/* 距离下界认证（2026-10-17，方案 §8.3 / §4.4）
 * 关节直线段 a→b 安全 ⇔ 对每个组对 (gA,gB)（gB ≥ gA+2）：
 *     gap_ab(a) + gap_ab(b) > Σ_{k=gA}^{gB-1} r_k·|Δθ_k|
 * gap 取 S.gapMatrix（距离 − need，含 margin），r_k 为 S.leverBounds 的每轴杠杆上界（mm/°）。
 * 不满足就二分，子段 < MIN_DEG 仍不过则判不安全。连续轴按 unwrapTo 口径展开后再插值。 */
'use strict';
module.exports = function makeCert(S, opt) {
  opt = opt || {};
  const CAP = opt.cap || 40, MIN_DEG = opt.minDeg || 0.002;
  const R = opt.lever || S.leverBounds(4000);
  const L = S.LIM, O = S.ORDER, w = S.wrap180;
  const memo = new Map();
  const key = q => q.map(v => v.toFixed(5)).join(',');
  let queries = 0;
  const gm = q => { const k = key(q); let M = memo.get(k); if (!M) { M = S.gapMatrix(q, CAP); queries++; if (memo.size > 50000) memo.clear(); memo.set(k, M); } return M; };
  const minGap = M => { let m = Infinity; for (let a = 0; a < 7; a++) for (let b = a + 2; b < 7; b++) m = Math.min(m, M[a * 7 + b]); return m; };
  const inBox = q => O.every((id, i) => L[id].cont || (q[i] >= L[id].lo - 1e-6 && q[i] <= L[id].hi + 1e-6));
  function seg(a, b, depth) {
    const Ma = gm(a), Mb = gm(b);
    const dq = a.map((v, i) => Math.abs(b[i] - v));
    let ok = true;
    for (let ga = 0; ga < 7 && ok; ga++) for (let gb = ga + 2; gb < 7; gb++) {
      const lhs = Ma[ga * 7 + gb] + Mb[ga * 7 + gb];
      let rhs = 0; for (let k = ga; k < gb; k++) rhs += R[k] * dq[k];
      if (!(lhs > rhs)) { ok = false; break; }
    }
    if (ok) return true;
    if (minGap(Ma) <= 0 || minGap(Mb) <= 0) return false;
    if (Math.max.apply(null, dq) < MIN_DEG || depth > 40) return false;
    const m = a.map((v, i) => 0.5 * (v + b[i]));
    return seg(a, m, depth + 1) && seg(m, b, depth + 1);
  }
  /* 整条折线：返回 {ok, queries, minGap, failAt} */
  function path(pts) {
    const q0 = queries; let mg = Infinity;
    const P = [pts[0].slice()];
    for (let i = 1; i < pts.length; i++) P.push(P[i - 1].map((v, k) => L[O[k]].cont ? v + w(pts[i][k] - v) : pts[i][k]));
    for (let i = 0; i < P.length; i++) { if (!inBox(P[i])) return { ok: false, queries: queries - q0, minGap: mg, failAt: i, why: 'box' }; mg = Math.min(mg, minGap(gm(P[i]))); }
    for (let i = 1; i < P.length; i++) if (!seg(P[i - 1], P[i], 0)) return { ok: false, queries: queries - q0, minGap: mg, failAt: i, why: 'cert' };
    return { ok: true, queries: queries - q0, minGap: mg, unwrapped: P };
  }
  return { seg: (a, b) => seg(a, b, 0), path, lever: R, gapMin: q => minGap(gm(q)) };
};