Documentation: describe MIDX-based bitmaps

Update the technical documentation to describe the multi-pack bitmap
format. This patch merely introduces the new format, and describes its
high-level ideas. Git does not yet know how to read nor write these
multi-pack variants, and so the subsequent patches will:

  - Introduce code to interpret multi-pack bitmaps, according to this
    document.

  - Then, introduce code to write multi-pack bitmaps from the 'git
    multi-pack-index write' sub-command.

Finally, the implementation will gain tests in subsequent patches (as
opposed to inline with the patch teaching Git how to write multi-pack
bitmaps) to avoid a cyclic dependency.

Signed-off-by: Taylor Blau <me@ttaylorr.com>
Signed-off-by: Junio C Hamano <gitster@pobox.com>

Documentation/technical/bitmap-format.txt

@@ -1,6 +1,44 @@
 GIT bitmap v1 format
 ====================
 
+== Pack and multi-pack bitmaps
+
+Bitmaps store reachability information about the set of objects in a packfile,
+or a multi-pack index (MIDX). The former is defined obviously, and the latter is
+defined as the union of objects in packs contained in the MIDX.
+
+A bitmap may belong to either one pack, or the repository's multi-pack index (if
+it exists). A repository may have at most one bitmap.
+
+An object is uniquely described by its bit position within a bitmap:
+
+	- If the bitmap belongs to a packfile, the __n__th bit corresponds to
+	the __n__th object in pack order. For a function `offset` which maps
+	objects to their byte offset within a pack, pack order is defined as
+	follows:
+
+		o1 <= o2 <==> offset(o1) <= offset(o2)
+
+	- If the bitmap belongs to a MIDX, the __n__th bit corresponds to the
+	__n__th object in MIDX order. With an additional function `pack` which
+	maps objects to the pack they were selected from by the MIDX, MIDX order
+	is defined as follows:
+
+		o1 <= o2 <==> pack(o1) <= pack(o2) /\ offset(o1) <= offset(o2)
+
+	The ordering between packs is done according to the MIDX's .rev file.
+	Notably, the preferred pack sorts ahead of all other packs.
+
+The on-disk representation (described below) of a bitmap is the same regardless
+of whether or not that bitmap belongs to a packfile or a MIDX. The only
+difference is the interpretation of the bits, which is described above.
+
+Certain bitmap extensions are supported (see: Appendix B). No extensions are
+required for bitmaps corresponding to packfiles. For bitmaps that correspond to
+MIDXs, both the bit-cache and rev-cache extensions are required.
+
+== On-disk format
+
 	- A header appears at the beginning:
 
 		4-byte signature: {'B', 'I', 'T', 'M'}
@@ -14,17 +52,19 @@ GIT bitmap v1 format
 			The following flags are supported:
 
 			- BITMAP_OPT_FULL_DAG (0x1) REQUIRED
-			This flag must always be present. It implies that the bitmap
-			index has been generated for a packfile with full closure
-			(i.e. where every single object in the packfile can find
-			 its parent links inside the same packfile). This is a
-			requirement for the bitmap index format, also present in JGit,
-			that greatly reduces the complexity of the implementation.
+			This flag must always be present. It implies that the
+			bitmap index has been generated for a packfile or
+			multi-pack index (MIDX) with full closure (i.e. where
+			every single object in the packfile/MIDX can find its
+			parent links inside the same packfile/MIDX). This is a
+			requirement for the bitmap index format, also present in
+			JGit, that greatly reduces the complexity of the
+			implementation.
 
 			- BITMAP_OPT_HASH_CACHE (0x4)
 			If present, the end of the bitmap file contains
 			`N` 32-bit name-hash values, one per object in the
-			pack. The format and meaning of the name-hash is
+			pack/MIDX. The format and meaning of the name-hash is
 			described below.
 
 		4-byte entry count (network byte order)
@@ -33,7 +73,8 @@ GIT bitmap v1 format
 
 		20-byte checksum
 
-			The SHA1 checksum of the pack this bitmap index belongs to.
+			The SHA1 checksum of the pack/MIDX this bitmap index
+			belongs to.
 
 	- 4 EWAH bitmaps that act as type indexes
 
@@ -50,7 +91,7 @@ GIT bitmap v1 format
 			- Tags
 
 		In each bitmap, the `n`th bit is set to true if the `n`th object
-		in the packfile is of that type.
+		in the packfile or multi-pack index is of that type.
 
 		The obvious consequence is that the OR of all 4 bitmaps will result
 		in a full set (all bits set), and the AND of all 4 bitmaps will
@@ -62,8 +103,9 @@ GIT bitmap v1 format
 		Each entry contains the following:
 
 		- 4-byte object position (network byte order)
-			The position **in the index for the packfile** where the
-			bitmap for this commit is found.
+			The position **in the index for the packfile or
+			multi-pack index** where the bitmap for this commit is
+			found.
 
 		- 1-byte XOR-offset
 			The xor offset used to compress this bitmap. For an entry
@@ -146,10 +188,11 @@ Name-hash cache
 ---------------
 
 If the BITMAP_OPT_HASH_CACHE flag is set, the end of the bitmap contains
-a cache of 32-bit values, one per object in the pack. The value at
+a cache of 32-bit values, one per object in the pack/MIDX. The value at
 position `i` is the hash of the pathname at which the `i`th object
-(counting in index order) in the pack can be found.  This can be fed
-into the delta heuristics to compare objects with similar pathnames.
+(counting in index or multi-pack index order) in the pack/MIDX can be found.
+This can be fed into the delta heuristics to compare objects with similar
+pathnames.
 
 The hash algorithm used is:
 

Documentation/technical/multi-pack-index.txt

@@ -71,14 +71,10 @@ Future Work
   still reducing the number of binary searches required for object
   lookups.
 
-- The reachability bitmap is currently paired directly with a single
-  packfile, using the pack-order as the object order to hopefully
-  compress the bitmaps well using run-length encoding. This could be
-  extended to pair a reachability bitmap with a multi-pack-index. If
-  the multi-pack-index is extended to store a "stable object order"
+- If the multi-pack-index is extended to store a "stable object order"
   (a function Order(hash) = integer that is constant for a given hash,
-  even as the multi-pack-index is updated) then a reachability bitmap
-  could point to a multi-pack-index and be updated independently.
+  even as the multi-pack-index is updated) then MIDX bitmaps could be
+  updated independently of the MIDX.
 
 - Packfiles can be marked as "special" using empty files that share
   the initial name but replace ".pack" with ".keep" or ".promisor".