Fix the fixed-timestep loop in a game engine

Your engine's main loop adds each frame's time to an accumulator and runs physics in fixed steps until the accumulator is drained. On a slow laptop, physics took longer than a step, each frame queued more work than it could run, and the game froze: a death spiral. The fix clamps long frames, caps the steps per frame and drops any backlog the cap leaves behind.

An assistant wrote simulate_fixed_steps(frame_times_ms, fixed_dt_ms, max_frame_ms, max_steps_per_frame). It is in the editor. It has a bug. Find it and fix it.

Input and output:

• frame_times_ms: each frame's measured time in milliseconds, in order.
• fixed_dt_ms: the length of one physics step.
• max_frame_ms: the most time one frame may add (0 or more). max_steps_per_frame: the most steps one frame may run.
• Return the number of physics steps each frame runs.

Rules the tests check:

• If fixed_dt_ms is 0 or less, return [].
• The accumulator starts at 0. For each frame:
  1. A negative frame time counts as 0, and a frame time above max_frame_ms counts as max_frame_ms. Add it to the accumulator.
  2. While the accumulator is at least fixed_dt_ms and fewer than max_steps_per_frame steps have run this frame, run a step: subtract fixed_dt_ms.
  3. Then keep only the accumulator's remainder after dividing by fixed_dt_ms. Whole steps the cap left over are dropped, never carried into the next frame.
  4. Record the number of steps run.