mergeInPlace

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;
    }
}