Gate error by gate, and H4's distance prediction

Complete · updated 2026-10-29 · branes-ai/racing-drone#35 · racing-drone/docs/plan/gate-error-by-gate/README.md

Approved: 2026-10-27; implemented in racing-drone#43 Issue: racing-drone#35, part of the Phase 2 epic racing-drone#9 Related: precision sweep plan, time-base plan, mixed-precision assessment §9 (H4)

Issues and pull requests

Item	What	State
racing-drone#35	This plan	Closed
racing-drone#43	The per-gate statistics, the regenerated sweep, and H4’s verdict; this document landed with it	Merged
racing-drone#40	The controller’s dt defect #35 found, fixed first	Closed

Problem

#35 had two questions.

1. Why posit<16,1> flew B0 faster than double and above the velocity cap. The cause was the controller’s dt, which #40 fixed before this measurement.
2. H4’s second prediction: gate errors grow with distance from the origin. The sweep’s table didn’t split gate error by position, so that prediction was unmeasured.

A gate’s error is measured in the gate’s plane. So rounding coarsens it only through the coordinates that span that plane, not through the distance from the origin. On a2rl-2025:

• the gates facing ±x (1–5, 7–10) resolve in y and z, whose values are small wherever the gate is;
• gate 6 faces y at x = 72 m, where posit<16,1> has 9 fraction bits.

Plan

1. sim::ulp_at<T>(x) (sim/sweep_types.hpp): the gap from T(|x|) to the next value of T above it. Built-in floats use std::nextafter; Universal types step to the next encoding.

2. sim::in_plane_ulp<T>(gate): the largest ulp_at<T> of the gate center’s coordinates on the world axes that span the gate’s plane. Those are the axes on which the gate’s y or z axis has a component.

3. Per-gate statistics (apps/precision_sweep/main.cpp), for every built type and gate:

   • the passages, with true gate error p50 and p99;
   • the median paired excess over double, the difference in true error for the same seed, lap and gate;
   • the in-plane ULP, and ¼ of it.

   They go to gate_error.jsonl and a “Gate error by gate” section of summary.md.

4. Smoke test (sweep.b0.smoke):

   • gate_error.jsonl reruns byte-identically;
   • each built type has 11 lines;
   • its per-gate passages add up to its run’s;
   • double’s paired excess is exactly 0 where it has pairs.

5. Results: docs/assessments/data/precision-sweep-b0.* is regenerated with .gate_error.jsonl, and H4’s verdict goes into assessment §9.

H4 distance criterion (approved 2026-10-27, before the run)

The comparison is posit<16,1> against double, paired by seed, lap and gate, on the controller fixed by #40.

• Holds iff gate 6 has a larger median paired excess true gate error than every other gate, and that excess is ≥ ¼ of its in-plane ULP.
• Refuted otherwise.
• This re-keys H4’s “x > 32 m” to the in-plane coordinate, the mechanism H4 names. The assessment discloses it as a refinement of H4.

Acceptance criteria (stated before the tests ran)

1. For every sweep type, ulp_at<T> equals the neighbor gap at the course’s magnitudes. In posit<16,1>, ulp_at(72) is 0.125.
2. in_plane_ulp uses y and z for the gates facing ±x, and x and z for gates 6 and 11.
3. Per-gate passages add up to each type’s passages.
4. A rerun is byte-identical.
5. double’s paired excess is exactly 0.
6. The H4 verdict follows from the generated columns alone.

Implementation notes (departures disclosed)

• The populations: passages are counted over runs without a run error, the population of the summary’s gate-error column. Pairs need the same seed, lap and gate in both runs, not two successful runs.
  • The plan said “successful seeds”. With every posit<16,1> seed succeeding, the H4 numbers are the same either way.
  • The smoke scenario is shorter than two laps, so with “successful seeds” it would have had no pairs, and criterion 5 couldn’t be checked.
• Criterion 3 is checked in the smoke test, against the passages in that run’s JSONL line.

Out of scope

• Why posit<16,1>’s excess grows along each straight (assessment §9): the table shows it, but its cause isn’t established here. Filed as #44.