Thanks for your reviews.

In the original "trivial merge" mode, the command takes three trees
without having to have this new option.  In the new "write-tree"
mode, currently it is incapable of taking the base, but it does not
have to stay that way.  Wouldn't it be sufficient to update the UI
to

    git merge-tree [--write-tree] [<options>] [<base-commit>] <branch1> <branch2>
    git merge-tree [--trivial-merge] <base-commit> <branch1> <branch2>

IOW, when you want to supply the base, you'd be explicit and ask for
the new "write-tree" mode, i.e.

    $ git merge-tree --write-tree $(git merge-base branch^ branch) HEAD branch 

would be how you would use merge-tree to cherry-pick the commit at
the tip of the branch on top of the current commit.

Referring to Newren's reply, if we need to implement octopus merges for git-merge-tree in the future,  still need a new option, 
so I haven't modified it yet.

quoted

@@ -402,6 +403,7 @@ struct merge_tree_options {
 	int allow_unrelated_histories;
 	int show_messages;
 	int name_only;
+	char* merge_base;

Style.  We write in C, not in C++, and our asterisks stick to variables and members of structs, not types.

Done.