merge base between 'A' and 'B' is '1'.
Given three commits 'A', 'B', and 'C', `git merge-base A B C` will compute the
merge base between 'A' and a hypothetical commit 'M', which is a merge
between 'B' and 'C'. For example, with this topology:
....
o---o---o---o---C
/
/ o---o---o---B
/ /
---2---1---o---o---o---A
....
the result of `git merge-base A B C` is '1'. This is because the
equivalent topology with a merge commit 'M' between 'B' and 'C' is:
....
o---o---o---o---o
/ \
/ o---o---o---o---M
/ /
---2---1---o---o---o---A
....
and the result of `git merge-base A M` is '1'. Commit '2' is also a
common ancestor between 'A' and 'M', but '1' is a better common ancestor,
because '2' is an ancestor of '1'. Hence, '2' is not a merge base.
The result of `git merge-base --octopus A B C` is '2', because '2' is
the best common ancestor of all commits.
When the history involves criss-cross merges, there can be more than one
'best' common ancestor for two commits. For example, with this topology:
....
---1---o---A
\ /
X
/ \
---2---o---o---B
....
both '1' and '2' are merge bases of A and B. Neither one is better than
the other (both are 'best' merge bases). When the `--all` option is not given,
it is unspecified which best one is output.
A common idiom to check "fast-forward-ness" between two commits A
and B is (or at least used to be) to compute the merge base between
A and B, and check if it is the same as A, in which case, A is an
ancestor of B. You will see this idiom used often in older scripts.
....
A=$(git rev-parse --verify A)
if test "$A" = "$(git merge-base A B)"
then
... A is an ancestor of B ...
fi
....
In modern git, you can say this in a more direct way:
....
if git merge-base --is-ancestor A B
then
... A is an ancestor of B ...
fi
....
instead.
Discussion on fork-point mode
-----------------------------
After working on the `topic` branch created with `git switch -c
topic origin/master`, the history of remote-tracking branch
`origin/master` may have been rewound and rebuilt, leading to a
history of this shape:
....
o---B2
/
---o---o---B1--o---o---o---B (origin/master)
\
B0
\
D0---D1---D (topic)
....
where `origin/master` used to point at commits B0, B1, B2 and now it
points at B, and your `topic` branch was started on top of it back
when `origin/master` was at B0, and you