feedback7: the battle sim uses engine-independent math — Chrome, Firefox, Safari and the server agree bit for bit (PR #373 by @Cloudnyco)

- server/sim/detmath.js: hypot (sqrt of the squares, rescaled outside 2^±500), powi (integer powers in double-double,
  one rounding), sin / cos (fdlibm 5.3) and atan2 (fdlibm / FreeBSD msun) built only from correctly rounded IEEE
  operations; the sim's Math.hypot / sin / cos / atan2 / pow calls go through it (65 files); eslint.config.js forbids
  the approximated Math functions under server/sim and test/sim/detmath.test.js scans for them.
- sin / cos / atan2 are the algorithms V8 runs in Node, so the server's results stay; only hypot differs from V8's.
  Golden: 2 moved — diy-027 (a hypot distance, damage +80) and coop3-ABYSS-5 (a later card pick from round 9, same end).
- Applied unchanged after review (Grok static review: MERGE; the diff read in full: no network, no new dependency).
- Tests: broad node --test 5155 / 5155 with the new file tracked (detmath 7 / 7, package 10 / 10); lint 0 errors,
  typecheck, check:imports.

server/sim/content/enemies/archetypes.js

@@ -8,6 +8,7 @@ import {
   HUSK_REBIRTH, BOOM_RADIUS, POLLUTION_INTERVAL, STEALTH_RESTORE_BY_KEY, DUCK_STEALTH_RESTORE, nthOf, stOf, safe, num, T, elem, hurt,
   areaAllies, areaAlliesInTiles, zone, spawnChildren, stepToward, setHits, hitCount, setForm, absorbArts, auraBuff,
 } from './helpers.js';
+import { hypot } from '../../detmath.js';
 
 // ---------------------------------------------------------------------------------------------------------------
 // archetypes
@@ -105,7 +106,7 @@ function pathKeysAhead(e) {
   if (!R || !Array.isArray(R.pts)) return keys;
   let x = e.x, y = e.y;
   for (let i = R.ptIdx ?? 0; i < R.pts.length; i++) {
-    const p = R.pts[i], n = Math.max(1, Math.ceil(Math.hypot(p.x - x, p.y - y) * 4));
+    const p = R.pts[i], n = Math.max(1, Math.ceil(hypot(p.x - x, p.y - y) * 4));
     for (let k = 1; k <= n; k++) keys.add(Math.round(y + ((p.y - y) * k) / n) * COLS + Math.round(x + ((p.x - x) * k) / n));
     x = p.x; y = p.y;
   }
@@ -405,7 +406,7 @@ function unbalanced(onMove) {
       a.px = e.x; a.py = e.y; a.hid = e.hidden;
       if (px == null || hid || e.hidden) return;
       const own = e.s.moveSpeed * MOVE_SCALE * dt * 1.5 + 1e-3;
-      const extra = Math.hypot(e.x - px, e.y - py) - own;
+      const extra = hypot(e.x - px, e.y - py) - own;
       a.lx = px; a.ly = py;                                          // where the move started (direction for onMove)
       if (extra > 0.05) onMove(b, e, a, extra);
     },
@@ -605,7 +606,7 @@ export function blinkForward(b, e, dist) {
     let i = R.ptIdx;
     while (left > 1e-9 && i < R.pts.length) {
       const p = R.pts[i];
-      const d = Math.hypot(p.x - e.x, p.y - e.y);
+      const d = hypot(p.x - e.x, p.y - e.y);
       if (d <= left) { e.x = p.x; e.y = p.y; left -= d; i++; } else { stepToward(e, p.x, p.y, left); left = 0; }
     }
   } else if (R && R.legs && R.legs[R.legIdx] && R.legs[R.legIdx].r != null) {

server/sim/content/enemies/fly.js

@@ -7,6 +7,7 @@ import {
   stepToward, setForm, expose,
 } from './helpers.js';
 import { enemyAura, allyAura, selfFear, skill, kitSelfFear } from './archetypes.js';
+import { hypot } from '../../detmath.js';
 
 // ---------------------------------------------------------------------------------------------------------------
 // constants (numbers that exist nowhere in the data)
@@ -62,7 +63,7 @@ function kitBlackCloud(ab, e) {
   const prey = (b, e2) => b.enemiesInRadius(e2.x, e2.y, grabR).filter((o) => isPrey(b, e2, o));
   return [
     skill(k, (b, e2) => {
-      const list = prey(b, e2).sort((p, q) => Math.hypot(p.x - e2.x, p.y - e2.y) - Math.hypot(q.x - e2.x, q.y - e2.y)).slice(0, GRAB_MAX_PREY);
+      const list = prey(b, e2).sort((p, q) => hypot(p.x - e2.x, p.y - e2.y) - hypot(q.x - e2.x, q.y - e2.y)).slice(0, GRAB_MAX_PREY);
       if (!list.length) return;
       b.addBuff(e2, { key: 'ab:grabbing', duration: dur, flags: { bind: true, noMove: true } });   // 技能持续4秒，期间持有束缚
       b.fx('beam', { x: e2.x, y: e2.y, from: e2.id, to: list[0].id, kind: 'devour' });
@@ -250,12 +251,12 @@ export const FLY_KITS = Object.freeze({
     tick(b, e, a, dt) {
       if (a.t && !a.t.alive) { a.t = null; b.removeBuff(e, 'ab:dive'); }
       if (!a.t) {
-        const l = targetsNear(b, e, e.base.rangeRadius || 1).sort((p, q) => Math.hypot(p.x - e.x, p.y - e.y) - Math.hypot(q.x - e.x, q.y - e.y));
+        const l = targetsNear(b, e, e.base.rangeRadius || 1).sort((p, q) => hypot(p.x - e.x, p.y - e.y) - hypot(q.x - e.x, q.y - e.y));
         if (!l.length) return;
         a.t = l[0];
         b.addBuff(e, { key: 'ab:dive', flags: { noMove: true } });
       }
-      if (!stepToward(e, a.t.x, a.t.y, Math.max(e.s.moveSpeed, 0.5) * MOVE_SCALE * dt) && Math.hypot(a.t.x - e.x, a.t.y - e.y) > 0.3) return;
+      if (!stepToward(e, a.t.x, a.t.y, Math.max(e.s.moveSpeed, 0.5) * MOVE_SCALE * dt) && hypot(a.t.x - e.x, a.t.y - e.y) > 0.3) return;
       hurt(b, e, a.t, e.s.atk, 'phys');
       b.fx('explode', { x: e.x, y: e.y, r: 0.5, kind: 'seed' });
       b.kill(e, null);

server/sim/content/enemies/helpers.js

@@ -6,6 +6,7 @@
 import { ELEMENT } from '../../constants.js';
 import { canTargetAlly, sortAllyTargets, areaSelectable, auraSelectable } from '../../targeting.js';
 import { mitigate } from '../../damage.js';
+import { hypot } from '../../detmath.js';
 
 // ---------------------------------------------------------------------------------------------------------------
 // constants (numbers that exist nowhere in the data)
@@ -295,7 +296,7 @@ export function spawnChildren(b, parent, key, n, opts = {}) {
 /** Move a unit straight toward (tx, ty) by `dist` tiles. Returns true on arrival. */
 export function stepToward(u, tx, ty, dist) {
   const dx = tx - u.x, dy = ty - u.y;
-  const d = Math.hypot(dx, dy);
+  const d = hypot(dx, dy);
   if (d <= dist + 1e-9) { u.x = tx; u.y = ty; return true; }
   u.x += (dx / d) * dist;
   u.y += (dy / d) * dist;

server/sim/content/enemies/invisible.js

@@ -4,6 +4,7 @@
 import { canTargetAlly, enemyStealthed } from '../../targeting.js';
 import { T, elem, hurt, targetsNear, byPriority, auraBuff } from './helpers.js';
 import { stealth, onHitStatus, skill, kitStealth } from './archetypes.js';
+import { hypot } from '../../detmath.js';
 
 // ---------------------------------------------------------------------------------------------------------------
 // constants (numbers that exist nowhere in the data)
@@ -20,8 +21,8 @@ const CROSS_REACH = 6, CROSS_SKILL = 2.5, CROSS_CHARGE = 1.4;
 
 function kitCrossbow(ab) {
   const s = ab.sk.CrossAttack;
-  const aligned = (b, e) => b.allies().filter((u) => canTargetAlly(e, u, true) && (Math.abs(u.y - e.y) < 0.5 || Math.abs(u.x - e.x) < 0.5) && Math.hypot(u.x - e.x, u.y - e.y) <= CROSS_REACH);
-  const nearest = (b, e, l) => l.sort((p, q) => Math.hypot(p.x - e.x, p.y - e.y) - Math.hypot(q.x - e.x, q.y - e.y))[0];
+  const aligned = (b, e) => b.allies().filter((u) => canTargetAlly(e, u, true) && (Math.abs(u.y - e.y) < 0.5 || Math.abs(u.x - e.x) < 0.5) && hypot(u.x - e.x, u.y - e.y) <= CROSS_REACH);
+  const nearest = (b, e, l) => l.sort((p, q) => hypot(p.x - e.x, p.y - e.y) - hypot(q.x - e.x, q.y - e.y))[0];
   // PRTS 重弩突袭者: 天赋 "隐匿（被阻挡，主动攻击期间均可解除）"; 直击 "蓄力1.4s后向目标方向发射1支弩箭，对击中的首个目标造成攻击力100%
   // 的法术伤害与5s晕眩 ※技能持续2.5s": revealed for the whole skill, the bolt leaves CROSS_CHARGE s in — at the nearest unit still
   // in line in the aimed direction; it stands meanwhile [ASSUMED], and a stun / silence or its death before the release
@@ -108,7 +109,7 @@ function kitShadowBlade(ab) {
     tick(b, e) {
       const partner = b.enemiesInRadius(e.x, e.y, 3).find((o) => /enemy_1174_duholy/.test(o.defId));
       const r = partner && partner.mem.ab ? (T(partner.mem.ab, 'traitAbility.range_radius') ?? 1.1) : 1.1;
-      if (partner && Math.hypot(partner.x - e.x, partner.y - e.y) <= r + 1e-9 && e.base.bat > 0) auraBuff(b, e, 'ab:shadowSync', 0.5, { batPct: bat / e.base.bat });
+      if (partner && hypot(partner.x - e.x, partner.y - e.y) <= r + 1e-9 && e.base.bat > 0) auraBuff(b, e, 'ab:shadowSync', 0.5, { batPct: bat / e.base.bat });
     },
   }];
 }

server/sim/content/enemies/leaders.js

@@ -12,6 +12,7 @@ import {
   unblockable, maxTargets, onHitStatus, splashAttack, pathKeysAhead, noAirTargets, resist, nthAttackStatus, lowHpBuff,
   freeAllPrisoners, reborn, frontGuard, faceCrowd, unbalanced, artsBarrier, skill, blinkForward,
 } from './archetypes.js';
+import { hypot, powi } from '../../detmath.js';
 
 // ---------------------------------------------------------------------------------------------------------------
 // constants (numbers that exist nowhere in the data)
@@ -312,7 +313,7 @@ function kitLeaderMisc(key, ab, e) {
             const nx = areaAllies(b, e2, prev.x, prev.y, jr).find((u) => !hit.has(u));
             if (!nx) break;
             hit.add(nx);
-            hurt(b, e2, nx, e2.s.atk * Math.pow(fall, k), 'arts');
+            hurt(b, e2, nx, e2.s.atk * powi(fall, k), 'arts');
             if (nx.alive && cold > 0) b.applyStatus(nx, 'cold', { duration: cold, source: e2 });
             prev = nx;
           }
@@ -323,7 +324,7 @@ function kitLeaderMisc(key, ab, e) {
       skill(cb, (b, e2) => {
         const bb = cb.bb, jump = bb.projectile_range ?? jr, max = bb['chain.max_target'] ?? 3;
         const near = (x, y, r, seen) => b.enemiesInRadius(x, y, r).filter((o) => o !== e2 && !seen.has(o))
-          .sort((p, q) => Math.hypot(p.x - x, p.y - y) - Math.hypot(q.x - x, q.y - y) || p.spawnSeq - q.spawnSeq)[0];
+          .sort((p, q) => hypot(p.x - x, p.y - y) - hypot(q.x - x, q.y - y) || p.spawnSeq - q.spawnSeq)[0];
         const seen = new Set();
         let prev = e2, cur = near(e2.x, e2.y, e2.base.rangeRadius || 3.5, seen);
         while (cur && seen.size < max) {
@@ -357,7 +358,7 @@ function kitLeaderMisc(key, ab, e) {
 function segDist(px, py, ax, ay, bx, by) {
   const dx = bx - ax, dy = by - ay, L = dx * dx + dy * dy;
   const t = L > 0 ? Math.max(0, Math.min(1, ((px - ax) * dx + (py - ay) * dy) / L)) : 0;
-  return Math.hypot(px - (ax + t * dx), py - (ay + t * dy));
+  return hypot(px - (ax + t * dx), py - (ay + t * dy));
 }
 
 /** A second normal hit on the same target ("二连击"): same damage type, no further on-hit procs. */
@@ -454,7 +455,7 @@ function kitWarden(ab) {
 function kitXi(ab) {
   const cross = ab.sk.CrossAttack, sb = ab.sk.ShieldBurst, sb2 = ab.sk.ShieldBurstReborn;
   const P = { form2: false };
-  const byDist = (b, e) => allTargets(b, e).sort((p, q) => Math.hypot(p.x - e.x, p.y - e.y) - Math.hypot(q.x - e.x, q.y - e.y) || aggroCmp(p, q));
+  const byDist = (b, e) => allTargets(b, e).sort((p, q) => hypot(p.x - e.x, p.y - e.y) - hypot(q.x - e.x, q.y - e.y) || aggroCmp(p, q));
   const crossAt = (b, e, t) => {
     const r0 = t.tileR, c0 = t.tileC;
     b.fx('telegraph', { x: c0, y: r0, r: XI_CROSS_REACH, kind: 'xiCross', tiles: 'plus', id: e.id });
@@ -783,7 +784,7 @@ export const LEADER_KITS = Object.freeze({
     if (st > 0) b.applyStatus(e, 'stun', { duration: st, source: null });
   })],
   enemy_10138_xdsnow: (ab) => [unbalanced((b, e, a) => {             // 雪孩子 · pushed / pulled into high ground ⇒ hitWall.value damage
-    const dx = e.x - a.lx, dy = e.y - a.ly, d = Math.hypot(dx, dy);
+    const dx = e.x - a.lx, dy = e.y - a.ly, d = hypot(dx, dy);
     if (!(d > 0)) return;
     const r = Math.round(e.y + (dy / d) * 0.6), c = Math.round(e.x + (dx / d) * 0.6);
     if (b.grid.isLow(r, c) && b.grid.groundPassable(r, c)) return;   // stopped by nothing: no collision

server/sim/content/enemies/special.js

@@ -12,6 +12,7 @@ import {
   unblockable, runWhenHit, blockWeight, taunt, maxTargets, ep, nthAttackPower, lowHpBuff, deathBoom, setFloat, float,
   reborn, frontGuard, faceMove, unbalanced, skill, kitEp, kitPrisoner, kitStun3,
 } from './archetypes.js';
+import { hypot } from '../../detmath.js';
 
 // ---------------------------------------------------------------------------------------------------------------
 // constants (numbers that exist nowhere in the data)
@@ -245,7 +246,7 @@ export const SPECIAL_KITS = Object.freeze({
   enemy_1183_mlasrt: (ab) => [ep('erosion', T(ab, 'EpDamage.attack@ep_damage_ratio') ?? 0), nthAttackPower(nthOf(ab.sk.PowerAttack), (ab.sk.PowerAttack && ab.sk.PowerAttack.bb.atk_scale) || 1)], // 无胄盟清扫小队 · erosion; every 4th attack ×1.5
   enemy_1273_stmgun_2: (ab) => {                                     // 高准度伦蒂尼姆城防自行炮 · locks the highest max-HP unit in range, bombards the highest HP% on its 9 tiles
     // the allies in its range (the engine's ranged reach: radius + the ally collider)
-    const inRange = (b, e) => allTargets(b, e).filter((a) => Math.hypot(a.x - e.x, a.y - e.y) <= (e.base.rangeRadius || 0) + ALLY_COLLIDER_RADIUS + 1e-9);
+    const inRange = (b, e) => allTargets(b, e).filter((a) => hypot(a.x - e.x, a.y - e.y) <= (e.base.rangeRadius || 0) + ALLY_COLLIDER_RADIUS + 1e-9);
     return [skill(ab.sk.Cannon, (b, e) => {
       const lock = inRange(b, e).sort((p, q) => q.s.maxHp - p.s.maxHp)[0];
       if (!lock) return;
@@ -279,7 +280,7 @@ export const SPECIAL_KITS = Object.freeze({
     spawn(b, e) { watchDeaths(b, e); },
     otherDeath(c, b, e) {
       const u = c.unit;
-      if (!u || u === e || c.reason !== 'killed' || Math.hypot(u.x - e.x, u.y - e.y) > (T(ab, 'Attack.range_radius') ?? TORTURER_RADIUS) + 1e-9) return;
+      if (!u || u === e || c.reason !== 'killed' || hypot(u.x - e.x, u.y - e.y) > (T(ab, 'Attack.range_radius') ?? TORTURER_RADIUS) + 1e-9) return;
       b.heal(e, e, e.s.maxHp * (T(ab, 'Attack.hp_ratio') ?? 0), { self: true });
       b.addBuff(e, { key: 'ab:torture', refresh: 'stack', stacks: 1, maxStacks: T(ab, 'Attack.max_stack_cnt') ?? 1, persist: true, mods: { atkPct: T(ab, 'Attack.atk') ?? 0 } });
     },