#!/usr/bin/env python3 """Precompute mpmath high-precision O3 vectors for engineering.tolerance.stackup. Independent of Node/V8 binary64 and of the IUT. Basic RSS = √Σ Tᵢ², WCA = Σ|Tᵢ|; Engineering a=(T++T−)/2, u = a | a/3 | a/√3. 80 dps, round-to-nearest binary64. Does not pin a gmpy2 backend. Re-run: python3 scripts/lib/cvp/oracles/generate-tolerance-stackup-o3.py """ from __future__ import annotations import json import math import shutil from pathlib import Path import mpmath as mp DPS = 80 GENERATOR_ID = "tolerance-stackup-mpmath-o3" GENERATOR_VERSION = "1.0.0" SEED = "20260916.stackup-o3" ENG_SYM = [ {"name": "A", "nom": 10, "tol_plus": 0.1, "tol_minus": 0.1, "direction": "+"}, {"name": "B", "nom": 5, "tol_plus": 0.2, "tol_minus": 0.2, "direction": "-"}, {"name": "C", "nom": 3, "tol_plus": 0.1, "tol_minus": 0.1, "direction": "+"}, ] ENG_ASYM = [ {"name": "A", "nom": 10, "tol_plus": 0.05, "tol_minus": 0.15, "direction": "+"}, {"name": "B", "nom": 5, "tol_plus": 0.2, "tol_minus": 0.2, "direction": "-"}, {"name": "C", "nom": 3, "tol_plus": 0.1, "tol_minus": 0.1, "direction": "+"}, ] def f64(x: mp.mpf) -> float: return float(x) def mp_fields(**kwargs) -> dict: out = {} for k, v in kwargs.items(): if v is None: continue out[f"{k}_f64"] = f64(v) out[f"{k}_decimal"] = mp.nstr(v, 40, strip_zeros=False) return out def rss_contributor(a: mp.mpf, basis: str) -> mp.mpf: if a <= 0: return mp.mpf(0) if basis == "uniform": return a / mp.sqrt(3) if basis == "3sigma": return a / 3 return a def basic(mode: str, tols: list[float]) -> dict: abs_t = [abs(mp.mpf(t)) for t in tols] stack_worst = sum(abs_t, mp.mpf(0)) stack_rss = mp.sqrt(sum((t * t for t in abs_t), mp.mpf(0))) stack = stack_rss if mode == "rss" else stack_worst return mp_fields( stack=stack, stack_rss=stack_rss, stack_worst=stack_worst, stack_worst_plus=stack_worst, stack_worst_minus=stack_worst, ) | {"profile": "basic", "mode": mode} def engineering(mode: str, dimensions: list[dict]) -> dict: stack_nom = mp.mpf(0) stack_stat_center = mp.mpf(0) pos_exc = mp.mpf(0) neg_exc = mp.mpf(0) rss_sq = mp.mpf(0) for d in dimensions: nom = mp.mpf(d.get("nom", 0)) if "tol" in d and d.get("tol_plus") is None and d.get("tol_minus") is None: t = abs(mp.mpf(d["tol"])) tol_plus = t tol_minus = t else: tol_plus = mp.mpf(d.get("tol_plus", 0)) tol_minus = mp.mpf(d.get("tol_minus", 0)) direction = 1 if str(d.get("direction", "+")) in ("+", "1", "plus") else -1 basis = str(d.get("statistical_basis") or d.get("distribution") or "magnitude") half = (tol_plus + tol_minus) / 2 t_rss = rss_contributor(half, basis) d_max = tol_plus if direction == 1 else tol_minus d_min = -tol_minus if direction == 1 else -tol_plus center_shift = (tol_plus - tol_minus) / 2 if basis == "uniform" else mp.mpf(0) stack_nom += direction * nom stack_stat_center += direction * (nom + center_shift) pos_exc += d_max neg_exc += d_min rss_sq += t_rss * t_rss stack_max = stack_nom + pos_exc stack_min = stack_nom + neg_exc stack_worst_plus = pos_exc stack_worst_minus = -neg_exc stack_worst = max(stack_worst_plus, stack_worst_minus) stack_rss = mp.sqrt(rss_sq) stack = stack_rss if mode == "rss" else stack_worst return mp_fields( stack=stack, stack_rss=stack_rss, stack_worst=stack_worst, stack_worst_plus=stack_worst_plus, stack_worst_minus=stack_worst_minus, stack_nom=stack_nom, stack_stat_center=stack_stat_center, stack_min=stack_min, stack_max=stack_max, ) | {"profile": "engineering", "mode": mode} def row(vid: str, inputs: dict, *, kind: str, extra: dict) -> dict: return {"id": vid, "kind": kind, "inputs": inputs, **extra} def vectors() -> list[dict]: return [ row("o3-rss", {"mode": "rss", "tol": [0.1, 0.2, 0.1]}, kind="basic-rss", extra=basic("rss", [0.1, 0.2, 0.1])), row( "o3-wca", {"mode": "worst_case", "tol1": 0.1, "tol2": 0.2, "tol3": 0.1}, kind="basic-wca", extra=basic("worst_case", [0.1, 0.2, 0.1]), ), row( "o3-rss-fields", {"mode": "rss", "tol1": 0.1, "tol2": 0.2, "tol3": 0.1}, kind="basic-rss-fields", extra=basic("rss", [0.1, 0.2, 0.1]), ), row( "o3-eng-symmetric", {"mode": "rss", "dimensions": ENG_SYM}, kind="engineering-symmetric", extra=engineering("rss", ENG_SYM), ), row( "o3-eng-asymmetric", {"mode": "worst_case", "dimensions": ENG_ASYM}, kind="engineering-asymmetric-wca", extra=engineering("worst_case", ENG_ASYM), ), row( "o3-eng-asymm-rss", {"mode": "rss", "dimensions": ENG_ASYM}, kind="engineering-asymmetric-rss", extra=engineering("rss", ENG_ASYM), ), row( "o3-eng-1sigma", { "mode": "rss", "dimensions": [{"name": "A", "nom": 0, "tol": 0.3, "direction": "+", "statistical_basis": "1sigma"}], }, kind="engineering-1sigma", extra=engineering( "rss", [{"name": "A", "nom": 0, "tol": 0.3, "direction": "+", "statistical_basis": "1sigma"}], ), ), row( "o3-eng-3sigma", { "mode": "rss", "dimensions": [{"name": "A", "nom": 0, "tol": 0.3, "direction": "+", "statistical_basis": "3sigma"}], }, kind="engineering-3sigma", extra=engineering( "rss", [{"name": "A", "nom": 0, "tol": 0.3, "direction": "+", "statistical_basis": "3sigma"}], ), ), row( "o3-eng-uniform", { "mode": "rss", "dimensions": [{"name": "A", "nom": 0, "tol": 0.3, "direction": "+", "statistical_basis": "uniform"}], }, kind="engineering-uniform", extra=engineering( "rss", [{"name": "A", "nom": 0, "tol": 0.3, "direction": "+", "statistical_basis": "uniform"}], ), ), row( "o3-eng-uniform-center", { "mode": "rss", "dimensions": [{**row, "statistical_basis": "uniform"} for row in ENG_ASYM], }, kind="engineering-uniform-center", extra=engineering("rss", [{**row, "statistical_basis": "uniform"} for row in ENG_ASYM]), ), ] def main() -> None: mp.mp.dps = DPS here = Path(__file__).resolve().parent table = { "family": "tolerance_stackup", "generator_id": GENERATOR_ID, "generator_version": GENERATOR_VERSION, "seed": SEED, "mpmath_dps": DPS, "precision_bits": int(DPS * math.log2(10)), "library": f"mpmath {mp.__version__}", "notes": "Basic RSS/WCA and Engineering dimensions[]; independent of Node Math and the IUT.", "vectors": vectors(), } dest = here / "tolerance-stackup-o3-tables.json" dest.write_text(json.dumps(table, indent=2) + "\n", encoding="utf-8") public = here.parents[3] / "public/developers/cvp/reproduce" public.mkdir(parents=True, exist_ok=True) shutil.copy2(dest, public / "tolerance-stackup-o3-tables.json") shutil.copy2(Path(__file__), public / "generate-tolerance-stackup-o3.py") print(f"wrote {dest} ({len(table['vectors'])} vectors)") if __name__ == "__main__": main()