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+Git Commit Graph Design Notes
+=============================
+
+Git walks the commit graph for many reasons, including:
+
+1. Listing and filtering commit history.
+2. Computing merge bases.
+
+These operations can become slow as the commit count grows. The merge
+base calculation shows up in many user-facing commands, such as 'merge-base'
+or 'status' and can take minutes to compute depending on history shape.
+
+There are two main costs here:
+
+1. Decompressing and parsing commits.
+2. Walking the entire graph to satisfy topological order constraints.
+
+The commit-graph file is a supplemental data structure that accelerates
+commit graph walks. If a user downgrades or disables the 'core.commitGraph'
+config setting, then the existing ODB is sufficient. The file is stored
+as "commit-graph" either in the .git/objects/info directory or in the info
+directory of an alternate.
+
+The commit-graph file stores the commit graph structure along with some
+extra metadata to speed up graph walks. By listing commit OIDs in lexi-
+cographic order, we can identify an integer position for each commit and
+refer to the parents of a commit using those integer positions. We use
+binary search to find initial commits and then use the integer positions
+for fast lookups during the walk.
+
+A consumer may load the following info for a commit from the graph:
+
+1. The commit OID.
+2. The list of parents, along with their integer position.
+3. The commit date.
+4. The root tree OID.
+5. The generation number (see definition below).
+
+Values 1-4 satisfy the requirements of parse_commit_gently().
+
+Define the "generation number" of a commit recursively as follows:
+
+ * A commit with no parents (a root commit) has generation number one.
+
+ * A commit with at least one parent has generation number one more than
+   the largest generation number among its parents.
+
+Equivalently, the generation number of a commit A is one more than the
+length of a longest path from A to a root commit. The recursive definition
+is easier to use for computation and observing the following property:
+
+    If A and B are commits with generation numbers N and M, respectively,
+    and N <= M, then A cannot reach B. That is, we know without searching
+    that B is not an ancestor of A because it is further from a root commit
+    than A.
+
+    Conversely, when checking if A is an ancestor of B, then we only need
+    to walk commits until all commits on the walk boundary have generation
+    number at most N. If we walk commits using a priority queue seeded by
+    generation numbers, then we always expand the boundary commit with highest
+    generation number and can easily detect the stopping condition.
+
+This property can be used to significantly reduce the time it takes to
+walk commits and determine topological relationships. Without generation
+numbers, the general heuristic is the following:
+
+    If A and B are commits with commit time X and Y, respectively, and
+    X < Y, then A _probably_ cannot reach B.
+
+This heuristic is currently used whenever the computation is allowed to
+violate topological relationships due to clock skew (such as "git log"
+with default order), but is not used when the topological order is
+required (such as merge base calculations, "git log --graph").
+
+In practice, we expect some commits to be created recently and not stored
+in the commit graph. We can treat these commits as having "infinite"
+generation number and walk until reaching commits with known generation
+number.
+
+We use the macro GENERATION_NUMBER_INFINITY = 0xFFFFFFFF to mark commits not
+in the commit-graph file. If a commit-graph file was written by a version
+of Git that did not compute generation numbers, then those commits will
+have generation number represented by the macro GENERATION_NUMBER_ZERO = 0.
+
+Since the commit-graph file is closed under reachability, we can guarantee
+the following weaker condition on all commits:
+
+    If A and B are commits with generation numbers N amd M, respectively,
+    and N < M, then A cannot reach B.
+
+Note how the strict inequality differs from the inequality when we have
+fully-computed generation numbers. Using strict inequality may result in
+walking a few extra commits, but the simplicity in dealing with commits
+with generation number *_INFINITY or *_ZERO is valuable.
+
+We use the macro GENERATION_NUMBER_MAX = 0x3FFFFFFF to for commits whose
+generation numbers are computed to be at least this value. We limit at
+this value since it is the largest value that can be stored in the
+commit-graph file using the 30 bits available to generation numbers. This
+presents another case where a commit can have generation number equal to
+that of a parent.
+
+Design Details
+--------------
+
+- The commit-graph file is stored in a file named 'commit-graph' in the
+  .git/objects/info directory. This could be stored in the info directory
+  of an alternate.
+
+- The core.commitGraph config setting must be on to consume graph files.
+
+- The file format includes parameters for the object ID hash function,
+  so a future change of hash algorithm does not require a change in format.
+
+- Commit grafts and replace objects can change the shape of the commit
+  history. The latter can also be enabled/disabled on the fly using
+  `--no-replace-objects`. This leads to difficultly storing both possible
+  interpretations of a commit id, especially when computing generation
+  numbers. The commit-graph will not be read or written when
+  replace-objects or grafts are present.
+
+- Shallow clones create grafts of commits by dropping their parents. This
+  leads the commit-graph to think those commits have generation number 1.
+  If and when those commits are made unshallow, those generation numbers
+  become invalid. Since shallow clones are intended to restrict the commit
+  history to a very small set of commits, the commit-graph feature is less
+  helpful for these clones, anyway. The commit-graph will not be read or
+  written when shallow commits are present.
+
+Commit Graphs Chains
+--------------------
+
+Typically, repos grow with near-constant velocity (commits per day). Over time,
+the number of commits added by a fetch operation is much smaller than the
+number of commits in the full history. By creating a "chain" of commit-graphs,
+we enable fast writes of new commit data without rewriting the entire commit
+history -- at least, most of the time.
+
+## File Layout
+
+A commit-graph chain uses multiple files, and we use a fixed naming convention
+to organize these files. Each commit-graph file has a name
+`$OBJDIR/info/commit-graphs/graph-{hash}.graph` where `{hash}` is the hex-
+valued hash stored in the footer of that file (which is a hash of the file's
+contents before that hash). For a chain of commit-graph files, a plain-text
+file at `$OBJDIR/info/commit-graphs/commit-graph-chain` contains the
+hashes for the files in order from "lowest" to "highest".
+
+For example, if the `commit-graph-chain` file contains the lines
+
+```
+	{hash0}
+	{hash1}
+	{hash2}
+```
+
+then the commit-graph chain looks like the following diagram:
+
+ +-----------------------+
+ |  graph-{hash2}.graph  |
+ +-----------------------+
+	  |
+ +-----------------------+
+ |                       |
+ |  graph-{hash1}.graph  |
+ |                       |
+ +-----------------------+
+	  |
+ +-----------------------+
+ |                       |
+ |                       |
+ |                       |
+ |  graph-{hash0}.graph  |
+ |                       |
+ |                       |
+ |                       |
+ +-----------------------+
+
+Let X0 be the number of commits in `graph-{hash0}.graph`, X1 be the number of
+commits in `graph-{hash1}.graph`, and X2 be the number of commits in
+`graph-{hash2}.graph`. If a commit appears in position i in `graph-{hash2}.graph`,
+then we interpret this as being the commit in position (X0 + X1 + i), and that
+will be used as its "graph position". The commits in `graph-{hash2}.graph` use these
+positions to refer to their parents, which may be in `graph-{hash1}.graph` or
+`graph-{hash0}.graph`. We can navigate to an arbitrary commit in position j by checking
+its containment in the intervals [0, X0), [X0, X0 + X1), [X0 + X1, X0 + X1 +
+X2).
+
+Each commit-graph file (except the base, `graph-{hash0}.graph`) contains data
+specifying the hashes of all files in the lower layers. In the above example,
+`graph-{hash1}.graph` contains `{hash0}` while `graph-{hash2}.graph` contains
+`{hash0}` and `{hash1}`.
+
+## Merging commit-graph files
+
+If we only added a new commit-graph file on every write, we would run into a
+linear search problem through many commit-graph files.  Instead, we use a merge
+strategy to decide when the stack should collapse some number of levels.
+
+The diagram below shows such a collapse. As a set of new commits are added, it
+is determined by the merge strategy that the files should collapse to
+`graph-{hash1}`. Thus, the new commits, the commits in `graph-{hash2}` and
+the commits in `graph-{hash1}` should be combined into a new `graph-{hash3}`
+file.
+
+			    +---------------------+
+			    |                     |
+			    |    (new commits)    |
+			    |                     |
+			    +---------------------+
+			    |                     |
+ +-----------------------+  +---------------------+
+ |  graph-{hash2} |->|                     |
+ +-----------------------+  +---------------------+
+	  |                 |                     |
+ +-----------------------+  +---------------------+
+ |                       |  |                     |
+ |  graph-{hash1} |->|                     |
+ |                       |  |                     |
+ +-----------------------+  +---------------------+
+	  |                  tmp_graphXXX
+ +-----------------------+
+ |                       |
+ |                       |
+ |                       |
+ |  graph-{hash0} |
+ |                       |
+ |                       |
+ |                       |
+ +-----------------------+
+
+During this process, the commits to write are combined, sorted and we write the
+contents to a temporary file, all while holding a `commit-graph-chain.lock`
+lock-file.  When the file is flushed, we rename it to `graph-{hash3}`
+according to the computed `{hash3}`. Finally, we write the new chain data to
+`commit-graph-chain.lock`:
+
+```
+	{hash3}
+	{hash0}
+```
+
+We then close the lock-file.
+
+## Merge Strategy
+
+When writing a set of commits that do not exist in the commit-graph stack of
+height N, we default to creating a new file at level N + 1. We then decide to
+merge with the Nth level if one of two conditions hold:
+
+  1. `--size-multiple=<X>` is specified or X = 2, and the number of commits in
+     level N is less than X times the number of commits in level N + 1.
+
+  2. `--max-commits=<C>` is specified with non-zero C and the number of commits
+     in level N + 1 is more than C commits.
+
+This decision cascades down the levels: when we merge a level we create a new
+set of commits that then compares to the next level.
+
+The first condition bounds the number of levels to be logarithmic in the total
+number of commits.  The second condition bounds the total number of commits in
+a `graph-{hashN}` file and not in the `commit-graph` file, preventing
+significant performance issues when the stack merges and another process only
+partially reads the previous stack.
+
+The merge strategy values (2 for the size multiple, 64,000 for the maximum
+number of commits) could be extracted into config settings for full
+flexibility.
+
+## Deleting graph-{hash} files
+
+After a new tip file is written, some `graph-{hash}` files may no longer
+be part of a chain. It is important to remove these files from disk, eventually.
+The main reason to delay removal is that another process could read the
+`commit-graph-chain` file before it is rewritten, but then look for the
+`graph-{hash}` files after they are deleted.
+
+To allow holding old split commit-graphs for a while after they are unreferenced,
+we update the modified times of the files when they become unreferenced. Then,
+we scan the `$OBJDIR/info/commit-graphs/` directory for `graph-{hash}`
+files whose modified times are older than a given expiry window. This window
+defaults to zero, but can be changed using command-line arguments or a config
+setting.
+
+## Chains across multiple object directories
+
+In a repo with alternates, we look for the `commit-graph-chain` file starting
+in the local object directory and then in each alternate. The first file that
+exists defines our chain. As we look for the `graph-{hash}` files for
+each `{hash}` in the chain file, we follow the same pattern for the host
+directories.
+
+This allows commit-graphs to be split across multiple forks in a fork network.
+The typical case is a large "base" repo with many smaller forks.
+
+As the base repo advances, it will likely update and merge its commit-graph
+chain more frequently than the forks. If a fork updates their commit-graph after
+the base repo, then it should "reparent" the commit-graph chain onto the new
+chain in the base repo. When reading each `graph-{hash}` file, we track
+the object directory containing it. During a write of a new commit-graph file,
+we check for any changes in the source object directory and read the
+`commit-graph-chain` file for that source and create a new file based on those
+files. During this "reparent" operation, we necessarily need to collapse all
+levels in the fork, as all of the files are invalid against the new base file.
+
+It is crucial to be careful when cleaning up "unreferenced" `graph-{hash}.graph`
+files in this scenario. It falls to the user to define the proper settings for
+their custom environment:
+
+ 1. When merging levels in the base repo, the unreferenced files may still be
+    referenced by chains from fork repos.
+
+ 2. The expiry time should be set to a length of time such that every fork has
+    time to recompute their commit-graph chain to "reparent" onto the new base
+    file(s).
+
+ 3. If the commit-graph chain is updated in the base, the fork will not have
+    access to the new chain until its chain is updated to reference those files.
+    (This may change in the future [5].)
+
+Related Links
+-------------
+[0] https://bugs.chromium.org/p/git/issues/detail?id=8
+    Chromium work item for: Serialized Commit Graph
+
+[1] https://public-inbox.org/git/20110713070517.GC18566@sigill.intra.peff.net/
+    An abandoned patch that introduced generation numbers.
+
+[2] https://public-inbox.org/git/20170908033403.q7e6dj7benasrjes@sigill.intra.peff.net/
+    Discussion about generation numbers on commits and how they interact
+    with fsck.
+
+[3] https://public-inbox.org/git/20170908034739.4op3w4f2ma5s65ku@sigill.intra.peff.net/
+    More discussion about generation numbers and not storing them inside
+    commit objects. A valuable quote:
+
+    "I think we should be moving more in the direction of keeping
+     repo-local caches for optimizations. Reachability bitmaps have been
+     a big performance win. I think we should be doing the same with our
+     properties of commits. Not just generation numbers, but making it
+     cheap to access the graph structure without zlib-inflating whole
+     commit objects (i.e., packv4 or something like the "metapacks" I
+     proposed a few years ago)."
+
+[4] https://public-inbox.org/git/20180108154822.54829-1-git@jeffhostetler.com/T/#u
+    A patch to remove the ahead-behind calculation from 'status'.
+
+[5] https://public-inbox.org/git/f27db281-abad-5043-6d71-cbb083b1c877@gmail.com/
+    A discussion of a "two-dimensional graph position" that can allow reading
+    multiple commit-graph chains at the same time.