Derrick Stolee authored Jul 20, 2018 and Junio C Hamano committed Jul 20, 2018

The can_all_from_reach_with_flags() algorithm is currently quadratic in
the worst case, because it calls the reachable() method for every 'from'
without tracking which commits have already been walked or which can
already reach a commit in 'to'.

Rewrite the algorithm to walk each commit a constant number of times.

We also add some optimizations that should work for the main consumer of
this method: fetch negotitation (haves/wants).

The first step includes using a depth-first-search (DFS) from each
'from' commit, sorted by ascending generation number. We do not walk
beyond the minimum generation number or the minimum commit date. This
DFS is likely to be faster than the existing reachable() method because
we expect previous ref values to be along the first-parent history.

If we find a target commit, then we mark everything in the DFS stack as
a RESULT. This expands the set of targets for the other 'from' commits.
We also mark the visited commits using 'assign_flag' to prevent re-
walking the same commits.

We still need to clear our flags at the end, which is why we will have a
total of three visits to each commit.

Performance was measured on the Linux repository using
'test-tool reach can_all_from_reach'. The input included rows seeded by
tag values. The "small" case included X-rows as v4.[0-9]* and Y-rows as
v3.[0-9]*. This mimics a (very large) fetch that says "I have all major
v3 releases and want all major v4 releases." The "large" case included
X-rows as "v4.*" and Y-rows as "v3.*". This adds all release-candidate
tags to the set, which does not greatly increase the number of objects
that are considered, but does increase the number of 'from' commits,
demonstrating the quadratic nature of the previous code.

Small Case:

Before: 1.52 s
 After: 0.26 s

Large Case:

Before: 3.50 s
 After: 0.27 s

Note how the time increases between the two cases in the two versions.
The new code increases relative to the number of commits that need to be
walked, but not directly relative to the number of 'from' commits.

Signed-off-by: Derrick Stolee <dstolee@microsoft.com>
Signed-off-by: Junio C Hamano <gitster@pobox.com>