Documentation/technical: describe multi-pack reverse indexes

As a prerequisite to implementing multi-pack bitmaps, motivate and
describe the format and ordering of the multi-pack reverse index.

The subsequent patch will implement reading this format, and the patch
after that will implement writing it while producing a multi-pack index.

Co-authored-by: Jeff King <peff@peff.net>
Signed-off-by: Jeff King <peff@peff.net>
Signed-off-by: Taylor Blau <me@ttaylorr.com>
Signed-off-by: Junio C Hamano <gitster@pobox.com>

Documentation/technical/pack-format.txt

@@ -379,3 +379,86 @@ CHUNK DATA:
 TRAILER:
 
 	Index checksum of the above contents.
+
+== multi-pack-index reverse indexes
+
+Similar to the pack-based reverse index, the multi-pack index can also
+be used to generate a reverse index.
+
+Instead of mapping between offset, pack-, and index position, this
+reverse index maps between an object's position within the MIDX, and
+that object's position within a pseudo-pack that the MIDX describes
+(i.e., the ith entry of the multi-pack reverse index holds the MIDX
+position of ith object in pseudo-pack order).
+
+To clarify the difference between these orderings, consider a multi-pack
+reachability bitmap (which does not yet exist, but is what we are
+building towards here). Each bit needs to correspond to an object in the
+MIDX, and so we need an efficient mapping from bit position to MIDX
+position.
+
+One solution is to let bits occupy the same position in the oid-sorted
+index stored by the MIDX. But because oids are effectively random, their
+resulting reachability bitmaps would have no locality, and thus compress
+poorly. (This is the reason that single-pack bitmaps use the pack
+ordering, and not the .idx ordering, for the same purpose.)
+
+So we'd like to define an ordering for the whole MIDX based around
+pack ordering, which has far better locality (and thus compresses more
+efficiently). We can think of a pseudo-pack created by the concatenation
+of all of the packs in the MIDX. E.g., if we had a MIDX with three packs
+(a, b, c), with 10, 15, and 20 objects respectively, we can imagine an
+ordering of the objects like:
+
+    |a,0|a,1|...|a,9|b,0|b,1|...|b,14|c,0|c,1|...|c,19|
+
+where the ordering of the packs is defined by the MIDX's pack list,
+and then the ordering of objects within each pack is the same as the
+order in the actual packfile.
+
+Given the list of packs and their counts of objects, you can
+naïvely reconstruct that pseudo-pack ordering (e.g., the object at
+position 27 must be (c,1) because packs "a" and "b" consumed 25 of the
+slots). But there's a catch. Objects may be duplicated between packs, in
+which case the MIDX only stores one pointer to the object (and thus we'd
+want only one slot in the bitmap).
+
+Callers could handle duplicates themselves by reading objects in order
+of their bit-position, but that's linear in the number of objects, and
+much too expensive for ordinary bitmap lookups. Building a reverse index
+solves this, since it is the logical inverse of the index, and that
+index has already removed duplicates. But, building a reverse index on
+the fly can be expensive. Since we already have an on-disk format for
+pack-based reverse indexes, let's reuse it for the MIDX's pseudo-pack,
+too.
+
+Objects from the MIDX are ordered as follows to string together the
+pseudo-pack. Let `pack(o)` return the pack from which `o` was selected
+by the MIDX, and define an ordering of packs based on their numeric ID
+(as stored by the MIDX). Let `offset(o)` return the object offset of `o`
+within `pack(o)`. Then, compare `o1` and `o2` as follows:
+
+  - If one of `pack(o1)` and `pack(o2)` is preferred and the other
+    is not, then the preferred one sorts first.
++
+(This is a detail that allows the MIDX bitmap to determine which
+pack should be used by the pack-reuse mechanism, since it can ask
+the MIDX for the pack containing the object at bit position 0).
+
+  - If `pack(o1) ≠ pack(o2)`, then sort the two objects in descending
+    order based on the pack ID.
+
+  - Otherwise, `pack(o1) = pack(o2)`, and the objects are sorted in
+    pack-order (i.e., `o1` sorts ahead of `o2` exactly when `offset(o1)
+    < offset(o2)`).
+
+In short, a MIDX's pseudo-pack is the de-duplicated concatenation of
+objects in packs stored by the MIDX, laid out in pack order, and the
+packs arranged in MIDX order (with the preferred pack coming first).
+
+Finally, note that the MIDX's reverse index is not stored as a chunk in
+the multi-pack-index itself. This is done because the reverse index
+includes the checksum of the pack or MIDX to which it belongs, which
+makes it impossible to write in the MIDX. To avoid races when rewriting
+the MIDX, a MIDX reverse index includes the MIDX's checksum in its
+filename (e.g., `multi-pack-index-xyz.rev`).