Set Algorithms Performance Improvements

[danhoeflinger]

Implement balanced path with reduce then scan skeleton.
Performance improvements for set_intersection, set_difference, set_union, and set_symmetric_difference.

Adds a non-exhaustive set of unit tests for balanced path building block functions in balanced_path_unit_tests.pass.
Changes set tests to encourage more overlap between inputs (better coverage).

[adamfidel]

Suggested change

	Sequence<T1> in1(n, [](::std::size_t k) { return rand() % (std::max(std::size_t{3},k>>4)); });
	Sequence<T2> in2(m, [m](::std::size_t k) { return ((m % 2) * rand() + rand()) % (std::max(std::size_t{3},k>>4)); });
	Sequence<T1> in1(n, [](::std::size_t k) { return rand() % (std::max(3ul,k>>4)); });
	Sequence<T2> in2(m, [m](::std::size_t k) { return ((m % 2) * rand() + rand()) % (std::max({3ul,k>>4)); });

[danhoeflinger]

I don't know if we can be sure about 3ul matching type with std::size_t. 3ul type depends upon the system environment. What is there is more verbose, but more reliable cross platform I believe,.

[adamfidel]

I know you're just moving this code but it's a good opportunity to modernize.

Suggested change

	typedef typename ::std::iterator_traits<_OutputIterator>::value_type _ValueType;
	using _ValueType = typename std::iterator_traits<_OutputIterator>::value_type;

[danhoeflinger]

done

[adamfidel]

Since TempData is defined right above this, it could make sense to use that instead.

Suggested change

	operator()(const _InRng& __in_rng, _IndexT __id, __noop_temp_data& __temp_data) const
	operator()(const _InRng& __in_rng, _IndexT __id, TempData& __temp_data) const

[danhoeflinger]

done

[adamfidel]

Sorry if this has already been asked, but is it safe to use the sign bit here? Is there a potential for the position to not fit in this integral type if it now can only store half of its range?

[danhoeflinger]

This variable has the same type as the rng1.size() (or the difference_type of the first input iterator). A diagonal may only be as large as the minimum size of the two sets, so the index into the diagonal should fit in this type's positive section. All indices into the diagonal will be positive on their own, which leaves the sign bit available for this sort of info.
It would be good to add a comment or perhaps find a way to make this type more explicit.
I'll look into this.

[adamfidel]

This comment is referring to a return value but this function returns void.

[danhoeflinger]

Good point. Clarified this comment, returns by reference.

[adamfidel]

__shift_right_div is of type _Size1. Is that type signed or unsigned? Is there a risk for this subtraction to underflow? I suppose since it starts at 10 and is decremented by 3 each time, it shouldn't enter the loop when it reaches 1 due to the loop predicate. But is it possible to count up instead of down here?

[danhoeflinger]

How about we just change this to be std::int8_t?

[mmichel11]

Small nitpicks. Otherwise, this PR LGTM.

[mmichel11]

LGTM