Times printed by the game differ by a hundredth from the same values printed by a tool

Symptoms

A time read from memory and printed by our reader is a hundredth away from the game's screen. In POD the gap behind the winner read +23"21 in our reader and +23"20 on the results screen; the other times matched.

Cause

POD's format_time (FUN_0047e4d0) converts a 16.16 time in x87 floating point: minutes = v × 2.5431e-7, seconds = rem / 65536, each through FUN_004d18ac, then hundredths = frac × 0.0015259 + 0.5, with a carry into the seconds at 100 and into the minutes at 60 (0x47e543, 0x47e560). FUN_004d18ac is not a bare frndint: it saves the control word, loads one with the rounding set to chop (mov byte [esp+1], 0x1f; fldcw), runs frndint and puts the old word back (observed). So these conversions truncate whatever mode the game runs in. The game itself runs with round to nearest (measured: its gate test, an fadd of 1.5 × 2^68 that does depend on the mode, matches under the control word 0x037f on 20,000 cases and not under truncation; x87-magic-add-rounding).

An earlier version of this entry inferred from the results screens that the whole game ran truncated. The screens fit, because the rounding happens inside the helper; the inference about the mode did not.

Evidence

The three instructions of FUN_004d18ac (0x4d18ae..0x4d18bd); format_time run under Unicorn on 20,000 values, stopped at its sprintf call to read the minutes, seconds and hundredths (measure/race_rules.py).

What to do

Print times the game's way: the whole of format_time is exact in integers (minutes = v / 3,932,160, truncated; seconds rem / 65536, truncated; hundredths (frac × 100 + 32768) / 65536, truncated; then both carries). crates/pod-race time::parts and run/vm/racelog.py clock() do this. Compute a gap as the difference of the raw values, then format it. When a game's float conversions disagree with a tool by one unit, read the rounding helper's own instructions before blaming the FPU's mode, and measure any mode-dependent code under both control words.