{ "item": "a1", "batch": "e09-stack-confirm-a", "blocked": null, "code": "// SPDX-License-Identifier: MIT\npragma solidity ^0.8.24;\n\nimport {AMMStrategyBase} from \"./AMMStrategyBase.sol\";\nimport {TradeInfo} from \"./IAMMStrategy.sol\";\n\ncontract Strategy is AMMStrategyBase {\n uint256 constant ELAPSED_CAP = 8;\n uint256 constant SIGNAL_THRESHOLD = WAD / 650;\n uint256 constant DIR_DECAY = 750000000000000000;\n uint256 constant ACT_DECAY = 530000000000000000;\n uint256 constant SIZE_DECAY = 530000000000000000;\n uint256 constant TOX_DECAY = 910000000000000000;\n uint256 constant SIGMA_DECAY = 690000000000000000;\n uint256 constant LAMBDA_DECAY = 990000000000000000;\n uint256 constant SIZE_BLEND_DECAY = 828000000000000000;\n uint256 constant TOX_BLEND_DECAY = 51000000000000000;\n uint256 constant ACT_BLEND_DECAY = 985000000000000000;\n uint256 constant PHAT_ALPHA = 270000000000000000;\n uint256 constant PHAT_ALPHA_RETAIL = 60000000000000000;\n uint256 constant PHAT_ALPHA_SAME = 120000000000000000;\n uint256 constant REVERT_U = 0;\n uint256 constant DIR_IMPACT_MULT = 4;\n uint256 constant GATE_SIGMA_MULT = 7200000000000000000;\n uint256 constant MIN_GATE = 30000000000000000;\n uint256 constant TRADE_TOX_BOOST = 3500 * BPS;\n uint256 constant STALE_ATTRACT_FRAC = 1050000000000000000;\n uint256 constant RET_CAP = WAD / 35;\n uint256 constant TOX_CAP = WAD / 5;\n uint256 constant TRADE_RATIO_CAP = WAD / 5;\n uint256 constant LAMBDA_CAP = 1820000000000000000;\n uint256 constant STEP_COUNT_CAP = 64;\n uint256 constant BASE_FEE = 4 * BPS;\n uint256 constant SIGMA_COEF = 200000000000000000;\n uint256 constant LAMBDA_COEF = 12 * BPS;\n uint256 constant FLOW_SIZE_COEF = 4842 * BPS;\n uint256 constant TOX_COEF = 300 * BPS;\n uint256 constant TOX_QUAD_COEF = 15000 * BPS;\n uint256 constant ACT_COEF = 91843 * BPS;\n uint256 constant DIR_COEF = 20 * BPS;\n uint256 constant DIR_TOX_COEF = 100 * BPS;\n uint256 constant STALE_DIR_COEF = 6850 * BPS;\n uint256 constant SIGMA_TOX_COEF = 500 * BPS;\n uint256 constant TAIL_KNEE = 600 * BPS;\n uint256 constant TAIL_SLOPE_PROTECT = 930000000000000000;\n uint256 constant TAIL_SLOPE_ATTRACT = 850000000000000000;\n\n function afterInitialize(uint256 initialX, uint256 initialY) external override returns (uint256, uint256) {\n slots[0] = BASE_FEE; slots[1] = BASE_FEE; slots[3] = WAD; \n slots[5] = initialX > 0 ? wdiv(initialY, initialX) : 100 * WAD;\n slots[6] = 950000000000000; slots[7] = 800000000000000000; slots[8] = 2000000000000000;\n slots[13] = 902500000000; slots[14] = slots[5]; \n return (BASE_FEE, BASE_FEE);\n }\n\n function afterSwap(TradeInfo calldata trade) external override returns (uint256, uint256) {\n uint256 prevBidFee = slots[0]; uint256 prevAskFee = slots[1]; uint256 lastTs = uint64(slots[2]);\n uint256 dirState = slots[3]; uint256 actEma = slots[4]; uint256 pHat = slots[5];\n uint256 sigmaHat = slots[6]; uint256 lambdaHat = slots[7]; uint256 sizeHat = slots[8];\n uint256 toxEma = slots[9]; uint256 stepTradeCount = slots[10];\n\n uint256 sigmaForFast = sigmaHat;\n uint256 fastHat = slots[14];\n uint256 uncertainty = slots[13];\n uint256 silent = trade.timestamp > lastTs ? trade.timestamp - lastTs : 0;\n bool isNewStep = trade.timestamp > lastTs;\n if (isNewStep) {\n uint256 elapsedRaw = trade.timestamp - lastTs;\n uint256 elapsed = elapsedRaw > ELAPSED_CAP ? ELAPSED_CAP : elapsedRaw;\n dirState = _decayCentered(dirState, DIR_DECAY, elapsed);\n actEma = wmul(actEma, _powWad(ACT_DECAY, elapsed));\n sizeHat = wmul(sizeHat, _powWad(SIZE_DECAY, elapsed));\n toxEma = wmul(toxEma, _powWad(TOX_DECAY, elapsed));\n if (stepTradeCount > 0 && elapsedRaw > 0) {\n uint256 lambdaInst = (stepTradeCount * WAD) / elapsedRaw;\n if (lambdaInst > LAMBDA_CAP) lambdaInst = LAMBDA_CAP;\n lambdaHat = wmul(lambdaHat, LAMBDA_DECAY) + wmul(lambdaInst, WAD - LAMBDA_DECAY);\n }\n uncertainty += wmul(sigmaForFast, sigmaForFast) * elapsedRaw;\n if (uncertainty > 100000000000000) uncertainty = 100000000000000;\n stepTradeCount = 0;\n }\n\n bool firstInStep = stepTradeCount == 0;\n uint256 spot = trade.reserveX > 0 ? wdiv(trade.reserveY, trade.reserveX) : pHat;\n if (pHat == 0) pHat = spot;\n\n uint256 feeUsed = trade.isBuy ? prevBidFee : prevAskFee;\n uint256 gamma = feeUsed < WAD ? WAD - feeUsed : 0;\n uint256 pImplied;\n if (gamma == 0) { pImplied = spot; }\n else { pImplied = trade.isBuy ? wmul(spot, gamma) : wdiv(spot, gamma); }\n\n // S: infer a no-trade interval center from the last post-trade spot.\n uint256 silenceScale = WAD;\n if (firstInStep && silent > 1) {\n uint256 g = silent - 1;\n if (g > 1) g = 1;\n uint256 w = WAD - _powWad(800000000000000000, g);\n uint256 s = slots[2] >> 64;\n if (s == 0) s = pHat;\n uint256 c = (wmul(s, WAD - prevBidFee) + wdiv(s, WAD - prevAskFee)) / 2;\n if (c >= pHat) pHat += wmul(w, c - pHat);\n else pHat -= wmul(w, pHat - c);\n silenceScale = WAD - wmul(300000000000000000, w);\n }\n\n {\n uint256 ret = pHat > 0 ? wdiv(absDiff(pImplied, pHat), pHat) : 0;\n uint256 alpha = firstInStep ? PHAT_ALPHA : PHAT_ALPHA_RETAIL;\n uint256 prePhat = pHat;\n bool secondPrint = !firstInStep && stepTradeCount == 1;\n bool sameDir = false; bool oppDir = false;\n if (secondPrint) {\n bool up2 = pImplied >= pHat;\n uint256 d1 = slots[12];\n if (d1 != 0) { sameDir = (d1 == 1) == up2; oppDir = !sameDir; }\n if (sameDir) alpha = PHAT_ALPHA_SAME;\n }\n if (firstInStep) { slots[12] = pImplied >= pHat ? 1 : 2; }\n uint256 adaptiveGate = wmul(sigmaHat, GATE_SIGMA_MULT);\n if (adaptiveGate < MIN_GATE) adaptiveGate = MIN_GATE;\n alpha = wmul(alpha, silenceScale);\n adaptiveGate = wmul(adaptiveGate, silenceScale);\n if (ret <= adaptiveGate) { pHat = wmul(pHat, WAD - alpha) + wmul(pImplied, alpha); }\n if (oppDir && REVERT_U > 0) {\n uint256 pre = slots[11];\n if (pre > pHat) pHat = pHat + wmul(pre - pHat, REVERT_U);\n else pHat = pHat - wmul(pHat - pre, REVERT_U);\n }\n if (firstInStep) {\n if (ret > RET_CAP) ret = RET_CAP;\n sigmaHat = wmul(sigmaHat, SIGMA_DECAY) + wmul(ret, WAD - SIGMA_DECAY);\n }\n }\n\n // Interior retail routing equalizes fee-adjusted marginal prices.\n // Subsequent trades in a step cannot be the initial arbitrage trade.\n if (!firstInStep && feeUsed > 30 * BPS && gamma > 0) {\n uint256 normalSpot = trade.isBuy\n ? wdiv(wmul(spot, gamma), WAD - 30 * BPS)\n : wdiv(wmul(spot, WAD - 30 * BPS), gamma);\n pHat = wmul(pHat, 90 * WAD / 100) + wmul(normalSpot, 10 * WAD / 100);\n }\n\n {\n uint256 ret = fastHat > 0 ? wdiv(absDiff(pImplied, fastHat), fastHat) : 0;\n uint256 alpha;\n if (firstInStep) {\n uint256 processSigma = sigmaForFast;\n uint256 obsVar = uncertainty + wmul(processSigma, processSigma);\n uint256 probArb;\n uint256 z2 = wdiv(wmul(ret, ret), obsVar);\n uint256 density = _powWad(wdiv(WAD, WAD + z2 / 16), 8);\n uint256 sigmaObs = _isqrt(obsVar * WAD);\n uint256 odds = wmul(density, wdiv(6700000000000000, sigmaObs));\n bool arbFlag = ret <= wmul(sigmaForFast, 1220000000000000000);\n uint256 prior = arbFlag ? 650000000000000000 : 400000000000000000;\n uint256 tr = trade.reserveY > 0 ? wdiv(trade.amountY, trade.reserveY) : 0;\n if (tr > 3000000000000000) prior = wmul(prior, 6 * WAD / 10);\n if (silent > 1) prior = wmul(prior, 8 * WAD / 10);\n odds = wmul(odds, wdiv(prior, WAD - prior));\n probArb = wdiv(odds, WAD + odds);\n alpha = wmul(probArb, 600000000000000000) + wmul(WAD - probArb, 80000000000000000);\n slots[15] = pImplied >= fastHat ? 1 : 2;\n uncertainty = wmul(uncertainty, WAD - alpha);\n } else {\n if ((slots[15] == 1) == (pImplied >= fastHat)) alpha = PHAT_ALPHA_RETAIL;\n }\n uint256 gate = wmul(sigmaHat, GATE_SIGMA_MULT);\n if (gate < MIN_GATE) gate = MIN_GATE;\n if (ret <= gate) fastHat = wmul(fastHat, WAD - alpha) + wmul(pImplied, alpha);\n slots[13] = uncertainty;\n }\n\n if (!firstInStep && feeUsed > 30 * BPS && gamma > 0) {\n uint256 normalObs = trade.isBuy\n ? wdiv(wmul(spot, gamma), WAD - 30 * BPS)\n : wdiv(wmul(spot, WAD - 30 * BPS), gamma);\n if ((slots[15] == 1) == (normalObs >= fastHat)) {\n fastHat = wmul(fastHat, 9 * WAD / 10) + wmul(normalObs, WAD / 10);\n }\n }\n slots[14] = fastHat;\n uint256 tradeRatio = trade.reserveY > 0 ? wdiv(trade.amountY, trade.reserveY) : 0;\n if (tradeRatio > TRADE_RATIO_CAP) tradeRatio = TRADE_RATIO_CAP;\n\n if (tradeRatio > SIGNAL_THRESHOLD) {\n uint256 push = tradeRatio * DIR_IMPACT_MULT;\n if (push > WAD / 4) push = WAD / 4;\n if (trade.isBuy) {\n dirState = dirState + push;\n if (dirState > 2 * WAD) dirState = 2 * WAD;\n } else {\n dirState = dirState > push ? dirState - push : 0;\n }\n actEma = wmul(actEma, ACT_BLEND_DECAY) + wmul(tradeRatio, WAD - ACT_BLEND_DECAY);\n sizeHat = wmul(sizeHat, SIZE_BLEND_DECAY) + wmul(tradeRatio, WAD - SIZE_BLEND_DECAY);\n if (sizeHat > WAD) sizeHat = WAD;\n }\n\n uint256 tox = pHat > 0 ? wdiv(absDiff(spot, pHat), pHat) : 0;\n if (tox > TOX_CAP) tox = TOX_CAP;\n toxEma = wmul(toxEma, TOX_BLEND_DECAY) + wmul(tox, WAD - TOX_BLEND_DECAY);\n uint256 toxSignal = toxEma;\n\n stepTradeCount = stepTradeCount + 1;\n if (stepTradeCount > STEP_COUNT_CAP) stepTradeCount = STEP_COUNT_CAP;\n\n uint256 flowSize = wmul(lambdaHat, sizeHat);\n uint256 fBase = BASE_FEE + wmul(SIGMA_COEF, sigmaHat) + wmul(LAMBDA_COEF, lambdaHat) + wmul(FLOW_SIZE_COEF, flowSize);\n uint256 fMid = fBase + wmul(TOX_COEF, toxSignal) + wmul(TOX_QUAD_COEF, wmul(toxSignal, toxSignal)) + wmul(ACT_COEF, actEma);\n fMid = fMid + wmul(SIGMA_TOX_COEF, wmul(sigmaHat, toxSignal));\n\n uint256 dirDev; bool sellPressure;\n if (dirState >= WAD) { dirDev = dirState - WAD; sellPressure = true; }\n else { dirDev = WAD - dirState; sellPressure = false; }\n\n uint256 skew = wmul(DIR_COEF, dirDev) + wmul(DIR_TOX_COEF, wmul(dirDev, toxSignal));\n uint256 bidFee; uint256 askFee;\n if (sellPressure) {\n bidFee = fMid + skew;\n askFee = fMid > skew ? fMid - skew : 0;\n } else {\n askFee = fMid + skew;\n bidFee = fMid > skew ? fMid - skew : 0;\n }\n\n {\n uint256 staleHat = wmul(pHat, 700000000000000000) + wmul(fastHat, 300000000000000000);\n uint256 staleTox = wdiv(absDiff(spot, staleHat), staleHat);\n if (staleTox > TOX_CAP) staleTox = TOX_CAP;\n uint256 staleShift = wmul(STALE_DIR_COEF, staleTox);\n uint256 attractShift = wmul(staleShift, STALE_ATTRACT_FRAC);\n if (spot >= staleHat) {\n bidFee = bidFee + staleShift;\n askFee = askFee > attractShift ? askFee - attractShift : 0;\n } else {\n askFee = askFee + staleShift;\n bidFee = bidFee > attractShift ? bidFee - attractShift : 0;\n }\n }\n\n {\n bool tradeAligned = (trade.isBuy && spot >= pHat) || (!trade.isBuy && spot < pHat);\n if (tradeAligned) {\n uint256 tradeBoost = wmul(TRADE_TOX_BOOST, tradeRatio);\n if (!firstInStep && tradeBoost > 16 * BPS) tradeBoost = 16 * BPS;\n if (trade.isBuy) { bidFee = bidFee + tradeBoost; }\n else { askFee = askFee + tradeBoost; }\n }\n }\n\n if (sellPressure) {\n bidFee = clampFee(_compressTailWithSlope(bidFee, TAIL_SLOPE_PROTECT));\n askFee = clampFee(_compressTailWithSlope(askFee, TAIL_SLOPE_ATTRACT));\n } else {\n askFee = clampFee(_compressTailWithSlope(askFee, TAIL_SLOPE_PROTECT));\n bidFee = clampFee(_compressTailWithSlope(bidFee, TAIL_SLOPE_ATTRACT));\n }\n\n if (firstInStep) {\n if (askFee > bidFee && bidFee > 30 * BPS) bidFee = 30 * BPS;\n else if (bidFee > askFee && askFee > 30 * BPS) askFee = 30 * BPS;\n }\n\n if (bidFee > askFee && askFee > 36 * BPS) askFee = 36 * BPS;\n else if (askFee > bidFee && bidFee > 36 * BPS) bidFee = 36 * BPS;\n\n slots[0] = bidFee; slots[1] = askFee; slots[2] = (spot << 64) | trade.timestamp;\n slots[3] = dirState; slots[4] = actEma; slots[5] = pHat;\n slots[6] = sigmaHat; slots[7] = lambdaHat; slots[8] = sizeHat;\n slots[9] = toxEma; slots[10] = stepTradeCount;\n\n return (bidFee, askFee);\n }\n\n function _compressTailWithSlope(uint256 fee, uint256 slope) internal pure returns (uint256) {\n if (fee <= TAIL_KNEE) return fee;\n return TAIL_KNEE + wmul(fee - TAIL_KNEE, slope);\n }\n\n function _powWad(uint256 factor, uint256 exp) internal pure returns (uint256 result) {\n result = WAD;\n while (exp > 0) {\n if (exp & 1 == 1) result = wmul(result, factor);\n factor = wmul(factor, factor);\n exp >>= 1;\n }\n }\n\n function _decayCentered(uint256 centered, uint256 decayFactor, uint256 elapsed) internal pure returns (uint256) {\n uint256 mul = _powWad(decayFactor, elapsed);\n if (centered >= WAD) { return WAD + wmul(centered - WAD, mul); }\n uint256 below = wmul(WAD - centered, mul);\n return below < WAD ? WAD - below : 0;\n }\n\n // Floor square root: bit-length seed and seven Newton steps (all uint256).\n function _isqrt(uint256 x) internal pure returns (uint256 r) {\n if (x == 0) return 0;\n unchecked {\n uint256 y = x;\n r = 1;\n if (y >> 128 != 0) { y >>= 128; r <<= 64; }\n if (y >> 64 != 0) { y >>= 64; r <<= 32; }\n if (y >> 32 != 0) { y >>= 32; r <<= 16; }\n if (y >> 16 != 0) { y >>= 16; r <<= 8; }\n if (y >> 8 != 0) { y >>= 8; r <<= 4; }\n if (y >> 4 != 0) { y >>= 4; r <<= 2; }\n if (y >> 2 != 0) { r <<= 1; }\n r = (r + x / r) >> 1;\n r = (r + x / r) >> 1;\n r = (r + x / r) >> 1;\n r = (r + x / r) >> 1;\n r = (r + x / r) >> 1;\n r = (r + x / r) >> 1;\n r = (r + x / r) >> 1;\n uint256 t = x / r;\n return r < t ? r : t;\n }\n }\n\n function getName() external pure override returns (string memory) { return \"no_cubic\"; }\n}\n", "sha256": "2eaafc7960e520b8a7fd322ec8afaff8fa677c730228a961efb509cc30b25719", "base_sha256": "610c1905e7dd5559b84e40a3b2d6f8e0b53a7b0ac7574ae33b6c1770a28367cb", "v2_sha256": "28417e116f57f1029fdd1803832e852574902c1ae7253c05657f317db76da4ab", "harness_sha_a": "2eaafc7960e520b8a7fd322ec8afaff8fa677c730228a961efb509cc30b25719", "harness_sha_b": "28417e116f57f1029fdd1803832e852574902c1ae7253c05657f317db76da4ab", "simulator_commit": "6b6921f8d463314aa7c96234e1be25a25245f704", "command": "python scratch/harness.py scratch/STACK.sol 4380000 4382000 scratch/confirm.json --ref scratch/V2.sol", "runs": [ { "name": "confirm_STACK_vs_V2", "seeds": [ 4380000, 4382000 ], "seeds_note": "half-open, 2000 seeds, each once, 10000 steps, 250000 gas", "paired": { "n": 2000, "mean_diff": 0.043224891299790416, "se": 0.003943530703625499, "sd": 0.17636005449328385, "n_nonzero": 2000, "worst": [ { "seed": 4380438, "diff": -0.9886365963045591, "edge_a": 528.96533285053, "edge_b": 529.9539694468345 }, { "seed": 4380970, "diff": -0.9525905042601153, "edge_a": 534.2685609204252, "edge_b": 535.2211514246853 }, { "seed": 4381653, "diff": -0.8596011420399918, "edge_a": 546.3548481829575, "edge_b": 547.2144493249975 }, { "seed": 4380519, "diff": -0.5986106075174575, "edge_a": 505.38666642563646, "edge_b": 505.9852770331539 }, { "seed": 4381375, "diff": -0.5608844022336825, "edge_a": 646.4949273424215, "edge_b": 647.0558117446552 } ] }, "valid": true, "invalid_reasons": [], "gas": { "afterSwap_max_ok": 213581, "init_max": 220962, "oog": 0, "other_errors": 0, "oog_seeds": [], "afterSwap_calls": 20695584, "afterSwap_oog": 0 }, "v2_gas": { "afterSwap_max_ok": 244105, "init_max": 236377, "oog": 39, "other_errors": 0, "oog_seeds": [ [ 4380041, 2 ], [ 4380082, 1 ], [ 4380230, 1 ], [ 4380275, 2 ], [ 4380281, 2 ], [ 4380538, 2 ], [ 4380553, 2 ], [ 4380644, 2 ], [ 4380710, 1 ], [ 4380879, 2 ], [ 4380925, 2 ], [ 4381054, 2 ], [ 4381084, 1 ], [ 4381179, 2 ], [ 4381392, 1 ], [ 4381412, 2 ], [ 4381511, 1 ], [ 4381522, 2 ], [ 4381544, 1 ], [ 4381577, 2 ], [ 4381581, 1 ], [ 4381673, 2 ], [ 4381977, 3 ] ], "afterSwap_calls": 20681259, "afterSwap_oog": 39 }, "vanilla_failures": { "cand_run": [ 0, 0 ], "v2_run": [ 0, 0 ] }, "complete": [ true, true ], "counters_per_seed_match_global": [ true, true ], "max_abs_reconciliation_error": [ 8.810729923425242e-12, 7.105427357601002e-12 ], "execution_note": "The 10-min per-command limit on this machine kills detached jobs, so the one 2000-seed command could not finish in one call. The unmodified harness was run on five consecutive half-open sub-ranges 4380000-4380400, -4380800, -4381200, -4381600, -4382000 (each seed once; each sub-range exit 0, valid). Per-seed results do not depend on chunking since each seed is an independent simulation. Pooled with the harness own validity() and summary(): counters summed, max_ok taken as max, paired stats recomputed over all 2000 per-seed diffs.", "chunk_valid": [ true, true, true, true, true ], "chunk_paired": [ { "n": 400, "mean_diff": 0.039192930592139276, "se": 0.007924734061971299 }, { "n": 400, "mean_diff": 0.04650572978119442, "se": 0.009637771622206321 }, { "n": 400, "mean_diff": 0.037770760515090984, "se": 0.008554044943730302 }, { "n": 400, "mean_diff": 0.05612605247910892, "se": 0.008980492800607951 }, { "n": 400, "mean_diff": 0.036528983131418474, "se": 0.008909803894327373 } ], "seconds": [ 819.242, 877.522 ], "retail_edge_delta": { "mean": 0.04446169481007647, "se": 0.003991404835856817 }, "arb_edge_delta": { "mean": -0.0012368035102822716, "se": 0.0014601906103536863 }, "terciles_by_v2_retail_volume": [ { "n": 666, "mean_diff": 0.03125986238734993, "se": 0.004842771951981862, "name": "low", "v2_retail_volume_y_range": [ 55008.020608732586, 71187.0740729544 ] }, { "n": 667, "mean_diff": 0.04186359848416489, "se": 0.0065960622225986225, "name": "mid", "v2_retail_volume_y_range": [ 71193.97716330917, 81658.97193074343 ] }, { "n": 667, "mean_diff": 0.0565332744537748, "se": 0.008519945498688107, "name": "high", "v2_retail_volume_y_range": [ 81673.87176794877, 97746.11075685479 ] } ], "terciles_note": "seeds sorted by V2-run submission retail_volume_y (ties by seed), split n//3, 2n//3" } ], "setup_notes": "Linux x86_64; host lacked python3 and cc, so uv-managed CPython 3.12 was linked as scratch/bin/python3 and conda-forge gcc pre-installed into scratch/cenv before running setup.sh (its cc/uv steps then skipped); instrumentation.patch applied, release rebuild, tests.py all_pass true; amm-match validate passed for G, V2, STACK. No tuning; seeds used only 4380000..4381999 (plus a 64-seed timing smoke run on 10000..10063).", "no_board_claim": true }