Under what exact condition does Git perform a fast-forward merge, rather than creating a new merge commit?

Git performs a fast-forward merge when the tip commit of the branch being merged into (the destination branch) is a direct ancestor of the tip commit of the branch being merged (the source branch). This specific condition means that the destination branch has not diverged from the source branch; all commits on the destination branch are already present in the history of the source branch, and no new commits have been added to the destination branch since the source branch branched off or was last merged from the destination branch. A fast-forward merge simply moves the destination branch's pointer forward to point to the same commit as the source branch's tip, effectively incorporating all changes from the source branch by advancing the history linearly. It does not create a new merge commit. An ancestor commit is a commit that can be reached by following the parent links from another commit. When the destination branch's tip is an ancestor of the source branch's tip, it signifies a linear progression of history, allowing the pointer to simply fast-forward. If the branches have diverged, meaning both branches have new commits that are not shared, the destination branch's tip commit is not an ancestor of the source branch's tip commit, and Git would then create a new merge commit to reconcile the two divergent histories.