Does a float32 simulation of a bouncing, chaotic system lose its statistics? Sinai billiard against float64
research/free-f32bounce
Does a float32 simulation of a bouncing, chaotic system lose its statistics? Sinai billiard: float32 leaves the float64 trajectory after a median 21 collisions, like a float64 start error of about one unit roundoff, and changes the event order one collision later, but the mean free path and circle-hit share agree with float64 and with Cauchy's exact value (stylised).
What it found
A point particle in a unit square with a circular obstacle (Sinai billiard), event-driven with specular reflection, run in float32 and float64 from the same start. Float32 leaves the float64 trajectory (position differs by > 0.1) after a median 21 collisions, equal to a float64 start error of 4.6×10−8, about one float32 unit roundoff (the smooth flows of free-f32shadow needed about 100×). The first different surface is hit exactly one collision after the position departs, at every error size tried. Mean free path (0.45296 vs 0.45325) and the circle's share of collisions agree within sampling error (|z| < 0.6), and match Cauchy’s exact mean free path 0.45321; no particle escaped and the direction vector’s length drifted by about 10−5 after 2000 collisions. Stylised: straight-line flights, no time-stepped contact; a first attempt on a vibrating-table bouncing ball was not chaotic and is not used.
A figure from its own output
Paper, code and results
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Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.