{ "item": "a", "batch": "e09-combine-anchors", "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 _anchorSigma(uint256 current, uint256 packed) internal pure returns (uint256) {\n uint256 mean = uint80(packed >> 80);\n if (uint32(packed >> 160) == 0) mean = current;\n return wmul(1047182309813441000, _blend(current, mean, 682794863439784300));\n }\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[15] = 400000000000000000 | (uint256(2000000000000000) << 160); 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 packedSigma = slots[6]; uint256 sigmaHat = uint80(packedSigma); uint256 lambdaHat = slots[7]; uint256 sizeHat = slots[8];\n uint256 toxEma = slots[9]; uint256 stepTradeCount = uint8(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 // Process variance is propagated inside the censored update.\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(_anchorSigma(sigmaHat, packedSigma), 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 if (682794863439784300 > 0) {\n uint256 count = uint32(packedSigma >> 160);\n uint256 mean = uint80(packedSigma >> 80);\n if (count < 5377) count++;\n if (sigmaHat >= mean) mean += (sigmaHat - mean) / count;\n else mean -= (mean - sigmaHat) / count;\n packedSigma = (mean << 80) | (count << 160);\n }\n\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 // Censored assumed-density posterior. No external or future inputs.\n uint256 arbProbability;\n (fastHat, uncertainty, arbProbability) = _posterior(PosteriorInput(\n fastHat, uncertainty, pImplied, spot, slots[2] >> 64,\n prevBidFee, prevAskFee, firstInStep, silent, trade.isBuy,\n trade.reserveY > 0 ? wdiv(trade.amountY, trade.reserveY) : 0\n ));\n slots[13] = uncertainty;\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 uint256 toxLinear;\n uint256 toxQuadratic;\n {\n uint256 packedAnchor = slots[16];\n uint256 runMean = uint64(packedAnchor);\n uint256 sampleCount = packedAnchor >> 64;\n if (sampleCount < 674) sampleCount++;\n if (toxEma >= runMean) runMean += (toxEma-runMean)/sampleCount;\n else runMean -= (runMean-toxEma)/sampleCount;\n slots[16] = runMean | (sampleCount << 64);\n toxLinear = _anchorBlend(runMean, toxEma, 712696014807650816);\n toxQuadratic = _anchorBlend(runMean, toxEma, 1295240753826310656);\n }\n\n\n stepTradeCount = stepTradeCount + 1;\n if (stepTradeCount > STEP_COUNT_CAP) stepTradeCount = STEP_COUNT_CAP;\n\n uint256 originalLambda = lambdaHat; uint256 originalSize = sizeHat;\n\n if (342406799193418304 > 0) {\n uint256 packedFlow = slots[15];\n uint256 rate = uint80(packedFlow);\n uint256 count = uint80(packedFlow >> 80);\n uint256 meanSize = uint80(packedFlow >> 160);\n if (rate == 0) rate = 400000000000000000;\n if (meanSize == 0) meanSize = 2000000000000000;\n if (isNewStep) {\n uint256 inst = count / silent;\n if (inst > 3 * WAD) inst = 3 * WAD;\n uint256 retention = _powWad(999000000000000000, silent > 64 ? 64 : silent);\n rate = wmul(rate, retention) + wmul(inst, WAD-retention);\n count = 0;\n }\n uint256 weight = firstInStep ? WAD-arbProbability : WAD;\n uint256 correctedWeight = weight;\n if (2 == 2) {\n uint256 missing = wmul(feeUsed, 196030880396139429888);\n if (missing > 333333333333333376) missing = 333333333333333376;\n correctedWeight = wdiv(weight, WAD-missing);\n }\n count += correctedWeight;\n uint256 learning = wmul(WAD-999000000000000000, weight);\n meanSize = _blend(meanSize, tradeRatio, learning);\n slots[15]=rate | (count << 80) | (meanSize << 160);\n uint256 retailRate = wmul(rate, 366383424913407168);\n uint256 retailSize = 2 == 0 ? sizeHat : wmul(meanSize,1883296158119298304);\n lambdaHat = _blend(lambdaHat,retailRate,342406799193418304);\n sizeHat = _blend(sizeHat,retailSize,342406799193418304);\n }\n uint256 flowSize = wmul(lambdaHat, sizeHat);\n // Run-level means, observed after RS2's flow correction on each callback.\n // Packed in unused bits of slots[10]; zero means no observations yet.\n uint256 anchor = slots[10] >> 8;\n uint256 runAct = uint96(anchor);\n uint256 runFlow = uint96(anchor >> 96);\n uint256 runN = anchor >> 192;\n if (runN < 4646) ++runN;\n if (actEma >= runAct) runAct += (actEma-runAct)/runN;\n else runAct -= (runAct-actEma)/runN;\n if (flowSize >= runFlow) runFlow += (flowSize-runFlow)/runN;\n else runFlow -= (runFlow-flowSize)/runN;\n uint256 feeAct = _anchorValue(runAct,actEma,1332392442189290496);\n flowSize = _anchorValue(runFlow,flowSize,216073432653406016);\n anchor = runAct | (runFlow << 96) | (runN << 192);\n uint256 fBase = BASE_FEE + wmul(SIGMA_COEF, _anchorSigma(sigmaHat, packedSigma)) + wmul(LAMBDA_COEF, lambdaHat) + wmul(FLOW_SIZE_COEF, flowSize);\n uint256 fMid = fBase + wmul(TOX_COEF, toxLinear) + wmul(TOX_QUAD_COEF, wmul(toxQuadratic, toxQuadratic)) + wmul(ACT_COEF, feeAct);\n fMid = fMid + wmul(SIGMA_TOX_COEF, wmul(_anchorSigma(sigmaHat, packedSigma), toxLinear));\n\n lambdaHat = originalLambda; sizeHat = originalSize;\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 | (682794863439784300 > 0 ? (packedSigma & ~uint256(type(uint80).max)) : 0); slots[7] = lambdaHat; slots[8] = sizeHat;\n slots[9] = toxEma; slots[10] = stepTradeCount | (anchor << 8);\n\n return (bidFee, askFee);\n }\n\n\n\n function _anchorBlend(uint256 mean, uint256 value, uint256 k) internal pure returns (uint256) {\n if (k == WAD) return value;\n if (value >= mean) return mean + wmul(value-mean,k);\n uint256 delta = wmul(mean-value,k);\n return delta < mean ? mean-delta : 0;\n }\n\n function _anchorValue(uint256 mean,uint256 value,uint256 k) internal pure returns(uint256) {\n if (value>=mean) return mean+wmul(value-mean,k);\n uint256 delta=wmul(mean-value,k);\n return mean>delta ? mean-delta : 0;\n }\n\n struct PosteriorInput {\n uint256 mu; uint256 v; uint256 obs; uint256 spot; uint256 preSpot;\n uint256 bid; uint256 ask; bool first; uint256 silent; bool buy; uint256 size;\n }\n function _posterior(PosteriorInput memory x) internal pure returns (uint256, uint256, uint256) {\n if (x.mu == 0) x.mu = x.spot;\n if (x.v < 10000000000) x.v = 10000000000;\n uint256 lo = wmul(x.preSpot, WAD-x.bid);\n uint256 hi = wdiv(x.preSpot, WAD-x.ask);\n if (x.first) {\n if (x.silent>1 && x.preSpot>0) {\n uint256 elapsed=x.silent>8?8:x.silent;\n x.v += 902500000000*(elapsed-1);\n (x.mu,x.v)=_band(x.mu,x.v,lo,hi);\n }\n x.v+=902500000000;\n }\n uint256 mRetail = x.mu;\n uint256 vRetail = x.v;\n // A missing own-pool trade is a censored price observation.\n if (x.first && x.preSpot > 0) {\n (mRetail, vRetail) = _band(x.mu, x.v, lo, hi);\n }\n if (!x.first) {\n // A later print is retail. Only an interior route is an observation\n // of the other pool, with explicit observation uncertainty.\n uint256 fee = x.buy ? x.bid : x.ask;\n if (fee > 30 * BPS) {\n uint256 normal = x.buy ? wdiv(wmul(x.spot, WAD-fee), WAD-30*BPS)\n : wdiv(wmul(x.spot, WAD-30*BPS), WAD-fee);\n uint256 residual = wdiv(absDiff(normal, x.mu),x.mu);\n uint256 noise = 9000000000000 + wmul(residual,residual);\n uint256 k = wdiv(x.v,x.v+noise);\n return (_blend(x.mu,normal,k),wmul(x.v,WAD-k),0);\n }\n return (x.mu,x.v,0);\n }\n uint256 e = wdiv(absDiff(x.obs,x.mu),x.mu);\n uint256 totalV = x.v + 22500000000;\n uint256 z = wdiv(wmul(e,e),totalV);\n uint256 density = _powWad(wdiv(WAD,WAD+z/8),4);\n uint256 odds = wmul(density,wdiv(4000000000000000,_isqrt(totalV*WAD)));\n if (x.size > 3000000000000000) odds = wmul(odds,4*WAD/10);\n if (x.silent > 1) odds = wmul(odds,8*WAD/10);\n uint256 sd = _isqrt(x.v*WAD);\n uint256 width = wdiv(hi-lo,x.mu);\n uint256 distance = x.muhi?x.mu-hi:0);\n uint256 zBand = wdiv(wdiv(distance,x.mu),sd);\n uint256 mass = wmul(wdiv(width,width+2*sd),wdiv(WAD,WAD+wmul(zBand,zBand)));\n if (mass < WAD/100) mass = WAD/100;\n odds = wdiv(odds,mass);\n uint256 prob = wdiv(odds,WAD+odds);\n uint256 kArb = wdiv(x.v,totalV);\n uint256 mArb = _blend(x.mu,x.obs,kArb);\n uint256 mean = _blend(mRetail,mArb,prob);\n uint256 between = wdiv(absDiff(mArb,mRetail),x.mu);\n uint256 variance = wmul(prob,wmul(x.v,WAD-kArb)) + wmul(WAD-prob,vRetail)\n + wmul(wmul(prob,WAD-prob),wmul(between,between));\n if (variance > 100000000000000) variance = 100000000000000;\n return (mean,variance,prob);\n }\n function _blend(uint256 a,uint256 b,uint256 w) internal pure returns(uint256) {\n return b>=a ? a+wmul(b-a,w) : a-wmul(a-b,w);\n }\n function _band(uint256 mu,uint256 v,uint256 lo,uint256 hi) internal pure returns(uint256,uint256) {\n // Soft interval likelihood avoids discontinuities at quadrature nodes.\n uint256 sd=wmul(mu,_isqrt(v*WAD));\n uint256[3] memory acc;\n for(uint256 j=0;j<7;j++) {\n uint256 p=j<3 ? (mu>(3-j)*sd?mu-(3-j)*sd:1) : mu+(j-3)*sd;\n uint256 w=j==3?72:(j==2||j==4?45:(j==1||j==5?10:1));\n uint256 distance=phi?p-hi:0);\n uint256 z=sd>0?wdiv(distance,sd):0;\n uint256 likelihood=wdiv(WAD,WAD+4*wmul(z,z));\n w=wmul(w*WAD,likelihood);\n acc[0]+=w;acc[1]+=wmul(w,p);\n uint256 d=wdiv(absDiff(p,mu),mu);\n acc[2]+=wmul(w,wmul(d,d));\n }\n uint256 m=wdiv(acc[1],acc[0]);\n uint256 d=wdiv(absDiff(m,mu),mu);\n uint256 second=wdiv(acc[2],acc[0]);\n return(m,second>wmul(d,d)?second-wmul(d,d):10000000000);\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 \"censored_10\"; }\n}\n", "sha256": "64a233b9f2f7df836092797d15490b435818cf9a680386cde7d787102b902421", "composition_source": { "base": "R.code (RS2) from https://api.imd.fun/artifacts/19f2ec857df536e8ab62ab1da89ec6623332521ce46849f15bccff402c63e1e5, sha256 f24b6ca198b744c380842c3a17964a6dc21f311bb04984b26733afa3fee8eaf2", "order": [ "T.generate(s,[0.7126960148076509,1.2952407538263107,674])", "H.generate(s,[1.3323924421892905,0.216073432653406,4646])", "S.generate(s,[0.6827948634397843,1.047182309813441,5377])", "s.replace(\"wmul(sigmaHat, toxLinear)\",\"wmul(_anchorSigma(sigmaHat, packedSigma), toxLinear)\") (exactly 1 occurrence)" ], "generators": { "T": "https://api.imd.fun/artifacts/6ac5e013b7b1fb4c5e7bdcdfec0aba28b16824e18ccf39500f258533879faffe", "H": "https://api.imd.fun/artifacts/26cb8e86f05170308de2a4b24821ac7fad2a17077f8d94af6e0f31985343fe89", "S": "https://api.imd.fun/artifacts/9045cab1f8a51e8f1c6a4c2c93daa2b2f0d9bd274a68de064a1167c079c2a8b4" }, "generator_hash_checks": { "T_on_RS2_reproduces_ebd9de9b...": true, "H_on_RS2_reproduces_0c3836cd...": true, "S_on_RS2_reproduces_014ad7bd...": true, "T.RS2_SOURCE_equals_R.code": true, "R_generator": "not re-run: its base is RS1, whose source is not in any of the named artifacts; R.code itself was verified against sha256 f24b6ca1..." }, "storage": "T: slots[16] (runMean low 64 bits, count above); H: slots[10] bits >=8 (uint8 step count kept in low byte); S: slots[6] bits >=80 (raw sigmaHat in low 80). afterInitialize body unchanged by all three. No other edits; no fitting.", "neutral_variant": "T k_linear=k_quadratic=1 (N=674), H act_k=flow_k=1 with force_overlay=True (N=4646, state updates run), S w=0,g=1 (N=5377); sha256 4094c125f605f09e5240ad694e633a7f3722611662ff82d6f8f56f217a952ebc" }, "blocked": null, "valid": true, "complete": false, "completion_note": "The fresh block 5120000..5121999 was only partly run. This machine has 2 CPU cores; one 20-seed chunk of 3 arms (union, RS2, STACK) took about 87 s, so 2000 seeds would have taken about 2.4 h against a 114-minute task budget. The block was run in ascending 20-seed chunks, every arm on every chunk, with no seed dropped, until the time ran out: 5120000..5120779 (n=780). Seeds 5120780..5121999 were never run. The union bytes were frozen (sha256 above) before any fresh seed was run, nothing was changed afterwards, and each chunk was run exactly once. The seeds that were not run remain unseen.", "calibration": { "source": "https://raw.githubusercontent.com/ChengHua926/amm-challenge/d34a5199c59a4c44d5336a25f1436b4ae1f21104/contracts/src/Strategy.sol", "ch_sha256": "6dd68f77a70900319460215374143dbd5d924198450a46d9f5f91f6b1e3d35c3", "seeds": "0..999", "mean": 525.5258821780834, "expected": 525.5258821780834, "abs_diff": 0.0, "pass": true }, "parity": { "seeds": "786100..786131", "n": 32, "neutral_vs_rs2_edges_identical": true, "neutral_vs_rs2_fee_traces_identical": true, "steps_compared": 320000, "max_abs_edge_diff": 0.0, "gas_neutral": { "init_max_ok": 243118, "max_ok": 227336, "oog": 0, "revert": 0, "other_halt": 0, "tx_error": 0, "bad_return": 0, "other_halts": 0 }, "gas_union": { "init_max_ok": 243143, "max_ok": 228697, "oog": 0, "revert": 0, "other_halt": 0, "tx_error": 0, "bad_return": 0, "other_halts": 0 }, "gas_rs2": { "init_max_ok": 243099, "max_ok": 202480, "oog": 0, "revert": 0, "other_halt": 0, "tx_error": 0, "bad_return": 0, "other_halts": 0 }, "union_gas_ok": true, "mean_edge_union": 520.6552350421681, "mean_edge_rs2": 520.3632302791513 }, "seeds": { "start": 5120000, "end_inclusive": 5120779, "n": 780 }, "paired": { "n": 780, "mean_diff": 0.19890157528467742, "se": 0.03707916182114838, "worst": [ { "seed": 5120166, "d": -7.2550272966645935 }, { "seed": 5120329, "d": -5.850160586499783 }, { "seed": 5120200, "d": -4.534495057084882 }, { "seed": 5120374, "d": -4.397802609153246 }, { "seed": 5120731, "d": -4.135962415093445 } ] }, "vs_rs2": { "paired": { "n": 780, "mean_diff": 0.19890157528467742, "se": 0.03707916182114838, "worst": [ { "seed": 5120166, "d": -7.2550272966645935 }, { "seed": 5120329, "d": -5.850160586499783 }, { "seed": 5120200, "d": -4.534495057084882 }, { "seed": 5120374, "d": -4.397802609153246 }, { "seed": 5120731, "d": -4.135962415093445 } ] }, "retail_edge_delta": { "mean": -1.1743546643430198, "se": 0.0404688934216256 }, "arb_edge_delta": { "mean": 1.3732562396276957, "se": 0.021144407059659087 }, "reconciliation_max_abs": 1.0658141036401503e-13 }, "vs_stack": { "paired": { "n": 780, "mean_diff": 0.5729534132476635, "se": 0.03642423115603716, "worst": [ { "seed": 5120166, "d": -6.54806236875902 }, { "seed": 5120302, "d": -4.985429799679196 }, { "seed": 5120087, "d": -4.726360355196448 }, { "seed": 5120329, "d": -4.273356085565069 }, { "seed": 5120200, "d": -4.2363210374913365 } ] }, "retail_edge_delta": { "mean": -0.746491746817483, "se": 0.04077756442377857 }, "arb_edge_delta": { "mean": 1.3194451600651476, "se": 0.022141421668992235 }, "reconciliation_max_abs": 1.1368683772161603e-13 }, "mean_edge_fresh": { "union.sol": 524.2326367666947, "rs2.sol": 524.03373519141, "stack.sol": 523.659683353447 }, "gas": { "union": { "init_max_ok": 243143, "max_ok": 228616, "oog": 0, "revert": 0, "other_halt": 0, "tx_error": 0, "bad_return": 0, "other_halts": 0 }, "rs2": { "init_max_ok": 243099, "max_ok": 202398, "oog": 0, "revert": 0, "other_halt": 0, "tx_error": 0, "bad_return": 0, "other_halts": 0 }, "stack": { "init_max_ok": 220962, "max_ok": 213524, "oog": 0, "revert": 0, "other_halt": 0, "tx_error": 0, "bad_return": 0, "other_halts": 0 }, "note": "max_ok = afterSwap max successful gas; init_max_ok = afterInitialize; summed over every chunk of the fresh run (stats reset and collected per arm per chunk)" }, "harness": { "checkout": "https://github.com/benedictbrady/amm-challenge @ 6b6921f8d463314aa7c96234e1be25a25245f704", "harness_source": "H.harness_source (https://api.imd.fun/artifacts/26cb8e86f05170308de2a4b24821ac7fad2a17077f8d94af6e0f31985343fe89): configs(), decomposition(), aggregate(), compare() used verbatim; SE = sample SD (ddof=1)/sqrt(n)", "method": "each arm alone: amm_sim_rs.run_batch(arm_bytecode, VanillaStrategy_bytecode, configs(first,20), 8), n_steps 10000, chunks of 20 seeds, gas_stats_reset() before and gas_stats() after each arm/chunk; solc 0.8.24 via amm_competition SolidityCompiler; simulator wheel sha256 aedb68280aca34c110968f00148387c95885207913fb2cf19a1ab4c5cfd6887a", "commands": [ "sh scratch/setup.sh", ". scratch/env.sh && python run.py parity 786100 32 parity.json", ". scratch/env.sh && python drive.py ch.jsonl 0 1000 ch.sol", ". scratch/env.sh && python drive.py fresh.jsonl 5120000 2000 union.sol rs2.sol stack.sol (resumable across 6 invocations, 20-seed chunks in order)" ], "stack": "K https://api.imd.fun/artifacts/c33720874aa1285e9dc766540b8a90410118a8e8b840d949ea0dcc211bdb27c1 code sha256 2eaafc7960e520b8a7fd322ec8afaff8fa677c730228a961efb509cc30b25719" }, "notes": [ "All figures are local simulator measurements, not leaderboard claims.", "The union beat STACK by +0.573 (se 0.036) over n=780 fresh seeds, far short of the about +5.0 the top 10 needs. Against RS2 the gain is +0.199 (se 0.037). Against both references it loses retail edge and gains arb edge." ] }