压力 ES — 最差滚动窗口历史 ES
Stressed Expected Shortfall — Worst Rolling-Window Historical ES
开始编码在 FRTB（交易账簿基本审查）市场风险框架下，使用内部 ES 模型计算资本的银行需同时报告普通期望损失（用最近观测窗口计算）与压力期望损失（sES，在历史样本中找出"重大金融压力期"的滚动窗口计算）。资本附加项取两者最大值。标准的量化口径就是「在历史 PnL 样本所有长度-W 滚动窗口上取历史 ES 的最大值」。请实现 solution(pnl_samples: list[float], window_size: int, alpha: float) -> float：给定历史区间 PnL 序列（正数=盈利、负数=亏损）、滚动窗口长度 W 与 ES 置信度 alpha，返回压力 ES 并以正损失数值报告。当 len(pnl_samples) < window_size（没有完整长度窗口能放下）时，返回 float('nan') 作为哨兵。
每个窗口的历史 ES 沿用与 ES 管线 (coding-historical-expected-shortfall) 相同的边界 ceil 约定。对长度 W 的窗口，先升序排序，取 k = max(1, ceil(W * (1 - alpha) - 1e-12))，再令 ES_window = -(sum(sorted_window[0..k-1]) / k)——升序后前 k 个观测均值的相反数；亏损尾部下为正数。压力 ES 是 ES_window 在所有 (N - W + 1) 个滚动窗口上的最大值。风控部门把这个数值与普通历史 ES、压力 VaR 一起送入资本归因仪表盘。
例
solution([0.01, -0.02, 0.005, -0.03, 0.008, -0.05, 0.012, -0.015, 0.003, -0.025, 0.006, -0.04], 5, 0.6) 应返回 0.04。W = 5、alpha = 0.6 时 k = ceil(5 * 0.4 - 1e-12) = 2，所以每个窗口的 ES 等于该窗口最差两笔观测的均值取相反数。从下标 1 开始的窗口 [-0.02, 0.005, -0.030, 0.008, -0.050] 升序排序为 [-0.050, -0.030, -0.020, 0.005, 0.008]；最差两笔均值为 (-0.050 + -0.030) / 2 = -0.040，故该窗口 ES = +0.040，没有其他窗口能超过。注意：相同输入下兄弟题 coding-stressed-var-worst-rolling-window 在 k = 2 取阈值 -sorted[k-1] = +0.030；sES 取尾部均值汇报 +0.040，是最差两笔的平均。
实践背景
四个常见正确性陷阱。第一，*ES 是尾部均值，不是阈值*：ES_window = -(sum(sorted[0..k-1]) / k)，是最差 k 笔观测的平均值。写成 -sorted[k - 1] 的作者计算的是压力 VaR，而不是压力 ES——这是完全不同的指标。两个兄弟题在 FRTB 资本仪表盘上比邻而居，最常见的 bug 就是把 VaR 公式贴在 ES 名下。第二，k 必须用*边界 ceil* 约定：与历史 ES 兄弟题相同的 ceil(W * (1 - alpha) - 1e-12) 兜底。W = 100、alpha = 0.99 时 100 * (1 - 0.99) 的浮点值是 1.0000000000000009，朴素 ceil 会得 2，而 100 个观测下 99% 置信度 ES 的教科书 k 是 1——ceil 前先减 1e-12 才能恢复教科书答案。第三，*最差窗口 vs 全样本*：sES 是滚动窗口内 ES 的最大值，而不是全样本一次 ES。压力期输入下全样本会把坏窗口稀释到整段样本里、低估真实风险——实现滚动最大值正是该指标的核心。聚合是 max，不是 min 也不是 mean；mutation tests 三种都会盯。第四，*符号约定*：ES 报告为正损失数；升序后前 k 笔 PnL 是最负的几笔，对其均值取相反数即可翻成正损失。若所有窗口的所有观测都是正数（无任何亏损），每个窗口的 ES 是负数、sES 也为负数——这是正确的，不是 bug。
参考实现就是教科书算法。先一次性算出 k。对每个起点 i ∈ 0..N-W，取 window = pnl_samples[i:i+W] 排序，对前 k 个求和、除以 k、取相反数得到 ES_window，并跟踪最大值。朴素的 O(N * W log W) 在 N ≤ 1200、W ≤ N 范围内 2s 预算绰绰有余。如果想过度工程化，sortedcontainers.SortedList 的滚动维护可达 O(N log W)，但在给定上下界完全没必要。
约束条件
- 1 ≤ window_size ≤ len(pnl_samples) ≤ 1200。若 `len(pnl_samples) < window_size`，返回 `float('nan')`——没有完整长度窗口能放下，结果未定义。
- |pnl_samples[i]| ≤ 1e6，均为有限浮点数。
- 0.5 ≤ alpha < 1.0（常见 ES 置信度：0.5、0.9、0.95、0.975、0.99）。
- 窗口内 k = ceil(W * (1 - alpha))（数学口径）；IEEE-754 浮点下用 `1e-12` 量级 epsilon 兜底，并 clamp 到 `k ≥ 1`。
- 损失尾部典型样本下输出 sES 为正损失数；若所有窗口都没有任何亏损，sES 会是负数（这是正确的，不是 bug）。
- 浮点容忍：rel_tol=1e-9，abs_tol=1e-9。
样例
Case 1 · statement-example, N=12 W=5 alpha=0.6 k=2
输入: [[0.01,-0.02,0.005,-0.03,0.008,-0.05,0.012,-0.015,0.003,-0.025,0.006,-0.04],5,0.6]
期望: 0.04
N=12、W=5、alpha=0.6。k=ceil(5*0.4-eps)=2，每个窗口 ES = -(最差两笔均值)。下标 1 起的窗口 [-0.02, 0.005, -0.030, 0.008, -0.050] 排序后最差两笔为 -0.050 与 -0.030，均值 -0.040，故该窗口 ES = +0.040 即为 sES。
Case 2 · statement-context, sES vs full-sample ES — worst window dominates
输入: [[0.001,-0.005,0.003,-0.008,0.002,-0.01,0.005,-0.003,0.001,-0.006,0.004,-0.04,0.002,-0.035,0.001,-0.03,0,0.005,-0.001,0.002,0.003,-0.002,0.001,-0.004,0.002],10,0.8]
期望: 0.037500000000000006
N=25、W=10、alpha=0.8、k=2。全样本 ES（25 个观测、k=5）只有约 0.0246，但下标 [4..13] 的窗口聚集了三笔大损失 [-0.040, -0.035, -0.010]，最差两笔均值 -0.0375，该窗口 ES = +0.0375。sES 把这段压力期挑出来，避免被全样本均化掉。
Case 3 · typical, N=W=10 single window equals full-sample ES
输入: [[0.012,-0.018,0.005,-0.025,0.014,-0.04,0.002,-0.011,0.008,-0.022],10,0.95]
期望: 0.04
W=N=10 时只有一个窗口，sES 退化为该窗口的历史 ES。alpha=0.95、k=ceil(10*0.05-eps)=1，ES = -最小值 = +0.040。
Case 4 · typical, W=1 every window is single observation, sES = -min(pnl)
输入: [[0.01,-0.02,0.03,-0.05,0.02,-0.01,0.04,-0.03],1,0.5]
期望: 0.05
W=1，每个窗口只有一个观测；k=ceil(1*0.5-eps)=1，所以每个窗口 ES = -该观测。max 即为 -min(pnl) = -(-0.05) = +0.05。
Case 5 · typical, W=N-1 two rolling windows take worse
输入: [[0.005,-0.01,0.008,-0.025,0.002,-0.045,0.01,-0.008],7,0.7]
期望: 0.02666666666666667
N=8、W=7、alpha=0.7、k=ceil(7*0.3-eps)=3。两个窗口的最差三笔分别为 [-0.045,-0.025,-0.010] 与 [-0.045,-0.025,-0.008]，均值 -0.02667 与 -0.026，故 sES = +0.02667 取自第一个窗口（更差）。
Case 6 · boundary, N<W returns NaN sentinel
输入: [[0.01,-0.02,0.03],5,0.95]
期望: "NaN"
N=3 < W=5，没有完整窗口能放下，返回 NaN。
Case 7 · boundary, N=W=1 single observation
输入: [[-0.05],1,0.5]
期望: 0.05
唯一观测 -0.05，sES = -(-0.05) = +0.05。
Case 8 · boundary, alpha=0.999 very high tail squeezes k to 1 for typical W
输入: [[0.01,-0.02,0.005,-0.03,0.008,-0.05,0.012,-0.015,0.003,-0.025,0.006,-0.04],5,0.999]
期望: 0.05
alpha=0.999、W=5 时 5*(1-0.999)=0.005，ceil 后 k=1，clamp 不触发；每窗 ES = -最小值。最差窗口含 -0.05，sES = +0.05。
Case 9 · boundary, epsilon-snap W=100 alpha=0.99 k=1 (IEEE-754 boundary)
输入: [[-0.013112053688159792,-0.00748864306344733,-0.011499595660845921,0.0009374738333989241,-0.010679027712774868,0.01564390113180378,-0.00033912118906973226,0.00452797720441735,0.00602871562939312,0.011257131175325417,0.008407494988119477,-0.009131187112259803,0.007354396221378821,0.0018360286376905156,0.0070501329131859546,0.005090030429073245,-0.010360923204152472,0.019131244008969643,-0.018382594475107,0.0018932907513332237,0.0017100406624565609,-0.004752487269045439,0.015836799337729725,0.017847246424777915,0.010783173844490752,0.0003220332764031089,0.002166725607238634,-0.0071201764493905645,0.0012627937475428697,-0.020675073973199728,0.0045363239209714745,-0.007020968227557774,-0.0010593047766014445,0.009205300507700393,0.00206374904596311,0.00040410253392124656,0.0005648480680207156,0.00638800883496896,-0.0007119076260398609,-0.009002788806165398,0.007991771272403145,0.002888240538030924,0.0015085429180744972,0.0015109643270047716,-0.0060062602072141445,-0.0043666258578975384,-0.0007302249407689914,0.006496100677012316,-0.013814419086228507,-0.011109473577140904,0.020854882565160895,-0.008555955501746666,0.0013036371066794683,0.01384671335706266,-0.0011693705448371015,0.005075790539659064,-0.02322664887480081,0.001549550166380092,-0.0067628208033466575,0.009855182678548272,0.00047604457405554866,-0.004140963506804216,0.020233170767372872,0.0007103498884153931,0.010075205370280331,-0.00979103351250045,0.006680500669406385,-0.01995536629472714,-0.0047347689908009884,-0.025275675398085628,0.013426076428977814,-0.02522151451407971,0.0013224818857358255,-0.0024581792779798366,-0.0038706508488168985,0.0007202243709383716,-0.00044367841345814134,-0.00291318499694612,-0.0016522367965677365,-0.01700684552311982,0.0037460527069299587,0.0010802244697144794,-0.025427404423924826,-0.002770944721803686,0.016944646059173975,-0.00244238258804072,0.003029694514128398,-0.008292985501392928,0.0023642538979977527,-0.012703008914333454,-0.014293221213458988,0.004376872448828541,0.008797099346174763,0.001219193719504798,-0.0066880716598674205,0.0008915249169552663,-0.006882248495372554,-0.026959102678411985,-0.00004949598740278035,0.008014114441666087],100,0.99]
期望: 0.026959102678411985
W=100、alpha=0.99 时 W*(1-alpha) 的浮点值落在整数附近；不减 1e-12 epsilon 会让 ceil 多漂一格 (k=2)，正确教科书 k=1。reference 减 epsilon 命中 k=1。
Case 10 · boundary, all-profit history yields negative sES (correct)
输入: [[0.001,0.005,0.003,0.008,0.002,0.01,0.005,0.003,0.001,0.006,0.004,0.04],5,0.8]
期望: -0.001
所有 PnL 均为正，每窗最差观测仍为正，ES = -mean(正数) 为负。sES 取最大值仍是负数；这是正确结果。
Case 11 · adversarial, ES-vs-VaR distinction k=2 (ES > VaR)
输入: [[0.01,-0.1,0.02,-0.05,0.03,-0.02,0.04,0.01],5,0.6]
期望: 0.07500000000000001
W=5、alpha=0.6、k=2。第一个窗口 [0.01,-0.10,0.02,-0.05,0.03] 排序为 [-0.10,-0.05,0.01,0.02,0.03]；ES = -(-0.10+-0.05)/2 = +0.075；VaR 形式 -sorted[k-1] = -(-0.05) = +0.05，差距很大。sES 取 +0.075。
Case 12 · adversarial, max-not-mean rolling aggregation
输入: [[0.001,-0.001,0.002,-0.002,0.003,-0.003,0.001,-0.1,0.002,-0.08,0.001,-0.09,0.001,-0.001,0.002,-0.002,0.003,-0.003],6,0.5]
期望: 0.09000000000000001
压力簇仅在中段 [6..11]。窗口 mean ES 远低于 max ES。max 拣出最差窗口；mean/min 错答。
Case 13 · adversarial, epsilon-snap rolling W=100 alpha=0.99
输入: [[-0.011149298967472744,-0.004999049259460595,-0.011438620155055496,0.009633284816208051,0.0000497176108048333,-0.012271508921357682,-0.006658860859956316,0.0031575473411602157,-0.00652932917145945,0.0035678447570392713,0.0026225403621188605,-0.009959180817476156,0.006554169410040809,-0.014248145677751605,-0.0009928568634324792,0.02591921078488241,0.00560351790435422,0.0062320010941962194,-0.018602573050766427,-0.00033261063012061373,-0.0013411261485536809,0.018271012952008666,0.007847809767378809,0.0018669466440662784,-0.014589728671150787,0.006287989165423251,0.016632462449550273,-0.027216065429669242,-0.007210881027860881,0.0023122835583020496,-0.018009037940197547,0.02004037416555216,0.00712528899052319,0.009425153582456268,-0.007043396604659802,0.00046109180200194295,0.0006421816268565185,-0.004742405293478989,-0.021642042388511067,0.014804906293753778,0.010246789123602438,0.020683854943131578,-0.0008012100523633732,-0.0013455300696804814,0.0012379104101340932,0.006084874893595527,0.010027197929222362,0.01397736007629474,-0.0007168116145556458,-0.001783624588743347,0.009983126610327445,0.020631125974431643,0.017249704209085528,-0.0020800403552316566,0.003933891912780858,-0.007382676607665465,0.01120703484698137,-0.003346033864719677,0.006298914548107048,-0.012336310667451002,0.0013489844157172448,-0.010132618804006238,-0.011628404962325182,-0.00559622903142745,-0.01499585545321304,-0.03526441167088841,0.009878762034524112,0.004474046362080074,0.010099259884770442,-0.0012755186837236237,0.0009885319216541375,-0.01579905913141974,-0.0030859229831712194,0.025404386268783982,-0.006355193428787243,-0.023745291605321527,-0.05626224201472549,-0.05681931048885472,-0.0532159579138479,-0.038877017923180546,-0.042268157125404646,-0.0335305455835027,-0.04110131740435686,-0.039726635144564676,-0.04280717346187144,-0.06092248616444681,-0.04722573062482094,-0.05962500514719829,-0.05671707483803759,-0.05628497948592277,-0.038213569063668136,-0.048841470911418314,-0.05318680418683856,-0.05321403662364574,-0.04508375358678593,-0.05016490358267769,-0.06288005587176523,-0.024327124417149976,-0.05200478085043446,-0.0503453374472038,-0.048222228178388504,-0.05513900946272604,-0.060284026824727846,-0.03789819470868398,-0.037904259233723946,-0.04709994379287389,-0.03837640706362899,-0.04851856904427966,-0.053710667127281994,-0.056262578650622064,-0.04039444340300581,-0.061398003339606114,-0.041096390121192025,-0.06445453962643644,-0.04457590200946479,-0.06886108687885907,-0.056612689638477875,-0.04273088135506057,-0.0497239809229955,-0.06310494861365945,-0.058681217424672374,-0.0453605625674646,-0.042697945254900456,-0.055875988286022735,-0.05487080563293404,-0.008980479493292042,0.007330665487602931,0.011466782569388028,-0.013779401381764863,-0.021974868676909055,0.003182192761583656,0.007328020946452584,0.011237052755616359,-0.008997769829249012,-0.01627198854418559,0.01641757832532185,0.0005767588297899436,0.007880437118833416,0.01789970400389449,0.0026945203160041132,0.009049210332955535,0.002321614341365397,0.0037440241026355297,-0.014284895253282012,0.011301892022837365,-0.008370476769426753,0.002930092136548833,0.0027106894240812624,0.0005149794466998552,-0.016031197770495383,0.01099266829194361,-0.01004131859407689,-0.003940901311304236,0.011085017129226302,-0.003462272326934582,-0.005665675755621504,0.014373069494276476,0.007360230833557459,-0.010506495807472314,-0.003679775419480732,0.01979501574980781,-0.007637598919476555,-0.008032930389801341,-0.018432737565290395,0.013032549878466556,0.00025196254422326573,0.007896000667208771,-0.0046801706198572775,-0.0026020328932172634,-0.000358775417992628,-0.00030713672510183275,0.005117499456084514,-0.004707284257963626,-0.0067388026204893885,0.0034559966348593762,-0.004177645886051338,0.0021911728786211176,0.015651138875178036,0.0077839372191088755,-0.0025502675552212585,-0.005877887709748986,-0.006019994905296687,0.007292618534453118,-0.0071451426996325465,0.009389775241278604,0.01124877493160787,-0.005334011106136605,-0.011131383091304152,-0.00809409661770658,-0.017476872611663034,-0.01745425750995701,0.0018467515602044358,0.008419962020298358,0.012300021411405402,0.011829462362197401,0.003940058216711551,-0.014069792347524568,0.014980130863855246,-0.00211144990608551,0.01054943337572727],100,0.99]
期望: 0.06886108687885907
W=100、alpha=0.99 滑动；W*(1-alpha) IEEE-754 漂移使朴素 ceil 多取一格。reference 用 1e-12 兜底；mutation 测试盯这个。
Case 14 · large, N=1200 W=250 alpha=0.95 stress test
输入: [[-0.005117605768952009,0.01022863025033028,-0.004521923295662094,-0.006301368446623708,-0.01860036380645535,-0.004266038948424073,0.022238347619726415,0.008482933682518724,0.02073758157779333,0.004978054553301827,0.007895392692275155,0.0037065332085679755,-0.03332125050623887,0.017105019375294742,0.010127696917894408,0.00997636076323888,-0.03382729103696845,-0.03487776234551207,-0.017792306896138595,-0.009363785514664692,0.0061089198366488144,-0.0009182346102517071,0.010419497968418042,-0.012844694997489876,0.0061740629842176225,0.007883089537184201,-0.013222746950642848,0.034350606346674854,0.011132187117349111,0.02394010475958016,-0.012406658289656876,-0.014790317924495464,-0.006880933583263361,-0.0021284266307708796,0.012641574900642978,0.004968545071393843,-0.00894709790464331,-0.019138246273247436,-0.010411806201330776,0.024418426297998078,-0.01615892856615671,0.004895174946321504,0.008530379493483273,-0.029794862697222296,0.0009694871561192407,0.026124871996141434,-0.040287276494205264,-0.006431877021313409,-0.0021227833725136745,-0.016345206048740287,0.009947800223985084,-0.001245597898659108,-0.029293133143081112,0.016556917569826288,0.01338671379642002,0.018916835848148277,0.02881194826385206,0.007244873406966834,0.002385483007002376,-0.025983361694625,0.012308864254299508,-0.01223517839220763,-0.009054037992376744,-0.025295755486026465,-0.01935228654421679,-0.010622421852317383,0.025776750861519742,-0.04063584094897351,-0.029154111071577338,0.004787021927490091,0.02886699508312992,0.011569939007496297,-0.03799886553863904,-0.05036469660062477,0.007147944314220529,-0.014725238794729036,-0.02239573147054152,0.01954742482839126,0.022035724083608082,0.0031450376087697263,0.0049155302055848725,0.008687256196642644,0.03188008113862558,0.012380572065107703,0.010372990779515414,0.010954751472624622,-0.031366210451099184,0.025634670368081806,0.019102041669922562,0.010592474435993836,-0.0394775087107326,-0.012673600511726732,0.01684607187694962,-0.03622428505042651,-0.003680444586520812,0.020390553437045857,-0.02622377226022933,0.032202123967497484,0.011039279435897243,-0.0030027750255957014,0.006497336420094367,0.012996619828903046,0.0024078745240709077,0.022913204717159234,-0.013230891315047922,-0.008294723117866857,0.020833691061471874,0.0005359788309455363,-0.01760928162238881,0.01892910530986423,0.029309951486054937,-0.008896521703114942,-0.0275998637432099,-0.0026949640338622604,-0.002980376072804778,-0.005959992992671605,0.028095406071551303,-0.02053872947831589,0.025211732896766478,-0.02536643958147239,-0.01574078934365458,0.012630425577963473,0.022573806110988078,0.0171800470050708,0.006904494923840602,0.0028471267590551162,0.0030496358091368675,0.01150560541668083,-0.0035239491551258195,0.0055487199369459485,0.011454530672659542,0.000016789529474801217,0.015279647770758605,0.011317562582806886,0.040212643927301096,0.006498852735454427,-0.008551859038864674,-0.007451024318257412,-0.0002621119553136872,0.018475692088497028,-0.006731273769955129,0.007716519841143595,0.03674602555298932,-0.05129358948427868,-0.022478171706780646,0.004877940338066021,0.00796670788834928,0.004771466577221392,-0.008623029981295037,0.013102923866582867,0.005642601319065422,-0.010441026765468028,0.04860107750333505,0.007102657247697899,-0.011084579414937505,-0.0019889710435377394,-0.004511905800500649,-0.0012548309321526114,-0.05456170681900401,-0.00973798059754989,0.020171390161008204,-0.023371245289199573,-0.0013340038169667367,0.01907010747562288,0.017123535317196154,0.02982103993269301,-0.03402826688895825,-0.007067520135277605,-0.006818999771985304,0.012465796918843865,0.02183575007740135,-0.05365659141564643,0.021773585805396123,-0.028950868445253075,0.01366299752204612,-0.029842768067419298,0.003517054667942324,0.023893092206850142,-0.0029863922177190867,0.003822061822970299,0.015942472896890002,0.0028275439029442446,-0.0017696276370506698,0.030665121189214925,0.020969414517521254,-0.0058763011898004345,0.054906504454260284,-0.022936780886352905,0.01829218231373315,-0.0053142915462351115,0.0026473143378144552,0.014100112363318046,0.004444442643877687,0.012772906153241632,-0.030546507253272886,-0.030190221642432794,0.01229885179302808,-0.019263169909320362,-0.020532964954314083,-0.02940278774543313,0.025327601021395033,0.014931160177582215,0.029461494446331754,-0.018754753852916205,0.00002012722352802332,-0.02280613804734019,0.015320747703585689,0.031788457867754624,-0.01780442003272933,0.03120663445754948,0.01976058987238415,-0.0035566933396540172,-0.03943941371859593,0.02813263473871566,-0.0019252098369312181,-0.01205656490583079,0.007991907609694414,0.008199286689365032,0.029961900777757337,-0.020402816214532483,0.022724746410689597,0.029747207628150762,0.029044720198034155,-0.0036124914646844565,-0.014880571038376847,0.020371454492231864,0.0023037062522056413,0.002483789717283113,0.02848429258257904,-0.005268729342097462,-0.04593450421618129,-0.007743824143326385,-0.037078463642182403,0.01637566661819729,0.006340695743279089,-0.012224143026582953,-0.00019198595487592427,0.016652480261401707,0.0015789018138222786,0.026530430243908946,-0.0012256963101086667,0.020806695335633982,0.029829615239550977,0.03219785967488852,-0.013436387507862316,0.017598084170644093,-0.03751991813930565,-0.02166698789903222,-0.03925583026631989,0.02137971245086699,-0.02463869445739107,-0.00025528085651701485,-0.0038442796104925627,-0.0005719505554715704,-0.011830435530702897,0.0046732635062872495,0.03582534176440611,0.0008853710713447864,0.010619642978388322,0.020010387355344182,-0.003958953817836576,-0.025193822636772657,-0.011107909430747145,0.02147189478734735,-0.032924511416984256,-0.011956916411010255,0.02014821305258943,0.015854732997152118,0.00015236256465365027,0.01610471591744901,0.0033195886465967866,-0.023578309149145365,-0.03127884738430396,-0.012779042730768598,0.018454602204418247,-0.0113109030351279,-0.018047172009208298,-0.015419210235579505,-0.030635339049953615,-0.002345498405996903,-0.023592139046435767,0.007282919336173511,-0.04720192825230913,0.006555624191321884,-0.012832215135986353,-0.03884295853242953,0.01449418896805712,-0.00551016502882416,-0.04460073566317155,-0.017501263940300583,0.005820484896382393,-0.009171644210184089,0.01559967375051662,0.014951138828249604,0.013324732832846105,0.0065325057619087116,0.026673938992711563,0.013196683403158476,0.00902436348797779,-0.04167957805088333,0.017931115601757194,0.02618850311153937,-0.005937961653628217,-0.00939014881366837,0.038805969178590936,-0.03516265078968568,0.009377138659832267,0.04847431554563956,-0.018552014816702017,0.013791775206207241,0.0377276168680895,-0.002404214239647993,0.0112239368584501,0.018051512877517516,-0.01811536659790749,-0.0017819160231933237,0.005856034444469836,0.01650769813190758,-0.0006906823383726404,-0.0039068063080057586,-0.02032152120158908,-0.0071795035499387936,0.01783344910522349,0.0020348643405936756,-0.017060568924706695,-0.016832081766347526,0.05333359650591174,0.022797885828139287,0.0127479088324407,-0.05185837796181348,0.01242963141553516,0.009613870008768746,0.03368193911888594,0.008555216905234008,-0.0013497665440498625,0.010448885461964574,-0.038884168928592165,0.02066506483539082,0.006497697468549536,-0.014041426052890129,0.02651144631355944,0.03618679069644611,-0.028048024572232683,-0.01332668477388379,0.005825308863149138,0.003669300835591225,-0.00796961314706485,-0.01948421614338369,0.04240934811724503,0.02074774821859269,-0.023884571914170247,-0.026900159640496486,0.03406256984151939,0.01978297578313163,0.03641941214540926,0.016202867962450743,-0.017441509987726415,0.005213309494659687,-0.043201248331365946,-0.014962376604798867,-0.00117817964459734,0.010455096187886068,-0.014551026345411396,-0.002484484399831349,0.00917094387691721,0.0075337757551831,0.012759925682475356,0.004179634370582069,-0.006478693932469552,0.015783139265480344,0.000987188358028874,-0.016521912045288693,-0.012518563344829986,-0.0000069689516128634306,-0.0021920738694003526,0.0031398849219043856,-0.000009917699359528155,0.0035173813998067185,-0.002685779792382096,-0.025168632022674227,0.008427071184896958,0.021073809009601305,0.008692858705651384,-0.0037849191645152698,0.008928933130189678,-0.01931402084748096,-0.0379230635136505,0.001191404993240779,-0.018609952658439573,0.014797198962666432,-0.02168181343530314,-0.052570228641502056,-0.020790453768247525,0.031561934802580634,-0.00763606657241045,-0.027388336134035678,-0.015267125679705632,0.01041797310112404,0.009937284762269962,0.0035345750637376227,0.029677285316126234,0.014130050894561558,-0.00041959818282947425,0.011933338241667018,0.03309172187003588,0.019426098911868982,0.020475195653405467,-0.021656745688114657,-0.002968703891399211,0.014596885828635931,-0.005928864907563374,0.021377264288546444,0.011926839270960846,0.018165069379650494,-0.0042474177980156595,0.050927529673295426,0.02480032379418639,-0.004308602095351727,0.0018118601729410874,0.051904050279246675,-0.0068645554941837075,0.017482814760877458,0.01960900051552197,0.0001316997666483591,-0.02334276033732612,0.003750728367928228,0.007187585489717591,0.022593571934005224,0.015657782257876313,0.00048719412424675745,0.017071525661253657,0.010796851532864436,0.004120868899378386,0.0011041915699734235,-0.004867203692889949,0.013723210564384596,-0.02108417760056843,-0.012573671622556322,0.00009945873422997987,-0.02927932755624385,-0.008717628080160774,-0.04017679179686643,-0.013657700150381518,0.011368699248372232,0.01132790205301203,-0.0010902599143493873,-0.004642270211322769,-0.02833649308396713,0.03655630250607531,0.010319383233249104,0.021869012075272396,-0.017646542059341394,-0.003704888773108924,-0.03639033595775297,0.015609847895639382,0.01870280105438531,-0.03794810367893277,-0.0010424735821095677,0.012606868773867559,-0.03524074455511524,-0.03650895631041416,-0.021301767007897345,-0.012584498899973779,-0.028057204569637954,0.0006325868317364784,0.004992485152360391,0.012680232021417165,0.0140401649805134,0.030053076883281328,0.023286303480473426,-0.02623756233594308,-0.010108351856556754,-0.021203014381182956,-0.02153234249810484,-0.001625997076027936,0.00010953926012588368,0.009807136881024067,-0.03173836650508102,-0.024752869992894406,-0.0004621321545417786,-0.003989159321012707,-0.006225175768182282,-0.001264269926493611,-0.01519508060729471,0.01402544428242647,0.007085376216163095,-0.0017551188745870939,-0.013441317432739061,-0.003483431467255842,-0.0544320222352719,-0.019626053352430214,0.000746560847519753,-0.030081870449638358,0.003990450534595241,0.002948785347123069,-0.027550437809987807,-0.005011462768960977,-0.006276553623127762,0.009197482337234254,0.012237892920042872,-0.0007260309151786103,-0.01702577418756631,-0.002885445537837208,-0.0013085446490645615,0.014689220345102007,0.005886562371384526,-0.01445122751913577,-0.0270881437598013,-0.0074622372894156555,-0.014807865830404408,-0.022237584714194902,-0.002318763904591811,-0.009821407488115982,0.002108737702864564,0.010466005152565959,-0.008260021693209708,0.046485955038954474,-0.006429567375745942,0.02203418012414615,0.0024332205383562613,0.02232318154439103,-0.047518437956302784,-0.015029541948475928,0.004940779166087995,0.012049312879018727,0.046730502636170214,0.0064507746989310175,0.025596823967218914,0.015328806452904855,0.018947508580880977,0.010201236826684827,-0.0031214554273248786,0.010182550489665036,-0.021562656680970956,0.023627317101910034,-0.020343961335519835,0.004984111191767063,0.04241555919780238,-0.004468356483272541,0.00039009470136236186,0.02326080780485408,0.0005248435329869857,-0.01615283957712924,0.005163197012265479,0.011642499150145414,0.014201380395174395,-0.01545024783324154,0.03505012148256062,0.0333354890706681,0.0003647523183120096,0.005371853583258264,-0.008570150284050265,0.02828256701510258,-0.014098955455770652,0.0134819088730271,-0.009593861954140638,-0.01388009183699984,0.01437329613429926,0.02667644309630869,-0.0002023956537871557,-0.013548623261545803,0.01622965247218858,-0.000990200424204401,0.006212650125950094,0.030457354575353226,0.02263245464529356,-0.01039674618231545,0.04567160369790327,0.00006669628930214794,0.015719292775683374,-0.012947194964651312,-0.0008932481562421348,-0.0349997808792419,0.035733434279315954,0.02731497135270512,-0.024306016643607455,-0.03010396390759557,-0.032421234208337896,0.02351512188206728,-0.009190984403374451,-0.0012106664802738185,-0.006255222591228057,-0.002423136314582569,-0.02176351339466784,0.00048216417137552265,-0.028759878945352316,-0.001429570185201181,0.006174939229650649,0.009352195467446436,-0.004634388546529934,-0.018074269253334285,0.003191446899517766,-0.009692864299241667,0.03131670348841134,0.015354445079922454,-0.002303882188626336,-0.009422910866462216,-0.014053648583935189,-0.018744513357854372,-0.007058974133330482,0.005895402346303528,0.010310507157249002,0.011377162235739861,0.04197365197527105,-0.014097087843012836,0.00025904033916756273,0.05589233670195686,-0.03734129563564871,-0.010429721812962974,0.003391688147516001,0.003087843698147373,0.008157337224599165,-0.004774164152333445,0.007322467897541376,0.00105561941431963,0.01542712246176478,-0.037851795294052554,-0.017700784930964913,-0.00004439670720377748,-0.020636978520129627,-0.020893243826262037,0.01255487733906807,-0.012999604900049035,0.012698327732863907,0.014915518410261824,0.006129901990627528,0.010161113762397863,-0.002091933278850274,-0.028182155107310206,-0.0006013888630481493,0.009084721889047817,-0.010588069917597644,-0.0019907122363303454,0.014984491335237495,-0.017561825081965864,0.012800402811500142,0.03725170759384437,-0.011091280380659754,0.002930359069752501,-0.003009068962833002,0.030804480588527507,0.006327542390338451,0.017954594250954505,-0.013801582735921436,-0.0003227880070135599,-0.00019690335519010875,-0.03551860184285668,0.028816227001648737,0.01798810952529125,-0.03498288023265115,0.014887214262511262,-0.002623194756470927,0.00896830704934225,0.007329126519885264,-0.029979441245178737,-0.004240881557229828,0.029852327687410998,-0.011497150425952148,-0.02045663689815629,-0.027191600180011887,-0.024422402702156055,0.006710078689948792,0.03385168551452677,0.008588839146863984,0.004910116241601405,0.04467298028457251,-0.010388777738445883,-0.013481378162812023,0.010569097931115124,0.010970672852549792,-0.020294502325288014,-0.023399546459912747,0.005820425270214451,0.0049479266463015835,-0.02613741092550435,-0.0040449796611902395,-0.010853212497890922,0.009201099863830954,-0.0023352064731815684,-0.0017205257190471578,-0.007069786682167898,0.021071090002207468,0.027815200305444897,-0.007339542835361255,0.016922197192748942,-0.015152180142903633,0.0014397836839177402,0.01499803636507005,0.030284380072126613,-0.0076512478180378865,-0.0014813401648976357,0.003927877091540851,-0.02996202205308862,0.00031812010677988563,-0.013517560793176977,0.007429586527347303,-0.022599420638392275,-0.03953728948621883,0.0007656830752837564,0.0052122520272286,-0.010978645580773385,0.017776937698131007,-0.005463527824889205,-0.012113902929193733,0.009554843896714214,-0.031363817299417764,-0.013549093614814123,-0.0004154343801008318,0.016977983520433067,-0.003254345545243077,0.006169507782322391,-0.013109910439685853,0.006034421471602003,0.03326934798177334,-0.013727321606376333,0.04732426847815617,-0.012876728107216847,0.00034274338624944384,0.0034661805415620527,0.020486092218650723,-0.02474046652328657,-0.042010921344274525,0.012120164143081303,0.01590877965541189,0.01247367925006701,0.05261013260212955,0.0040990261164359255,0.0050778000680687186,0.018584741091204574,0.0073764953220876095,0.033273861737540836,-0.024765214927705545,-0.007507951696138018,-0.06889410210653636,0.01624831978537105,-0.00744785208495262,0.01847924948876412,0.04308289518487803,-0.0001181021273907001,-0.0050908495106723765,-0.009991611269792545,-0.016757593119302912,-0.012607310685155491,0.012785429042195038,0.0007367601598040159,0.0013255438743083284,-0.003465438643549329,0.018287276293404025,0.009879482630816575,-0.0028356319774038175,0.013294242287768843,-0.0030355982283050056,-0.023058263663938604,0.02910635368576944,0.009305882941500712,-0.019145253880939125,0.02157650585953787,0.006899487742260381,-0.031287191638887095,0.032198973731244945,0.006669738122992355,0.017828994968989598,0.003956808883417576,-0.0029905996086962267,-0.030963116513107992,0.019431668116396652,0.0006023263231164223,-0.005730289554775117,0.007018473023471778,0.0015620737786757898,0.013513049426891861,-0.007420381325740358,-0.0007293442381116675,-0.042778891225281584,-0.00846600738943448,0.013514287310067027,0.02673461379833026,-0.007279540603209419,-0.0024268423645868614,0.03166904026394329,-0.00651580749993808,0.0146801562669513,0.0335663182302627,0.0007955955514553279,0.02453841548769826,-0.014209859280993907,0.004153434134372183,-0.0015471200694424467,0.0022982669292372043,0.02259406387254084,0.047797469832129645,-0.013309371304745021,-0.011502389944261929,0.009947767206933175,-0.021102928955370973,0.009940313970927242,0.011438070765818702,-0.005550133564961593,0.010623861370639776,-0.030986346933354444,0.015197621469600454,-0.030896682734231455,-0.013928993321020823,-0.011123956624965112,-0.008022704926085155,0.017175340409671797,0.001633014819733217,-0.007948734141931537,0.010869639386650348,0.03162553211739585,0.00012377884317747766,0.007315960909959216,0.024793945272144707,0.005356536538504401,-0.02567694216327604,0.049805721183619235,0.04416717381024419,-0.03969735940458447,-0.0007831470029921743,0.008345654742105711,0.01931461216932308,0.01338012117947009,-0.005443897046728028,-0.021076727244905346,0.0020591256553929584,0.020668715917241568,-0.02179233659197578,-0.020543781966064396,-0.0004925593029904767,-0.03874975728339148,-0.005205945680979969,-0.008730657500330795,0.009015239637602795,-0.014035336350523514,-0.017642428934530382,-0.007883827686432202,-0.0009985210663172985,-0.013293167316922259,0.00024239123842569984,0.015004397057068802,0.02370239780717162,0.03409819089840864,-0.015669695774810383,-0.008395353495035054,-0.04965740871762597,0.03798648467167655,-0.014494215135581556,-0.0006675135678320258,0.010451446752148657,-0.027171030019754183,0.009278241553835977,-0.0005278259035335137,-0.03652059388256338,0.005840111278356752,0.023890452607112336,-0.03735604147442467,0.016144295339273067,0.004184300045626488,0.009496459591192523,0.008830211852787288,0.026078721023194494,-0.0044729603596318284,0.0174717477177783,-0.008198295123871071,0.014558668605523717,-0.016279645945631912,-0.0021668139046202984,0.03462024593716067,0.008912351120261243,-0.0031643028543990727,-0.02289616298969199,-0.01580264006426114,0.0038729173049534206,0.018788044754137475,0.008521266986920635,0.010482805103694265,-0.0008350973736185169,0.02704039139613357,-0.007815805867971986,-0.010994418335855394,0.017761921326428298,0.0012721749210730542,-0.005571197039777547,-0.011522063091730036,-0.005137854636219815,0.012471260628146526,0.007074974797570248,-0.02419261390115775,0.00852666355355589,0.003580355329926559,-0.020003538588806793,0.015456690428926601,-0.00560837212088963,-0.006708846492315146,0.015916194504879105,0.026413914639968453,-0.013771369764410426,0.008765218591202127,-0.017521489660104608,0.04628503281243242,-0.009875369954085276,0.023899892943268865,-0.012946351675851604,0.016226082719083774,0.0443775265891009,-0.050819513484259275,-0.008689952733907567,0.010010296486954891,-0.0018572022916374079,-0.013369414438552272,0.0430429095221775,0.0015900280739810637,-0.03288847664335075,0.017082934896389616,-0.03443220262314574,0.023016976475394708,-0.011555015623708316,0.0028967931390614745,0.025219142478714707,0.0023574344974810987,-0.027821624435456997,-0.03391886239215431,0.02365173748893493,0.01480865044342103,-0.01631512529688296,0.017190328471753634,0.0099330644670211,0.01295403433357121,-0.04517807874270887,-0.006041843102069011,0.01800819030147492,0.014669034562847485,0.017628339731903666,-0.049145103048557334,0.003381264455382117,0.009843905989797445,0.051038487382418535,-0.019075142371317445,-0.0065853735749830935,0.0007171292719589229,0.017721890404198692,-0.008866566018617933,0.022944953188473304,-0.015758131463238772,0.005337386878860452,-0.010547893334597633,0.0031636571587979868,-0.013816348693561567,-0.031945712156002455,0.021861862862506767,0.006068324942562423,-0.011172942359649855,0.00401850227803447,0.019803357992751174,-0.01954956150894363,-0.00220710713552781,0.01078326957796486,0.010523103859134604,-0.006706096410850821,-0.04213957788279591,0.024858509406512436,0.006565883417719036,0.0002613429177531019,-0.005570583259325141,0.005268098182200031,-0.008511978622737806,-0.0204938041830082,-0.014795347482202587,-0.011936662104097726,-0.012247025851779253,-0.02317433462615941,0.012726574914317034,-0.026196061240500685,0.013194532514064515,-0.020293161307223334,0.007049284897887193,0.027481081019981014,0.004065454125807345,-0.014616215066431385,0.0009655360385648228,0.0029627146672424097,-0.03467611871397737,-0.012153664780289253,0.0032601901096947577,-0.009384124664869818,0.0015941502449322918,0.014679519860391333,0.015331274718012084,0.018113981748437053,0.011770879296182132,-0.005758585200934815,-0.0003681572675872476,-0.005423232262408601,-0.006264577899221063,-0.0035932871960378666,-0.034494061488169185,-0.00666350873242772,-0.0004815535732350684,-0.019479341073193008,-0.0004803725449577169,0.010310519760027764,-0.0032880337084320193,0.041532598158649583,-0.05212909243089594,-0.00412705706740425,-0.036508099592968545,0.019599428253623746,0.05308271613341005,-0.05004014178167653,0.0025584018034520402,0.01038180344063113,-0.006048458518539093,0.01103296218404574,-0.04485953688629293,0.01704055900892162,0.007439820921671824,0.00045652982655461664,-0.011751650640868184,0.012767881770690699,-0.009707724759503837,0.004462445617780938,-0.010201709514514082,-0.04493628116998764,-0.0006262584334162904,0.004043749365697927,0.015087689187048036,-0.01752163488589821,-0.0006616319181931635,0.012342953158373795,0.0029086308229181435,0.024849324489995453,0.0398330494385519,-0.018172608973875067,-0.03841804119710267,0.017132618243936765,0.030588904385895514,0.018446005836819105,0.016278559795993557,-0.012372991229335814,-0.014271045026019176,0.01776784567697316,-0.018231081611044666,-0.03626654546251907,-0.019950667388265602,0.049845020101146796,0.038467898326246315,-0.01372922107686747,-0.014579001714623938,0.004628287747699126,-0.014987301153994445,0.026201827877872143,-0.001566143590447963,-0.021726052726238856,0.026177988921908403,-0.011662724188051048,0.004425272686967967,-0.0002531819133514209,-0.006287531428567785,0.00649859697710562,-0.01384988857108513,-0.03688952478808859,-0.044159493498317375,-0.02533189065297643,-0.01516882162297892,-0.0004593062134942628,0.001105937298207441,0.011120704083822246,0.002397380143787374,-0.015868934603032472,-0.014177872289370492,-0.04237613169882776,-0.003382761451894863,0.009697172643457621,0.010593138421123761,-0.0024284999623204115,-0.0034836386565631414,0.01872599352836568,0.0003077637364414564,0.014756489104649084,0.011650023537980852,0.004263139049784742,0.026128439558528598,-0.011453961629214663,-0.007177531361005915,-0.016159639079951618,-0.015943715730377426,0.031119792248687307,0.035186319033768246,0.00045809207132546485,0.011364816059050372,0.02350645160404928,0.016149304110449514,0.02410699958094478,-0.025259333302309728,-0.012787584706010189,0.009053095806880176,0.028706738336234845,0.0020771512307268076,-0.017168724563949033,-0.007090191575792355,-0.013211641853812467,-0.01716649559212918,0.030023664518435942,-0.012512056760250738,0.00040842987885730906,0.043248488643457574,0.023694369395500882,0.006723019420645811,-0.012237660701121955,0.008206034640289862,0.03243361917314996,0.012460820753642084,0.025230932739966447,0.001961807413031102,0.010325475040470445,-0.0040192131087353035,0.00853795390476733,0.026008987649037422,-0.02862261379124764,-0.0012503697235092743,0.0048052863522383615,-0.011421786779268368,-0.006160661042587925,0.015738184726562594,0.04003297600414734,0.012589079675896994,0.006522247754355524,-0.03102890365324267,0.03855090747644643,0.0015387845606643453,-0.0006765755139299663,-0.02236806326913801,-0.0011367253709647913,-0.021922670078176144,0.0014202249719237451,0.009326308989553469,0.0006247150139262336,0.005593082245936971,-0.017036543121879938,0.028595199762683904,-0.013064479070426335,-0.03636627486747364,-0.003750072121616121,-0.01527483422254256,-0.020195551846173467,-0.007097555538751196,0.005824047346976228,-0.02363645269398438,-0.0027509012541704824,0.028534496576173282,0.013654842233038103,-0.003039536712092919,0.00255476401101858,-0.002397718033763475,-0.0009556144639098083,0.01464756784509796,-0.0018504787445267382,-0.04808878432884993,-0.00043026817661151814,-0.017789602904575704,0.013025440935087498,-0.012206347050538465,0.0029683416498513904,0.043545585197413444,-0.020937785720595774,-0.02249279961863848,-0.028230437450878273,-0.04789717825314276,-0.03756947949612237,0.00729088616487243,-0.01276128365046157,-0.03736319079690185,-0.029652845128171776,0.012345083498127131,-0.015505419914724372,-0.00733685294526712,0.00660916832338194,0.027127944903741145,0.03882048389080429,0.020648905895533146,0.002872181149089932,0.003683396992381384,0.0360434010413587,0.028571966538641906,-0.00621006499924147,0.00915468986916295,0.005738997886257925,0.0010474798152211309,-0.010000820639537406,-0.026529508069292565,-0.010680430222411882,-0.030882948083845597,0.024475262346320605,0.010731407124723669,-0.024119245453946586,0.027916594901788973,0.01783467224761526,-0.0381721058614467,0.03682826825841744,0.016198251683611248],250,0.95]
期望: 0.046472146288435684
N=1200、W=250、alpha=0.95；规模接近上限，验证 O(N*W log W) 在 2s 预算内完成且数值精确。
Case 15 · large, N=500 W=50 alpha=0.9 stress test
输入: [[-0.0359144142147632,-0.004992614195724789,0.01603303581287113,-0.004063497451776182,0.0031539738498687366,-0.031057423656814943,-0.005106577225831005,-0.008203389375857259,0.019411984797117168,0.0033171890444808018,-0.00034547407600048023,-0.015250345580826946,-0.017478190455217275,-0.0001760091627689759,0.027423609919751898,-0.03963721549982467,-0.05861305183657054,0.04169611687852445,0.033842054076241954,0.013941367455950362,0.008105484898230297,-0.008073311030456247,-0.007051132658663715,-0.024597839709544173,0.013191971634554399,-0.003815742059785065,-0.04008761067262188,-0.01028290987140183,-0.011067082731250455,-0.013169779103796827,0.04127574691952954,0.02332511111960674,-0.06608683981158701,0.010851213693248157,0.023029655045266936,0.028417516999383153,0.017429755716870127,-0.04143110902519207,0.01917709618602587,0.0021579545044216096,0.031655502115192566,0.010653768645040591,-0.030952628316790222,0.040089905700510395,-0.02437770695282229,0.02443014319296544,0.009966776123455826,-0.010913511786044841,-0.04707734094183619,-0.01755841552032286,-0.01861609925864214,-0.0031788970059714824,-0.003790853213959226,0.034940100641255405,0.00958155778860617,0.02547660495949772,-0.023866070228910182,-0.008684989375113318,0.020140042034848885,0.021308622423757237,0.015171661455852716,-0.008776840512868337,-0.021595802052940392,0.03809850874647111,-0.014061641645695636,-0.007541135211462705,0.033396988841494946,0.0020513106167884976,-0.012962118597871065,0.018319637177702283,-0.003991134048638148,0.02803939999505415,-0.002267496342982259,-0.01707230937659972,0.0524166041583788,0.026719964991987696,0.0034511983755432536,-0.002188946521124319,-0.02799939422329784,-0.0119465267098811,-0.026600589004653487,0.01856746634919676,0.025865676618856144,-0.006673177306727993,-0.010251560666208186,0.008311455640868447,-0.00010191687667002725,0.011435009886368782,0.010626140434741027,0.00883666445962407,0.013564152616572428,-0.020784568057550513,0.01521650218949731,-0.042319035395096946,0.002373796753352713,-0.005910224453937683,0.00788846880103468,-0.003959681108125916,0.0050202944491386774,-0.03788927097368323,-0.01117056643036674,-0.01699424370174568,0.007517865999136915,0.0038315596944512305,-0.00973298280941889,-0.011252312586500926,-0.015380165611282217,-0.0031631589033621287,0.008660144773739168,0.0143149702937447,-0.0036330138546864506,-0.022814345042283787,-0.01804507223443388,0.014406673414711493,-0.022710781799266822,-0.008012963855278185,-0.04924263189114496,0.017707835295486387,0.00015700662515215618,-0.014425405396854588,-0.005379293808481173,0.011766697529235882,-0.0031530743540878242,0.003617855882352686,-0.000894659803114687,-0.025893199802441053,-0.03742583169892397,0.019761550489428802,-0.012484741560568,0.02313956392471252,0.023039500790250425,-0.010884543795622505,-0.014530733512898226,-0.012485681403106123,0.03353098307396395,-0.00040080713586496954,-0.006166513441440915,0.01770361523923874,-0.020296141327445023,-0.013151895487778203,-0.012923226480840735,-0.0019060983456015686,-0.027741334754637765,-0.014289569168991054,0.0020549817617123807,-0.021751910475934576,-0.022320290153662707,0.007947549911194394,-0.022115421981232335,-0.005126546391067371,0.015594448870673879,0.0011878850873217309,0.03731260702316781,-0.002864115501004099,-0.032698136286189956,0.00679867050803211,0.0038017137677064513,0.015304303744374578,-0.030814824151676287,-0.0034273521335609807,0.022256045126144694,0.003893550029253081,0.022874882058301904,-0.015318970299591363,0.009108575865751858,-0.0003956416681871045,0.03200534282154245,-0.02070790355366148,0.024471086577943852,0.004058645007548871,0.0008259030044646516,-0.0141490299778543,-0.023057091879545483,-0.03144455214893098,0.005764349972603219,-0.020342491117221896,0.023241195644988694,0.008923639108818923,0.009436990736158264,0.02301978715240684,-0.002250453660171173,0.018337464411308284,-0.03562496004604513,-0.01004300385943802,0.020152954467756137,-0.00315056714900199,0.03327328753554573,0.0015598112131022164,-0.017910443615186674,0.02851386469066111,0.0025327076581764256,-0.004567914062359311,-0.001967491735791088,-0.016257794852998934,-0.007849614262827254,0.016243555662669044,-0.014500608862113627,-0.003566227458770968,-0.016314626237146895,0.0005672808713242514,0.010751248228483343,0.010701942469054964,-0.007251146214440827,-0.015648376547654434,0.005860917597529195,0.018156982298866794,0.01307797994031991,0.05622853713250686,0.0026594253324813584,-0.01115799350942299,-0.0058175461387449615,0.02059528726862703,-0.019526330043296684,-0.0034806495074376593,-0.03343305963498642,-0.0049349027024805404,0.014502430874996511,0.021096189114499574,0.012666346426835718,0.02125510562452333,-0.01475647742157606,0.032902399445205524,0.03674945059114814,-0.03407369034748561,-0.02311669901822279,0.015259100282044594,0.015431835079203586,0.027507155636455987,0.003697191283495618,-0.020781137475021964,-0.014669401903391582,0.03033298045254833,0.00007865595545365676,-0.035843878630037664,-0.003587611025093796,0.014471411111339656,-0.00005273402754768162,0.013022366422583307,0.010211344532176645,0.0004502538259651677,-0.021201807890033834,0.0009713594259133436,0.014997698405977823,-0.012457905451918015,0.022187079619660564,0.040559220550100465,0.016350179527361616,0.00805019712683746,0.0015047387857333328,-0.01754573489494356,0.03214977638023562,-0.007408300127777574,-0.014295860998012824,0.03726070209805248,0.021181186835162746,-0.01133958298700303,0.0058145874868348905,0.00735668051715198,0.01732313483860676,-0.03809244378056882,-0.019585695011687446,-0.028384771285666167,0.0039861375752804065,-0.014164904768526932,0.009209506055829274,0.039151401149830775,0.01138649157232413,-0.018131248433774304,-0.0010273131496730161,0.008035025025432473,-0.03612851428680829,0.024741397954775268,0.005032019015921685,0.016683646898349298,0.025313067679704253,0.005689044177508247,0.027870192449681114,0.011051684823943905,-0.02095380840944476,0.0010499488217163308,-0.0009937251235053125,0.016950148361274082,0.037205813758214135,-0.0296065269831111,0.00017214348362870412,-0.013840863635049801,0.004946504283369611,0.018330952476894143,0.034012931834497884,-0.0336555866669687,0.003554160064448545,0.028110339359894283,-0.016052133970190584,0.015124024812767764,0.010335362827247395,0.0302665620692097,0.00947738288707952,-0.04640899290310627,-0.02148762372415493,0.0021422033102983158,-0.006435416543210663,-0.008437115514415705,0.024694038587460172,-0.023642541601048672,0.00282673334389608,0.02007811404689931,-0.03893760738002782,0.0034261643618697037,-0.005205739296452531,-0.013840833386979261,0.04395663969839495,-0.013934881218515152,0.014602537801494874,-0.018156317350874723,-0.02014146792267697,0.0034234896783138192,0.022697936217297668,-0.003197063004010381,0.01234245692676784,-0.0032095047625048867,0.022200614364897557,0.00427854325836408,0.004870299424111684,0.014610652568554188,0.010046958872282989,0.0023122348371141374,-0.00798165966307018,0.0030961280991389207,-0.007911130323689626,0.026378921567364166,-0.0010796366533668631,0.017241833335367853,-0.011290292536640998,0.010814996881175144,-0.031929699745956414,-0.013431858701981306,0.024328764246155377,0.004817929337743053,-0.04369664437247429,-0.009693117908160687,-0.0045592836720653234,-0.015366504970297843,-0.03204712453900906,-0.028642655629868136,0.03258383260145533,-0.010266708813400796,0.015048366215363703,0.012067763833811031,-0.017714884600324388,0.0023850841823663065,0.0012678044741704798,-0.023275752339857885,0.002484216485715203,-0.0003368690231573565,0.0034948588358908565,-0.009178156110466868,-0.011278512868415231,-0.0013229289138457809,-0.02031216686049921,0.018530923793884945,0.005586033225062457,-0.0014789646561590597,-0.00748802436033226,0.006058794898915588,-0.000490388885740547,-0.011125015838981352,0.011911545370563544,0.03437558253753813,0.0398145359833379,0.01213415116168559,-0.0075959734466124335,0.06613321294030461,0.0070642689755257265,0.005565774591225771,-0.016999640072442437,0.0025780218502916264,-0.0104890715501312,-0.013361433022941278,-0.0017792790030575964,0.0032031896237514935,0.0013409985603220168,0.0008336425972761929,-0.03966557848169189,0.009824233941769643,-0.017206658955829648,-0.004054737588442918,-0.03296031967549815,0.008633734486252561,0.006076342264781551,-0.006425665834089418,-0.010166254454169705,-0.013358924508394415,0.02899737165521434,-0.013845444386104178,-0.02500226658622324,-0.01588707884817959,0.0005787564432300619,-0.007652705681424581,-0.0024733761253826116,0.005071208661676803,0.025972675111756337,0.037778056596878794,-0.012024984077134862,-0.005853597317922249,-0.005816782218108412,0.02002891494548368,0.03157817675309282,0.01876384516824841,-0.004998344755498932,0.004629791044954685,-0.020582329225353902,-0.0018958421045345325,0.0012759006626215552,-0.015586747003632993,0.0017239472738516434,0.02354002645146137,-0.00869951619624524,0.005928875768102725,-0.0036560591739753312,-0.03993573446357183,0.01428453342091432,-0.025568023608033216,-0.034766903201863555,0.006429894797492444,0.0022140885792999183,0.008857921863270887,0.006864283845798694,0.023620636999177606,0.005557226280986019,0.020661742452571286,0.010620089661031715,-0.02561833995063184,0.003214106295482626,0.009676618155921269,0.006475684925041918,0.00023323614175118474,-0.0022885310141733954,0.03147545209141012,0.009463153540056184,-0.0173521214914121,0.024560596990298368,0.007272623605798254,0.00332178370838499,-0.0011165929836809733,-0.04886675389405258,-0.0513130674482959,-0.01198017458138008,0.02394600216290648,0.011098267911427566,-0.027464866991473835,0.016400708869189137,0.031073141972429844,-0.025207446557661252,-0.015100681684757637,-0.030394924256610296,-0.021767305836627285,-0.04081291518985325,-0.019667674314113766,0.003376014897848796,0.002815215085324812,0.015449486137500322,0.018107471516979518,-0.008765295440932812,-0.0438188705530466,0.0025006116826284835,0.00011455116061810132,-0.02165439767293813,0.019693128919777387,-0.013045349978126073,0.009615066166277412,0.009265296856372342,0.030198896012484693,-0.038732675558941866,-0.03064718579062972,-0.01059411865502813,0.020121179735055814,0.030151544870038804,-0.007319508379132075,-0.0023054507053611845,0.03222893702333623,-0.008194341244752016,0.0028207742593996006,0.018538574856919884,0.014421227337128369,-0.005832712508629972,0.014367351071210701,-0.0025774930948954263,-0.015224659336472046,-0.022713523644941495,0.007227308332612721,0.03607039518798126,0.0018059919920683262,-0.0013177016049010257,0.011806993520985723,-0.013792132994610804,-0.0012614907210830232,0.009625664309226767,0.001980792110509817,0.018112473383231253,0.004684370893896551],50,0.9]
期望: 0.050659190457561544
N=500、W=50、alpha=0.9；规模接近上限，验证 O(N*W log W) 在 2s 预算内完成且数值精确。
Case 16 · adversarial, duplicate values at tail boundary
输入: [[-0.05,-0.05,0.01,0.02,0.03,-0.05,-0.05,0.01,0.02],5,0.6]
期望: 0.05
排序后多个相同值挤在尾部边界。W=5、alpha=0.6、k=2。多个窗口含两笔 -0.05，ES = +0.05。
Case 17 · adversarial, large PnL magnitudes near 1e6 limit
输入: [[100000,-200000,300000,-500000,200000,-900000,400000,-300000,100000,-700000],5,0.6]
期望: 800000
大量级 PnL。W=5、alpha=0.6、k=2，最差窗口含 -9e5 与 -7e5，sES = +800000。
Case 18 · adversarial, monotone-increasing PnL with one stress cluster
输入: [[-0.001,-0.002,-0.003,-0.05,-0.06,-0.07,-0.001,-0.002,-0.003,-0.001],3,0.66]
期望: 0.065
单一压力簇 [3..5]。W=3、alpha=0.66、k=2，最差窗口含 -0.07 与 -0.06，sES = +0.065。
Case 19 · boundary, W=2 alpha=0.5 k=1
输入: [[0.01,-0.02,0.005,-0.03,0.008,-0.05,0.012,-0.015],2,0.5]
期望: 0.05
W=2、alpha=0.5、k=ceil(2*0.5-eps)=1，每窗 ES = -最小。最差窗口含 -0.05，sES = +0.05。
Case 20 · random, N=100 W=20 alpha=0.95 seed=1
输入: [[0.020322771297331944,0.022741684130496563,0.001995037134073929,-0.010468154764574477,-0.01538259822656212,0.001470017752475753,-0.014331547550163092,-0.020552441676537945,0.003989679647256307,0.0030006190698790725,0.009197024505073474,-0.012709564156029689,0.0010750792543985867,0.000028873594409681747,-0.021587435018911125,0.009069957679915506,0.005810666514982724,0.03683668064861029,0.004044537659649463,-0.0011705346224738077,0.019491357625433855,0.003981868722901382,0.014635465392298135,-0.004483163993487751,0.004272577200408736,0.01636433017730527,0.011443705336794424,0.002927083729492846,-0.015234620368940667,0.007678326585415728,0.002152952225788785,0.011807013952888804,0.004243494067001096,0.017322781167032848,0.00022659601864111873,0.004029460901191319,0.011001646579384742,-0.01530326918261719,-0.0050249039011102834,-0.006500428534285526,0.03070923579284869,-0.00039293038484126855,0.01078330335711358,0.010290625932605785,-0.003213101452803389,-0.022262552406956706,0.015472659560142148,-0.0051079515449538775,0.011769349851173498,-0.018578972376649468,-0.005569745029547446,0.01985232016908042,0.022465059820787774,-0.018536879317075358,-0.018992112186334148,0.0003360334359725209,0.011923619849780794,0.003407570190689946,0.005553320617404756,-0.013832546374619194,0.009801875707207055,0.017752785117052534,-0.005535087804259744,-0.020502320954951987,-0.010382312355256232,0.012424870087554739,-0.025005457877546506,-0.00037815181708405815,-0.013865124277182402,-0.0009670166296657811,-0.0026678238012205788,0.0012378517490847403,0.023518110944551012,0.007310656654118205,0.02100569118047839,-0.001121190714551809,-0.006193799117404486,0.006682158733989835,-0.04153686180020056,0.00040166777961899217,0.003402546836128405,-0.017528131160203117,0.007965478338588263,-0.007388672064904403,-0.03588650285415435,-0.002199775855519199,-0.013682686164451691,-0.006808938089002196,-0.0012842662805805402,0.019764630238507348,0.0025472226841238526,0.0005727156252448831,0.006835066242510807,-0.02618138548736922,0.01960185805935352,-0.015156303804447262,0.0075864260670251045,-0.015901707432029552,-0.013647280469164105,-0.004944318129072505],20,0.95]
期望: 0.04153686180020056
随机 PnL，seed=1。验证滑动 ES 在常规分布上的正确性。
最近提交
还没有提交记录。
编码区
实现 solution(...)。本地运行当前支持 Python 可见样例；服务端提交会运行可见样例和隐藏测试。
默认展示公开样例。点击「运行样例」后会在这里显示实际输出；点击「提交评测」会进入隐藏测试。
Case 1 · statement-example, N=12 W=5 alpha=0.6 k=2
输入: [[0.01,-0.02,0.005,-0.03,0.008,-0.05,0.012,-0.015,0.003,-0.025,0.006,-0.04],5,0.6]
期望: 0.04
N=12、W=5、alpha=0.6。k=ceil(5*0.4-eps)=2，每个窗口 ES = -(最差两笔均值)。下标 1 起的窗口 [-0.02, 0.005, -0.030, 0.008, -0.050] 排序后最差两笔为 -0.050 与 -0.030，均值 -0.040，故该窗口 ES = +0.040 即为 sES。
Case 2 · statement-context, sES vs full-sample ES — worst window dominates
输入: [[0.001,-0.005,0.003,-0.008,0.002,-0.01,0.005,-0.003,0.001,-0.006,0.004,-0.04,0.002,-0.035,0.001,-0.03,0,0.005,-0.001,0.002,0.003,-0.002,0.001,-0.004,0.002],10,0.8]
期望: 0.037500000000000006
N=25、W=10、alpha=0.8、k=2。全样本 ES（25 个观测、k=5）只有约 0.0246，但下标 [4..13] 的窗口聚集了三笔大损失 [-0.040, -0.035, -0.010]，最差两笔均值 -0.0375，该窗口 ES = +0.0375。sES 把这段压力期挑出来，避免被全样本均化掉。
Case 3 · typical, N=W=10 single window equals full-sample ES
输入: [[0.012,-0.018,0.005,-0.025,0.014,-0.04,0.002,-0.011,0.008,-0.022],10,0.95]
期望: 0.04
W=N=10 时只有一个窗口，sES 退化为该窗口的历史 ES。alpha=0.95、k=ceil(10*0.05-eps)=1，ES = -最小值 = +0.040。
Case 4 · typical, W=1 every window is single observation, sES = -min(pnl)
输入: [[0.01,-0.02,0.03,-0.05,0.02,-0.01,0.04,-0.03],1,0.5]
期望: 0.05
W=1，每个窗口只有一个观测；k=ceil(1*0.5-eps)=1，所以每个窗口 ES = -该观测。max 即为 -min(pnl) = -(-0.05) = +0.05。
Case 5 · typical, W=N-1 two rolling windows take worse
输入: [[0.005,-0.01,0.008,-0.025,0.002,-0.045,0.01,-0.008],7,0.7]
期望: 0.02666666666666667
N=8、W=7、alpha=0.7、k=ceil(7*0.3-eps)=3。两个窗口的最差三笔分别为 [-0.045,-0.025,-0.010] 与 [-0.045,-0.025,-0.008]，均值 -0.02667 与 -0.026，故 sES = +0.02667 取自第一个窗口（更差）。
Case 6 · boundary, N<W returns NaN sentinel
输入: [[0.01,-0.02,0.03],5,0.95]
期望: "NaN"
N=3 < W=5，没有完整窗口能放下，返回 NaN。
Case 7 · boundary, N=W=1 single observation
输入: [[-0.05],1,0.5]
期望: 0.05
唯一观测 -0.05，sES = -(-0.05) = +0.05。
Case 8 · boundary, alpha=0.999 very high tail squeezes k to 1 for typical W
输入: [[0.01,-0.02,0.005,-0.03,0.008,-0.05,0.012,-0.015,0.003,-0.025,0.006,-0.04],5,0.999]
期望: 0.05
alpha=0.999、W=5 时 5*(1-0.999)=0.005，ceil 后 k=1，clamp 不触发；每窗 ES = -最小值。最差窗口含 -0.05，sES = +0.05。
Case 9 · boundary, epsilon-snap W=100 alpha=0.99 k=1 (IEEE-754 boundary)
输入: [[-0.013112053688159792,-0.00748864306344733,-0.011499595660845921,0.0009374738333989241,-0.010679027712774868,0.01564390113180378,-0.00033912118906973226,0.00452797720441735,0.00602871562939312,0.011257131175325417,0.008407494988119477,-0.009131187112259803,0.007354396221378821,0.0018360286376905156,0.0070501329131859546,0.005090030429073245,-0.010360923204152472,0.019131244008969643,-0.018382594475107,0.0018932907513332237,0.0017100406624565609,-0.004752487269045439,0.015836799337729725,0.017847246424777915,0.010783173844490752,0.0003220332764031089,0.002166725607238634,-0.0071201764493905645,0.0012627937475428697,-0.020675073973199728,0.0045363239209714745,-0.007020968227557774,-0.0010593047766014445,0.009205300507700393,0.00206374904596311,0.00040410253392124656,0.0005648480680207156,0.00638800883496896,-0.0007119076260398609,-0.009002788806165398,0.007991771272403145,0.002888240538030924,0.0015085429180744972,0.0015109643270047716,-0.0060062602072141445,-0.0043666258578975384,-0.0007302249407689914,0.006496100677012316,-0.013814419086228507,-0.011109473577140904,0.020854882565160895,-0.008555955501746666,0.0013036371066794683,0.01384671335706266,-0.0011693705448371015,0.005075790539659064,-0.02322664887480081,0.001549550166380092,-0.0067628208033466575,0.009855182678548272,0.00047604457405554866,-0.004140963506804216,0.020233170767372872,0.0007103498884153931,0.010075205370280331,-0.00979103351250045,0.006680500669406385,-0.01995536629472714,-0.0047347689908009884,-0.025275675398085628,0.013426076428977814,-0.02522151451407971,0.0013224818857358255,-0.0024581792779798366,-0.0038706508488168985,0.0007202243709383716,-0.00044367841345814134,-0.00291318499694612,-0.0016522367965677365,-0.01700684552311982,0.0037460527069299587,0.0010802244697144794,-0.025427404423924826,-0.002770944721803686,0.016944646059173975,-0.00244238258804072,0.003029694514128398,-0.008292985501392928,0.0023642538979977527,-0.012703008914333454,-0.014293221213458988,0.004376872448828541,0.008797099346174763,0.001219193719504798,-0.0066880716598674205,0.0008915249169552663,-0.006882248495372554,-0.026959102678411985,-0.00004949598740278035,0.008014114441666087],100,0.99]
期望: 0.026959102678411985
W=100、alpha=0.99 时 W*(1-alpha) 的浮点值落在整数附近；不减 1e-12 epsilon 会让 ceil 多漂一格 (k=2)，正确教科书 k=1。reference 减 epsilon 命中 k=1。
Case 10 · boundary, all-profit history yields negative sES (correct)
输入: [[0.001,0.005,0.003,0.008,0.002,0.01,0.005,0.003,0.001,0.006,0.004,0.04],5,0.8]
期望: -0.001
所有 PnL 均为正，每窗最差观测仍为正，ES = -mean(正数) 为负。sES 取最大值仍是负数；这是正确结果。
Case 11 · adversarial, ES-vs-VaR distinction k=2 (ES > VaR)
输入: [[0.01,-0.1,0.02,-0.05,0.03,-0.02,0.04,0.01],5,0.6]
期望: 0.07500000000000001
W=5、alpha=0.6、k=2。第一个窗口 [0.01,-0.10,0.02,-0.05,0.03] 排序为 [-0.10,-0.05,0.01,0.02,0.03]；ES = -(-0.10+-0.05)/2 = +0.075；VaR 形式 -sorted[k-1] = -(-0.05) = +0.05，差距很大。sES 取 +0.075。
Case 12 · adversarial, max-not-mean rolling aggregation
输入: [[0.001,-0.001,0.002,-0.002,0.003,-0.003,0.001,-0.1,0.002,-0.08,0.001,-0.09,0.001,-0.001,0.002,-0.002,0.003,-0.003],6,0.5]
期望: 0.09000000000000001
压力簇仅在中段 [6..11]。窗口 mean ES 远低于 max ES。max 拣出最差窗口；mean/min 错答。
Case 13 · adversarial, epsilon-snap rolling W=100 alpha=0.99
输入: [[-0.011149298967472744,-0.004999049259460595,-0.011438620155055496,0.009633284816208051,0.0000497176108048333,-0.012271508921357682,-0.006658860859956316,0.0031575473411602157,-0.00652932917145945,0.0035678447570392713,0.0026225403621188605,-0.009959180817476156,0.006554169410040809,-0.014248145677751605,-0.0009928568634324792,0.02591921078488241,0.00560351790435422,0.0062320010941962194,-0.018602573050766427,-0.00033261063012061373,-0.0013411261485536809,0.018271012952008666,0.007847809767378809,0.0018669466440662784,-0.014589728671150787,0.006287989165423251,0.016632462449550273,-0.027216065429669242,-0.007210881027860881,0.0023122835583020496,-0.018009037940197547,0.02004037416555216,0.00712528899052319,0.009425153582456268,-0.007043396604659802,0.00046109180200194295,0.0006421816268565185,-0.004742405293478989,-0.021642042388511067,0.014804906293753778,0.010246789123602438,0.020683854943131578,-0.0008012100523633732,-0.0013455300696804814,0.0012379104101340932,0.006084874893595527,0.010027197929222362,0.01397736007629474,-0.0007168116145556458,-0.001783624588743347,0.009983126610327445,0.020631125974431643,0.017249704209085528,-0.0020800403552316566,0.003933891912780858,-0.007382676607665465,0.01120703484698137,-0.003346033864719677,0.006298914548107048,-0.012336310667451002,0.0013489844157172448,-0.010132618804006238,-0.011628404962325182,-0.00559622903142745,-0.01499585545321304,-0.03526441167088841,0.009878762034524112,0.004474046362080074,0.010099259884770442,-0.0012755186837236237,0.0009885319216541375,-0.01579905913141974,-0.0030859229831712194,0.025404386268783982,-0.006355193428787243,-0.023745291605321527,-0.05626224201472549,-0.05681931048885472,-0.0532159579138479,-0.038877017923180546,-0.042268157125404646,-0.0335305455835027,-0.04110131740435686,-0.039726635144564676,-0.04280717346187144,-0.06092248616444681,-0.04722573062482094,-0.05962500514719829,-0.05671707483803759,-0.05628497948592277,-0.038213569063668136,-0.048841470911418314,-0.05318680418683856,-0.05321403662364574,-0.04508375358678593,-0.05016490358267769,-0.06288005587176523,-0.024327124417149976,-0.05200478085043446,-0.0503453374472038,-0.048222228178388504,-0.05513900946272604,-0.060284026824727846,-0.03789819470868398,-0.037904259233723946,-0.04709994379287389,-0.03837640706362899,-0.04851856904427966,-0.053710667127281994,-0.056262578650622064,-0.04039444340300581,-0.061398003339606114,-0.041096390121192025,-0.06445453962643644,-0.04457590200946479,-0.06886108687885907,-0.056612689638477875,-0.04273088135506057,-0.0497239809229955,-0.06310494861365945,-0.058681217424672374,-0.0453605625674646,-0.042697945254900456,-0.055875988286022735,-0.05487080563293404,-0.008980479493292042,0.007330665487602931,0.011466782569388028,-0.013779401381764863,-0.021974868676909055,0.003182192761583656,0.007328020946452584,0.011237052755616359,-0.008997769829249012,-0.01627198854418559,0.01641757832532185,0.0005767588297899436,0.007880437118833416,0.01789970400389449,0.0026945203160041132,0.009049210332955535,0.002321614341365397,0.0037440241026355297,-0.014284895253282012,0.011301892022837365,-0.008370476769426753,0.002930092136548833,0.0027106894240812624,0.0005149794466998552,-0.016031197770495383,0.01099266829194361,-0.01004131859407689,-0.003940901311304236,0.011085017129226302,-0.003462272326934582,-0.005665675755621504,0.014373069494276476,0.007360230833557459,-0.010506495807472314,-0.003679775419480732,0.01979501574980781,-0.007637598919476555,-0.008032930389801341,-0.018432737565290395,0.013032549878466556,0.00025196254422326573,0.007896000667208771,-0.0046801706198572775,-0.0026020328932172634,-0.000358775417992628,-0.00030713672510183275,0.005117499456084514,-0.004707284257963626,-0.0067388026204893885,0.0034559966348593762,-0.004177645886051338,0.0021911728786211176,0.015651138875178036,0.0077839372191088755,-0.0025502675552212585,-0.005877887709748986,-0.006019994905296687,0.007292618534453118,-0.0071451426996325465,0.009389775241278604,0.01124877493160787,-0.005334011106136605,-0.011131383091304152,-0.00809409661770658,-0.017476872611663034,-0.01745425750995701,0.0018467515602044358,0.008419962020298358,0.012300021411405402,0.011829462362197401,0.003940058216711551,-0.014069792347524568,0.014980130863855246,-0.00211144990608551,0.01054943337572727],100,0.99]
期望: 0.06886108687885907
W=100、alpha=0.99 滑动；W*(1-alpha) IEEE-754 漂移使朴素 ceil 多取一格。reference 用 1e-12 兜底；mutation 测试盯这个。
Case 14 · large, N=1200 W=250 alpha=0.95 stress test
输入: [[-0.005117605768952009,0.01022863025033028,-0.004521923295662094,-0.006301368446623708,-0.01860036380645535,-0.004266038948424073,0.022238347619726415,0.008482933682518724,0.02073758157779333,0.004978054553301827,0.007895392692275155,0.0037065332085679755,-0.03332125050623887,0.017105019375294742,0.010127696917894408,0.00997636076323888,-0.03382729103696845,-0.03487776234551207,-0.017792306896138595,-0.009363785514664692,0.0061089198366488144,-0.0009182346102517071,0.010419497968418042,-0.012844694997489876,0.0061740629842176225,0.007883089537184201,-0.013222746950642848,0.034350606346674854,0.011132187117349111,0.02394010475958016,-0.012406658289656876,-0.014790317924495464,-0.006880933583263361,-0.0021284266307708796,0.012641574900642978,0.004968545071393843,-0.00894709790464331,-0.019138246273247436,-0.010411806201330776,0.024418426297998078,-0.01615892856615671,0.004895174946321504,0.008530379493483273,-0.029794862697222296,0.0009694871561192407,0.026124871996141434,-0.040287276494205264,-0.006431877021313409,-0.0021227833725136745,-0.016345206048740287,0.009947800223985084,-0.001245597898659108,-0.029293133143081112,0.016556917569826288,0.01338671379642002,0.018916835848148277,0.02881194826385206,0.007244873406966834,0.002385483007002376,-0.025983361694625,0.012308864254299508,-0.01223517839220763,-0.009054037992376744,-0.025295755486026465,-0.01935228654421679,-0.010622421852317383,0.025776750861519742,-0.04063584094897351,-0.029154111071577338,0.004787021927490091,0.02886699508312992,0.011569939007496297,-0.03799886553863904,-0.05036469660062477,0.007147944314220529,-0.014725238794729036,-0.02239573147054152,0.01954742482839126,0.022035724083608082,0.0031450376087697263,0.0049155302055848725,0.008687256196642644,0.03188008113862558,0.012380572065107703,0.010372990779515414,0.010954751472624622,-0.031366210451099184,0.025634670368081806,0.019102041669922562,0.010592474435993836,-0.0394775087107326,-0.012673600511726732,0.01684607187694962,-0.03622428505042651,-0.003680444586520812,0.020390553437045857,-0.02622377226022933,0.032202123967497484,0.011039279435897243,-0.0030027750255957014,0.006497336420094367,0.012996619828903046,0.0024078745240709077,0.022913204717159234,-0.013230891315047922,-0.008294723117866857,0.020833691061471874,0.0005359788309455363,-0.01760928162238881,0.01892910530986423,0.029309951486054937,-0.008896521703114942,-0.0275998637432099,-0.0026949640338622604,-0.002980376072804778,-0.005959992992671605,0.028095406071551303,-0.02053872947831589,0.025211732896766478,-0.02536643958147239,-0.01574078934365458,0.012630425577963473,0.022573806110988078,0.0171800470050708,0.006904494923840602,0.0028471267590551162,0.0030496358091368675,0.01150560541668083,-0.0035239491551258195,0.0055487199369459485,0.011454530672659542,0.000016789529474801217,0.015279647770758605,0.011317562582806886,0.040212643927301096,0.006498852735454427,-0.008551859038864674,-0.007451024318257412,-0.0002621119553136872,0.018475692088497028,-0.006731273769955129,0.007716519841143595,0.03674602555298932,-0.05129358948427868,-0.022478171706780646,0.004877940338066021,0.00796670788834928,0.004771466577221392,-0.008623029981295037,0.013102923866582867,0.005642601319065422,-0.010441026765468028,0.04860107750333505,0.007102657247697899,-0.011084579414937505,-0.0019889710435377394,-0.004511905800500649,-0.0012548309321526114,-0.05456170681900401,-0.00973798059754989,0.020171390161008204,-0.023371245289199573,-0.0013340038169667367,0.01907010747562288,0.017123535317196154,0.02982103993269301,-0.03402826688895825,-0.007067520135277605,-0.006818999771985304,0.012465796918843865,0.02183575007740135,-0.05365659141564643,0.021773585805396123,-0.028950868445253075,0.01366299752204612,-0.029842768067419298,0.003517054667942324,0.023893092206850142,-0.0029863922177190867,0.003822061822970299,0.015942472896890002,0.0028275439029442446,-0.0017696276370506698,0.030665121189214925,0.020969414517521254,-0.0058763011898004345,0.054906504454260284,-0.022936780886352905,0.01829218231373315,-0.0053142915462351115,0.0026473143378144552,0.014100112363318046,0.004444442643877687,0.012772906153241632,-0.030546507253272886,-0.030190221642432794,0.01229885179302808,-0.019263169909320362,-0.020532964954314083,-0.02940278774543313,0.025327601021395033,0.014931160177582215,0.029461494446331754,-0.018754753852916205,0.00002012722352802332,-0.02280613804734019,0.015320747703585689,0.031788457867754624,-0.01780442003272933,0.03120663445754948,0.01976058987238415,-0.0035566933396540172,-0.03943941371859593,0.02813263473871566,-0.0019252098369312181,-0.01205656490583079,0.007991907609694414,0.008199286689365032,0.029961900777757337,-0.020402816214532483,0.022724746410689597,0.029747207628150762,0.029044720198034155,-0.0036124914646844565,-0.014880571038376847,0.020371454492231864,0.0023037062522056413,0.002483789717283113,0.02848429258257904,-0.005268729342097462,-0.04593450421618129,-0.007743824143326385,-0.037078463642182403,0.01637566661819729,0.006340695743279089,-0.012224143026582953,-0.00019198595487592427,0.016652480261401707,0.0015789018138222786,0.026530430243908946,-0.0012256963101086667,0.020806695335633982,0.029829615239550977,0.03219785967488852,-0.013436387507862316,0.017598084170644093,-0.03751991813930565,-0.02166698789903222,-0.03925583026631989,0.02137971245086699,-0.02463869445739107,-0.00025528085651701485,-0.0038442796104925627,-0.0005719505554715704,-0.011830435530702897,0.0046732635062872495,0.03582534176440611,0.0008853710713447864,0.010619642978388322,0.020010387355344182,-0.003958953817836576,-0.025193822636772657,-0.011107909430747145,0.02147189478734735,-0.032924511416984256,-0.011956916411010255,0.02014821305258943,0.015854732997152118,0.00015236256465365027,0.01610471591744901,0.0033195886465967866,-0.023578309149145365,-0.03127884738430396,-0.012779042730768598,0.018454602204418247,-0.0113109030351279,-0.018047172009208298,-0.015419210235579505,-0.030635339049953615,-0.002345498405996903,-0.023592139046435767,0.007282919336173511,-0.04720192825230913,0.006555624191321884,-0.012832215135986353,-0.03884295853242953,0.01449418896805712,-0.00551016502882416,-0.04460073566317155,-0.017501263940300583,0.005820484896382393,-0.009171644210184089,0.01559967375051662,0.014951138828249604,0.013324732832846105,0.0065325057619087116,0.026673938992711563,0.013196683403158476,0.00902436348797779,-0.04167957805088333,0.017931115601757194,0.02618850311153937,-0.005937961653628217,-0.00939014881366837,0.038805969178590936,-0.03516265078968568,0.009377138659832267,0.04847431554563956,-0.018552014816702017,0.013791775206207241,0.0377276168680895,-0.002404214239647993,0.0112239368584501,0.018051512877517516,-0.01811536659790749,-0.0017819160231933237,0.005856034444469836,0.01650769813190758,-0.0006906823383726404,-0.0039068063080057586,-0.02032152120158908,-0.0071795035499387936,0.01783344910522349,0.0020348643405936756,-0.017060568924706695,-0.016832081766347526,0.05333359650591174,0.022797885828139287,0.0127479088324407,-0.05185837796181348,0.01242963141553516,0.009613870008768746,0.03368193911888594,0.008555216905234008,-0.0013497665440498625,0.010448885461964574,-0.038884168928592165,0.02066506483539082,0.006497697468549536,-0.014041426052890129,0.02651144631355944,0.03618679069644611,-0.028048024572232683,-0.01332668477388379,0.005825308863149138,0.003669300835591225,-0.00796961314706485,-0.01948421614338369,0.04240934811724503,0.02074774821859269,-0.023884571914170247,-0.026900159640496486,0.03406256984151939,0.01978297578313163,0.03641941214540926,0.016202867962450743,-0.017441509987726415,0.005213309494659687,-0.043201248331365946,-0.014962376604798867,-0.00117817964459734,0.010455096187886068,-0.014551026345411396,-0.002484484399831349,0.00917094387691721,0.0075337757551831,0.012759925682475356,0.004179634370582069,-0.006478693932469552,0.015783139265480344,0.000987188358028874,-0.016521912045288693,-0.012518563344829986,-0.0000069689516128634306,-0.0021920738694003526,0.0031398849219043856,-0.000009917699359528155,0.0035173813998067185,-0.002685779792382096,-0.025168632022674227,0.008427071184896958,0.021073809009601305,0.008692858705651384,-0.0037849191645152698,0.008928933130189678,-0.01931402084748096,-0.0379230635136505,0.001191404993240779,-0.018609952658439573,0.014797198962666432,-0.02168181343530314,-0.052570228641502056,-0.020790453768247525,0.031561934802580634,-0.00763606657241045,-0.027388336134035678,-0.015267125679705632,0.01041797310112404,0.009937284762269962,0.0035345750637376227,0.029677285316126234,0.014130050894561558,-0.00041959818282947425,0.011933338241667018,0.03309172187003588,0.019426098911868982,0.020475195653405467,-0.021656745688114657,-0.002968703891399211,0.014596885828635931,-0.005928864907563374,0.021377264288546444,0.011926839270960846,0.018165069379650494,-0.0042474177980156595,0.050927529673295426,0.02480032379418639,-0.004308602095351727,0.0018118601729410874,0.051904050279246675,-0.0068645554941837075,0.017482814760877458,0.01960900051552197,0.0001316997666483591,-0.02334276033732612,0.003750728367928228,0.007187585489717591,0.022593571934005224,0.015657782257876313,0.00048719412424675745,0.017071525661253657,0.010796851532864436,0.004120868899378386,0.0011041915699734235,-0.004867203692889949,0.013723210564384596,-0.02108417760056843,-0.012573671622556322,0.00009945873422997987,-0.02927932755624385,-0.008717628080160774,-0.04017679179686643,-0.013657700150381518,0.011368699248372232,0.01132790205301203,-0.0010902599143493873,-0.004642270211322769,-0.02833649308396713,0.03655630250607531,0.010319383233249104,0.021869012075272396,-0.017646542059341394,-0.003704888773108924,-0.03639033595775297,0.015609847895639382,0.01870280105438531,-0.03794810367893277,-0.0010424735821095677,0.012606868773867559,-0.03524074455511524,-0.03650895631041416,-0.021301767007897345,-0.012584498899973779,-0.028057204569637954,0.0006325868317364784,0.004992485152360391,0.012680232021417165,0.0140401649805134,0.030053076883281328,0.023286303480473426,-0.02623756233594308,-0.010108351856556754,-0.021203014381182956,-0.02153234249810484,-0.001625997076027936,0.00010953926012588368,0.009807136881024067,-0.03173836650508102,-0.024752869992894406,-0.0004621321545417786,-0.003989159321012707,-0.006225175768182282,-0.001264269926493611,-0.01519508060729471,0.01402544428242647,0.007085376216163095,-0.0017551188745870939,-0.013441317432739061,-0.003483431467255842,-0.0544320222352719,-0.019626053352430214,0.000746560847519753,-0.030081870449638358,0.003990450534595241,0.002948785347123069,-0.027550437809987807,-0.005011462768960977,-0.006276553623127762,0.009197482337234254,0.012237892920042872,-0.0007260309151786103,-0.01702577418756631,-0.002885445537837208,-0.0013085446490645615,0.014689220345102007,0.005886562371384526,-0.01445122751913577,-0.0270881437598013,-0.0074622372894156555,-0.014807865830404408,-0.022237584714194902,-0.002318763904591811,-0.009821407488115982,0.002108737702864564,0.010466005152565959,-0.008260021693209708,0.046485955038954474,-0.006429567375745942,0.02203418012414615,0.0024332205383562613,0.02232318154439103,-0.047518437956302784,-0.015029541948475928,0.004940779166087995,0.012049312879018727,0.046730502636170214,0.0064507746989310175,0.025596823967218914,0.015328806452904855,0.018947508580880977,0.010201236826684827,-0.0031214554273248786,0.010182550489665036,-0.021562656680970956,0.023627317101910034,-0.020343961335519835,0.004984111191767063,0.04241555919780238,-0.004468356483272541,0.00039009470136236186,0.02326080780485408,0.0005248435329869857,-0.01615283957712924,0.005163197012265479,0.011642499150145414,0.014201380395174395,-0.01545024783324154,0.03505012148256062,0.0333354890706681,0.0003647523183120096,0.005371853583258264,-0.008570150284050265,0.02828256701510258,-0.014098955455770652,0.0134819088730271,-0.009593861954140638,-0.01388009183699984,0.01437329613429926,0.02667644309630869,-0.0002023956537871557,-0.013548623261545803,0.01622965247218858,-0.000990200424204401,0.006212650125950094,0.030457354575353226,0.02263245464529356,-0.01039674618231545,0.04567160369790327,0.00006669628930214794,0.015719292775683374,-0.012947194964651312,-0.0008932481562421348,-0.0349997808792419,0.035733434279315954,0.02731497135270512,-0.024306016643607455,-0.03010396390759557,-0.032421234208337896,0.02351512188206728,-0.009190984403374451,-0.0012106664802738185,-0.006255222591228057,-0.002423136314582569,-0.02176351339466784,0.00048216417137552265,-0.028759878945352316,-0.001429570185201181,0.006174939229650649,0.009352195467446436,-0.004634388546529934,-0.018074269253334285,0.003191446899517766,-0.009692864299241667,0.03131670348841134,0.015354445079922454,-0.002303882188626336,-0.009422910866462216,-0.014053648583935189,-0.018744513357854372,-0.007058974133330482,0.005895402346303528,0.010310507157249002,0.011377162235739861,0.04197365197527105,-0.014097087843012836,0.00025904033916756273,0.05589233670195686,-0.03734129563564871,-0.010429721812962974,0.003391688147516001,0.003087843698147373,0.008157337224599165,-0.004774164152333445,0.007322467897541376,0.00105561941431963,0.01542712246176478,-0.037851795294052554,-0.017700784930964913,-0.00004439670720377748,-0.020636978520129627,-0.020893243826262037,0.01255487733906807,-0.012999604900049035,0.012698327732863907,0.014915518410261824,0.006129901990627528,0.010161113762397863,-0.002091933278850274,-0.028182155107310206,-0.0006013888630481493,0.009084721889047817,-0.010588069917597644,-0.0019907122363303454,0.014984491335237495,-0.017561825081965864,0.012800402811500142,0.03725170759384437,-0.011091280380659754,0.002930359069752501,-0.003009068962833002,0.030804480588527507,0.006327542390338451,0.017954594250954505,-0.013801582735921436,-0.0003227880070135599,-0.00019690335519010875,-0.03551860184285668,0.028816227001648737,0.01798810952529125,-0.03498288023265115,0.014887214262511262,-0.002623194756470927,0.00896830704934225,0.007329126519885264,-0.029979441245178737,-0.004240881557229828,0.029852327687410998,-0.011497150425952148,-0.02045663689815629,-0.027191600180011887,-0.024422402702156055,0.006710078689948792,0.03385168551452677,0.008588839146863984,0.004910116241601405,0.04467298028457251,-0.010388777738445883,-0.013481378162812023,0.010569097931115124,0.010970672852549792,-0.020294502325288014,-0.023399546459912747,0.005820425270214451,0.0049479266463015835,-0.02613741092550435,-0.0040449796611902395,-0.010853212497890922,0.009201099863830954,-0.0023352064731815684,-0.0017205257190471578,-0.007069786682167898,0.021071090002207468,0.027815200305444897,-0.007339542835361255,0.016922197192748942,-0.015152180142903633,0.0014397836839177402,0.01499803636507005,0.030284380072126613,-0.0076512478180378865,-0.0014813401648976357,0.003927877091540851,-0.02996202205308862,0.00031812010677988563,-0.013517560793176977,0.007429586527347303,-0.022599420638392275,-0.03953728948621883,0.0007656830752837564,0.0052122520272286,-0.010978645580773385,0.017776937698131007,-0.005463527824889205,-0.012113902929193733,0.009554843896714214,-0.031363817299417764,-0.013549093614814123,-0.0004154343801008318,0.016977983520433067,-0.003254345545243077,0.006169507782322391,-0.013109910439685853,0.006034421471602003,0.03326934798177334,-0.013727321606376333,0.04732426847815617,-0.012876728107216847,0.00034274338624944384,0.0034661805415620527,0.020486092218650723,-0.02474046652328657,-0.042010921344274525,0.012120164143081303,0.01590877965541189,0.01247367925006701,0.05261013260212955,0.0040990261164359255,0.0050778000680687186,0.018584741091204574,0.0073764953220876095,0.033273861737540836,-0.024765214927705545,-0.007507951696138018,-0.06889410210653636,0.01624831978537105,-0.00744785208495262,0.01847924948876412,0.04308289518487803,-0.0001181021273907001,-0.0050908495106723765,-0.009991611269792545,-0.016757593119302912,-0.012607310685155491,0.012785429042195038,0.0007367601598040159,0.0013255438743083284,-0.003465438643549329,0.018287276293404025,0.009879482630816575,-0.0028356319774038175,0.013294242287768843,-0.0030355982283050056,-0.023058263663938604,0.02910635368576944,0.009305882941500712,-0.019145253880939125,0.02157650585953787,0.006899487742260381,-0.031287191638887095,0.032198973731244945,0.006669738122992355,0.017828994968989598,0.003956808883417576,-0.0029905996086962267,-0.030963116513107992,0.019431668116396652,0.0006023263231164223,-0.005730289554775117,0.007018473023471778,0.0015620737786757898,0.013513049426891861,-0.007420381325740358,-0.0007293442381116675,-0.042778891225281584,-0.00846600738943448,0.013514287310067027,0.02673461379833026,-0.007279540603209419,-0.0024268423645868614,0.03166904026394329,-0.00651580749993808,0.0146801562669513,0.0335663182302627,0.0007955955514553279,0.02453841548769826,-0.014209859280993907,0.004153434134372183,-0.0015471200694424467,0.0022982669292372043,0.02259406387254084,0.047797469832129645,-0.013309371304745021,-0.011502389944261929,0.009947767206933175,-0.021102928955370973,0.009940313970927242,0.011438070765818702,-0.005550133564961593,0.010623861370639776,-0.030986346933354444,0.015197621469600454,-0.030896682734231455,-0.013928993321020823,-0.011123956624965112,-0.008022704926085155,0.017175340409671797,0.001633014819733217,-0.007948734141931537,0.010869639386650348,0.03162553211739585,0.00012377884317747766,0.007315960909959216,0.024793945272144707,0.005356536538504401,-0.02567694216327604,0.049805721183619235,0.04416717381024419,-0.03969735940458447,-0.0007831470029921743,0.008345654742105711,0.01931461216932308,0.01338012117947009,-0.005443897046728028,-0.021076727244905346,0.0020591256553929584,0.020668715917241568,-0.02179233659197578,-0.020543781966064396,-0.0004925593029904767,-0.03874975728339148,-0.005205945680979969,-0.008730657500330795,0.009015239637602795,-0.014035336350523514,-0.017642428934530382,-0.007883827686432202,-0.0009985210663172985,-0.013293167316922259,0.00024239123842569984,0.015004397057068802,0.02370239780717162,0.03409819089840864,-0.015669695774810383,-0.008395353495035054,-0.04965740871762597,0.03798648467167655,-0.014494215135581556,-0.0006675135678320258,0.010451446752148657,-0.027171030019754183,0.009278241553835977,-0.0005278259035335137,-0.03652059388256338,0.005840111278356752,0.023890452607112336,-0.03735604147442467,0.016144295339273067,0.004184300045626488,0.009496459591192523,0.008830211852787288,0.026078721023194494,-0.0044729603596318284,0.0174717477177783,-0.008198295123871071,0.014558668605523717,-0.016279645945631912,-0.0021668139046202984,0.03462024593716067,0.008912351120261243,-0.0031643028543990727,-0.02289616298969199,-0.01580264006426114,0.0038729173049534206,0.018788044754137475,0.008521266986920635,0.010482805103694265,-0.0008350973736185169,0.02704039139613357,-0.007815805867971986,-0.010994418335855394,0.017761921326428298,0.0012721749210730542,-0.005571197039777547,-0.011522063091730036,-0.005137854636219815,0.012471260628146526,0.007074974797570248,-0.02419261390115775,0.00852666355355589,0.003580355329926559,-0.020003538588806793,0.015456690428926601,-0.00560837212088963,-0.006708846492315146,0.015916194504879105,0.026413914639968453,-0.013771369764410426,0.008765218591202127,-0.017521489660104608,0.04628503281243242,-0.009875369954085276,0.023899892943268865,-0.012946351675851604,0.016226082719083774,0.0443775265891009,-0.050819513484259275,-0.008689952733907567,0.010010296486954891,-0.0018572022916374079,-0.013369414438552272,0.0430429095221775,0.0015900280739810637,-0.03288847664335075,0.017082934896389616,-0.03443220262314574,0.023016976475394708,-0.011555015623708316,0.0028967931390614745,0.025219142478714707,0.0023574344974810987,-0.027821624435456997,-0.03391886239215431,0.02365173748893493,0.01480865044342103,-0.01631512529688296,0.017190328471753634,0.0099330644670211,0.01295403433357121,-0.04517807874270887,-0.006041843102069011,0.01800819030147492,0.014669034562847485,0.017628339731903666,-0.049145103048557334,0.003381264455382117,0.009843905989797445,0.051038487382418535,-0.019075142371317445,-0.0065853735749830935,0.0007171292719589229,0.017721890404198692,-0.008866566018617933,0.022944953188473304,-0.015758131463238772,0.005337386878860452,-0.010547893334597633,0.0031636571587979868,-0.013816348693561567,-0.031945712156002455,0.021861862862506767,0.006068324942562423,-0.011172942359649855,0.00401850227803447,0.019803357992751174,-0.01954956150894363,-0.00220710713552781,0.01078326957796486,0.010523103859134604,-0.006706096410850821,-0.04213957788279591,0.024858509406512436,0.006565883417719036,0.0002613429177531019,-0.005570583259325141,0.005268098182200031,-0.008511978622737806,-0.0204938041830082,-0.014795347482202587,-0.011936662104097726,-0.012247025851779253,-0.02317433462615941,0.012726574914317034,-0.026196061240500685,0.013194532514064515,-0.020293161307223334,0.007049284897887193,0.027481081019981014,0.004065454125807345,-0.014616215066431385,0.0009655360385648228,0.0029627146672424097,-0.03467611871397737,-0.012153664780289253,0.0032601901096947577,-0.009384124664869818,0.0015941502449322918,0.014679519860391333,0.015331274718012084,0.018113981748437053,0.011770879296182132,-0.005758585200934815,-0.0003681572675872476,-0.005423232262408601,-0.006264577899221063,-0.0035932871960378666,-0.034494061488169185,-0.00666350873242772,-0.0004815535732350684,-0.019479341073193008,-0.0004803725449577169,0.010310519760027764,-0.0032880337084320193,0.041532598158649583,-0.05212909243089594,-0.00412705706740425,-0.036508099592968545,0.019599428253623746,0.05308271613341005,-0.05004014178167653,0.0025584018034520402,0.01038180344063113,-0.006048458518539093,0.01103296218404574,-0.04485953688629293,0.01704055900892162,0.007439820921671824,0.00045652982655461664,-0.011751650640868184,0.012767881770690699,-0.009707724759503837,0.004462445617780938,-0.010201709514514082,-0.04493628116998764,-0.0006262584334162904,0.004043749365697927,0.015087689187048036,-0.01752163488589821,-0.0006616319181931635,0.012342953158373795,0.0029086308229181435,0.024849324489995453,0.0398330494385519,-0.018172608973875067,-0.03841804119710267,0.017132618243936765,0.030588904385895514,0.018446005836819105,0.016278559795993557,-0.012372991229335814,-0.014271045026019176,0.01776784567697316,-0.018231081611044666,-0.03626654546251907,-0.019950667388265602,0.049845020101146796,0.038467898326246315,-0.01372922107686747,-0.014579001714623938,0.004628287747699126,-0.014987301153994445,0.026201827877872143,-0.001566143590447963,-0.021726052726238856,0.026177988921908403,-0.011662724188051048,0.004425272686967967,-0.0002531819133514209,-0.006287531428567785,0.00649859697710562,-0.01384988857108513,-0.03688952478808859,-0.044159493498317375,-0.02533189065297643,-0.01516882162297892,-0.0004593062134942628,0.001105937298207441,0.011120704083822246,0.002397380143787374,-0.015868934603032472,-0.014177872289370492,-0.04237613169882776,-0.003382761451894863,0.009697172643457621,0.010593138421123761,-0.0024284999623204115,-0.0034836386565631414,0.01872599352836568,0.0003077637364414564,0.014756489104649084,0.011650023537980852,0.004263139049784742,0.026128439558528598,-0.011453961629214663,-0.007177531361005915,-0.016159639079951618,-0.015943715730377426,0.031119792248687307,0.035186319033768246,0.00045809207132546485,0.011364816059050372,0.02350645160404928,0.016149304110449514,0.02410699958094478,-0.025259333302309728,-0.012787584706010189,0.009053095806880176,0.028706738336234845,0.0020771512307268076,-0.017168724563949033,-0.007090191575792355,-0.013211641853812467,-0.01716649559212918,0.030023664518435942,-0.012512056760250738,0.00040842987885730906,0.043248488643457574,0.023694369395500882,0.006723019420645811,-0.012237660701121955,0.008206034640289862,0.03243361917314996,0.012460820753642084,0.025230932739966447,0.001961807413031102,0.010325475040470445,-0.0040192131087353035,0.00853795390476733,0.026008987649037422,-0.02862261379124764,-0.0012503697235092743,0.0048052863522383615,-0.011421786779268368,-0.006160661042587925,0.015738184726562594,0.04003297600414734,0.012589079675896994,0.006522247754355524,-0.03102890365324267,0.03855090747644643,0.0015387845606643453,-0.0006765755139299663,-0.02236806326913801,-0.0011367253709647913,-0.021922670078176144,0.0014202249719237451,0.009326308989553469,0.0006247150139262336,0.005593082245936971,-0.017036543121879938,0.028595199762683904,-0.013064479070426335,-0.03636627486747364,-0.003750072121616121,-0.01527483422254256,-0.020195551846173467,-0.007097555538751196,0.005824047346976228,-0.02363645269398438,-0.0027509012541704824,0.028534496576173282,0.013654842233038103,-0.003039536712092919,0.00255476401101858,-0.002397718033763475,-0.0009556144639098083,0.01464756784509796,-0.0018504787445267382,-0.04808878432884993,-0.00043026817661151814,-0.017789602904575704,0.013025440935087498,-0.012206347050538465,0.0029683416498513904,0.043545585197413444,-0.020937785720595774,-0.02249279961863848,-0.028230437450878273,-0.04789717825314276,-0.03756947949612237,0.00729088616487243,-0.01276128365046157,-0.03736319079690185,-0.029652845128171776,0.012345083498127131,-0.015505419914724372,-0.00733685294526712,0.00660916832338194,0.027127944903741145,0.03882048389080429,0.020648905895533146,0.002872181149089932,0.003683396992381384,0.0360434010413587,0.028571966538641906,-0.00621006499924147,0.00915468986916295,0.005738997886257925,0.0010474798152211309,-0.010000820639537406,-0.026529508069292565,-0.010680430222411882,-0.030882948083845597,0.024475262346320605,0.010731407124723669,-0.024119245453946586,0.027916594901788973,0.01783467224761526,-0.0381721058614467,0.03682826825841744,0.016198251683611248],250,0.95]
期望: 0.046472146288435684
N=1200、W=250、alpha=0.95；规模接近上限，验证 O(N*W log W) 在 2s 预算内完成且数值精确。
Case 15 · large, N=500 W=50 alpha=0.9 stress test
输入: [[-0.0359144142147632,-0.004992614195724789,0.01603303581287113,-0.004063497451776182,0.0031539738498687366,-0.031057423656814943,-0.005106577225831005,-0.008203389375857259,0.019411984797117168,0.0033171890444808018,-0.00034547407600048023,-0.015250345580826946,-0.017478190455217275,-0.0001760091627689759,0.027423609919751898,-0.03963721549982467,-0.05861305183657054,0.04169611687852445,0.033842054076241954,0.013941367455950362,0.008105484898230297,-0.008073311030456247,-0.007051132658663715,-0.024597839709544173,0.013191971634554399,-0.003815742059785065,-0.04008761067262188,-0.01028290987140183,-0.011067082731250455,-0.013169779103796827,0.04127574691952954,0.02332511111960674,-0.06608683981158701,0.010851213693248157,0.023029655045266936,0.028417516999383153,0.017429755716870127,-0.04143110902519207,0.01917709618602587,0.0021579545044216096,0.031655502115192566,0.010653768645040591,-0.030952628316790222,0.040089905700510395,-0.02437770695282229,0.02443014319296544,0.009966776123455826,-0.010913511786044841,-0.04707734094183619,-0.01755841552032286,-0.01861609925864214,-0.0031788970059714824,-0.003790853213959226,0.034940100641255405,0.00958155778860617,0.02547660495949772,-0.023866070228910182,-0.008684989375113318,0.020140042034848885,0.021308622423757237,0.015171661455852716,-0.008776840512868337,-0.021595802052940392,0.03809850874647111,-0.014061641645695636,-0.007541135211462705,0.033396988841494946,0.0020513106167884976,-0.012962118597871065,0.018319637177702283,-0.003991134048638148,0.02803939999505415,-0.002267496342982259,-0.01707230937659972,0.0524166041583788,0.026719964991987696,0.0034511983755432536,-0.002188946521124319,-0.02799939422329784,-0.0119465267098811,-0.026600589004653487,0.01856746634919676,0.025865676618856144,-0.006673177306727993,-0.010251560666208186,0.008311455640868447,-0.00010191687667002725,0.011435009886368782,0.010626140434741027,0.00883666445962407,0.013564152616572428,-0.020784568057550513,0.01521650218949731,-0.042319035395096946,0.002373796753352713,-0.005910224453937683,0.00788846880103468,-0.003959681108125916,0.0050202944491386774,-0.03788927097368323,-0.01117056643036674,-0.01699424370174568,0.007517865999136915,0.0038315596944512305,-0.00973298280941889,-0.011252312586500926,-0.015380165611282217,-0.0031631589033621287,0.008660144773739168,0.0143149702937447,-0.0036330138546864506,-0.022814345042283787,-0.01804507223443388,0.014406673414711493,-0.022710781799266822,-0.008012963855278185,-0.04924263189114496,0.017707835295486387,0.00015700662515215618,-0.014425405396854588,-0.005379293808481173,0.011766697529235882,-0.0031530743540878242,0.003617855882352686,-0.000894659803114687,-0.025893199802441053,-0.03742583169892397,0.019761550489428802,-0.012484741560568,0.02313956392471252,0.023039500790250425,-0.010884543795622505,-0.014530733512898226,-0.012485681403106123,0.03353098307396395,-0.00040080713586496954,-0.006166513441440915,0.01770361523923874,-0.020296141327445023,-0.013151895487778203,-0.012923226480840735,-0.0019060983456015686,-0.027741334754637765,-0.014289569168991054,0.0020549817617123807,-0.021751910475934576,-0.022320290153662707,0.007947549911194394,-0.022115421981232335,-0.005126546391067371,0.015594448870673879,0.0011878850873217309,0.03731260702316781,-0.002864115501004099,-0.032698136286189956,0.00679867050803211,0.0038017137677064513,0.015304303744374578,-0.030814824151676287,-0.0034273521335609807,0.022256045126144694,0.003893550029253081,0.022874882058301904,-0.015318970299591363,0.009108575865751858,-0.0003956416681871045,0.03200534282154245,-0.02070790355366148,0.024471086577943852,0.004058645007548871,0.0008259030044646516,-0.0141490299778543,-0.023057091879545483,-0.03144455214893098,0.005764349972603219,-0.020342491117221896,0.023241195644988694,0.008923639108818923,0.009436990736158264,0.02301978715240684,-0.002250453660171173,0.018337464411308284,-0.03562496004604513,-0.01004300385943802,0.020152954467756137,-0.00315056714900199,0.03327328753554573,0.0015598112131022164,-0.017910443615186674,0.02851386469066111,0.0025327076581764256,-0.004567914062359311,-0.001967491735791088,-0.016257794852998934,-0.007849614262827254,0.016243555662669044,-0.014500608862113627,-0.003566227458770968,-0.016314626237146895,0.0005672808713242514,0.010751248228483343,0.010701942469054964,-0.007251146214440827,-0.015648376547654434,0.005860917597529195,0.018156982298866794,0.01307797994031991,0.05622853713250686,0.0026594253324813584,-0.01115799350942299,-0.0058175461387449615,0.02059528726862703,-0.019526330043296684,-0.0034806495074376593,-0.03343305963498642,-0.0049349027024805404,0.014502430874996511,0.021096189114499574,0.012666346426835718,0.02125510562452333,-0.01475647742157606,0.032902399445205524,0.03674945059114814,-0.03407369034748561,-0.02311669901822279,0.015259100282044594,0.015431835079203586,0.027507155636455987,0.003697191283495618,-0.020781137475021964,-0.014669401903391582,0.03033298045254833,0.00007865595545365676,-0.035843878630037664,-0.003587611025093796,0.014471411111339656,-0.00005273402754768162,0.013022366422583307,0.010211344532176645,0.0004502538259651677,-0.021201807890033834,0.0009713594259133436,0.014997698405977823,-0.012457905451918015,0.022187079619660564,0.040559220550100465,0.016350179527361616,0.00805019712683746,0.0015047387857333328,-0.01754573489494356,0.03214977638023562,-0.007408300127777574,-0.014295860998012824,0.03726070209805248,0.021181186835162746,-0.01133958298700303,0.0058145874868348905,0.00735668051715198,0.01732313483860676,-0.03809244378056882,-0.019585695011687446,-0.028384771285666167,0.0039861375752804065,-0.014164904768526932,0.009209506055829274,0.039151401149830775,0.01138649157232413,-0.018131248433774304,-0.0010273131496730161,0.008035025025432473,-0.03612851428680829,0.024741397954775268,0.005032019015921685,0.016683646898349298,0.025313067679704253,0.005689044177508247,0.027870192449681114,0.011051684823943905,-0.02095380840944476,0.0010499488217163308,-0.0009937251235053125,0.016950148361274082,0.037205813758214135,-0.0296065269831111,0.00017214348362870412,-0.013840863635049801,0.004946504283369611,0.018330952476894143,0.034012931834497884,-0.0336555866669687,0.003554160064448545,0.028110339359894283,-0.016052133970190584,0.015124024812767764,0.010335362827247395,0.0302665620692097,0.00947738288707952,-0.04640899290310627,-0.02148762372415493,0.0021422033102983158,-0.006435416543210663,-0.008437115514415705,0.024694038587460172,-0.023642541601048672,0.00282673334389608,0.02007811404689931,-0.03893760738002782,0.0034261643618697037,-0.005205739296452531,-0.013840833386979261,0.04395663969839495,-0.013934881218515152,0.014602537801494874,-0.018156317350874723,-0.02014146792267697,0.0034234896783138192,0.022697936217297668,-0.003197063004010381,0.01234245692676784,-0.0032095047625048867,0.022200614364897557,0.00427854325836408,0.004870299424111684,0.014610652568554188,0.010046958872282989,0.0023122348371141374,-0.00798165966307018,0.0030961280991389207,-0.007911130323689626,0.026378921567364166,-0.0010796366533668631,0.017241833335367853,-0.011290292536640998,0.010814996881175144,-0.031929699745956414,-0.013431858701981306,0.024328764246155377,0.004817929337743053,-0.04369664437247429,-0.009693117908160687,-0.0045592836720653234,-0.015366504970297843,-0.03204712453900906,-0.028642655629868136,0.03258383260145533,-0.010266708813400796,0.015048366215363703,0.012067763833811031,-0.017714884600324388,0.0023850841823663065,0.0012678044741704798,-0.023275752339857885,0.002484216485715203,-0.0003368690231573565,0.0034948588358908565,-0.009178156110466868,-0.011278512868415231,-0.0013229289138457809,-0.02031216686049921,0.018530923793884945,0.005586033225062457,-0.0014789646561590597,-0.00748802436033226,0.006058794898915588,-0.000490388885740547,-0.011125015838981352,0.011911545370563544,0.03437558253753813,0.0398145359833379,0.01213415116168559,-0.0075959734466124335,0.06613321294030461,0.0070642689755257265,0.005565774591225771,-0.016999640072442437,0.0025780218502916264,-0.0104890715501312,-0.013361433022941278,-0.0017792790030575964,0.0032031896237514935,0.0013409985603220168,0.0008336425972761929,-0.03966557848169189,0.009824233941769643,-0.017206658955829648,-0.004054737588442918,-0.03296031967549815,0.008633734486252561,0.006076342264781551,-0.006425665834089418,-0.010166254454169705,-0.013358924508394415,0.02899737165521434,-0.013845444386104178,-0.02500226658622324,-0.01588707884817959,0.0005787564432300619,-0.007652705681424581,-0.0024733761253826116,0.005071208661676803,0.025972675111756337,0.037778056596878794,-0.012024984077134862,-0.005853597317922249,-0.005816782218108412,0.02002891494548368,0.03157817675309282,0.01876384516824841,-0.004998344755498932,0.004629791044954685,-0.020582329225353902,-0.0018958421045345325,0.0012759006626215552,-0.015586747003632993,0.0017239472738516434,0.02354002645146137,-0.00869951619624524,0.005928875768102725,-0.0036560591739753312,-0.03993573446357183,0.01428453342091432,-0.025568023608033216,-0.034766903201863555,0.006429894797492444,0.0022140885792999183,0.008857921863270887,0.006864283845798694,0.023620636999177606,0.005557226280986019,0.020661742452571286,0.010620089661031715,-0.02561833995063184,0.003214106295482626,0.009676618155921269,0.006475684925041918,0.00023323614175118474,-0.0022885310141733954,0.03147545209141012,0.009463153540056184,-0.0173521214914121,0.024560596990298368,0.007272623605798254,0.00332178370838499,-0.0011165929836809733,-0.04886675389405258,-0.0513130674482959,-0.01198017458138008,0.02394600216290648,0.011098267911427566,-0.027464866991473835,0.016400708869189137,0.031073141972429844,-0.025207446557661252,-0.015100681684757637,-0.030394924256610296,-0.021767305836627285,-0.04081291518985325,-0.019667674314113766,0.003376014897848796,0.002815215085324812,0.015449486137500322,0.018107471516979518,-0.008765295440932812,-0.0438188705530466,0.0025006116826284835,0.00011455116061810132,-0.02165439767293813,0.019693128919777387,-0.013045349978126073,0.009615066166277412,0.009265296856372342,0.030198896012484693,-0.038732675558941866,-0.03064718579062972,-0.01059411865502813,0.020121179735055814,0.030151544870038804,-0.007319508379132075,-0.0023054507053611845,0.03222893702333623,-0.008194341244752016,0.0028207742593996006,0.018538574856919884,0.014421227337128369,-0.005832712508629972,0.014367351071210701,-0.0025774930948954263,-0.015224659336472046,-0.022713523644941495,0.007227308332612721,0.03607039518798126,0.0018059919920683262,-0.0013177016049010257,0.011806993520985723,-0.013792132994610804,-0.0012614907210830232,0.009625664309226767,0.001980792110509817,0.018112473383231253,0.004684370893896551],50,0.9]
期望: 0.050659190457561544
N=500、W=50、alpha=0.9；规模接近上限，验证 O(N*W log W) 在 2s 预算内完成且数值精确。
Case 16 · adversarial, duplicate values at tail boundary
输入: [[-0.05,-0.05,0.01,0.02,0.03,-0.05,-0.05,0.01,0.02],5,0.6]
期望: 0.05
排序后多个相同值挤在尾部边界。W=5、alpha=0.6、k=2。多个窗口含两笔 -0.05，ES = +0.05。
Case 17 · adversarial, large PnL magnitudes near 1e6 limit
输入: [[100000,-200000,300000,-500000,200000,-900000,400000,-300000,100000,-700000],5,0.6]
期望: 800000
大量级 PnL。W=5、alpha=0.6、k=2，最差窗口含 -9e5 与 -7e5，sES = +800000。
Case 18 · adversarial, monotone-increasing PnL with one stress cluster
输入: [[-0.001,-0.002,-0.003,-0.05,-0.06,-0.07,-0.001,-0.002,-0.003,-0.001],3,0.66]
期望: 0.065
单一压力簇 [3..5]。W=3、alpha=0.66、k=2，最差窗口含 -0.07 与 -0.06，sES = +0.065。
Case 19 · boundary, W=2 alpha=0.5 k=1
输入: [[0.01,-0.02,0.005,-0.03,0.008,-0.05,0.012,-0.015],2,0.5]
期望: 0.05
W=2、alpha=0.5、k=ceil(2*0.5-eps)=1，每窗 ES = -最小。最差窗口含 -0.05，sES = +0.05。
Case 20 · random, N=100 W=20 alpha=0.95 seed=1
输入: [[0.020322771297331944,0.022741684130496563,0.001995037134073929,-0.010468154764574477,-0.01538259822656212,0.001470017752475753,-0.014331547550163092,-0.020552441676537945,0.003989679647256307,0.0030006190698790725,0.009197024505073474,-0.012709564156029689,0.0010750792543985867,0.000028873594409681747,-0.021587435018911125,0.009069957679915506,0.005810666514982724,0.03683668064861029,0.004044537659649463,-0.0011705346224738077,0.019491357625433855,0.003981868722901382,0.014635465392298135,-0.004483163993487751,0.004272577200408736,0.01636433017730527,0.011443705336794424,0.002927083729492846,-0.015234620368940667,0.007678326585415728,0.002152952225788785,0.011807013952888804,0.004243494067001096,0.017322781167032848,0.00022659601864111873,0.004029460901191319,0.011001646579384742,-0.01530326918261719,-0.0050249039011102834,-0.006500428534285526,0.03070923579284869,-0.00039293038484126855,0.01078330335711358,0.010290625932605785,-0.003213101452803389,-0.022262552406956706,0.015472659560142148,-0.0051079515449538775,0.011769349851173498,-0.018578972376649468,-0.005569745029547446,0.01985232016908042,0.022465059820787774,-0.018536879317075358,-0.018992112186334148,0.0003360334359725209,0.011923619849780794,0.003407570190689946,0.005553320617404756,-0.013832546374619194,0.009801875707207055,0.017752785117052534,-0.005535087804259744,-0.020502320954951987,-0.010382312355256232,0.012424870087554739,-0.025005457877546506,-0.00037815181708405815,-0.013865124277182402,-0.0009670166296657811,-0.0026678238012205788,0.0012378517490847403,0.023518110944551012,0.007310656654118205,0.02100569118047839,-0.001121190714551809,-0.006193799117404486,0.006682158733989835,-0.04153686180020056,0.00040166777961899217,0.003402546836128405,-0.017528131160203117,0.007965478338588263,-0.007388672064904403,-0.03588650285415435,-0.002199775855519199,-0.013682686164451691,-0.006808938089002196,-0.0012842662805805402,0.019764630238507348,0.0025472226841238526,0.0005727156252448831,0.006835066242510807,-0.02618138548736922,0.01960185805935352,-0.015156303804447262,0.0075864260670251045,-0.015901707432029552,-0.013647280469164105,-0.004944318129072505],20,0.95]
期望: 0.04153686180020056
随机 PnL，seed=1。验证滑动 ES 在常规分布上的正确性。