pack-revindex: radix-sort the revindex
pack-revindex: radix-sort the revindex

The pack revindex stores the offsets of the objects in the
pack in sorted order, allowing us to easily find the on-disk
size of each object. To compute it, we populate an array
with the offsets from the sha1-sorted idx file, and then use
qsort to order it by offsets.

That does O(n log n) offset comparisons, and profiling shows
that we spend most of our time in cmp_offset. However, since
we are sorting on a simple off_t, we can use numeric sorts
that perform better. A radix sort can run in O(k*n), where k
is the number of "digits" in our number. For a 64-bit off_t,
using 16-bit "digits" gives us k=4.

On the linux.git repo, with about 3M objects to sort, this
yields a 400% speedup. Here are the best-of-five numbers for
running

  echo HEAD | git cat-file --batch-check="%(objectsize:disk)

on a fully packed repository, which is dominated by time
spent building the pack revindex:

          before     after
  real    0m0.834s   0m0.204s
  user    0m0.788s   0m0.164s
  sys     0m0.040s   0m0.036s

This matches our algorithmic expectations. log(3M) is ~21.5,
so a traditional sort is ~21.5n. Our radix sort runs in k*n,
where k is the number of radix digits. In the worst case,
this is k=4 for a 64-bit off_t, but we can quit early when
the largest value to be sorted is smaller. For any
repository under 4G, k=2. Our algorithm makes two passes
over the list per radix digit, so we end up with 4n. That
should yield ~5.3x speedup. We see 4x here; the difference
is probably due to the extra bucket book-keeping the radix
sort has to do.

On a smaller repo, the difference is less impressive, as
log(n) is smaller. For git.git, with 173K objects (but still
k=2), we see a 2.7x improvement:

          before     after
  real    0m0.046s   0m0.017s
  user    0m0.036s   0m0.012s
  sys     0m0.008s   0m0.000s

On even tinier repos (e.g., a few hundred objects), the
speedup goes away entirely, as the small advantage of the
radix sort gets erased by the book-keeping costs (and at
those sizes, the cost to generate the the rev-index gets
lost in the noise anyway).

Signed-off-by: Jeff King <696e3fbcf235d40b6ea1ebd61c87cbea79d444e7@peff.net>
Reviewed-by: Brandon Casey <8846602a89ca53d44af0c0033a3c79dc5d05ea84@gmail.com>
Signed-off-by: Junio C Hamano <a6723cc3f76163bf7adb636a73ac3b0ceb3e6b9b@pobox.com>

destenson/git,destenson/git,destenson/git,destenson/git,destenson/git,destenson/git,destenson/git,destenson/git