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To retrieve the number of modifications made between branch A and branch B in a VSCode extension, you can use the Git API provided by VSCode. Here's how to achieve this:

1. Get the Git Repository object representing the current workspace:

   const repository = await workspace.getWorkspaceFolder(uri)?.uri.fsPath;
   const gitExtension = extensions.getExtension<GitExtension>('vscode.git')!.exports;
   const git = gitExtension.getAPI(1);
   
   const repo = git.getRepository(repository!);
   

2. Get the commit hash of the two branches, A and B:

   const branchA = repo.refs.find(ref => ref.name === 'refs/heads/A')?.commit;
   const branchB = repo.refs.find(ref => ref.name === 'refs/heads/B')?.commit;
   

3. Use the Git.diffWith method to get the difference between the two commit trees:

   const diff = await git.diffWith(branchA!.hash, branchB!.hash);
   

4. Use the GitDiffParser class provided by the git extension and parse the diff output to get the number of modifications:

   const changes = GitDiffParser.parse(diff);
   const numModifications = changes.chunks.reduce((total, chunk) => {
      return total + chunk.newLines - chunk.oldLines;
   }, 0);
   

The numModifications variable will now hold the number of modifications made between branch A and B.