
RotateBlocks(w1_begin, w1_begin + w1_length, v1_begin, right_begin);
v1_begin = w1_begin;
w1_begin += v1_length;
if (right_begin < right_end) {
if (w1_length < external_buffer_length) {
MoveBlock(w1_begin, external_buffer_begin, w1_length);
InternalBufferMerge(compare, external_buffer_begin, external_buffer_begin + w1_length, right_begin, right_end, w1_begin);
}
else {
ExternalSmallBufferRotationMerge(compare, w1_begin, w1_length, right_begin, right_end - right_begin, external_buffer_begin, external_buffer_length);
}
}
right_begin = v1_begin;
right_end = right_begin + v1_length;
if (right_begin < right_end) {
RandomAccessIterator v1_begin = right_begin;
right_begin = std::lower_bound(right_begin, right_end, s1_begin[bds_length - 1], compare);
std::size_t v1_length = right_begin - v1_begin;
RotateBlocks(s1_begin + bds_length, v1_begin, v1_begin, right_begin);
s2_begin += v1_length;
ExternalSmallBufferRotationMerge(compare, s1_begin, bds_length, s1_begin + bds_length, v1_length, external_buffer_begin, external_buffer_length);
ExternalSmallBufferRotationMerge(compare, s2_begin, right_begin - s2_begin, right_begin, right_end - right_begin, external_buffer_begin, external_buffer_length);
}
}
}
// changed to use external buffer, not sort the internal buffer etc.
template <class RandomAccessIterator, class SortedTypePointer, class Comparator>
inline void HybridMerge(Comparator compare, RandomAccessIterator left_begin, std::size_t left_length, RandomAccessIterator right_begin, std::size_t right_length, SortedTypePointer external_buffer_begin, std::size_t external_buffer_length) {
std::size_t max_block_length = external_buffer_length;
std::size_t bds_length = left_length / max_block_length + right_length / max_block_length;
if (bds_length == 0) bds_length = 1;
RandomAccessIterator s1_begin = left_begin, s2_begin = left_begin + bds_length, left_end = left_begin + left_length, right_end = right_begin + right_length, array_end = right_end;
while (s2_begin < left_end && !(compare(s2_begin[-1], *s2_begin))) ++s2_begin;
if (s2_begin + bds_length >= left_end) {
ExternalSmallBufferRotationMerge(compare, left_begin, left_length, right_begin, right_length, external_buffer_begin, external_buffer_length);
return;
}
left_begin = s2_begin + bds_length;
std::size_t buffer_length = ExtractBuffer(compare, left_begin, left_end, left_length / max_block_length), block_length = max_block_length;
bool enough_buffer = (buffer_length >= left_length / max_block_length);
if (!enough_buffer) block_length = left_length / buffer_length;
RandomAccessIterator buffer_begin = left_begin;
left_begin += buffer_length;
left_length = left_end - left_begin;
RandomAccessIterator w1_begin = left_begin;
std::size_t w1_length = left_length % block_length;
left_begin += w1_length;
left_length -= w1_length;
std::size_t bds_id = RearrangeBlocks(compare, s1_begin, s2_begin, left_begin, left_length / block_length, right_begin, right_length / block_length, buffer_begin, block_length);
right_end = ExternalMergeBlocks(compare, s1_begin, s2_begin, left_begin, right_end, external_buffer_begin, external_buffer_length, bds_id, block_length, enough_buffer);
right_begin = left_begin;
if (right_begin < right_end) {
RandomAccessIterator v1_begin = right_begin;
right_begin = std::lower_bound(right_begin, right_end, s2_begin[bds_length - 1], compare);
std::size_t v1_length = right_begin - v1_begin;
RotateBlocks(buffer_begin, w1_begin + w1_length, v1_begin, right_begin);
w1_begin += v1_length;
v1_begin = buffer_begin;
buffer_begin += v1_length;
if (right_begin < right_end) {
if (w1_length < external_buffer_length) {
MoveBlock(w1_begin, external_buffer_begin, w1_length);
InternalBufferMerge(compare, external_buffer_begin, external_buffer_begin + w1_length, right_begin, right_end, w1_begin);
}
else {
ExternalSmallBufferRotationMerge(compare, w1_begin, w1_length, right_begin, right_end - right_begin, external_buffer_begin, external_buffer_length);
}
}
right_begin = v1_begin;
right_end = right_begin + v1_length;
if (right_begin < right_end) {
RandomAccessIterator v1_begin = right_begin;
right_begin = std::lower_bound(right_begin, right_end, s1_begin[bds_length - 1], compare);
std::size_t v1_length = right_begin - v1_begin;
RotateBlocks(s1_begin + bds_length, v1_begin, v1_begin, right_begin);
s2_begin += v1_length;
ExternalSmallBufferRotationMerge(compare, s1_begin, bds_length, s1_begin + bds_length, v1_length, external_buffer_begin, external_buffer_length);
ExternalSmallBufferRotationMerge(compare, s2_begin, right_begin - s2_begin, right_begin, right_end - right_begin, external_buffer_begin, external_buffer_length);
}
}
RotationMerge(compare, buffer_begin, buffer_length, w1_begin, array_end - w1_begin);
}
// changed to use external buffer, not sort the internal buffer etc.
template <class RandomAccessIterator, class SortedTypePointer, class Comparator>
inline void HybridMergeRight(Comparator compare, RandomAccessIterator left_begin, std::size_t left_length, RandomAccessIterator right_begin, std::size_t right_length, SortedTypePointer external_buffer_begin, std::size_t external_buffer_length) {
RandomAccessIterator array_begin = left_begin;
std::size_t max_block_length = external_buffer_length;
std::size_t bds_length = left_length / max_block_length + right_length / max_block_length;
if (bds_length == 0) bds_length = 1;
RandomAccessIterator s1_begin = left_begin, s2_begin = left_begin + bds_length, left_end = left_begin + left_length, right_end = right_begin + right_length;
while (s2_begin < left_end && !(compare(s2_begin[-1], *s2_begin))) ++s2_begin;
if (s2_begin + bds_length >= left_end) {
ExternalSmallBufferRotationMerge(compare, left_begin, left_length, right_begin, right_length, external_buffer_begin, external_buffer_length);
return;
}
left_begin = s2_begin + bds_length;
left_length = left_end - left_begin;
std::size_t buffer_length = ExtractBufferBack(compare, right_begin, right_end, right_length / max_block_length), block_length = max_block_length;
bool enough_buffer = (buffer_length >= right_length / max_block_length);
if (!enough_buffer) block_length = right_length / buffer_length;
RandomAccessIterator buffer_begin = right_end - buffer_length;
right_end -= buffer_length;
right_length -= buffer_length;
RandomAccessIterator w1_begin = left_begin;
std::size_t w1_length = left_length % block_length;
left_begin += w1_length;
left_length -= w1_length;