async def schedule_formatting(
    sources: set[Path],
    fast: bool,
    write_back: WriteBack,
    mode: Mode,
    report: "Report",
    loop: asyncio.AbstractEventLoop,
    executor: "Executor",
) -> None:
    """Run formatting of `sources` in parallel using the provided `executor`.

    (Use ProcessPoolExecutors for actual parallelism.)

    `write_back`, `fast`, and `mode` options are passed to
    :func:`format_file_in_place`.
    """
    cache = Cache.read(mode)
    if write_back not in (WriteBack.DIFF, WriteBack.COLOR_DIFF):
        sources, cached = cache.filtered_cached(sources)
        for src in sorted(cached):
            report.done(src, Changed.CACHED)
    if not sources:
        return

    cancelled = []
    sources_to_cache = []
    lock = None
    if write_back in (WriteBack.DIFF, WriteBack.COLOR_DIFF):
        # For diff output, we need locks to ensure we don't interleave output
        # from different processes.
        manager = Manager()
        lock = manager.Lock()
    tasks = {
        asyncio.ensure_future(
            loop.run_in_executor(
                executor, format_file_in_place, src, fast, mode, write_back, lock
            )
        ): src
        for src in sorted(sources)
    }
    pending = tasks.keys()
    try:
        loop.add_signal_handler(signal.SIGINT, cancel, pending)
        loop.add_signal_handler(signal.SIGTERM, cancel, pending)
    except NotImplementedError:
        # There are no good alternatives for these on Windows.
        pass
    while pending:
        done, _ = await asyncio.wait(pending, return_when=asyncio.FIRST_COMPLETED)
        for task in done:
            src = tasks.pop(task)
            if task.cancelled():
                cancelled.append(task)
            elif exc := task.exception():
                if report.verbose:
                    traceback.print_exception(type(exc), exc, exc.__traceback__)
                report.failed(src, str(exc))
            else:
                changed = Changed.YES if task.result() else Changed.NO
                # If the file was written back or was successfully checked as
                # well-formatted, store this information in the cache.
                if write_back is WriteBack.YES or (
                    write_back is WriteBack.CHECK and changed is Changed.NO
                ):
                    sources_to_cache.append(src)
                report.done(src, changed)
    if cancelled:
        await asyncio.gather(*cancelled, return_exceptions=True)
    if sources_to_cache:
        cache.write(sources_to_cache)
Run formatting of `sources` in parallel using the provided `executor`.

    (Use ProcessPoolExecutors for actual parallelism.)

    `write_back`, `fast`, and `mode` options are passed to
    :func:`format_file_in_place`.
    
src/black/concurrency.py