test(skills): add comprehensive Blizzard missile physics stress verification suite (Ref #400)

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/**
* Diablo II: Lord of Destruction v1.13c — Blizzard (Skill 59) Empirical Challenger Suite
*
* EMPIRICAL CHALLENGER VERIFICATION (solution-stress-testing playbook):
* 1. 5-band damage progression across slvl 1 to 50 matches 1.13c formula exactly
* (base 45-75, bands [15/16, 30/31, 45/46, 55/56, 65/66]).
* 2. Synergy multiplier matches +5% per hard point in Ice Bolt, Ice Blast, Glacial Spike.
* 3. Authoritative 64-entry circle table values in `src/game/engine/blizzard-table.ts`
* match D2Game.dll 0x6FD1C960 and 0x6FD1CA60 with 0 errors.
* 4. Exactly 25 shards dropped over 100 ticks (cadence 4, step 13 mod 64).
* 5. 2:1 isometric aspect ratio scaling on ground plane (`dy = tblY * scale * 0.5`).
* 6. Altitude descent (120 px to 0 over 9 ticks) and ground detonation.
* 7. NextDelay = 0 sweet-spot burst collision.
* 8. High-density performance stress test (100 concurrent Blizzard centers = 2,500 shards).
*/
import { describe, expect, it } from 'vitest'
import fs from 'node:fs'
import path from 'node:path'
import {
calculateBlizzardDamage,
calculateBlizzardSynergyMultiplier,
tickProjectiles,
ISO_GROUND_ASPECT_RATIO,
type Projectile,
} from '../src/game/skills.ts'
import {
BLIZZARD_CIRCLE_X,
BLIZZARD_CIRCLE_Y,
getBlizzardDropOffset,
SUBTILE_TO_PX,
} from '../src/game/engine/blizzard-table.ts'
import { getSharedDataRegistry } from '../src/game/engine/data-registry.ts'
import { UnitStatList } from '../src/game/engine/stat-list.ts'
import { skillModule } from '../src/game/skills/impl/sor/skill-059-blizzard.ts'
/**
* Independent mathematical oracle for 1.13c Blizzard 5-band damage.
* Derived directly from D2Common.dll disassembly VA 0x6FD9DDB0 & 0x6FDBA580:
* Base: 45 - 75
* Band 1 (slvl 2..8): +15 / +16 per slvl (7 levels)
* Band 2 (slvl 9..16): +30 / +31 per slvl (8 levels)
* Band 3 (slvl 17..22): +45 / +46 per slvl (6 levels)
* Band 4 (slvl 23..28): +55 / +56 per slvl (6 levels)
* Band 5 (slvl 29+): +65 / +66 per slvl
*/
function oracle113cBlizzardDamage(
slvl: number,
synergies: { iceBolt?: number; iceBlast?: number; glacialSpike?: number } = {},
): { min: number; max: number } {
const lvl = Math.max(1, Math.floor(slvl))
let min = 45
let max = 75
if (lvl > 1) {
const b1 = Math.min(lvl, 8) - 1
min += b1 * 15
max += b1 * 16
}
if (lvl > 8) {
const b2 = Math.min(lvl, 16) - 8
min += b2 * 30
max += b2 * 31
}
if (lvl > 16) {
const b3 = Math.min(lvl, 22) - 16
min += b3 * 45
max += b3 * 46
}
if (lvl > 22) {
const b4 = Math.min(lvl, 28) - 22
min += b4 * 55
max += b4 * 56
}
if (lvl > 28) {
const b5 = lvl - 28
min += b5 * 65
max += b5 * 66
}
const hardPoints =
(synergies.iceBolt ?? 0) + (synergies.iceBlast ?? 0) + (synergies.glacialSpike ?? 0)
const synMultiplier = 1.0 + hardPoints * 0.05
return {
min: Math.floor(min * synMultiplier),
max: Math.floor(max * synMultiplier),
}
}
describe('[Skill #059 Challenger] Empirical Stress Testing & Oracle Verification Suite', () => {
it('1. 5-band damage progression across slvl 1 to 50 matches 1.13c formula exactly with 0 deviations', async () => {
const registry = await getSharedDataRegistry()
const skillRec = registry.getSkillById(59)!
expect(skillRec).toBeDefined()
// Test every level from 1 to 50
for (let slvl = 1; slvl <= 50; slvl++) {
const expected = oracle113cBlizzardDamage(slvl)
const actual = calculateBlizzardDamage(slvl)
expect(actual.min).toBe(expected.min)
expect(actual.max).toBe(expected.max)
// Also compare against D2Common UnitStatList AST evaluation
const stats = new UnitStatList()
stats.setBaseSkillLevel(59, slvl)
const evalRes = skillModule.evaluate!({
registry,
skill: skillRec,
slvl,
blvl: slvl,
statList: stats,
})
// HitShift = 8 -> 256 fixed point
expect(evalRes.minElemDmg256).toBe(expected.min * 256)
expect(evalRes.maxElemDmg256).toBe(expected.max * 256)
}
// Explicit checkpoint assertions for all 5 band transition points
// Band 1: slvl 1 (base 45-75), slvl 8 (150-187)
expect(calculateBlizzardDamage(1)).toEqual({ min: 45, max: 75 })
expect(calculateBlizzardDamage(8)).toEqual({ min: 150, max: 187 })
// Band 2: slvl 9 (180-218), slvl 10 (210-249), slvl 16 (390-435)
expect(calculateBlizzardDamage(9)).toEqual({ min: 180, max: 218 })
expect(calculateBlizzardDamage(10)).toEqual({ min: 210, max: 249 })
expect(calculateBlizzardDamage(16)).toEqual({ min: 390, max: 435 })
// Band 3: slvl 17 (435-481), slvl 20 (570-619), slvl 22 (660-711)
expect(calculateBlizzardDamage(17)).toEqual({ min: 435, max: 481 })
expect(calculateBlizzardDamage(20)).toEqual({ min: 570, max: 619 })
expect(calculateBlizzardDamage(22)).toEqual({ min: 660, max: 711 })
// Band 4: slvl 23 (715-767), slvl 28 (990-1047)
expect(calculateBlizzardDamage(23)).toEqual({ min: 715, max: 767 })
expect(calculateBlizzardDamage(28)).toEqual({ min: 990, max: 1047 })
// Band 5: slvl 29 (1055-1113), slvl 30 (1120-1179), slvl 50 (2420-2499)
expect(calculateBlizzardDamage(29)).toEqual({ min: 1055, max: 1113 })
expect(calculateBlizzardDamage(30)).toEqual({ min: 1120, max: 1179 })
expect(calculateBlizzardDamage(50)).toEqual({ min: 2420, max: 2499 })
})
it('2. Synergy multiplier matches +5% per hard point with 1,000 randomized combination fuzzing', async () => {
const registry = await getSharedDataRegistry()
const skillRec = registry.getSkillById(59)!
// Test zero synergies
expect(calculateBlizzardSynergyMultiplier({})).toBe(1.0)
expect(calculateBlizzardDamage(20, {})).toEqual({ min: 570, max: 619 })
// Test individual synergies
expect(calculateBlizzardSynergyMultiplier({ iceBolt: 1 })).toBeCloseTo(1.05, 5)
expect(calculateBlizzardSynergyMultiplier({ iceBlast: 1 })).toBeCloseTo(1.05, 5)
expect(calculateBlizzardSynergyMultiplier({ glacialSpike: 1 })).toBeCloseTo(1.05, 5)
// Test 20 in single skill: +100% (2.0x)
expect(calculateBlizzardSynergyMultiplier({ iceBolt: 20 })).toBe(2.0)
expect(calculateBlizzardDamage(20, { iceBolt: 20 })).toEqual({ min: 1140, max: 1238 })
// Test 20 in two skills: +200% (3.0x)
expect(calculateBlizzardSynergyMultiplier({ iceBolt: 20, iceBlast: 20 })).toBe(3.0)
expect(calculateBlizzardDamage(20, { iceBolt: 20, iceBlast: 20 })).toEqual({ min: 1710, max: 1857 })
// Test max legal synergies (60 points total): +300% (4.0x)
expect(
calculateBlizzardSynergyMultiplier({ iceBolt: 20, iceBlast: 20, glacialSpike: 20 }),
).toBe(4.0)
expect(
calculateBlizzardDamage(20, { iceBolt: 20, iceBlast: 20, glacialSpike: 20 }),
).toEqual({ min: 2280, max: 2476 })
// Fuzz test 1,000 random synergy triples (p1, p2, p3) in range [0..20]
for (let i = 0; i < 1000; i++) {
const p1 = Math.floor(Math.random() * 21)
const p2 = Math.floor(Math.random() * 21)
const p3 = Math.floor(Math.random() * 21)
const synObj = { iceBolt: p1, iceBlast: p2, glacialSpike: p3 }
const expectedSyn = 1.0 + (p1 + p2 + p3) * 0.05
const actualSyn = calculateBlizzardSynergyMultiplier(synObj)
expect(actualSyn).toBeCloseTo(expectedSyn, 5)
const slvl = 1 + Math.floor(Math.random() * 40)
const expectedDmg = oracle113cBlizzardDamage(slvl, synObj)
const actualDmg = calculateBlizzardDamage(slvl, synObj)
expect(actualDmg.min).toBe(expectedDmg.min)
expect(actualDmg.max).toBe(expectedDmg.max)
}
// Verify 1.13c hard point invariant: soft skills (+skills, charged skills) produce ZERO synergy
const statsSoft = new UnitStatList()
statsSoft.setBaseSkillLevel(59, 20)
statsSoft.addStat('item_allskills', 20) // +20 all skills
statsSoft.setChargedSkillLevel(39, 33) // 33 charges of Ice Bolt (Marrowwalk bug test)
statsSoft.setChargedSkillLevel(45, 33) // 33 charges of Ice Blast
statsSoft.setChargedSkillLevel(55, 33) // 33 charges of Glacial Spike
const evalSoft = skillModule.evaluate!({
registry,
skill: skillRec,
slvl: 40,
blvl: 20,
statList: statsSoft,
})
expect(evalSoft.synergyBonusPct).toBe(0)
})
it('3. Authoritative 64-entry circle table values match D2Game.dll 0x6FD1C960 & 0x6FD1CA60 with 0 errors', () => {
// Read D2Game.dll directly from 1.13c installation on disk
const dllPath = '/usr/local/google/home/taodao/d2-data/D2Game.dll'
expect(fs.existsSync(dllPath), `Missing D2Game.dll at ${dllPath}`).toBe(true)
const dllBuffer = fs.readFileSync(dllPath)
// Offsets in D2Game.dll file:
// ImageBase = 0x6FC20000, .rdata file offset = 0xF8000, VA = 0x6FD18000
// VA 0x6FD1C960 -> file offset 0xFC960
// VA 0x6FD1CA60 -> file offset 0xFCA60
const fileOffsetTableX = 0xFC960
const fileOffsetTableY = 0xFCA60
expect(BLIZZARD_CIRCLE_X.length).toBe(64)
expect(BLIZZARD_CIRCLE_Y.length).toBe(64)
expect(Object.isFrozen(BLIZZARD_CIRCLE_X)).toBe(true)
expect(Object.isFrozen(BLIZZARD_CIRCLE_Y)).toBe(true)
const dllCircleX: number[] = []
const dllCircleY: number[] = []
for (let i = 0; i < 64; i++) {
dllCircleX.push(dllBuffer.readInt32LE(fileOffsetTableX + i * 4))
dllCircleY.push(dllBuffer.readInt32LE(fileOffsetTableY + i * 4))
}
// Compare all 64 coordinates byte-for-byte against D2Game.dll
let mismatchCount = 0
const mismatches: string[] = []
for (let i = 0; i < 64; i++) {
const codeX = BLIZZARD_CIRCLE_X[i]
const codeY = BLIZZARD_CIRCLE_Y[i]
const binaryX = dllCircleX[i]
const binaryY = dllCircleY[i]
if (codeX !== binaryX || codeY !== binaryY) {
mismatchCount++
mismatches.push(
`Index ${i}: code=(${codeX}, ${codeY}) vs dll=(${binaryX}, ${binaryY})`,
)
}
}
expect(mismatchCount).toBe(0)
expect(mismatches).toEqual([])
})
it('4. Exactly 25 shards dropped over 100 ticks (cadence 4, step 13 mod 64) with zero clustering', () => {
let center: Projectile = {
skillId: '59',
x: 500,
y: 500,
vx: 0,
vy: 0,
damage: 250,
ttl: 100, // 100 ticks = 4.0s
fromPlayer: true,
missileType: 'blizzardcenter',
subMissileIdx: 0,
}
const emittedShards: Projectile[] = []
const angleIndicesUsed: number[] = []
const dummyTerrain = { overlap: () => 0 }
for (let tick = 1; tick <= 100; tick++) {
const outcome = tickProjectiles([center], [], dummyTerrain)
if (tick % 4 === 0) {
expect(outcome.spawnedProjectiles).toBeDefined()
expect(outcome.spawnedProjectiles!.length).toBe(1)
const shard = outcome.spawnedProjectiles![0]!
expect(['blizzard1', 'blizzard2', 'blizzard3', 'blizzard4']).toContain(shard.missileType)
expect(shard.ttl).toBe(9)
expect(shard.altitude).toBe(120)
expect(shard.damage).toBe(250)
expect(shard.statusEffect).toBe('chill')
expect(shard.statusDuration).toBe(100)
emittedShards.push(shard)
} else {
expect(outcome.spawnedProjectiles?.length ?? 0).toBe(0)
}
center = outcome.alive.find(p => p.missileType === 'blizzardcenter')!
if (tick < 100) {
expect(center).toBeDefined()
expect(center.ttl).toBe(100 - tick)
}
}
// 1. Total count is strictly 25 shards
expect(emittedShards.length).toBe(25)
// 2. Center expires at tick 101
const finalOutcome = tickProjectiles([center], [], dummyTerrain)
expect(finalOutcome.expired).toBe(1)
expect(finalOutcome.alive.length).toBe(0)
// 3. Step 13 mod 64 sequence: gcd(13, 64) = 1, ensuring zero duplicate indices in 25 drops
for (let k = 0; k < 25; k++) {
const expectedIndex = (k * 13) % 64
angleIndicesUsed.push(expectedIndex)
}
const uniqueIndices = new Set(angleIndicesUsed)
expect(uniqueIndices.size).toBe(25) // All 25 drops use distinct angle indices!
})
it('5. 2:1 isometric aspect ratio scaling on ground plane (dy = tblY * scale * 0.5)', () => {
expect(ISO_GROUND_ASPECT_RATIO).toBe(0.5)
const radiusSubtiles = 7
const subtileToPx = SUBTILE_TO_PX // 16
const scale = (radiusSubtiles * subtileToPx) / 30 // 112 / 30 = 3.7333333333333334
// Test all 64 drop offsets
for (let i = 0; i < 64; i++) {
const offset = getBlizzardDropOffset(i, radiusSubtiles, subtileToPx)
const rawX = BLIZZARD_CIRCLE_X[i]!
const rawY = BLIZZARD_CIRCLE_Y[i]!
const expectedDx = rawX * scale
const expectedDy = rawY * scale * 0.5
expect(offset.dx).toBeCloseTo(expectedDx, 10)
expect(offset.dy).toBeCloseTo(expectedDy, 10)
// When rawY is non-zero, aspect ratio dy / (rawY * scale) must be strictly 0.5
if (rawY !== 0) {
const uncompressedY = rawY * scale
expect(offset.dy / uncompressedY).toBeCloseTo(0.5, 10)
}
}
// Cardinal coordinate checks:
// East: index 16 (X=30, Y=0) -> dx = 112, dy = 0
const east = getBlizzardDropOffset(16, 7, 16)
expect(east.dx).toBe(112)
expect(east.dy).toBe(0)
// South: index 0 (X=0, Y=30) -> dx = 0, dy = 56
const south = getBlizzardDropOffset(0, 7, 16)
expect(south.dx).toBe(0)
expect(south.dy).toBe(56)
// West: index 48 (X=-30, Y=0) -> dx = -112, dy = 0
const west = getBlizzardDropOffset(48, 7, 16)
expect(west.dx).toBe(-112)
expect(west.dy).toBe(0)
// North: index 32 (X=0, Y=-30) -> dx = 0, dy = -56
const north = getBlizzardDropOffset(32, 7, 16)
expect(north.dx).toBe(0)
expect(north.dy).toBe(-56)
// Bounding ellipse width and height:
// Full width = 2 * 112 = 224 px (14 subtiles = 7 subtiles radius)
// Full height = 2 * 56 = 112 px (7 subtiles = 3.5 subtiles vertical radius)
// Ratio height / width = 112 / 224 = 0.5 (2:1 isometric ellipse)
expect(56 / 112).toBe(0.5)
})
it('6. Falling shard altitude descends vertically from 120 px to 0 over 9 ticks and detonates on impact', () => {
let shard: Projectile = {
skillId: '59',
x: 200,
y: 200,
vx: 0,
vy: 0,
altitude: 120,
damage: 180,
ttl: 9,
fromPlayer: true,
missileType: 'blizzard1',
}
const dummyTerrain = { overlap: () => 0 }
for (let t = 1; t <= 9; t++) {
const outcome = tickProjectiles([shard], [], dummyTerrain)
shard = outcome.alive.find(p => p.missileType === 'blizzard1')!
if (t < 9) {
expect(shard).toBeDefined()
expect(shard.ttl).toBe(9 - t)
const expectedAlt = 120 - t * (120 / 9)
expect(shard.altitude).toBeCloseTo(expectedAlt, 0.1)
} else {
expect(shard.ttl).toBe(0)
}
}
// Ttl = 0 expires and detonates ground explosion
const detonation = tickProjectiles([shard], [], dummyTerrain)
expect(detonation.expired).toBe(1)
expect(detonation.spawnedProjectiles!.length).toBe(1)
const exp = detonation.spawnedProjectiles![0]!
expect(exp.missileType).toBe('blizzardexplode1')
expect(exp.damage).toBe(180)
expect(exp.ttl).toBe(6)
expect(exp.statusEffect).toBe('chill')
expect(exp.statusDuration).toBe(100)
})
it('7. NextDelay = 0 sweet-spot burst collision: overlapping shards deal full stacked damage', () => {
const shardCount = 5
const shards: Projectile[] = []
for (let i = 0; i < shardCount; i++) {
shards.push({
skillId: '59',
x: 300 + (i % 2),
y: 300,
vx: 0,
vy: 0,
altitude: 10,
damage: 150,
ttl: 2,
fromPlayer: true,
missileType: `blizzard${(i % 4) + 1}`,
})
}
const bossMonster = [{ index: 42, x: 300, y: 300, radius: 25, alive: true }]
const outcome = tickProjectiles(shards, bossMonster, { overlap: () => 0 })
// All 5 shards must hit the target without being blocked by NextDelay immunity frames
expect(outcome.hits.length).toBe(shardCount)
for (const hit of outcome.hits) {
expect(hit.targetIndex).toBe(42)
expect(hit.damage).toBe(150)
expect(hit.statusEffect).toBe('chill')
expect(hit.statusDuration).toBe(100)
}
// Total damage dealt across the single frame is exactly 5 * 150 = 750
const totalDmg = outcome.hits.reduce((sum, h) => sum + h.damage, 0)
expect(totalDmg).toBe(750)
// All 5 shards must spawn explosion missiles
expect(outcome.spawnedProjectiles!.length).toBe(shardCount)
})
it('8. High-density performance stress test: 100 concurrent Blizzard centers execute well under 50% budget', () => {
// 100 concurrent Blizzard centers active simultaneously
const centers: Projectile[] = []
for (let c = 0; c < 100; c++) {
centers.push({
skillId: '59',
x: 100 + c * 5,
y: 100 + c * 5,
vx: 0,
vy: 0,
damage: 300,
ttl: 100,
fromPlayer: true,
missileType: 'blizzardcenter',
subMissileIdx: c % 64,
})
}
let activeProjectiles: Projectile[] = [...centers]
let totalShardsSpawned = 0
let totalExplosionsSpawned = 0
const dummyTerrain = { overlap: () => 0 }
const startTime = performance.now()
// Simulate 100 ticks (2,500 falling shards + 4,400 ground explosions spawned + simulated)
for (let tick = 1; tick <= 100; tick++) {
const outcome = tickProjectiles(activeProjectiles, [], dummyTerrain)
activeProjectiles = [...outcome.alive]
if (outcome.spawnedProjectiles) {
for (const p of outcome.spawnedProjectiles) {
if (['blizzard1', 'blizzard2', 'blizzard3', 'blizzard4'].includes(p.missileType ?? '')) {
totalShardsSpawned++
} else if (p.missileType?.startsWith('blizzardexplode')) {
totalExplosionsSpawned++
}
}
activeProjectiles.push(...outcome.spawnedProjectiles)
}
}
const elapsedMs = performance.now() - startTime
// 100 centers * 25 shards = 2,500 shards spawned
expect(totalShardsSpawned).toBe(2500)
expect(totalExplosionsSpawned).toBe(4400)
// 100 frames simulation of 100 centers + 2,500 shards + 4,400 explosions should execute in < 500ms
expect(elapsedMs).toBeLessThan(500)
})
})

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/**
* Diablo II: Lord of Destruction v1.13c — Skill #059: Blizzard
* Empirical Stress Testing & Adversarial Verification Suite
*
* Requirements (User Request & Solution Stress Testing Playbook):
* 1. Altitude descent: 120 px to 0 px over 9 ticks (linear 120/9 px/tick, clamped at 0).
* 2. Ground impact explosion at tick 9 vs immediate explosion on monster collision at tick t < 9.
* 3. NextDelay = 0: multiple shards hitting the same target deal damage without cooldown immunity
* (both simultaneous hits and consecutive tick hits, with differential oracle contrast).
* 4. Wall collisions: shards hitting walls explode and terminate cleanly without memory leak or hanging.
* 5. 100,000 tick continuous stress simulation: verifying stability, bounded active missile count,
* zero NaNs, zero crashes, and zero memory leaks over 2,222+ Blizzard casts.
*/
import { describe, expect, it } from 'vitest'
import {
tickProjectiles,
ISO_GROUND_ASPECT_RATIO,
calculateBlizzardDamage,
calculateBlizzardSynergyMultiplier,
CANONICAL_113C_MISSILES,
type Projectile,
type ProjectileTarget,
} from '../src/game/skills.ts'
import {
BLIZZARD_CIRCLE_X,
BLIZZARD_CIRCLE_Y,
getBlizzardDropOffset,
} from '../src/game/engine/blizzard-table.ts'
import { MissileEngine } from '../src/game/engine/missile-engine.ts'
import { getSharedDataRegistry } from '../src/game/engine/data-registry.ts'
import { UnitStatList } from '../src/game/engine/stat-list.ts'
import { StateBus } from '../src/game/engine/state-bus.ts'
import type { CombatUnitContext } from '../src/game/engine/combat-pipeline.ts'
import { drawMissileProjectile } from '../src/scene/act-scene.ts'
describe('[Skill #059] Blizzard — Empirical Stress & Physics Challenger Suite', () => {
const openTerrain = { overlap: () => 0 }
const wallTerrain = { overlap: () => 1 }
// =========================================================================
// Dimension 1: Shard Altitude Descent Physics (120 px -> 0 px over 9 ticks)
// =========================================================================
describe('Dimension 1: Shard Altitude Descent Physics (120 px -> 0 px over 9 ticks)', () => {
const shardVariants = ['blizzard1', 'blizzard2', 'blizzard3', 'blizzard4'] as const
for (const variant of shardVariants) {
it(`verifies altitude descent of ${variant} tick-by-tick from 120 px to 0 px over exactly 9 ticks`, () => {
let shard: Projectile = {
skillId: '59',
x: 200,
y: 200,
vx: 0,
vy: 0,
altitude: 120,
damage: 100,
ttl: 9,
fromPlayer: true,
missileType: variant,
}
const descentRate = 120 / 9 // 13.333333333333334 px/tick
for (let tick = 1; tick <= 9; tick++) {
const outcome = tickProjectiles([shard], [], openTerrain)
shard = outcome.alive.find(p => p.missileType === variant)!
expect(shard).toBeDefined()
expect(shard.ttl).toBe(9 - tick)
const expectedAltitude = Math.max(0, 120 - tick * descentRate)
expect(shard.altitude).toBeCloseTo(expectedAltitude, 0.001)
if (tick === 9) {
// At tick 9, altitude reaches ground level (within IEEE-754 float precision ~1e-14)
expect(shard.altitude).toBeCloseTo(0, 5)
expect(shard.ttl).toBe(0)
} else {
expect(shard.altitude).toBeGreaterThan(0)
}
}
})
}
it('verifies altitude never drops below zero and remains non-negative even if ticked past 0', () => {
let shard: Projectile = {
skillId: '59',
x: 100,
y: 100,
vx: 0,
vy: 0,
altitude: 5, // very close to ground
damage: 100,
ttl: 5,
fromPlayer: true,
missileType: 'blizzard1',
}
// Tick once: 5 - (120/9) < 0, must be clamped to exactly 0
const outcome = tickProjectiles([shard], [], openTerrain)
const ticked = outcome.alive.find(p => p.missileType === 'blizzard1')!
expect(ticked.altitude).toBe(0)
expect(Number.isNaN(ticked.altitude!)).toBe(false)
expect(Number.isFinite(ticked.altitude!)).toBe(true)
})
it('verifies visual screen projection offset: drawY = WorldY - altitude', () => {
const drawnSprites: { x: number; y: number }[] = []
const mockRenderer = {
draw: (_frame: any, x: number, y: number) => {
drawnSprites.push({ x, y })
},
drawSolid: (_x: number, _y: number) => {},
} as any
const mockArt = {
meta: { name: 'blizzard1', directions: 1, framesPerDirection: 6, animSpeed: 16 },
frames: { 0: [{ anchorX: 0, anchorY: 0, width: 32, height: 64 }] },
handle: 'atlas',
} as any
// Shard at World (200, 200), altitude 120 -> screen Y should be 200 - 120 = 80
const shardHigh: Projectile = {
skillId: '59',
x: 200,
y: 200,
vx: 0,
vy: 0,
altitude: 120,
damage: 100,
ttl: 9,
fromPlayer: true,
missileType: 'blizzard1',
}
drawMissileProjectile(mockRenderer, shardHigh, mockArt)
expect(drawnSprites.length).toBe(1)
expect(drawnSprites[0]!.y).toBe(200 - 120) // 80 px
// Shard at World (200, 200), altitude 0 (ground level) -> screen Y should be 200
drawnSprites.length = 0
const shardGround: Projectile = {
...shardHigh,
altitude: 0,
ttl: 0,
}
drawMissileProjectile(mockRenderer, shardGround, mockArt)
expect(drawnSprites.length).toBe(1)
expect(drawnSprites[0]!.y).toBe(200) // 200 px
})
it('verifies all 25 shards spawned from blizzardcenter initialize with altitude 120 px', () => {
const center: Projectile = {
skillId: '59',
x: 300,
y: 300,
vx: 0,
vy: 0,
damage: 200,
ttl: 100,
fromPlayer: true,
missileType: 'blizzardcenter',
subMissileIdx: 0,
}
let current: Projectile[] = [center]
const spawnedShards: Projectile[] = []
for (let t = 1; t <= 100; t++) {
const res = tickProjectiles(current, [], openTerrain)
current = res.alive as Projectile[]
if (res.spawnedProjectiles && res.spawnedProjectiles.length > 0) {
for (const p of res.spawnedProjectiles) {
if (p.missileType?.startsWith('blizzard') && !p.missileType.includes('explode')) {
spawnedShards.push(p)
}
}
}
}
expect(spawnedShards.length).toBe(25)
for (const shard of spawnedShards) {
expect(shard.altitude).toBe(120)
expect(shard.ttl).toBe(9)
expect(shard.damage).toBe(200)
expect(shard.statusEffect).toBe('chill')
expect(shard.statusDuration).toBe(100)
}
})
})
// =========================================================================
// Dimension 2: Ground Impact Explosion (t = 9) vs Immediate Collision (t < 9)
// =========================================================================
describe('Dimension 2: Ground Impact Explosion (t = 9) vs Immediate Collision (t < 9)', () => {
it('Case A (Ground Impact): shard reaches altitude 0 at tick 9 and detonates ground impact explosion on expiry', () => {
let shard: Projectile = {
skillId: '59',
x: 250,
y: 250,
vx: 0,
vy: 0,
altitude: 120,
damage: 150,
ttl: 9,
fromPlayer: true,
missileType: 'blizzard1',
}
// Over ticks 1..9, no monster is present
for (let tick = 1; tick <= 9; tick++) {
const res = tickProjectiles([shard], [], openTerrain)
expect(res.hits.length).toBe(0)
expect(res.expired).toBe(0)
shard = res.alive.find(p => p.missileType === 'blizzard1')!
expect(shard).toBeDefined()
}
// At tick 9, shard is at ground level (altitude ~0 within IEEE-754 precision, ttl 0)
expect(shard.altitude).toBeCloseTo(0, 5)
expect(shard.ttl).toBe(0)
// On next tick (tick 10), shard expires and detonates ground explosion
const detonateRes = tickProjectiles([shard], [], openTerrain)
expect(detonateRes.expired).toBe(1)
expect(detonateRes.alive.some(p => p.missileType === 'blizzard1')).toBe(false)
expect(detonateRes.spawnedProjectiles).toBeDefined()
expect(detonateRes.spawnedProjectiles!.length).toBe(1)
const exp = detonateRes.spawnedProjectiles![0]!
expect(exp.missileType).toBe('blizzardexplode1')
expect(exp.ttl).toBe(6) // 1.13c Range = 6
expect(exp.statusEffect).toBe('chill')
expect(exp.statusDuration).toBe(100) // 1.13c ElemLen = 100
expect(exp.x).toBe(250)
expect(exp.y).toBe(250)
})
it('Case B (Immediate Monster Collision at t < 9): parametric sweep across all ticks t in [1..8]', () => {
// Test collision at every possible mid-air tick: t = 1, 2, 3, 4, 5, 6, 7, 8
for (let collisionTick = 1; collisionTick <= 8; collisionTick++) {
let shard: Projectile = {
skillId: '59',
x: 200,
y: 200,
vx: 0,
vy: 0,
altitude: 120,
damage: 120,
ttl: 9,
fromPlayer: true,
missileType: 'blizzard2',
}
// Ticks before collision: target is distant/inactive
const distantTarget: ProjectileTarget = { index: 1, x: 9999, y: 9999, radius: 20, alive: true }
for (let t = 1; t < collisionTick; t++) {
const res = tickProjectiles([shard], [distantTarget], openTerrain)
expect(res.hits.length).toBe(0)
shard = res.alive.find(p => p.missileType === 'blizzard2')!
expect(shard).toBeDefined()
expect(shard.altitude).toBeGreaterThan(0)
}
// At collisionTick, place target directly under the falling shard
const closeTarget: ProjectileTarget = { index: 1, x: 200, y: 200, radius: 20, alive: true }
const hitRes = tickProjectiles([shard], [closeTarget], openTerrain)
// 1. Hit must register IMMEDIATELY at collisionTick
expect(hitRes.hits.length).toBe(1)
const hit = hitRes.hits[0]!
expect(hit.targetIndex).toBe(1)
expect(hit.damage).toBe(120)
expect(hit.statusEffect).toBe('chill')
expect(hit.statusDuration).toBe(100)
// 2. Shard must be destroyed IMMEDIATELY on collision (not survive to tick 9)
expect(hitRes.alive.some(p => p.missileType === 'blizzard2')).toBe(false)
// 3. Impact explosion must be spawned IMMEDIATELY at collisionTick
expect(hitRes.spawnedProjectiles).toBeDefined()
expect(hitRes.spawnedProjectiles!.length).toBe(1)
const exp = hitRes.spawnedProjectiles![0]!
expect(exp.missileType).toBe('blizzardexplode2')
expect(exp.ttl).toBe(6)
expect(exp.x).toBe(200)
expect(exp.y).toBe(200)
}
})
it('empirical finding: blizzardexplode spawned on monster hit carries damage: 0 to prevent double damage', () => {
const shard: Projectile = {
skillId: '59',
x: 200,
y: 200,
vx: 0,
vy: 0,
altitude: 60,
damage: 150,
ttl: 4,
fromPlayer: true,
missileType: 'blizzard3',
}
const target: ProjectileTarget = { index: 1, x: 200, y: 200, radius: 20, alive: true }
const res = tickProjectiles([shard], [target], openTerrain)
expect(res.hits.length).toBe(1)
expect(res.hits[0]!.damage).toBe(150) // shard dealt full damage
// Spawned explosion must have damage = 0
const exp = res.spawnedProjectiles![0]!
expect(exp.missileType).toBe('blizzardexplode3')
expect(exp.damage).toBe(0)
})
})
// =========================================================================
// Dimension 3: NextDelay = 0 Invariant (No Cooldown Immunity / Sweet-Spot Burst)
// =========================================================================
describe('Dimension 3: NextDelay = 0 Invariant (No Cooldown Immunity / Sweet-Spot Burst)', () => {
it('verifies simultaneous hits: 5 overlapping shards hitting the same target on the same tick all deal full damage', () => {
const shards: Projectile[] = [1, 2, 3, 4, 5].map(i => ({
skillId: '59',
x: 200,
y: 200,
vx: 0,
vy: 0,
damage: 100,
ttl: 5,
fromPlayer: true,
missileType: `blizzard${((i - 1) % 4) + 1}`,
}))
const target: ProjectileTarget = { index: 99, x: 200, y: 200, radius: 20, alive: true }
const res = tickProjectiles(shards, [target], openTerrain)
// All 5 shards must hit the target without being blocked by immunity frames
expect(res.hits.length).toBe(5)
let totalDamage = 0
for (const hit of res.hits) {
expect(hit.targetIndex).toBe(99)
expect(hit.damage).toBe(100)
expect(hit.statusEffect).toBe('chill')
totalDamage += hit.damage
}
expect(totalDamage).toBe(500)
})
it('verifies consecutive tick hits: shards hitting on ticks t, t+1, t+2, t+3 all deal damage without NextDelay lockout', () => {
const target: ProjectileTarget = { index: 42, x: 200, y: 200, radius: 20, alive: true }
let totalDamage = 0
const recordedHits: number[] = []
// On 4 consecutive ticks, a new shard hits the target
for (let t = 1; t <= 4; t++) {
const shard: Projectile = {
skillId: '59',
x: 200,
y: 200,
vx: 0,
vy: 0,
damage: 150,
ttl: 5,
fromPlayer: true,
missileType: 'blizzard1',
}
const res = tickProjectiles([shard], [target], openTerrain)
expect(res.hits.length).toBe(1)
expect(res.hits[0]!.damage).toBe(150)
recordedHits.push(res.hits[0]!.damage)
totalDamage += res.hits[0]!.damage
}
expect(recordedHits.length).toBe(4)
expect(totalDamage).toBe(600) // 150 * 4
})
it('differential contrast oracle: compares NextDelay = 0 (Blizzard) against NextDelay = 4 (Nova / Chain Lightning)', async () => {
const registry = await getSharedDataRegistry()
const engine = new MissileEngine(registry)
const ownerStatList = new UnitStatList(registry, {})
const owner: CombatUnitContext = {
id: 'sorc',
name: 'Sorceress',
isUndead: false,
isDemon: false,
statList: ownerStatList,
stateBus: new StateBus(ownerStatList, registry),
}
const dummyStatList = new UnitStatList(registry, { maxhp: 50000 * 256, hitpoints: 50000 * 256 })
const dummy: CombatUnitContext = {
id: 'boss-target',
name: 'BossDummy',
isUndead: false,
isDemon: true,
statList: dummyStatList,
stateBus: new StateBus(dummyStatList, registry),
}
const targetPositions = new Map([['boss-target', { x: 100, y: 100 }]])
// 1. Contrast Test: Nova with nextDelay = 4
// Spawn 2 Nova missiles hitting on tick 1 and tick 2
engine.spawnMissile({
missileNameOrId: 'nova',
sourceSkillId: 48,
slvl: 20,
owner,
startX: 100,
startY: 100,
targetX: 100,
targetY: 100,
dmgPacket: { skillId: 48, attackKind: 'spell', elemType: 'ltng', elemMin256: 100 * 256, elemMax256: 100 * 256, autoHit: true },
})
engine.spawnMissile({
missileNameOrId: 'nova',
sourceSkillId: 48,
slvl: 20,
owner,
startX: 100,
startY: 100,
targetX: 100,
targetY: 100,
dmgPacket: { skillId: 48, attackKind: 'spell', elemType: 'ltng', elemMin256: 100 * 256, elemMax256: 100 * 256, autoHit: true },
})
const novaRes = engine.tick(1, [dummy], targetPositions)
// Under NextDelay = 4, first Nova hits, second Nova is locked out on the same tick!
expect(novaRes.hits.length).toBe(1)
expect(engine.isTargetInNextDelay('boss-target', 1)).toBe(true)
// 2. Blizzard Test: NextDelay = 0
// In contrast, Blizzard has NextDelay = 0 (empty in Missiles.txt)
const b1 = registry.getMissileByName('blizzard1')!
expect(b1.nextHit).toBe(false)
expect(b1.nextDelay).toBe(0)
})
})
// =========================================================================
// Dimension 4: Wall Collisions & Resource Cleanup
// =========================================================================
describe('Dimension 4: Wall Collisions & Resource Cleanup', () => {
it('verifies descending shard hitting a wall detonates immediately and spawns impact explosion', () => {
const shard: Projectile = {
skillId: '59',
x: 150,
y: 150,
vx: 0,
vy: 0,
altitude: 70,
damage: 100,
ttl: 6,
fromPlayer: true,
missileType: 'blizzard4',
}
const res = tickProjectiles([shard], [], wallTerrain)
// Shard halted and destroyed by wall
expect(res.wallHits).toBe(1)
expect(res.alive.some(p => p.missileType === 'blizzard4')).toBe(false)
// Wall hit event recorded
expect(res.wallHitEvents).toBeDefined()
expect(res.wallHitEvents!.length).toBe(1)
expect(res.wallHitEvents![0]!.missileType).toBe('blizzard4')
// Explosion spawned
expect(res.spawnedProjectiles).toBeDefined()
expect(res.spawnedProjectiles!.length).toBe(1)
const exp = res.spawnedProjectiles![0]!
expect(exp.missileType).toBe('blizzardexplode1')
expect(exp.ttl).toBe(6)
})
it('verifies 1,000 shards fired into solid walls terminate cleanly without memory leak or hanging', () => {
const shards: Projectile[] = []
for (let i = 0; i < 1000; i++) {
shards.push({
skillId: '59',
x: 100 + (i % 50),
y: 100 + Math.floor(i / 50),
vx: 0,
vy: 0,
altitude: 120,
damage: 50,
ttl: 9,
fromPlayer: true,
missileType: 'blizzard1',
})
}
// Tick 1: all 1,000 shards strike the wall immediately
const tick1 = tickProjectiles(shards, [], wallTerrain)
expect(tick1.wallHits).toBe(1000)
// None of the original shards should survive
expect(tick1.alive.every(p => p.missileType === 'blizzardexplode1')).toBe(true)
expect(tick1.alive.length).toBe(1000) // 1,000 spawned explosions
// Now tick the 1,000 explosions over open terrain until they all expire (range = 6)
let active = tick1.alive as Projectile[]
for (let t = 1; t <= 6; t++) {
const step = tickProjectiles(active, [], openTerrain)
active = step.alive as Projectile[]
}
// After 6 ticks, the explosions reached ttl = 0
// Next tick (tick 7): all 1,000 explosions expire
const finalStep = tickProjectiles(active, [], openTerrain)
expect(finalStep.expired).toBe(1000)
expect(finalStep.alive.length).toBe(0) // Clean zero active missiles!
})
})
// =========================================================================
// Dimension 5: 100,000-Tick Long-Run Stress Simulation (Crashes, NaNs, Leaks)
// =========================================================================
describe('Dimension 5: 100,000-Tick Long-Run Stress Simulation (Crashes, NaNs, Leaks)', () => {
it('runs 100,000 ticks of continuous Blizzard casting without crashes, NaNs, or memory leaks', () => {
const simStartMs = Date.now()
const heapBefore = process.memoryUsage().heapUsed
let activeProjectiles: Projectile[] = []
let totalCasts = 0
let totalHits = 0
let totalWallHits = 0
let totalExpired = 0
let peakActiveCount = 0
// Dynamic targets moving in combat arena
const targets: ProjectileTarget[] = [
{ index: 0, x: 200, y: 200, radius: 25, alive: true },
{ index: 1, x: 215, y: 210, radius: 20, alive: true },
{ index: 2, x: 190, y: 220, radius: 20, alive: true },
{ index: 3, x: 205, y: 185, radius: 20, alive: true },
{ index: 4, x: 300, y: 300, radius: 25, alive: true },
]
// Semi-solid map terrain with boundary walls
const hybridTerrain = {
overlap: (x: number, y: number) => (x > 380 || x < 20 || y > 380 || y < 20 ? 1 : 0),
}
// 100,000 ticks = 4,000 seconds = 66.6 minutes of non-stop game simulation
for (let tick = 0; tick < 100000; tick++) {
// Cast Blizzard on cooldown (every 45 ticks = 1.80s cast delay)
if (tick % 45 === 0) {
totalCasts++
// Settle Blizzard center with slight spatial variation across casts
const cx = 200 + ((tick / 45) % 5) * 10
const cy = 200 + ((tick / 45) % 7) * 8
activeProjectiles.push({
skillId: '59',
x: cx,
y: cy,
vx: 0,
vy: 0,
damage: 150,
ttl: 100,
fromPlayer: true,
missileType: 'blizzardcenter',
subMissileIdx: 0,
})
}
// Monsters oscillate positions slightly every 10 ticks
if (tick % 10 === 0) {
for (let m = 0; m < targets.length; m++) {
const angle = (tick * 0.05) + m
targets[m] = {
...targets[m]!,
x: 200 + Math.cos(angle) * 30,
y: 200 + Math.sin(angle) * 15 * ISO_GROUND_ASPECT_RATIO,
}
}
}
// Advance simulation tick
const outcome = tickProjectiles(activeProjectiles, targets, hybridTerrain)
activeProjectiles = outcome.alive as Projectile[]
totalHits += outcome.hits.length
totalWallHits += outcome.wallHits
totalExpired += outcome.expired
if (activeProjectiles.length > peakActiveCount) {
peakActiveCount = activeProjectiles.length
}
// INVARIANT 1: Bounded missile count — no runaway memory leak!
// At any tick, at most 3 blizzard centers (ttl 100 / 45 = 2.22) can exist concurrently,
// each emitting shards with ttl 9. Peak active projectiles must never exceed 60.
if (activeProjectiles.length > 60) {
throw new Error(`Memory leak detected at tick ${tick}: active projectile count reached ${activeProjectiles.length}`)
}
// INVARIANT 2: Zero NaNs or non-finite numbers in any active missile
for (const p of activeProjectiles) {
if (!Number.isFinite(p.x) || !Number.isFinite(p.y)) {
throw new Error(`NaN detected in position at tick ${tick}: x=${p.x}, y=${p.y}`)
}
if (p.altitude !== undefined && (!Number.isFinite(p.altitude) || p.altitude < 0)) {
throw new Error(`Invalid altitude at tick ${tick}: altitude=${p.altitude}`)
}
if (!Number.isFinite(p.ttl) || p.ttl < 0) {
throw new Error(`Invalid ttl at tick ${tick}: ttl=${p.ttl}`)
}
}
}
const simElapsedMs = Date.now() - simStartMs
const heapAfter = process.memoryUsage().heapUsed
const heapDiffMb = (heapAfter - heapBefore) / (1024 * 1024)
// Assertions on 100,000 tick completion
expect(totalCasts).toBe(Math.floor(100000 / 45) + 1) // 2,223 Blizzard casts
expect(totalHits).toBeGreaterThan(1000) // thousands of hits registered
expect(peakActiveCount).toBeLessThanOrEqual(45) // comfortably bounded
expect(activeProjectiles.length).toBeLessThanOrEqual(25) // final active count is bounded
expect(heapDiffMb).toBeLessThan(15) // stable heap (< 15 MB variance)
console.log(`[100,000-Tick Blizzard Stress Sim Completed]`)
console.log(` Duration: ${simElapsedMs} ms (${(100000 / (simElapsedMs / 1000)).toFixed(0)} ticks/sec)`)
console.log(` Total Casts: ${totalCasts}`)
console.log(` Total Hits: ${totalHits}`)
console.log(` Total Wall Hits: ${totalWallHits}`)
console.log(` Total Expired Missiles: ${totalExpired}`)
console.log(` Peak Active Projectiles: ${peakActiveCount}`)
console.log(` Final Active Projectiles: ${activeProjectiles.length}`)
console.log(` Heap Diff: ${heapDiffMb.toFixed(2)} MB`)
})
})
})