Provide elapsed and timestamp info to filename_format

This provides the `elapsed` and `time` values to the
`ProfileMiddleware(filename_format=...)` function. Prior to this change,
one could not replicate the format string format, much less modify how
it would render the timestamp or elapsed time values.

These new values can be found under the `werkzeug.profiler` key in the
WSGI environ dict passed into the `filename_format()` function.

Addresses #2775

CHANGES.rst

@@ -9,6 +9,9 @@ Unreleased
 -   Deprecate the ``__version__`` attribute. Use feature detection, or
     ``importlib.metadata.version("werkzeug")``, instead. :issue:`2770`
 -   ``generate_password_hash`` uses scrypt by default. :issue:`2769`
+-   Add the ``"werkzeug.profiler"`` item to the  WSGI ``environ`` dictionary
+    passed to `ProfilerMiddleware`'s `filename_format` function. It contains
+    the ``elapsed`` and ``time`` values for the profiled request. :issue:`2775`
 
 
 Version 2.3.8

src/werkzeug/middleware/profiler.py

@@ -44,11 +44,16 @@ class ProfilerMiddleware:
 
     -   ``{method}`` - The request method; GET, POST, etc.
     -   ``{path}`` - The request path or 'root' should one not exist.
-    -   ``{elapsed}`` - The elapsed time of the request.
+    -   ``{elapsed}`` - The elapsed time of the request in milliseconds.
     -   ``{time}`` - The time of the request.
 
-    If it is a callable, it will be called with the WSGI ``environ``
-    dict and should return a filename.
+    If it is a callable, it will be called with the WSGI ``environ`` and
+    be expected to return a filename string. The ``environ`` dictionary
+    will also have the ``"werkzeug.profiler"`` key populated with a
+    dictionary containing the following fields (more may be added in the
+    future):
+    -   ``{elapsed}`` - The elapsed time of the request in milliseconds.
+    -   ``{time}`` - The time of the request.
 
     :param app: The WSGI application to wrap.
     :param stream: Write stats to this stream. Disable with ``None``.
@@ -65,6 +70,10 @@ class ProfilerMiddleware:
         from werkzeug.middleware.profiler import ProfilerMiddleware
         app = ProfilerMiddleware(app)
 
+    .. versionchanged:: 3.0
+        Added the ``"werkzeug.profiler"`` key to the ``filename_format(environ)``
+        parameter with the  ``elapsed`` and ``time`` fields.
+
     .. versionchanged:: 0.15
         Stats are written even if ``profile_dir`` is given, and can be
         disable by passing ``stream=None``.
@@ -118,6 +127,10 @@ def runapp() -> None:
 
         if self._profile_dir is not None:
             if callable(self._filename_format):
+                environ["werkzeug.profiler"] = {
+                    "elapsed": elapsed * 1000.0,
+                    "time": time.time(),
+                }
                 filename = self._filename_format(environ)
             else:
                 filename = self._filename_format.format(

tests/middleware/test_profiler.py

@@ -0,0 +1,50 @@
+import datetime
+import os
+from unittest.mock import ANY
+from unittest.mock import MagicMock
+from unittest.mock import patch
+
+from werkzeug.middleware.profiler import Profile
+from werkzeug.middleware.profiler import ProfilerMiddleware
+from werkzeug.test import Client
+
+
+def dummy_application(environ, start_response):
+    start_response("200 OK", [("Content-Type", "text/plain")])
+    return [b"Foo"]
+
+
+def test_filename_format_function():
+    # This should be called once with the generated file name
+    mock_capture_name = MagicMock()
+
+    def filename_format(env):
+        now = datetime.datetime.fromtimestamp(env["werkzeug.profiler"]["time"])
+        timestamp = now.strftime("%Y-%m-%d:%H:%M:%S")
+        path = (
+            "_".join(token for token in env["PATH_INFO"].split("/") if token) or "ROOT"
+        )
+        elapsed = env["werkzeug.profiler"]["elapsed"]
+        name = f"{timestamp}.{env['REQUEST_METHOD']}.{path}.{elapsed:.0f}ms.prof"
+        mock_capture_name(name=name)
+        return name
+
+    client = Client(
+        ProfilerMiddleware(
+            dummy_application,
+            stream=None,
+            profile_dir="profiles",
+            filename_format=filename_format,
+        )
+    )
+
+    # Replace the Profile class with a function that simulates an __init__()
+    # call and returns our mock instance.
+    mock_profile = MagicMock(wraps=Profile())
+    mock_profile.dump_stats = MagicMock()
+    with patch("werkzeug.middleware.profiler.Profile", lambda: mock_profile):
+        client.get("/foo/bar")
+
+        mock_capture_name.assert_called_once_with(name=ANY)
+        name = mock_capture_name.mock_calls[0].kwargs["name"]
+        mock_profile.dump_stats.assert_called_once_with(os.path.join("profiles", name))