//using value_type = std::decay_t<decltype(*std::declval<I>())>;

using value_type = typename std::iterator_traits<I>::value_type;

constexpr size_t object_size = sizeof(value_type);

if constexpr(std::is_same_v<value_type, std::string>) {

return 65536 / sizeof(std::string);

}

else {

if constexpr(object_size < 16) return 4096;

else if constexpr(object_size < 32) return 2048;

else if constexpr(object_size < 64) return 1024;

else if constexpr(object_size < 128) return 768;

else if constexpr(object_size < 256) return 512;

else if constexpr(object_size < 512) return 256;

else return 128;

}

Iter first, Iter last,

unsigned char* offsets_l, unsigned char* offsets_r,

size_t num, bool use_swaps

) {

typedef typename std::iterator_traits<Iter>::value_type T;

if (use_swaps) {

// This case is needed for the descending distribution, where we need

// to have proper swapping for pdqsort to remain O(n).

for (size_t i = 0; i < num; ++i) {

std::iter_swap(first + offsets_l[i], last - offsets_r[i]);

}

} else if (num > 0) {

Iter l = first + offsets_l[0]; Iter r = last - offsets_r[0];

T tmp(std::move(*l)); *l = std::move(*r);

for (size_t i = 1; i < num; ++i) {

l = first + offsets_l[i]; *r = std::move(*l);

r = last - offsets_r[i]; *l = std::move(*r);

}

*r = std::move(tmp);

}

using T = typename std::iterator_traits<RandItr>::value_type;

if (begin == end) {

return;

}

for (RandItr cur = begin + 1; cur != end; ++cur) {

RandItr shift = cur;

RandItr shift_1 = cur - 1;

// Compare first to avoid 2 moves for an element

// already positioned correctly.

if (comp(*shift, *shift_1)) {

T tmp = std::move(*shift);

do {

*shift-- = std::move(*shift_1);

}while (shift != begin && comp(tmp, *--shift_1));

*shift = std::move(tmp);

}

}

using T = typename std::iterator_traits<RandItr>::value_type;

if (begin == end) {

return;

}

for (RandItr cur = begin + 1; cur != end; ++cur) {

RandItr shift = cur;

RandItr shift_1 = cur - 1;

// Compare first so we can avoid 2 moves

// for an element already positioned correctly.

if (comp(*shift, *shift_1)) {

T tmp = std::move(*shift);

do {

*shift-- = std::move(*shift_1);

}while (comp(tmp, *--shift_1));

*shift = std::move(tmp);

}

}

using T = typename std::iterator_traits<RandItr>::value_type;

using D = typename std::iterator_traits<RandItr>::difference_type;

// When we detect an already sorted partition, attempt an insertion sort

// that allows this amount of element moves before giving up.

constexpr auto partial_insertion_sort_limit = D{8};

if (begin == end) return true;

auto limit = D{0};

for (RandItr cur = begin + 1; cur != end; ++cur) {

if (limit > partial_insertion_sort_limit) {

return false;

}

RandItr shift = cur;

RandItr shift_1 = cur - 1;

// Compare first so we can avoid 2 moves

// for an element already positioned correctly.

if (comp(*shift, *shift_1)) {

T tmp = std::move(*shift);

do {

*shift-- = std::move(*shift_1);

}while (shift != begin && comp(tmp, *--shift_1));

*shift = std::move(tmp);

limit += cur - shift;

}

}

return true;

typedef typename std::iterator_traits<Iter>::value_type T;

constexpr size_t block_size = 64;

constexpr size_t cacheline_size = 64;

// Move pivot into local for speed.

T pivot(std::move(*begin));

Iter first = begin;

Iter last = end;

// Find the first element greater than or equal than the pivot (the median of 3 guarantees

// this exists).

while (comp(*++first, pivot));

// Find the first element strictly smaller than the pivot. We have to guard this search if

// there was no element before *first.

if (first - 1 == begin) while (first < last && !comp(*--last, pivot));

else while ( !comp(*--last, pivot));

// If the first pair of elements that should be swapped to partition are the same element,

// the passed in sequence already was correctly partitioned.

bool already_partitioned = first >= last;

if (!already_partitioned) {

std::iter_swap(first, last);

++first;

// The following branchless partitioning is derived from "BlockQuicksort: How Branch

// Mispredictions don't affect Quicksort" by Stefan Edelkamp and Armin Weiss, but

// heavily micro-optimized.

unsigned char offsets_l_storage[block_size + cacheline_size];

unsigned char offsets_r_storage[block_size + cacheline_size];

unsigned char* offsets_l = align_cacheline(offsets_l_storage);

unsigned char* offsets_r = align_cacheline(offsets_r_storage);

Iter offsets_l_base = first;

Iter offsets_r_base = last;

size_t num_l, num_r, start_l, start_r;

num_l = num_r = start_l = start_r = 0;

while (first < last) {

// Fill up offset blocks with elements that are on the wrong side.

// First we determine how much elements are considered for each offset block.

size_t num_unknown = last - first;

size_t left_split = num_l == 0 ? (num_r == 0 ? num_unknown / 2 : num_unknown) : 0;

size_t right_split = num_r == 0 ? (num_unknown - left_split) : 0;

// Fill the offset blocks.

if (left_split >= block_size) {

for (size_t i = 0; i < block_size;) {

offsets_l[num_l] = i++; num_l += !comp(*first, pivot); ++first;

offsets_l[num_l] = i++; num_l += !comp(*first, pivot); ++first;

offsets_l[num_l] = i++; num_l += !comp(*first, pivot); ++first;

offsets_l[num_l] = i++; num_l += !comp(*first, pivot); ++first;

offsets_l[num_l] = i++; num_l += !comp(*first, pivot); ++first;

offsets_l[num_l] = i++; num_l += !comp(*first, pivot); ++first;

offsets_l[num_l] = i++; num_l += !comp(*first, pivot); ++first;

offsets_l[num_l] = i++; num_l += !comp(*first, pivot); ++first;

}

} else {

for (size_t i = 0; i < left_split;) {

offsets_l[num_l] = i++; num_l += !comp(*first, pivot); ++first;

}

}

if (right_split >= block_size) {

for (size_t i = 0; i < block_size;) {

offsets_r[num_r] = ++i; num_r += comp(*--last, pivot);

offsets_r[num_r] = ++i; num_r += comp(*--last, pivot);

offsets_r[num_r] = ++i; num_r += comp(*--last, pivot);

offsets_r[num_r] = ++i; num_r += comp(*--last, pivot);

offsets_r[num_r] = ++i; num_r += comp(*--last, pivot);

offsets_r[num_r] = ++i; num_r += comp(*--last, pivot);

offsets_r[num_r] = ++i; num_r += comp(*--last, pivot);

offsets_r[num_r] = ++i; num_r += comp(*--last, pivot);

}

} else {

for (size_t i = 0; i < right_split;) {

offsets_r[num_r] = ++i; num_r += comp(*--last, pivot);

}

}

// Swap elements and update block sizes and first/last boundaries.

size_t num = std::min(num_l, num_r);

swap_offsets(

offsets_l_base, offsets_r_base,

offsets_l + start_l, offsets_r + start_r,

num, num_l == num_r

);

num_l -= num; num_r -= num;

start_l += num; start_r += num;

if (num_l == 0) {

start_l = 0;

offsets_l_base = first;

}

if (num_r == 0) {

start_r = 0;

offsets_r_base = last;

}

}

// We have now fully identified [first, last)'s proper position. Swap the last elements.

if (num_l) {

offsets_l += start_l;

while (num_l--) std::iter_swap(offsets_l_base + offsets_l[num_l], --last);

first = last;

}

if (num_r) {

offsets_r += start_r;

while (num_r--) std::iter_swap(offsets_r_base - offsets_r[num_r], first), ++first;

last = first;

}

}

// Put the pivot in the right place.

Iter pivot_pos = first - 1;

*begin = std::move(*pivot_pos);

*pivot_pos = std::move(pivot);

return std::make_pair(pivot_pos, already_partitioned);

using T = typename std::iterator_traits<Iter>::value_type;

// Move pivot into local for speed.

T pivot(std::move(*begin));

Iter first = begin;

Iter last = end;

// Find the first element greater than or equal than the pivot

// (the median of 3 guarantees/ this exists).

while (comp(*++first, pivot));

// Find the first element strictly smaller than the pivot.

// We have to guard this search if there was no element before *first.

if (first - 1 == begin) while (first < last && !comp(*--last, pivot));

else while (!comp(*--last, pivot));

// If the first pair of elements that should be swapped to partition

// are the same element, the passed in sequence already was correctly

// partitioned.

bool already_partitioned = first >= last;

// Keep swapping pairs of elements that are on the wrong side of the pivot.

// Previously swapped pairs guard the searches,

// which is why the first iteration is special-cased above.

while (first < last) {

std::iter_swap(first, last);

while (comp(*++first, pivot));

while (!comp(*--last, pivot));

}

// Put the pivot in the right place.

Iter pivot_pos = first - 1;

*begin = std::move(*pivot_pos);

*pivot_pos = std::move(pivot);

return std::make_pair(pivot_pos, already_partitioned);

using T = typename std::iterator_traits<RandItr>::value_type;

T pivot(std::move(*begin));

RandItr first = begin;

RandItr last = end;

while (comp(pivot, *--last));

if (last + 1 == end) {

while (first < last && !comp(pivot, *++first));

}

else {

while (!comp(pivot, *++first));

}

while (first < last) {

std::iter_swap(first, last);

while (comp(pivot, *--last));

while (!comp(pivot, *++first));

}

RandItr pivot_pos = last;

*begin = std::move(*pivot_pos);

*pivot_pos = std::move(pivot);

return pivot_pos;

tf::Runtime& rt,

Iter begin, Iter end, Compare comp,

int bad_allowed, bool leftmost = true

) {

// Partitions below this size are sorted sequentially

constexpr auto cutoff = parallel_sort_cutoff<Iter>();

// Partitions below this size are sorted using insertion sort

constexpr auto insertion_sort_threshold = 24;

// Partitions above this size use Tukey's ninther to select the pivot.

constexpr auto ninther_threshold = 128;

//using diff_t = typename std::iterator_traits<Iter>::difference_type;

// Use a while loop for tail recursion elimination.

while (true) {

//diff_t size = end - begin;

size_t size = end - begin;

// Insertion sort is faster for small arrays.

if (size < insertion_sort_threshold) {

if (leftmost) {

insertion_sort(begin, end, comp);

}

else {

unguarded_insertion_sort(begin, end, comp);

}

return;

}

if(size <= cutoff) {

std::sort(begin, end, comp);

return;

}

// Choose pivot as median of 3 or pseudomedian of 9.

//diff_t s2 = size / 2;

size_t s2 = size >> 1;

if (size > ninther_threshold) {

sort3(begin, begin + s2, end - 1, comp);

sort3(begin + 1, begin + (s2 - 1), end - 2, comp);

sort3(begin + 2, begin + (s2 + 1), end - 3, comp);

sort3(begin + (s2 - 1), begin + s2, begin + (s2 + 1), comp);

std::iter_swap(begin, begin + s2);

}

else {

sort3(begin + s2, begin, end - 1, comp);

}

// If *(begin - 1) is the end of the right partition

// of a previous partition operation, there is no element in [begin, end)

// that is smaller than *(begin - 1).

// Then if our pivot compares equal to *(begin - 1) we change strategy,

// putting equal elements in the left partition,

// greater elements in the right partition.

// We do not have to recurse on the left partition,

// since it's sorted (all equal).

if (!leftmost && !comp(*(begin - 1), *begin)) {

begin = partition_left(begin, end, comp) + 1;

continue;

}

// Partition and get results.

const auto pair = Branchless ? partition_right_branchless(begin, end, comp) :

partition_right(begin, end, comp);

const auto pivot_pos = pair.first;

const auto already_partitioned = pair.second;

// Check for a highly unbalanced partition.

//diff_t l_size = pivot_pos - begin;

//diff_t r_size = end - (pivot_pos + 1);

const size_t l_size = pivot_pos - begin;

const size_t r_size = end - (pivot_pos + 1);

const bool highly_unbalanced = l_size < size / 8 || r_size < size / 8;

// If we got a highly unbalanced partition we shuffle elements

// to break many patterns.

if (highly_unbalanced) {

// If we had too many bad partitions, switch to heapsort

// to guarantee O(n log n).

if (--bad_allowed == 0) {

std::make_heap(begin, end, comp);

std::sort_heap(begin, end, comp);

return;

}

if (l_size >= insertion_sort_threshold) {

std::iter_swap(begin, begin + l_size / 4);

std::iter_swap(pivot_pos - 1, pivot_pos - l_size / 4);

if (l_size > ninther_threshold) {

std::iter_swap(begin + 1, begin + (l_size / 4 + 1));

std::iter_swap(begin + 2, begin + (l_size / 4 + 2));

std::iter_swap(pivot_pos - 2, pivot_pos - (l_size / 4 + 1));

std::iter_swap(pivot_pos - 3, pivot_pos - (l_size / 4 + 2));

}

}

if (r_size >= insertion_sort_threshold) {

std::iter_swap(pivot_pos + 1, pivot_pos + (1 + r_size / 4));

std::iter_swap(end - 1, end - r_size / 4);

if (r_size > ninther_threshold) {

std::iter_swap(pivot_pos + 2, pivot_pos + (2 + r_size / 4));

std::iter_swap(pivot_pos + 3, pivot_pos + (3 + r_size / 4));

std::iter_swap(end - 2, end - (1 + r_size / 4));

std::iter_swap(end - 3, end - (2 + r_size / 4));

}

}

}

// decently balanced

else {

// sequence try to use insertion sort.

if (already_partitioned &&

partial_insertion_sort(begin, pivot_pos, comp) &&

partial_insertion_sort(pivot_pos + 1, end, comp)

) {

return;

}

}

// Sort the left partition first using recursion and

// do tail recursion elimination for the right-hand partition.

rt.silent_async(

[&rt, begin, pivot_pos, comp, bad_allowed, leftmost] () mutable {

parallel_pdqsort<Iter, Compare, Branchless>(

rt, begin, pivot_pos, comp, bad_allowed, leftmost

);

}

);

begin = pivot_pos + 1;

leftmost = false;

}

using namespace std::string_literals;

constexpr auto cutoff = parallel_sort_cutoff<RandItr>();

sort_partition:

if(static_cast<size_t>(last - first) < cutoff) {

std::sort(first, last+1, compare);

return;

}

auto m = pseudo_median_of_nine(first, last, compare);

if(m != first) {

std::iter_swap(first, m);

}

auto l = first;

auto r = last;

auto f = std::next(first, 1);

bool is_swapped_l = false;

bool is_swapped_r = false;

while(f <= r) {

if(compare(*f, *l)) {

is_swapped_l = true;

std::iter_swap(l, f);

l++;

f++;

}

else if(compare(*l, *f)) {

is_swapped_r = true;

std::iter_swap(r, f);

r--;

}

else {

f++;

}

}

if(l - first > 1 && is_swapped_l) {

//rt.emplace([&](tf::Runtime& rtl) mutable {

// parallel_3wqsort(rtl, first, l-1, compare);

//});

rt.silent_async([&rt, first, l, &compare] () mutable {

parallel_3wqsort(rt, first, l-1, compare);

});

}

if(last - r > 1 && is_swapped_r) {

//rt.emplace([&](tf::Runtime& rtr) mutable {

// parallel_3wqsort(rtr, r+1, last, compare);

//});

//rt.silent_async([&rt, r, last, &compare] () mutable {

// parallel_3wqsort(rt, r+1, last, compare);

//});

first = r+1;

goto sort_partition;

}

//rt.join();

return [b, e, cmp] (Runtime& rt) mutable {

using B_t = std::decay_t<unwrap_ref_decay_t<B>>;

using E_t = std::decay_t<unwrap_ref_decay_t<E>>;

// fetch the iterator values

B_t beg = b;

E_t end = e;

if(beg == end) {

return;

}

size_t W = rt.executor().num_workers();

size_t N = std::distance(beg, end);

// only myself - no need to spawn another graph

if(W <= 1 || N <= detail::parallel_sort_cutoff<B_t>()) {

std::sort(beg, end, cmp);

return;

}

//parallel_3wqsort(rt, beg, end-1, cmp);

detail::parallel_pdqsort<B_t, C,

is_std_compare_v<std::decay_t<C>> &&

std::is_arithmetic_v<typename std::iterator_traits<B_t>::value_type>

>(rt, beg, end, cmp, log2(end - beg));

rt.corun_all();

};