    const builtin = @import("builtin");
    const std = @import("../std.zig");
    const sort = std.sort;
    const math = std.math;
    const mem = std.mem;

    const Range = struct {
        start: usize,
        end: usize,

        fn init(start: usize, end: usize) Range {
            return Range{
                .start = start,
                .end = end,
            };
        }

        fn length(self: Range) usize {
            return self.end - self.start;
        }
    };

    const Iterator = struct {
        size: usize,
        power_of_two: usize,
        numerator: usize,
        decimal: usize,
        denominator: usize,
        decimal_step: usize,
        numerator_step: usize,

        fn init(size2: usize, min_level: usize) Iterator {
            const power_of_two = math.floorPowerOfTwo(usize, size2);
            const denominator = power_of_two / min_level;
            return Iterator{
                .numerator = 0,
                .decimal = 0,
                .size = size2,
                .power_of_two = power_of_two,
                .denominator = denominator,
                .decimal_step = size2 / denominator,
                .numerator_step = size2 % denominator,
            };
        }

        fn begin(self: *Iterator) void {
            self.numerator = 0;
            self.decimal = 0;
        }

        fn nextRange(self: *Iterator) Range {
            const start = self.decimal;

            self.decimal += self.decimal_step;
            self.numerator += self.numerator_step;
            if (self.numerator >= self.denominator) {
                self.numerator -= self.denominator;
                self.decimal += 1;
            }

            return Range{
                .start = start,
                .end = self.decimal,
            };
        }

        fn finished(self: *Iterator) bool {
            return self.decimal >= self.size;
        }

        fn nextLevel(self: *Iterator) bool {
            self.decimal_step += self.decimal_step;
            self.numerator_step += self.numerator_step;
            if (self.numerator_step >= self.denominator) {
                self.numerator_step -= self.denominator;
                self.decimal_step += 1;
            }

            return (self.decimal_step < self.size);
        }

        fn length(self: *Iterator) usize {
            return self.decimal_step;
        }
    };

    const Pull = struct {
        from: usize,
        to: usize,
        count: usize,
        range: Range,
    };

    /// Stable in-place sort. O(n) best case, O(n*log(n)) worst case and average case.
    /// O(1) memory (no allocator required).
    /// Sorts in ascending order with respect to the given `lessThan` function.
    ///
    /// NOTE: the algorithm only work when the comparison is less-than or greater-than
    ///       (See https://github.com/ziglang/zig/issues/8289)
    pub fn block(
        comptime T: type,
        items: []T,
        context: anytype,
        comptime lessThanFn: fn (@TypeOf(context), lhs: T, rhs: T) bool,
    ) void {
        const lessThan = if (builtin.mode == .Debug) struct {
            fn lessThan(ctx: @TypeOf(context), lhs: T, rhs: T) bool {
                const lt = lessThanFn(ctx, lhs, rhs);
                const gt = lessThanFn(ctx, rhs, lhs);
                std.debug.assert(!(lt and gt));
                return lt;
            }
        }.lessThan else lessThanFn;

        // Implementation ported from https://github.com/BonzaiThePenguin/WikiSort/blob/master/WikiSort.c

        var cache: [512]T = undefined;

        if (items.len < 4) {
            if (items.len == 3) {
                // hard coded insertion sort

                if (lessThan(context, items[1], items[0])) mem.swap(T, &items[0], &items[1]);
                if (lessThan(context, items[2], items[1])) {
                    mem.swap(T, &items[1], &items[2]);
                    if (lessThan(context, items[1], items[0])) mem.swap(T, &items[0], &items[1]);
                }
            } else if (items.len == 2) {
                if (lessThan(context, items[1], items[0])) mem.swap(T, &items[0], &items[1]);
            }
            return;
        }

        // sort groups of 4-8 items at a time using an unstable sorting network,

        // but keep track of the original item orders to force it to be stable

        // http://pages.ripco.net/~jgamble/nw.html

        var iterator = Iterator.init(items.len, 4);
        while (!iterator.finished()) {
            var order = [_]u8{ 0, 1, 2, 3, 4, 5, 6, 7 };
            const range = iterator.nextRange();

            const sliced_items = items[range.start..];
            switch (range.length()) {
                8 => {
                    swap(T, sliced_items, &order, 0, 1, context, lessThan);
                    swap(T, sliced_items, &order, 2, 3, context, lessThan);
                    swap(T, sliced_items, &order, 4, 5, context, lessThan);
                    swap(T, sliced_items, &order, 6, 7, context, lessThan);
                    swap(T, sliced_items, &order, 0, 2, context, lessThan);
                    swap(T, sliced_items, &order, 1, 3, context, lessThan);
                    swap(T, sliced_items, &order, 4, 6, context, lessThan);
                    swap(T, sliced_items, &order, 5, 7, context, lessThan);
                    swap(T, sliced_items, &order, 1, 2, context, lessThan);
                    swap(T, sliced_items, &order, 5, 6, context, lessThan);
                    swap(T, sliced_items, &order, 0, 4, context, lessThan);
                    swap(T, sliced_items, &order, 3, 7, context, lessThan);
                    swap(T, sliced_items, &order, 1, 5, context, lessThan);
                    swap(T, sliced_items, &order, 2, 6, context, lessThan);
                    swap(T, sliced_items, &order, 1, 4, context, lessThan);
                    swap(T, sliced_items, &order, 3, 6, context, lessThan);
                    swap(T, sliced_items, &order, 2, 4, context, lessThan);
                    swap(T, sliced_items, &order, 3, 5, context, lessThan);
                    swap(T, sliced_items, &order, 3, 4, context, lessThan);
                },
                7 => {
                    swap(T, sliced_items, &order, 1, 2, context, lessThan);
                    swap(T, sliced_items, &order, 3, 4, context, lessThan);
                    swap(T, sliced_items, &order, 5, 6, context, lessThan);
                    swap(T, sliced_items, &order, 0, 2, context, lessThan);
                    swap(T, sliced_items, &order, 3, 5, context, lessThan);
                    swap(T, sliced_items, &order, 4, 6, context, lessThan);
                    swap(T, sliced_items, &order, 0, 1, context, lessThan);
                    swap(T, sliced_items, &order, 4, 5, context, lessThan);
                    swap(T, sliced_items, &order, 2, 6, context, lessThan);
                    swap(T, sliced_items, &order, 0, 4, context, lessThan);
                    swap(T, sliced_items, &order, 1, 5, context, lessThan);
                    swap(T, sliced_items, &order, 0, 3, context, lessThan);
                    swap(T, sliced_items, &order, 2, 5, context, lessThan);
                    swap(T, sliced_items, &order, 1, 3, context, lessThan);
                    swap(T, sliced_items, &order, 2, 4, context, lessThan);
                    swap(T, sliced_items, &order, 2, 3, context, lessThan);
                },
                6 => {
                    swap(T, sliced_items, &order, 1, 2, context, lessThan);
                    swap(T, sliced_items, &order, 4, 5, context, lessThan);
                    swap(T, sliced_items, &order, 0, 2, context, lessThan);
                    swap(T, sliced_items, &order, 3, 5, context, lessThan);
                    swap(T, sliced_items, &order, 0, 1, context, lessThan);
                    swap(T, sliced_items, &order, 3, 4, context, lessThan);
                    swap(T, sliced_items, &order, 2, 5, context, lessThan);
                    swap(T, sliced_items, &order, 0, 3, context, lessThan);
                    swap(T, sliced_items, &order, 1, 4, context, lessThan);
                    swap(T, sliced_items, &order, 2, 4, context, lessThan);
                    swap(T, sliced_items, &order, 1, 3, context, lessThan);
                    swap(T, sliced_items, &order, 2, 3, context, lessThan);
                },
                5 => {
                    swap(T, sliced_items, &order, 0, 1, context, lessThan);
                    swap(T, sliced_items, &order, 3, 4, context, lessThan);
                    swap(T, sliced_items, &order, 2, 4, context, lessThan);
                    swap(T, sliced_items, &order, 2, 3, context, lessThan);
                    swap(T, sliced_items, &order, 1, 4, context, lessThan);
                    swap(T, sliced_items, &order, 0, 3, context, lessThan);
                    swap(T, sliced_items, &order, 0, 2, context, lessThan);
                    swap(T, sliced_items, &order, 1, 3, context, lessThan);
                    swap(T, sliced_items, &order, 1, 2, context, lessThan);
                },
                4 => {
                    swap(T, sliced_items, &order, 0, 1, context, lessThan);
                    swap(T, sliced_items, &order, 2, 3, context, lessThan);
                    swap(T, sliced_items, &order, 0, 2, context, lessThan);
                    swap(T, sliced_items, &order, 1, 3, context, lessThan);
                    swap(T, sliced_items, &order, 1, 2, context, lessThan);
                },
                else => {},
            }
        }
        if (items.len < 8) return;

        // then merge sort the higher levels, which can be 8-15, 16-31, 32-63, 64-127, etc.

        while (true) {
            // if every A and B block will fit into the cache, use a special branch

            // specifically for merging with the cache

            // (we use < rather than <= since the block size might be one more than

            // iterator.length())

            if (iterator.length() < cache.len) {
                // if four subarrays fit into the cache, it's faster to merge both

                // pairs of subarrays into the cache,

                // then merge the two merged subarrays from the cache back into the original array

                if ((iterator.length() + 1) * 4 <= cache.len and iterator.length() * 4 <= items.len) {
                    iterator.begin();
                    while (!iterator.finished()) {
                        // merge A1 and B1 into the cache

                        var A1 = iterator.nextRange();
                        var B1 = iterator.nextRange();
                        var A2 = iterator.nextRange();
                        var B2 = iterator.nextRange();

                        if (lessThan(context, items[B1.end - 1], items[A1.start])) {
                            // the two ranges are in reverse order, so copy them in reverse order into the cache

                            const a1_items = items[A1.start..A1.end];
                            @memcpy(cache[B1.length()..][0..a1_items.len], a1_items);
                            const b1_items = items[B1.start..B1.end];
                            @memcpy(cache[0..b1_items.len], b1_items);
                        } else if (lessThan(context, items[B1.start], items[A1.end - 1])) {
                            // these two ranges weren't already in order, so merge them into the cache

                            mergeInto(T, items, A1, B1, cache[0..], context, lessThan);
                        } else {
                            // if A1, B1, A2, and B2 are all in order, skip doing anything else

                            if (!lessThan(context, items[B2.start], items[A2.end - 1]) and !lessThan(context, items[A2.start], items[B1.end - 1])) continue;

                            // copy A1 and B1 into the cache in the same order

                            const a1_items = items[A1.start..A1.end];
                            @memcpy(cache[0..a1_items.len], a1_items);
                            const b1_items = items[B1.start..B1.end];
                            @memcpy(cache[A1.length()..][0..b1_items.len], b1_items);
                        }
                        A1 = Range.init(A1.start, B1.end);

                        // merge A2 and B2 into the cache

                        if (lessThan(context, items[B2.end - 1], items[A2.start])) {
                            // the two ranges are in reverse order, so copy them in reverse order into the cache

                            const a2_items = items[A2.start..A2.end];
                            @memcpy(cache[A1.length() + B2.length() ..][0..a2_items.len], a2_items);
                            const b2_items = items[B2.start..B2.end];
                            @memcpy(cache[A1.length()..][0..b2_items.len], b2_items);
                        } else if (lessThan(context, items[B2.start], items[A2.end - 1])) {
                            // these two ranges weren't already in order, so merge them into the cache

                            mergeInto(T, items, A2, B2, cache[A1.length()..], context, lessThan);
                        } else {
                            // copy A2 and B2 into the cache in the same order

                            const a2_items = items[A2.start..A2.end];
                            @memcpy(cache[A1.length()..][0..a2_items.len], a2_items);
                            const b2_items = items[B2.start..B2.end];
                            @memcpy(cache[A1.length() + A2.length() ..][0..b2_items.len], b2_items);
                        }
                        A2 = Range.init(A2.start, B2.end);

                        // merge A1 and A2 from the cache into the items

                        const A3 = Range.init(0, A1.length());
                        const B3 = Range.init(A1.length(), A1.length() + A2.length());

                        if (lessThan(context, cache[B3.end - 1], cache[A3.start])) {
                            // the two ranges are in reverse order, so copy them in reverse order into the items

                            const a3_items = cache[A3.start..A3.end];
                            @memcpy(items[A1.start + A2.length() ..][0..a3_items.len], a3_items);
                            const b3_items = cache[B3.start..B3.end];
                            @memcpy(items[A1.start..][0..b3_items.len], b3_items);
                        } else if (lessThan(context, cache[B3.start], cache[A3.end - 1])) {
                            // these two ranges weren't already in order, so merge them back into the items

                            mergeInto(T, cache[0..], A3, B3, items[A1.start..], context, lessThan);
                        } else {
                            // copy A3 and B3 into the items in the same order

                            const a3_items = cache[A3.start..A3.end];
                            @memcpy(items[A1.start..][0..a3_items.len], a3_items);
                            const b3_items = cache[B3.start..B3.end];
                            @memcpy(items[A1.start + A1.length() ..][0..b3_items.len], b3_items);
                        }
                    }

                    // we merged two levels at the same time, so we're done with this level already

                    // (iterator.nextLevel() is called again at the bottom of this outer merge loop)

                    _ = iterator.nextLevel();
                } else {
                    iterator.begin();
                    while (!iterator.finished()) {
                        var A = iterator.nextRange();
                        var B = iterator.nextRange();

                        if (lessThan(context, items[B.end - 1], items[A.start])) {
                            // the two ranges are in reverse order, so a simple rotation should fix it

                            mem.rotate(T, items[A.start..B.end], A.length());
                        } else if (lessThan(context, items[B.start], items[A.end - 1])) {
                            // these two ranges weren't already in order, so we'll need to merge them!

                            const a_items = items[A.start..A.end];
                            @memcpy(cache[0..a_items.len], a_items);
                            mergeExternal(T, items, A, B, cache[0..], context, lessThan);
                        }
                    }
                }
            } else {
                // this is where the in-place merge logic starts!

                // 1. pull out two internal buffers each containing √A unique values

                //    1a. adjust block_size and buffer_size if we couldn't find enough unique values

                // 2. loop over the A and B subarrays within this level of the merge sort

                // 3. break A and B into blocks of size 'block_size'

                // 4. "tag" each of the A blocks with values from the first internal buffer

                // 5. roll the A blocks through the B blocks and drop/rotate them where they belong

                // 6. merge each A block with any B values that follow, using the cache or the second internal buffer

                // 7. sort the second internal buffer if it exists

                // 8. redistribute the two internal buffers back into the items

                var block_size: usize = math.sqrt(iterator.length());
                var buffer_size = iterator.length() / block_size + 1;

                // as an optimization, we really only need to pull out the internal buffers once for each level of merges

                // after that we can reuse the same buffers over and over, then redistribute it when we're finished with this level

                var A: Range = undefined;
                var B: Range = undefined;
                var index: usize = 0;
                var last: usize = 0;
                var count: usize = 0;
                var find: usize = 0;
                var start: usize = 0;
                var pull_index: usize = 0;
                var pull = [_]Pull{
                    Pull{
                        .from = 0,
                        .to = 0,
                        .count = 0,
                        .range = Range.init(0, 0),
                    },
                    Pull{
                        .from = 0,
                        .to = 0,
                        .count = 0,
                        .range = Range.init(0, 0),
                    },
                };

                var buffer1 = Range.init(0, 0);
                var buffer2 = Range.init(0, 0);

                // find two internal buffers of size 'buffer_size' each

                find = buffer_size + buffer_size;
                var find_separately = false;

                if (block_size <= cache.len) {
                    // if every A block fits into the cache then we won't need the second internal buffer,

                    // so we really only need to find 'buffer_size' unique values

                    find = buffer_size;
                } else if (find > iterator.length()) {
                    // we can't fit both buffers into the same A or B subarray, so find two buffers separately

                    find = buffer_size;
                    find_separately = true;
                }

                // we need to find either a single contiguous space containing 2√A unique values (which will be split up into two buffers of size √A each),

                // or we need to find one buffer of < 2√A unique values, and a second buffer of √A unique values,

                // OR if we couldn't find that many unique values, we need the largest possible buffer we can get

                // in the case where it couldn't find a single buffer of at least √A unique values,

                // all of the Merge steps must be replaced by a different merge algorithm (MergeInPlace)

                iterator.begin();
                while (!iterator.finished()) {
                    A = iterator.nextRange();
                    B = iterator.nextRange();

                    // just store information about where the values will be pulled from and to,

                    // as well as how many values there are, to create the two internal buffers

                    // check A for the number of unique values we need to fill an internal buffer

                    // these values will be pulled out to the start of A

                    last = A.start;
                    count = 1;
                    while (count < find) : ({
                        last = index;
                        count += 1;
                    }) {
                        index = findLastForward(T, items, items[last], Range.init(last + 1, A.end), find - count, context, lessThan);
                        if (index == A.end) break;
                    }
                    index = last;

                    if (count >= buffer_size) {
                        // keep track of the range within the items where we'll need to "pull out" these values to create the internal buffer

                        pull[pull_index] = Pull{
                            .range = Range.init(A.start, B.end),
                            .count = count,
                            .from = index,
                            .to = A.start,
                        };
                        pull_index = 1;

                        if (count == buffer_size + buffer_size) {
                            // we were able to find a single contiguous section containing 2√A unique values,

                            // so this section can be used to contain both of the internal buffers we'll need

                            buffer1 = Range.init(A.start, A.start + buffer_size);
                            buffer2 = Range.init(A.start + buffer_size, A.start + count);
                            break;
                        } else if (find == buffer_size + buffer_size) {
                            // we found a buffer that contains at least √A unique values, but did not contain the full 2√A unique values,

                            // so we still need to find a second separate buffer of at least √A unique values

                            buffer1 = Range.init(A.start, A.start + count);
                            find = buffer_size;
                        } else if (block_size <= cache.len) {
                            // we found the first and only internal buffer that we need, so we're done!

                            buffer1 = Range.init(A.start, A.start + count);
                            break;
                        } else if (find_separately) {
                            // found one buffer, but now find the other one

                            buffer1 = Range.init(A.start, A.start + count);
                            find_separately = false;
                        } else {
                            // we found a second buffer in an 'A' subarray containing √A unique values, so we're done!

                            buffer2 = Range.init(A.start, A.start + count);
                            break;
                        }
                    } else if (pull_index == 0 and count > buffer1.length()) {
                        // keep track of the largest buffer we were able to find

                        buffer1 = Range.init(A.start, A.start + count);
                        pull[pull_index] = Pull{
                            .range = Range.init(A.start, B.end),
                            .count = count,
                            .from = index,
                            .to = A.start,
                        };
                    }

                    // check B for the number of unique values we need to fill an internal buffer

                    // these values will be pulled out to the end of B

                    last = B.end - 1;
                    count = 1;
                    while (count < find) : ({
                        last = index - 1;
                        count += 1;
                    }) {
                        index = findFirstBackward(T, items, items[last], Range.init(B.start, last), find - count, context, lessThan);
                        if (index == B.start) break;
                    }
                    index = last;

                    if (count >= buffer_size) {
                        // keep track of the range within the items where we'll need to "pull out" these values to create the internal buffe

                        pull[pull_index] = Pull{
                            .range = Range.init(A.start, B.end),
                            .count = count,
                            .from = index,
                            .to = B.end,
                        };
                        pull_index = 1;

                        if (count == buffer_size + buffer_size) {
                            // we were able to find a single contiguous section containing 2√A unique values,

                            // so this section can be used to contain both of the internal buffers we'll need

                            buffer1 = Range.init(B.end - count, B.end - buffer_size);
                            buffer2 = Range.init(B.end - buffer_size, B.end);
                            break;
                        } else if (find == buffer_size + buffer_size) {
                            // we found a buffer that contains at least √A unique values, but did not contain the full 2√A unique values,

                            // so we still need to find a second separate buffer of at least √A unique values

                            buffer1 = Range.init(B.end - count, B.end);
                            find = buffer_size;
                        } else if (block_size <= cache.len) {
                            // we found the first and only internal buffer that we need, so we're done!

                            buffer1 = Range.init(B.end - count, B.end);
                            break;
                        } else if (find_separately) {
                            // found one buffer, but now find the other one

                            buffer1 = Range.init(B.end - count, B.end);
                            find_separately = false;
                        } else {
                            // buffer2 will be pulled out from a 'B' subarray, so if the first buffer was pulled out from the corresponding 'A' subarray,

                            // we need to adjust the end point for that A subarray so it knows to stop redistributing its values before reaching buffer2

                            if (pull[0].range.start == A.start) pull[0].range.end -= pull[1].count;

                            // we found a second buffer in an 'B' subarray containing √A unique values, so we're done!

                            buffer2 = Range.init(B.end - count, B.end);
                            break;
                        }
                    } else if (pull_index == 0 and count > buffer1.length()) {
                        // keep track of the largest buffer we were able to find

                        buffer1 = Range.init(B.end - count, B.end);
                        pull[pull_index] = Pull{
                            .range = Range.init(A.start, B.end),
                            .count = count,
                            .from = index,
                            .to = B.end,
                        };
                    }
                }

                // pull out the two ranges so we can use them as internal buffers

                pull_index = 0;
                while (pull_index < 2) : (pull_index += 1) {
                    const length = pull[pull_index].count;

                    if (pull[pull_index].to < pull[pull_index].from) {
                        // we're pulling the values out to the left, which means the start of an A subarray

                        index = pull[pull_index].from;
                        count = 1;
                        while (count < length) : (count += 1) {
                            index = findFirstBackward(T, items, items[index - 1], Range.init(pull[pull_index].to, pull[pull_index].from - (count - 1)), length - count, context, lessThan);
                            const range = Range.init(index + 1, pull[pull_index].from + 1);
                            mem.rotate(T, items[range.start..range.end], range.length() - count);
                            pull[pull_index].from = index + count;
                        }
                    } else if (pull[pull_index].to > pull[pull_index].from) {
                        // we're pulling values out to the right, which means the end of a B subarray

                        index = pull[pull_index].from + 1;
                        count = 1;
                        while (count < length) : (count += 1) {
                            index = findLastForward(T, items, items[index], Range.init(index, pull[pull_index].to), length - count, context, lessThan);
                            const range = Range.init(pull[pull_index].from, index - 1);
                            mem.rotate(T, items[range.start..range.end], count);
                            pull[pull_index].from = index - 1 - count;
                        }
                    }
                }

                // adjust block_size and buffer_size based on the values we were able to pull out

                buffer_size = buffer1.length();
                block_size = iterator.length() / buffer_size + 1;

                // the first buffer NEEDS to be large enough to tag each of the evenly sized A blocks,

                // so this was originally here to test the math for adjusting block_size above

                // assert((iterator.length() + 1)/block_size <= buffer_size);

                // now that the two internal buffers have been created, it's time to merge each A+B combination at this level of the merge sort!

                iterator.begin();
                while (!iterator.finished()) {
                    A = iterator.nextRange();
                    B = iterator.nextRange();

                    // remove any parts of A or B that are being used by the internal buffers

                    start = A.start;
                    if (start == pull[0].range.start) {
                        if (pull[0].from > pull[0].to) {
                            A.start += pull[0].count;

                            // if the internal buffer takes up the entire A or B subarray, then there's nothing to merge

                            // this only happens for very small subarrays, like √4 = 2, 2 * (2 internal buffers) = 4,

                            // which also only happens when cache.len is small or 0 since it'd otherwise use MergeExternal

                            if (A.length() == 0) continue;
                        } else if (pull[0].from < pull[0].to) {
                            B.end -= pull[0].count;
                            if (B.length() == 0) continue;
                        }
                    }
                    if (start == pull[1].range.start) {
                        if (pull[1].from > pull[1].to) {
                            A.start += pull[1].count;
                            if (A.length() == 0) continue;
                        } else if (pull[1].from < pull[1].to) {
                            B.end -= pull[1].count;
                            if (B.length() == 0) continue;
                        }
                    }

                    if (lessThan(context, items[B.end - 1], items[A.start])) {
                        // the two ranges are in reverse order, so a simple rotation should fix it

                        mem.rotate(T, items[A.start..B.end], A.length());
                    } else if (lessThan(context, items[A.end], items[A.end - 1])) {
                        // these two ranges weren't already in order, so we'll need to merge them!

                        var findA: usize = undefined;

                        // break the remainder of A into blocks. firstA is the uneven-sized first A block

                        var blockA = Range.init(A.start, A.end);
                        var firstA = Range.init(A.start, A.start + blockA.length() % block_size);

                        // swap the first value of each A block with the value in buffer1

                        var indexA = buffer1.start;
                        index = firstA.end;
                        while (index < blockA.end) : ({
                            indexA += 1;
                            index += block_size;
                        }) {
                            mem.swap(T, &items[indexA], &items[index]);
                        }

                        // start rolling the A blocks through the B blocks!

                        // whenever we leave an A block behind, we'll need to merge the previous A block with any B blocks that follow it, so track that information as well

                        var lastA = firstA;
                        var lastB = Range.init(0, 0);
                        var blockB = Range.init(B.start, B.start + @min(block_size, B.length()));
                        blockA.start += firstA.length();
                        indexA = buffer1.start;

                        // if the first unevenly sized A block fits into the cache, copy it there for when we go to Merge it

                        // otherwise, if the second buffer is available, block swap the contents into that

                        if (lastA.length() <= cache.len) {
                            const last_a_items = items[lastA.start..lastA.end];
                            @memcpy(cache[0..last_a_items.len], last_a_items);
                        } else if (buffer2.length() > 0) {
                            blockSwap(T, items, lastA.start, buffer2.start, lastA.length());
                        }

                        if (blockA.length() > 0) {
                            while (true) {
                                // if there's a previous B block and the first value of the minimum A block is <= the last value of the previous B block,

                                // then drop that minimum A block behind. or if there are no B blocks left then keep dropping the remaining A blocks.

                                if ((lastB.length() > 0 and !lessThan(context, items[lastB.end - 1], items[indexA])) or blockB.length() == 0) {
                                    // figure out where to split the previous B block, and rotate it at the split

                                    const B_split = binaryFirst(T, items, items[indexA], lastB, context, lessThan);
                                    const B_remaining = lastB.end - B_split;

                                    // swap the minimum A block to the beginning of the rolling A blocks

                                    var minA = blockA.start;
                                    findA = minA + block_size;
                                    while (findA < blockA.end) : (findA += block_size) {
                                        if (lessThan(context, items[findA], items[minA])) {
                                            minA = findA;
                                        }
                                    }
                                    blockSwap(T, items, blockA.start, minA, block_size);

                                    // swap the first item of the previous A block back with its original value, which is stored in buffer1

                                    mem.swap(T, &items[blockA.start], &items[indexA]);
                                    indexA += 1;

                                    // locally merge the previous A block with the B values that follow it

                                    // if lastA fits into the external cache we'll use that (with MergeExternal),

                                    // or if the second internal buffer exists we'll use that (with MergeInternal),

                                    // or failing that we'll use a strictly in-place merge algorithm (MergeInPlace)

                                    if (lastA.length() <= cache.len) {
                                        mergeExternal(T, items, lastA, Range.init(lastA.end, B_split), cache[0..], context, lessThan);
                                    } else if (buffer2.length() > 0) {
                                        mergeInternal(T, items, lastA, Range.init(lastA.end, B_split), buffer2, context, lessThan);
                                    } else {
                                        mergeInPlace(T, items, lastA, Range.init(lastA.end, B_split), context, lessThan);
                                    }

                                    if (buffer2.length() > 0 or block_size <= cache.len) {
                                        // copy the previous A block into the cache or buffer2, since that's where we need it to be when we go to merge it anyway

                                        if (block_size <= cache.len) {
                                            @memcpy(cache[0..block_size], items[blockA.start..][0..block_size]);
                                        } else {
                                            blockSwap(T, items, blockA.start, buffer2.start, block_size);
                                        }

                                        // this is equivalent to rotating, but faster

                                        // the area normally taken up by the A block is either the contents of buffer2, or data we don't need anymore since we memcopied it

                                        // either way, we don't need to retain the order of those items, so instead of rotating we can just block swap B to where it belongs

                                        blockSwap(T, items, B_split, blockA.start + block_size - B_remaining, B_remaining);
                                    } else {
                                        // we are unable to use the 'buffer2' trick to speed up the rotation operation since buffer2 doesn't exist, so perform a normal rotation

                                        mem.rotate(T, items[B_split .. blockA.start + block_size], blockA.start - B_split);
                                    }

                                    // update the range for the remaining A blocks, and the range remaining from the B block after it was split

                                    lastA = Range.init(blockA.start - B_remaining, blockA.start - B_remaining + block_size);
                                    lastB = Range.init(lastA.end, lastA.end + B_remaining);

                                    // if there are no more A blocks remaining, this step is finished!

                                    blockA.start += block_size;
                                    if (blockA.length() == 0) break;
                                } else if (blockB.length() < block_size) {
                                    // move the last B block, which is unevenly sized, to before the remaining A blocks, by using a rotation

                                    // the cache is disabled here since it might contain the contents of the previous A block

                                    mem.rotate(T, items[blockA.start..blockB.end], blockB.start - blockA.start);

                                    lastB = Range.init(blockA.start, blockA.start + blockB.length());
                                    blockA.start += blockB.length();
                                    blockA.end += blockB.length();
                                    blockB.end = blockB.start;
                                } else {
                                    // roll the leftmost A block to the end by swapping it with the next B block

                                    blockSwap(T, items, blockA.start, blockB.start, block_size);
                                    lastB = Range.init(blockA.start, blockA.start + block_size);

                                    blockA.start += block_size;
                                    blockA.end += block_size;
                                    blockB.start += block_size;

                                    if (blockB.end > B.end - block_size) {
                                        blockB.end = B.end;
                                    } else {
                                        blockB.end += block_size;
                                    }
                                }
                            }
                        }

                        // merge the last A block with the remaining B values

                        if (lastA.length() <= cache.len) {
                            mergeExternal(T, items, lastA, Range.init(lastA.end, B.end), cache[0..], context, lessThan);
                        } else if (buffer2.length() > 0) {
                            mergeInternal(T, items, lastA, Range.init(lastA.end, B.end), buffer2, context, lessThan);
                        } else {
                            mergeInPlace(T, items, lastA, Range.init(lastA.end, B.end), context, lessThan);
                        }
                    }
                }

                // when we're finished with this merge step we should have the one

                // or two internal buffers left over, where the second buffer is all jumbled up

                // insertion sort the second buffer, then redistribute the buffers

                // back into the items using the opposite process used for creating the buffer

                // while an unstable sort like quicksort could be applied here, in benchmarks

                // it was consistently slightly slower than a simple insertion sort,

                // even for tens of millions of items. this may be because insertion

                // sort is quite fast when the data is already somewhat sorted, like it is here

                sort.insertion(T, items[buffer2.start..buffer2.end], context, lessThan);

                pull_index = 0;
                while (pull_index < 2) : (pull_index += 1) {
                    var unique = pull[pull_index].count * 2;
                    if (pull[pull_index].from > pull[pull_index].to) {
                        // the values were pulled out to the left, so redistribute them back to the right

                        var buffer = Range.init(pull[pull_index].range.start, pull[pull_index].range.start + pull[pull_index].count);
                        while (buffer.length() > 0) {
                            index = findFirstForward(T, items, items[buffer.start], Range.init(buffer.end, pull[pull_index].range.end), unique, context, lessThan);
                            const amount = index - buffer.end;
                            mem.rotate(T, items[buffer.start..index], buffer.length());
                            buffer.start += (amount + 1);
                            buffer.end += amount;
                            unique -= 2;
                        }
                    } else if (pull[pull_index].from < pull[pull_index].to) {
                        // the values were pulled out to the right, so redistribute them back to the left

                        var buffer = Range.init(pull[pull_index].range.end - pull[pull_index].count, pull[pull_index].range.end);
                        while (buffer.length() > 0) {
                            index = findLastBackward(T, items, items[buffer.end - 1], Range.init(pull[pull_index].range.start, buffer.start), unique, context, lessThan);
                            const amount = buffer.start - index;
                            mem.rotate(T, items[index..buffer.end], amount);
                            buffer.start -= amount;
                            buffer.end -= (amount + 1);
                            unique -= 2;
                        }
                    }
                }
            }

            // double the size of each A and B subarray that will be merged in the next level

            if (!iterator.nextLevel()) break;
        }
    }
    // merge operation without a buffer

    fn mergeInPlace(
        comptime T: type,
        items: []T,
        A_arg: Range,
        B_arg: Range,
        context: anytype,
        comptime lessThan: fn (@TypeOf(context), lhs: T, rhs: T) bool,
    ) void {
        if (A_arg.length() == 0 or B_arg.length() == 0) return;

        // this just repeatedly binary searches into B and rotates A into position.

        // the paper suggests using the 'rotation-based Hwang and Lin algorithm' here,

        // but I decided to stick with this because it had better situational performance

        //

        // (Hwang and Lin is designed for merging subarrays of very different sizes,

        // but WikiSort almost always uses subarrays that are roughly the same size)

        //

        // normally this is incredibly suboptimal, but this function is only called

        // when none of the A or B blocks in any subarray contained 2√A unique values,

        // which places a hard limit on the number of times this will ACTUALLY need

        // to binary search and rotate.

        //

        // according to my analysis the worst case is √A rotations performed on √A items

        // once the constant factors are removed, which ends up being O(n)

        //

        // again, this is NOT a general-purpose solution – it only works well in this case!

        // kind of like how the O(n^2) insertion sort is used in some places

        var A = A_arg;
        var B = B_arg;

        while (true) {
            // find the first place in B where the first item in A needs to be inserted

            const mid = binaryFirst(T, items, items[A.start], B, context, lessThan);

            // rotate A into place

            const amount = mid - A.end;
            mem.rotate(T, items[A.start..mid], A.length());
            if (B.end == mid) break;

            // calculate the new A and B ranges

            B.start = mid;
            A = Range.init(A.start + amount, B.start);
            A.start = binaryLast(T, items, items[A.start], A, context, lessThan);
            if (A.length() == 0) break;
        }
    }

    // merge operation using an internal buffer

    fn mergeInternal(
        comptime T: type,
        items: []T,
        A: Range,
        B: Range,
        buffer: Range,
        context: anytype,
        comptime lessThan: fn (@TypeOf(context), lhs: T, rhs: T) bool,
    ) void {
        // whenever we find a value to add to the final array, swap it with the value that's already in that spot

        // when this algorithm is finished, 'buffer' will contain its original contents, but in a different order

        var A_count: usize = 0;
        var B_count: usize = 0;
        var insert: usize = 0;

        if (B.length() > 0 and A.length() > 0) {
            while (true) {
                if (!lessThan(context, items[B.start + B_count], items[buffer.start + A_count])) {
                    mem.swap(T, &items[A.start + insert], &items[buffer.start + A_count]);
                    A_count += 1;
                    insert += 1;
                    if (A_count >= A.length()) break;
                } else {
                    mem.swap(T, &items[A.start + insert], &items[B.start + B_count]);
                    B_count += 1;
                    insert += 1;
                    if (B_count >= B.length()) break;
                }
            }
        }

        // swap the remainder of A into the final array

        blockSwap(T, items, buffer.start + A_count, A.start + insert, A.length() - A_count);
    }

    fn blockSwap(comptime T: type, items: []T, start1: usize, start2: usize, block_size: usize) void {
        var index: usize = 0;
        while (index < block_size) : (index += 1) {
            mem.swap(T, &items[start1 + index], &items[start2 + index]);
        }
    }

    // combine a linear search with a binary search to reduce the number of comparisons in situations

    // where have some idea as to how many unique values there are and where the next value might be

    fn findFirstForward(
        comptime T: type,
        items: []T,
        value: T,
        range: Range,
        unique: usize,
        context: anytype,
        comptime lessThan: fn (@TypeOf(context), lhs: T, rhs: T) bool,
    ) usize {
        if (range.length() == 0) return range.start;
        const skip = @max(range.length() / unique, @as(usize, 1));

        var index = range.start + skip;
        while (lessThan(context, items[index - 1], value)) : (index += skip) {
            if (index >= range.end - skip) {
                return binaryFirst(T, items, value, Range.init(index, range.end), context, lessThan);
            }
        }

        return binaryFirst(T, items, value, Range.init(index - skip, index), context, lessThan);
    }

    fn findFirstBackward(
        comptime T: type,
        items: []T,
        value: T,
        range: Range,
        unique: usize,
        context: anytype,
        comptime lessThan: fn (@TypeOf(context), lhs: T, rhs: T) bool,
    ) usize {
        if (range.length() == 0) return range.start;
        const skip = @max(range.length() / unique, @as(usize, 1));

        var index = range.end - skip;
        while (index > range.start and !lessThan(context, items[index - 1], value)) : (index -= skip) {
            if (index < range.start + skip) {
                return binaryFirst(T, items, value, Range.init(range.start, index), context, lessThan);
            }
        }

        return binaryFirst(T, items, value, Range.init(index, index + skip), context, lessThan);
    }

    fn findLastForward(
        comptime T: type,
        items: []T,
        value: T,
        range: Range,
        unique: usize,
        context: anytype,
        comptime lessThan: fn (@TypeOf(context), lhs: T, rhs: T) bool,
    ) usize {
        if (range.length() == 0) return range.start;
        const skip = @max(range.length() / unique, @as(usize, 1));

        var index = range.start + skip;
        while (!lessThan(context, value, items[index - 1])) : (index += skip) {
            if (index >= range.end - skip) {
                return binaryLast(T, items, value, Range.init(index, range.end), context, lessThan);
            }
        }

        return binaryLast(T, items, value, Range.init(index - skip, index), context, lessThan);
    }

    fn findLastBackward(
        comptime T: type,
        items: []T,
        value: T,
        range: Range,
        unique: usize,
        context: anytype,
        comptime lessThan: fn (@TypeOf(context), lhs: T, rhs: T) bool,
    ) usize {
        if (range.length() == 0) return range.start;
        const skip = @max(range.length() / unique, @as(usize, 1));

        var index = range.end - skip;
        while (index > range.start and lessThan(context, value, items[index - 1])) : (index -= skip) {
            if (index < range.start + skip) {
                return binaryLast(T, items, value, Range.init(range.start, index), context, lessThan);
            }
        }

        return binaryLast(T, items, value, Range.init(index, index + skip), context, lessThan);
    }

    fn binaryFirst(
        comptime T: type,
        items: []T,
        value: T,
        range: Range,
        context: anytype,
        comptime lessThan: fn (@TypeOf(context), lhs: T, rhs: T) bool,
    ) usize {
        var curr = range.start;
        var size = range.length();
        if (range.start >= range.end) return range.end;
        while (size > 0) {
            const offset = size % 2;

            size /= 2;
            const mid_item = items[curr + size];
            if (lessThan(context, mid_item, value)) {
                curr += size + offset;
            }
        }
        return curr;
    }

    fn binaryLast(
        comptime T: type,
        items: []T,
        value: T,
        range: Range,
        context: anytype,
        comptime lessThan: fn (@TypeOf(context), lhs: T, rhs: T) bool,
    ) usize {
        var curr = range.start;
        var size = range.length();
        if (range.start >= range.end) return range.end;
        while (size > 0) {
            const offset = size % 2;

            size /= 2;
            const mid_item = items[curr + size];
            if (!lessThan(context, value, mid_item)) {
                curr += size + offset;
            }
        }
        return curr;
    }

    fn mergeInto(
        comptime T: type,
        from: []T,
        A: Range,
        B: Range,
        into: []T,
        context: anytype,
        comptime lessThan: fn (@TypeOf(context), lhs: T, rhs: T) bool,
    ) void {
        var A_index: usize = A.start;
        var B_index: usize = B.start;
        const A_last = A.end;
        const B_last = B.end;
        var insert_index: usize = 0;

        while (true) {
            if (!lessThan(context, from[B_index], from[A_index])) {
                into[insert_index] = from[A_index];
                A_index += 1;
                insert_index += 1;
                if (A_index == A_last) {
                    // copy the remainder of B into the final array

                    const from_b = from[B_index..B_last];
                    @memcpy(into[insert_index..][0..from_b.len], from_b);
                    break;
                }
            } else {
                into[insert_index] = from[B_index];
                B_index += 1;
                insert_index += 1;
                if (B_index == B_last) {
                    // copy the remainder of A into the final array

                    const from_a = from[A_index..A_last];
                    @memcpy(into[insert_index..][0..from_a.len], from_a);
                    break;
                }
            }
        }
    }

    fn mergeExternal(
        comptime T: type,
        items: []T,
        A: Range,
        B: Range,
        cache: []T,
        context: anytype,
        comptime lessThan: fn (@TypeOf(context), lhs: T, rhs: T) bool,
    ) void {
        // A fits into the cache, so use that instead of the internal buffer

        var A_index: usize = 0;
        var B_index: usize = B.start;
        var insert_index: usize = A.start;
        const A_last = A.length();
        const B_last = B.end;

        if (B.length() > 0 and A.length() > 0) {
            while (true) {
                if (!lessThan(context, items[B_index], cache[A_index])) {
                    items[insert_index] = cache[A_index];
                    A_index += 1;
                    insert_index += 1;
                    if (A_index == A_last) break;
                } else {
                    items[insert_index] = items[B_index];
                    B_index += 1;
                    insert_index += 1;
                    if (B_index == B_last) break;
                }
            }
        }

        // copy the remainder of A into the final array

        const cache_a = cache[A_index..A_last];
        @memcpy(items[insert_index..][0..cache_a.len], cache_a);
    }

    fn swap(
        comptime T: type,
        items: []T,
        order: *[8]u8,
        x: usize,
        y: usize,
        context: anytype,
        comptime lessThan: fn (@TypeOf(context), lhs: T, rhs: T) bool,
    ) void {
        if (lessThan(context, items[y], items[x]) or ((order.*)[x] > (order.*)[y] and !lessThan(context, items[x], items[y]))) {
            mem.swap(T, &items[x], &items[y]);
            mem.swap(u8, &(order.*)[x], &(order.*)[y]);
        }
    }