ZkEVM的定義與增強以太坊生態系的機制

來源: LBank時間: 2023-04-14 02:00:19

零知識證明與彙總技術的革新融合

在探討zkEVM之前,我們先回顧兩個關鍵基石——零知識證明和以太坊彙總機制。零知識證明這一密碼學概念,如同其名所示,能夠在不揭示具體信息內容的前提下,驗證某個陳述的真實性。這一突破性技術使得區塊鏈網絡能夠在保護用戶隱私的同時確保交易的有效性。


彙總技術則是以太坊爲應對網絡擁堵、提高交易處理效率而引入的一種Layer 2擴展解決方案。它通過將大量交易在主鏈之外進行處理並壓縮成單個交易提交至主網,從而大大提升了系統的吞吐量,並顯著降低了每筆交易的成本。


而零知識彙總(或稱ZK彙總)則是在此基礎之上引入零知識證明技術,使得彙總內部的所有交易數據無需完全公開到以太坊主網上,僅需發佈狀態變化及其相應的有效性證明。這樣一來,不僅實現了更高的隱私保護,還進一步減少了在以太坊主網上進行驗證所需的燃料費用。

以太坊虛擬機:智能合約運行的核心引擎

以太坊虛擬機(EVM)是支撐以太坊網絡運作的基石,它是一個去中心化的、圖靈完備的狀態機系統。在以太坊生態系統中,EVM不僅負責處理和執行賬戶間的交易,更是智能合約生命週期的承載者。每次智能合約被執行時,EVM都會依據預定義規則從當前狀態過渡到新的狀態,確保整個區塊鏈的狀態更新過程準確無誤。


“狀態”一詞在以太坊中具有核心地位,代表了整個網絡的當前狀況。這一狀態被編碼爲默克爾帕特里夏字典樹(Merkle Patricia Trie),這是一種高效的數據結構,可將所有賬戶餘額、合約代碼以及合約存儲等信息進行安全、透明且易於驗證的組織。通過這種數據結構,任何人都能通過遞歸地查詢哈希值,追溯至創世區塊以來的所有交易歷史記錄。


以太坊節點間的一致性與共識維護至關重要,每個參與維護以太坊網絡的節點都運行着同樣的EVM,共同確認和更新全局狀態。因此,以太坊虛擬機在保障整個網絡狀態轉換的確定性及達成分佈式共識方面扮演着不可替代的角色。

ZkEVM運作機制:零知識證明與以太坊生態的無縫融合

zkEVM,即零知識以太坊虛擬機,其核心目標是將零知識證明技術引入以太坊生態系統,實現安全、隱私保護下的高效交易驗證。通過整合零知識證明與以太坊虛擬機功能,zkEVM爲區塊鏈狀態轉換提供了一種全新的解決方案。


在具體運作中,zkEVM首先模擬以太坊環境構建一個零知識彙總層,該層能夠讀取並處理初始區塊鏈狀態及後續的所有交易數據。在執行交易過程中,zkEVM不僅計算出新的更新狀態,還會生成相應的零知識證明,這一證明能夠確保所有計算過程的真實性和完整性,而無需公開實際的交易詳情。


當這個零知識證明提交給鏈上的驗證者智能合約時,智能合約只需驗證初始狀態和新狀態之間的轉換是否有效,而不必逐一檢查每筆交易的具體內容,極大地提高了系統的效率和隱私性。


得益於與以太坊虛擬機的高度兼容性,開發者可以輕鬆地將現有的以太坊DApp和智能合約遷移到zkEVM環境中,無需從零開始學習和開發複雜的零知識證明邏輯。這不僅簡化了開發流程,也爲各類基於以太坊的應用提供了前所未有的安全保障。用戶則能在享受熟悉的DApp體驗的同時,享受到更強的安全性和隱私保護,從而進一步推動以太坊生態系統的創新與發展。

以太坊虛擬機兼容性與等效性的深入解讀

在區塊鏈領域,以太坊虛擬機(EVM)的兼容性意味着其他區塊鏈或Layer 2解決方案能夠支持以太坊原生編程語言Solidity編寫的智能合約,並且能夠無縫地執行這些智能合約。這意味着開發者可以便捷地將已有的以太坊DApp移植到這些兼容EVM的鏈上,只需進行細微調整,用戶則能夠在新的環境中繼續使用他們的以太坊地址,保持與主流錢包如Metamask和Trust Wallet的良好兼容性。


當前市場上,一些知名項目如LBK Chain、Avalanche的C鏈以及Polygon等均實現了與以太坊虛擬機的兼容,爲用戶提供了一種低成本、高效率的交易環境,同時保持了與以太坊生態系統的緊密聯繫。


然而,在討論以太坊虛擬機的兼容性時,我們還需區分其與等效性的概念。EVM等效性更強調的是運行環境在功能和體驗上的完全一致,就好比在一個操作系統中,不論是在新舊設備間遷移數據還是操作設置都能達到無差別效果。但在實際應用中,儘管某些區塊鏈宣稱與以太坊虛擬機兼容,但可能存在一定的差異性,就如同從Apple系統切換至Windows系統,雖然可以通過雲服務實現文件和設置的轉移,但仍需要經過轉換過程才能確保原有應用的正常運行和功能一致性。


因此,ZkEVM作爲對以太坊虛擬機技術的重要革新,它不僅實現了與以太坊虛擬機的兼容性,即允許在保護隱私的前提下執行現有的智能合約,還致力於通過零知識證明技術提供更爲高效、安全且具有更高隱私保護能力的等效性解決方案,從而極大地增強整個以太坊生態系統的性能和潛力。

ZkEVM的類型與權衡分析

在探索ZkEVM如何增強以太坊生態系統的過程中,有必要深入剖析不同類型的ZkEVM以及它們在零知識證明效率和以太坊虛擬機兼容性之間的取捨。Vitalik Buterin將zkEVM劃分爲四個主要類別:

1. 第1類(神聖彙總)zkEVM:

此類zkEVM在共識層面上與以太坊完全等效,這意味着鏈狀態、交易執行和區塊驗證規則都與以太坊主網保持一致。然而,其面臨的挑戰在於生成和驗證零知識證明所需的巨大計算資源。儘管如此,隨着技術進步,如大規模並行驗證或專用集成電路的應用,有望提升這類zkEVM的零知識證明性能。

2. 第2類zkEVM:

此類型 zkEVM 在字節碼級別實現對以太坊虛擬機的完全等效,使得現有的DApp、調試工具和開發者基礎架構能夠無縫遷移至該環境中。然而,爲了優化零知識證明,第2類zkEVM對數據結構進行調整,並移除了某些不利於零知識證明實現的操作。代價是高昂的費用和較低的執行效率,尤其在無法利用零知識證明的優勢時更爲明顯。

3. 第2.5類zkEVM:

作爲第2類的改進版,第2.5類zkEVM試圖在保證一定的零知識證明效率提升的同時,適度降低燃料費成本,但仍保留了較高的以太坊虛擬機兼容性。

4. 第3類zkEVM:

相較於前兩類,第3類zkEVM更注重提高零知識證明性能,因此可能犧牲一部分以太坊虛擬機兼容性。它通過剔除諸如預編譯等功能來簡化零知識證明的實施過程,但這意味着部分依賴於這些功能的DApp需要重新編寫代碼才能適應新的環境。

5. 第4類zkEVM:

這一類別的zkEVM在零知識證明性能方面達到了最優水平,但與此同時也犧牲了最大的兼容性,使得以太坊生態中的部分應用難以直接移植到該環境中。

ZkEVM的挑戰與未來展望

儘管ZkEVM(零知識以太坊虛擬機)在提升以太坊生態系統效率、隱私保護和擴展性方面展現出巨大潛力,但其發展也面臨諸多挑戰。首先,零知識證明技術的複雜性意味着實現高效的ZkEVM需要克服算法優化和計算資源消耗的難題。目前,生成和驗證零知識證明的過程相較於傳統的區塊鏈交易驗證更爲耗時且計算密集,這要求持續的技術突破以降低時間成本和提高處理能力。


其次,ZkEVM的普及和廣泛應用還依賴於開發者社區對其的理解和支持。雖然與以太坊虛擬機兼容有助於簡化遷移過程,但開發者仍需學習並掌握針對零知識證明的特定編程技巧。此外,確保ZkEVM的安全性和可靠性也是一個重要議題,尤其是在應對潛在的新型攻擊策略時。


然而,面對這些挑戰的同時,ZkEVM的未來前景一片光明。隨着研究者和工程師不斷攻克技術難關,ZkEVM有望成爲推動以太坊從Layer 1向Layer 2擴容解決方案的重要引擎,並在Web3.0時代爲去中心化應用提供兼具高效、安全和隱私保護的運行環境。同時,隨着更多項目採用和改進ZkEVM,我們有理由相信它將在區塊鏈生態系統的整體發展中扮演舉足輕重的角色,進一步推動區塊鏈技術在全球範圍內的大規模商業化應用。

結語

綜上所述,零知識證明與彙總技術的革新融合在zkEVM中得到充分體現,這一技術突破不僅極大地提升了以太坊生態系統的隱私保護和交易效率,同時也爲區塊鏈擴容問題提供了具有前瞻性的解決方案。


隨着研究和技術的不斷推進,ZkEVM有望克服現有挑戰,如優化算法性能、提高開發者友好度以及強化安全機制。未來,zkEVM將在保障去中心化應用高效運行的同時,進一步推動Web3.0時代下的隱私保護和安全性提升,對整個區塊鏈行業產生深遠影響。

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0.05397
0.73%
1.8134
-10.53%
0.4543
7.35%
0.0016299
0.98%
0.00542
1.31%
0.00286
0.00%
0.00004382
0.02%
0.0010863
-3.89%
6.713
-4.02%
0.011782
45.44%
0.020186
-5.39%
0.0002758
-3.19%
91.42
-2.30%
0.023572
-5.18%
0.01884
-1.46%
0.0005712
-2.86%
0.009345
0.53%
0.002251
0.27%
0.00010064
0.40%
0.013285
-2.01%
0.0203
-68.58%
0.004656
-5.50%
176.09
-6.22%
0.05274
8.61%
0.02531
-8.66%
0.002746
8.20%
0.002762
-0.65%
1.7403
1.26%
11.5784
1.27%
0.0675
11.02%
0.00001891
-5.92%
0.0003635
-3.07%
0.002821
-0.28%
0.0010017
0.11%
0.0006451
0.51%
0.00221
-7.92%
0.1920
-12.49%
0.002041
-14.85%
0.008238
15.83%
0.0001318
-4.15%
0.13861
-10.01%
0.0256
-2.66%
0.5941
-3.23%
5.84
-0.85%
0.6860
20.56%
0.00082109
-2.09%
0.00017868
0.56%
0.1267
-1.25%
0.2555
-0.27%
0.10354
-1.93%
0.000639
-0.16%
0.00007549
0.94%
0.00000487
-1.62%
0.000003527
15.30%
0.014626
10.72%
0.000001399
-2.71%
4.1299
6.92%
0.00000008078
-5.23%
0.00000014
-61.11%
0.16182
-10.59%
11.42
0.09%
0.00508
1.80%
3.0001
0.00%
0.000478
14.63%
3.7999
-2.19%
0.1348
-16.27%
0.02246
2.04%
0.10451
-8.88%
0.027683
7.72%
0.0000747
-30.90%
0.0001468
-12.62%
0.001299
-3.06%
22.01
-5.01%
0.00829
5.07%
0.0785
0.38%
0.0000000360
-1.64%
0.000032
-87.64%
0.000002247
0.36%
0.01590
0.00%
216.000
1.50%
0.00048
0.00%
0.002987
-0.93%
0.006975
-8.32%
0.19044
-2.70%
0.0000000026
-18.75%
0.00053
0.00%
0.1463
-3.62%
0.008871
6.07%
91.1358
0.42%
0.44869
-5.68%
0.0000813
-8.34%
0.68508
0.33%
0.003077
5.09%
0.0332
3.43%
0.01685
-6.44%
0.018780
-5.38%
0.48578
-0.31%
0.000006328
0.59%
0.00018760
0.59%
0.4039
-3.10%
0.5484
0.96%
0.00335
2.45%
0.002498
-3.96%
0.02128
15.21%
0.01114
15.20%
0.05930
-1.33%
0.1001
-23.24%
0.00017163
-0.13%
11.8274
0.01%
0.0107
1.90%
0.07445
44.03%
0.5939
-1.53%
0.00009653
-2.23%
0.035822
-2.05%
0.0892
-1.55%
0.0000569
0.18%
0.002460
-0.65%
6.4000
0.00%
0.03253
7.79%
0.1380
-0.07%
0.006764
-0.10%
0.000470
-31.88%
0.00230
16.75%
0.04480
-5.06%
3.034
-2.97%
0.0017
0.00%
0.0059
-1.67%
13.77
-30.59%
0.0000215
0.47%
13.65
-15.16%
2.951
-3.06%
0.00397
1.02%
1.976
0.10%
0.0021
5.00%
0.02602
-8.28%
0.3645
0.08%
0.01051
-6.74%
15.03
-2.53%
34.0606
-0.09%
0.8414
-10.35%
0.00001569
-2.00%
1.240
0.00%
0.2312
1.81%
9.47
-6.61%
0.01666
0.12%
0.17257
-1.88%
0.00058415
-0.18%
0.000975
-6.61%
0.0000397
-0.75%
6.05
-3.20%
0.3488
-0.26%
0.358
-3.24%
0.00460
0.22%
0.529
-3.29%
0.00153
-4.38%
0.0000000045
-8.16%
0.002235
-9.51%
0.2792
-0.61%
0.03790
2.10%
0.002821
22.07%
0.0082549
-7.05%
0.007572
-2.46%
0.000129
-0.77%
1.1503999
-3.52%
3019
-0.26%
0.05166
-13.18%
0.015000
77.10%
4.3163
-2.71%
0.0002305
0.39%
71.7998
-2.97%
0.00761
-8.09%
0.001000
0.00%
0.02341
32.26%
0.001600
-13.47%
0.00590000
-1.34%
0.000000000342
-2.56%
0.00699
0.72%
2.1111
0.00%
0.000600
-11.76%
1.0002
0.01%
0.1794
-1.32%
0.012403
-0.14%
0.0000001052
-14.12%
0.05036
-19.11%
0.00005992
-6.91%
0.0000008
-46.67%
0.000527
-9.14%
0.7905
-1.14%
0.8910
-3.51%
0.00049
4.26%
0.08996
2.81%
1.6002
-0.29%
0.2163
1.45%
0.014897
8.04%
0.01237
-1.20%
0.00000615
-0.32%
0.2075
-1.33%
0.0241
-1.23%
0.2340
-5.49%
0.005063
-8.21%
0.5065
-6.62%
0.01803
-8.10%
0.4572
-1.99%
0.988
0.30%
7.34
-3.55%
0.0036763
-0.23%
0.9489
3.80%
0.0000832
-2.23%
0.2043
-3.95%
0.1375
-4.18%
0.0000854
0.59%
0.00002495
2.63%
0.6008
-4.12%
2.858
-2.56%
0.0315
-0.94%
0.00000001383
-2.74%
0.0360
2.86%
0.002916
-19.96%
0.01816
-2.16%
0.09838
-7.85%
0.09020
-0.45%
0.000188
-6.93%
0.00020718
29.27%
0.5270
4.46%
0.03887
3.85%
0.3997
10.75%
0.2844
-2.84%
0.1800
-3.74%
0.1857
-10.38%
0.002829
5.21%
20.0001
0.97%
0.005331
-3.56%
0.01455
-6.97%
0.4424
-2.17%
18.42
-4.06%
0.0242
0.83%
0.000510
0.39%
0.0000000427
7.02%
0.0122431
-0.26%
0.007004
-6.24%
0.872
-5.22%
0.01256
-17.15%
0.0000603
-0.66%
0.01820
-0.60%
0.000000051075
-5.18%
0.002122
0.33%
0.9991
-16.67%
0.001049
2.74%
0.00030
42.86%
0.00240
0.00%
0.000162
-1.22%
3.931
-3.79%
0.00002386
-7.20%
0.000669
11.50%
0.04564
-7.14%
0.00060
-7.69%
0.2463
-0.20%
4.852
0.35%
0.004772
6.90%
3.496
-4.48%
0.0000018390
-9.96%
0.02613
-2.54%
0.1169
0.17%
0.00000333
-2.06%
0.7335
0.63%
0.008098
0.10%
19.0120
2.91%
0.546
-3.19%
0.000287
2.14%
0.0015
0.00%
0.1000
-0.10%
0.00896
-13.68%
0.00480
-4.76%
0.011377
-2.46%
0.000650
-9.09%
0.002751
-7.81%
0.006681
13.45%
0.065959
-2.29%
0.582
-6.28%
0.00514
-0.96%
0.00418
-6.49%
0.01836
1.72%
0.02318
34.92%
0.3153
0.22%
7.73
-10.01%
0.01934
-4.02%
0.03699
38.02%
17.88
-3.09%
0.05303
-19.65%
0.00770
-0.13%
0.08650
1.09%
0.003736
-0.05%
6.13
-1.45%
0.00003946
0.18%
0.1190
0.68%
0.0602
-4.14%
0.00141
0.71%
0.005519
0.49%
1.413
1.95%
0.5223
0.00%
0.2378
-6.16%
0.03724
48.07%
0.001836
-5.36%
0.00285
-6.56%
10.399
28.40%
0.0000618
0.49%
0.03700
1.96%
0.13085
1.18%
0.00001268
-7.04%
0.01483
29.97%
0.000000536
-3.77%
0.0093
-4.12%
24.94
11.69%
0.6319
0.75%
0.1148
4.27%
0.006207
1.01%
258.4
-3.62%
0.00000016021
-1.48%
0.9899
1.58%
0.004241
-6.32%
0.04888
0.76%
0.1972
-1.74%
0.00029883
5.38%
1.5926
-33.03%
0.000852
0.24%
332.2
-0.95%
0.352
-3.56%
0.000119
0.00%
0.3074
0.07%
0.00723
0.70%
0.001585
38.55%
0.003906
15.56%
10.49
-2.15%
0.02351
-1.55%
1.7629
-0.22%
0.002126
28.93%
0.00362
44.80%
0.6920
-2.07%
0.641
-4.75%
0.00876
-5.50%
0.25616
-5.36%
0.00357923
-1.38%
0.4241
0.28%
0.0002400
-9.71%
0.004943
-1.38%
0.1778
-5.83%
0.5140
-3.78%
0.00483
2.77%
0.02070
7.31%
0.001941
81.40%
0.002744
-10.24%
6.4617
61.51%
0.000366
-1.88%
0.000283
-8.41%
0.881
-2.22%
0.000697
-2.24%
0.7363
-8.47%
0.019964
2.22%
0.0889
0.00%
0.1411
-6.86%
0.00000000009545
3.36%
0.3121
-2.86%
0.1500
-0.40%
0.000382
-1.29%
0.00010121
8.12%
0.00818
-17.12%
0.000209802
-1.11%
0.0002811
-2.90%
0.06034
-3.38%
2.951
-3.12%
0.0590
22.66%
1.013
-4.34%
0.01048
-20.00%
0.6599
-21.96%
0.01466
0.14%
0.00003954
-1.54%
0.1090
0.00%
6.046
-1.79%
0.000000001497
0.00%
0.000721
-9.19%
0.002471
-6.33%
0.3405
-4.22%
0.00802
-5.65%
0.4276
6.55%
0.03811
-8.67%
0.000102
6.25%
43.94
-0.88%
0.001041
-10.10%
0.02589
-9.16%
5.819
-4.31%
17.429
-0.09%
0.1502
-0.40%
30.69
-0.62%
5.32
-3.45%
0.001011
-6.13%
0.0681
-4.89%
0.0000213
-0.47%
0.001362
-15.25%
0.1193
-5.77%
0.62198
6.59%
1.1586
-1.99%
0.00009706
15.55%
0.002052
-11.74%
0.001584
-0.44%
0.000616
-8.06%
0.0106
20.45%
0.005834
-24.20%
0.001493
-11.97%
0.00006552
-0.35%
0.013288
1.03%
2.203
0.18%
0.00498
0.81%
0.000001660
-1.19%
0.00000003785
-2.55%
0.05811
-5.39%
0.2476
-1.71%
2152.76
-2.08%
0.5757
0.26%
0.2580
-7.19%
0.02578
-7.76%
0.05149
5.71%
0.000389
18.24%
0.00000455
-7.14%
1.4918
-1.99%
0.0000046
17.95%
0.00095
0.00%
5.608
-4.67%
0.2080
-3.48%
0.004711
-24.38%
0.1795
-7.47%
0.01190
-0.42%
0.06203
-3.75%
7.64
-4.50%
0.000000000248
-1.98%
0.2118
-2.75%
0.019218
-14.59%
0.2692
-17.22%
0.0003201
-5.74%
0.000240
-10.11%
0.004762
14.64%
0.0058
-12.12%
0.0473
-2.67%
0.00120
-4.76%
1.2761
-7.00%
0.3407
-1.62%
0.00609
-2.40%
0.713
-1.25%
7.6116
-6.00%
2.405
0.00%
0.544
-3.55%
0.002021
-9.29%
0.02022
-6.43%
0.85421
0.04%
0.0042
0.00%
0.0924
-1.81%
1.030
-0.19%
0.1380
0.00%
0.3340
7.67%
0.002736
-1.19%
0.3928
-9.76%
0.00256
-1.16%
0.02144
-24.11%
0.003891
9.79%
0.00662
-7.15%
0.1183
1.72%
1.940
-0.51%
0.01820
0.22%
0.05510
22.44%
0.002255
-14.55%
0.01419
0.21%
6.4821
-4.62%
0.0005560
-3.67%
1.5365
-5.82%
0.05377
3.78%
0.01030
-21.43%
0.03545
-14.48%
0.0000003063
-4.10%
0.001271
-5.22%
0.00002833
-1.53%
0.03878
-5.21%
2.339
-3.35%
0.00003083
-0.32%
0.273
-3.87%
0.03407
-3.40%
0.0398
2.31%
0.003122
-2.28%
0.004670
-2.28%
0.00152
27.73%
0.1029
-8.29%
0.003893
-9.02%
0.0000000785
-4.38%
0.5360
-5.43%
9.814
0.45%
0.006889
42.54%
0.01786
0.56%
0.0235
1.29%
0.003377
-2.74%
0.00016984
-15.08%
165.67
-1.45%
0.766
-0.26%
0.1090
-2.77%
0.000853
-0.93%
0.012954
0.50%
3049.25
-0.46%
0.00000001301
-2.03%
0.19469
-4.89%
0.0119
-0.83%
0.008500
8.97%
0.000002530
-10.92%
0.01414
-18.27%
0.2090
-2.70%
0.006041
-9.90%
0.000596
1.71%
0.661
-4.48%
0.1415
-2.48%
0.012770
-1.77%
0.6246
-5.23%
0.001144
1.69%
1.351
-4.39%
0.001822
0.22%
0.0991
-1.78%
0.0027
-12.90%
0.018319
2.00%
0.002966
0.03%
0.0000508
4.10%
0.2811
-2.83%
0.00927
1.64%
0.03142
-0.10%
0.1032
-1.53%
0.01270
-24.45%
0.0004908
-11.85%
0.01698
-15.18%
0.002000
-14.02%
0.0804
-1.35%
0.0118
12.38%
0.4663
-2.73%
0.003999
-0.50%
0.13079
-4.72%
0.00004900
-1.23%
0.5865
-7.36%
3.0220
-2.33%
0.00000798
-1.36%
0.0767
-4.96%
0.0006858
-12.16%
7.046
-0.48%
0.1919
-0.93%
0.03035
-7.36%
0.001514
-8.52%
0.011992
-4.22%
0.0000689
4.55%
0.00000001531
0.86%
0.2201
-1.78%
0.07739
6.04%
0.04424
-26.17%
0.0004398
4.02%
0.03423
-5.47%
11.5002
-4.96%
0.0458
-2.55%
0.2965
-1.53%
0.00000021520
-34.79%
0.618
-2.37%
2.288
-2.22%
0.002249
-2.22%
0.0000521
6.54%
1337
4.53%
0.0002816
-1.33%
0.00421
0.24%
0.008950
-7.53%
0.01780
-5.42%
0.000001661
-0.66%
0.1457
-2.74%
0.000000516
-1.34%
0.0007500
-20.06%
0.1549
-5.89%
0.821
-0.85%
18.95
-3.46%
0.11128
-0.22%
0.7537
-2.42%
0.000349
-9.82%
0.423
-0.47%
0.00005367
-6.37%
0.7620
-0.09%
76.1
-3.30%
0.939
1.29%
0.07701
-4.19%
0.000921
-12.70%
0.007063
-3.71%
23.511
-1.81%
0.02986
0.57%
0.2739
-2.98%
0.03000
0.00%
0.1016
-3.15%
0.004402
-12.95%
0.0002212
-24.69%
0.004212
-7.25%
0.00002454
-5.21%
2.231
2.34%
0.2193
-2.88%
0.002421
-7.70%
0.01229
-5.90%
0.0098
-2.00%
3.440
-3.48%
0.0000086
-11.34%
0.002105
0.19%
0.6811
-5.34%
0.000023
0.00%
0.0006498
-3.32%
0.2733
2.36%
0.01825
-8.11%
0.0051066
0.10%
0.01571
-18.52%
0.2110
-2.36%
25.0000
-0.44%
0.0065104
0.04%
0.0001532
-49.93%
0.0000699
145.26%
0.0004784
20.14%
0.0100
1.01%
0.0538
-0.92%
0.004236
-1.35%
0.0000002725
-31.24%
0.003821
-19.86%
0.482
-1.03%
0.0268
-8.53%
0.3281
-2.79%
0.002867
-8.37%
0.000000000661
-7.29%
1.4238
-1.16%
0.000001891
-13.65%
0.0000000002063
-0.96%
0.00000000110
10.00%
0.00804
7.20%
0.0000266
-1.12%
0.0000683
-2.43%
0.2076
-2.35%
0.03929
-11.21%
0.0000000000000157
-12.78%
0.001947
-2.31%
0.0997
-4.41%
0.898
-1.10%
0.0001249
49.76%
0.0575
-2.21%
0.003432
-1.80%
0.03886
-10.17%
1.251
-0.32%
0.0760
-1.81%
0.01472
1.38%
0.0334
-3.47%
0.05808
1.27%
0.2831
-5.13%
0.05767
-2.85%
0.002473
3.34%
0.001279
-27.86%
0.0007601
-13.31%
3.34
-5.38%
0.001878
-0.84%
0.000000000598
-3.55%
17.35
-2.64%
0.0190
-0.52%
0.1735
-2.53%
0.0755
-1.44%
0.000000001795
-5.82%
0.1112
-5.60%
0.0006304
-3.15%
0.000000000000888
-4.41%
0.001261
-7.62%
0.004874
-12.16%
0.3599
-3.92%
0.09000
-21.62%
0.0000086
-2.27%
6.4140
-8.74%
0.005148
-3.56%
0.003912
0.00%
0.1096
-1.97%
0.1679
-3.45%
0.0382
50.39%
0.001150
-3.28%
0.00010610
-1.41%
0.00000000015505
-1.19%
0.0254
-4.51%
0.0473
-2.27%
0.006160
0.56%
0.032603
-3.50%
0.00009300
-27.34%
0.00120
-0.83%
0.02742
-2.04%
0.003500
2.19%
0.1503
-5.17%
0.01662
-2.35%
0.00000000001592
-5.63%
0.0000000626
0.48%
0.0004066
7.08%
17.87
-2.40%
0.0168
-1.18%
0.00524
-3.14%
0.00003
0.00%
0.000000002106
4.83%
0.0111
0.91%
0.0000000502
-5.82%
0.02482
-1.94%
0.0004
-33.33%
14.92
-4.36%
0.0022272
-7.65%
0.01274
-3.12%
0.931
-13.48%
0.000030
3.45%
0.013605
0.05%
0.000306
-0.33%
0.0062
-1.59%
0.0110
-5.17%
0.000104
-5.45%
0.000261
61.11%
0.00000709
-0.42%
0.00000398
-3.63%
0.1253
-3.91%
0.00894
-2.51%
0.0000018
-5.26%
0.000504
26.00%
0.00000000001076
-14.19%
0.002701
0.04%
0.0006748
-3.27%
0.00725
-0.55%
0.0950
23.06%
0.0003343
36.23%
0.0007492
-7.52%
0.00306
0.00%
0.0904
-5.54%
0.00006107
-37.58%
0.008231
0.00%
0.001038
-0.10%
0.797
-1.36%
0.04024
2.26%
0.0356
-2.73%
0.01105
-12.65%
0.000000000003
-25.00%
0.00000000000023
-11.54%
0.000012
-60.00%
0.000000000001766
-0.90%
0.1404
-7.57%
8.02
-3.26%
0.00000926
0.00%
0.2574
-3.85%
1.514
-2.45%
0.02658
0.00%
0.00853
-5.95%
0.00685
-19.70%
0.00237
-15.96%
0.01303
9.22%
0.0431
-2.05%
0.3781
-2.65%
82.10
-10.84%
0.002814
-17.55%
0.04993
-6.62%
2.49
96.06%
0.000777
-6.16%
0.0000301
-1.31%
0.0000013
30.00%
0.01308
-2.46%
0.01061
-4.24%
0.0474
1.50%
0.000706
-14.63%
0.0048
-26.15%
0.0000238
-6.67%
0.0972
-4.24%
0.000835
-0.95%
0.0000652
0.93%
0.05804
-1.46%
0.00003
-50.00%
0.169000
-26.52%
0.249
-17.00%
0.0555
-4.80%
0.3832
-3.52%
0.004173
-1.32%
0.1158
-2.53%
0.0000000030204
-29.16%
0.1332
-1.41%
18.30
-1.40%
12.32
-1.04%
0.650
-5.11%
0.9097
-1.30%
0.000823
-10.45%
0.000090
5.88%
0.003591
-11.62%
0.0098
10.11%
0.1268
-3.65%
450.00
80.00%
0.00648
0.31%
0.0591
1.90%
0.05804
-0.14%
0.0000119
-15.00%
0.03287
2.85%
0.02897
-3.34%
0.01050
0.00%
1.466
-3.30%
0.01658
-2.59%
0.000182
-9.90%
0.0018
5.88%
0.000025
-3.85%
1.640
-4.87%
0.00029
7.41%
0.001383
-16.59%
0.0002201
-8.37%
0.00113
-12.40%
0.02018
0.80%
0.002315
-6.46%
0.03745
-0.87%
0.00000000000099
1.02%
0.0504
-3.63%
0.00000000000012
0.00%
0.722
-2.83%
0.002213
-10.55%
0.0924
-4.84%
0.000037
-17.78%
0.000000000003846
-15.29%
0.0124
-4.62%
0.000001624
-3.22%
0.0856
-1.38%
0.1288
-13.85%
0.00000000000212
0.00%
0.00000058
0.00%
0.00002238
-1.63%
0.000075
-11.76%
0.00036
0.00%
0.0000000000000160
-1.84%
0.01276
-2.15%
0.000025
66.67%
0.0382
-3.78%
0.0794
-3.64%
2.992
-1.87%
0.0009038
-9.45%
0.0004361
-6.90%
0.02930
-7.25%
0.0680
-2.72%
0.0541
-0.18%
0.0001
0.00%
0.0872
-0.57%
0.1508
-1.76%
0.000017
21.43%
0.524
-3.68%
0.00014
-6.67%
0.000000000030
-57.14%
0.001100
-3.17%
0.00000000000651
-0.15%
0.000004
-55.56%
0.750
0.00%
0.1355
-0.51%
0.003637
-8.94%
0.00004089
-1.64%
0.0119
-2.46%
0.0000006650
0.15%
0.00000000000115
0.00%
0.0000138
39.39%
0.001002
-9.24%
0.1871
-3.41%
0.0350
-2.23%
0.00040
11.11%
0.8427
-0.19%
0.0007
-41.67%
0.0000000171
11.76%
0.00025
0.00%
0.1906
-2.21%
0.0791
-6.17%
0.00608
63.88%
0.001790
0.00%
0.00220
-8.33%
0.0364
-4.96%
0.2993
-0.03%
0.00000007
-41.67%
0.0001402
-0.07%
0.0005
0.00%
0.001018
-9.75%
0.00004
0.00%
0.0001513
-0.79%
0.0000002176
0.14%
0.003277
-13.60%
0.0000310
-0.64%
0.0004504
-14.31%
0.006338
-5.60%
0.1449
-2.42%
0.0006668
-7.31%
0.483
-4.17%
0.001749
-6.72%
0.0066
3.13%
0.000003220
101.25%
0.00000000001606
-4.18%
0.5320
0.40%
0.0014
55.56%
0.00000310
-5.78%
0.00242
-7.98%
0.000062
40.91%
0.0000329
0.00%
0.0000099
0.00%
2.957
-2.54%
0.001216
-2.01%
0.00000000057
1.79%
0.0000000190
1.06%
0.0182
0.00%
0.0009
0.00%
0.0700
39.44%
0.0657
-5.74%
49.775
-1.79%
0.00011
-8.33%
0.0582
-5.98%
0.3905
24.72%
0.00000042
2.44%
0.000000106
6.00%
0.0108
10.20%
0.0005
25.00%
0.01299
-1.59%
0.7000
0.00%
0.00000000000288
-0.69%
0.0026
0.00%
0.00009
-10.00%
0.000201
3.61%
0.000000000019
72.73%
0.3535
-8.18%
100.71
-0.94%
0.01200
0.00%
0.00011
-15.38%
0.003424
-5.99%
0.0027
0.00%
0.3023
-1.47%
0.00000000003625
5.26%
0.00004399
0.00%
0.000000000108
-4.42%
0.00000007783
0.00%
0.000400
-20.00%
0.000000000785
-2.00%
0.000056
-25.33%
0.00077
-8.33%
0.000445
-1.98%
0.000092
6.98%
0.000000001868
-0.05%
0.00011
0.00%
0.000000000746
-6.28%
0.0485
-2.22%
0.002013
0.65%
0.00006
-40.00%
0.00774
12.34%
0.000000000375
0.27%
0.000193218
1.67%
0.000028
-15.15%
0.00000000000040
5.26%
0.00000000000389
-1.52%
0.000000008400
0.00%
0.000000000533
0.00%
0.000000002313
-2.32%
0.000000039
-2.50%
0.000000000129
0.78%
0.00030000
-14.29%
0.00000152
4.83%
0.0239
-1.65%
0.0000326
7.95%
0.000033
-13.16%
0.001500
0.00%
0.2225
-0.98%
0.0000068
-33.33%
0.0562
28.60%
0.01082
-7.84%
0.001650
50.00%
0.0000235
0.00%
0.00021
0.00%
0.00083
0.00%
0.0085
41.67%
0.000700
38.34%
0.000057
1.79%
0.0000017
-41.38%
0.0000010
42.86%
0.0814
-0.85%
0.005018
-6.15%
0.02254
-17.19%
1.2610
-1.35%
0.01467
-7.74%
0.1133
-5.35%
0.0003805
-6.65%
0.4835
-0.68%
0.10435
0.04%
0.1352
-5.52%
0.3649
-4.70%
0.003189
-20.06%
0.2540
-0.66%
58.5600
0.00%
0.0582
-1.52%
0.0004419
-15.38%
0.0888
-6.82%
0.0004917
-6.86%
0.0003220
0.00%
0.002564
-8.00%
0.0009012
0.00%
0.0003988
-5.48%
0.00600
0.00%
0.0007993
0.00%
6.147
-1.03%
0.2166
-1.46%
0.0000675
-0.74%
0.0000397
0.00%
0.002730
-7.36%
0.0012
0.00%
0.7705
-3.25%
1899.00
0.00%
0.4351
-5.54%
0.5914
-3.24%
0.001326
-3.91%
0.00424
3.67%
0.00221
-4.74%
0.2042
-4.13%
2.5129
0.00%
0.464
1.53%
1.000000
0.00%
0.3771
0.00%
0.5732
0.00%
1.856
-2.78%
0.0558
-3.79%
0.000000100
0.00%
8.77
-4.15%
0.0001030
0.00%
0.00103
0.00%
0.6789
5.30%
0.0700
0.00%
0.00000000003010
63.06%
0.001119
-3.87%
0.00000085
-5.56%
0.1500
-2.66%
0.01891
-2.32%
0.1879
-3.84%
0.000216
0.00%
2.179
0.00%
1.5000
0.00%
3.9889
0.00%
1.1371
0.00%
6.332
-2.81%
0.000082
6.49%
0.4424
0.00%
0.000392
0.77%
0.0071
0.00%
0.000210
0.00%
14.08
0.14%
0.0754
-4.56%
0.1125
-2.60%
0.1759
-0.90%
0.004231
-2.35%
0.000452
0.00%
0.0272
0.00%
0.1204
0.00%
2.644
-1.16%
1.100
0.73%
0.006000
0.00%
0.000300
0.00%
0.0025
0.00%
0.00035
0.00%
0.0004
0.00%
0.00033
0.00%
0.011926
0.00%
0.001100
0.00%
0.000365
0.00%
0.001201
0.00%
0.0064
0.00%
0.0000002593
0.00%
0.00001584
0.00%
0.0000001013
0.00%
0.000024
0.00%
0.00005
0.00%
0.00006187
0.00%
0.000166
0.00%
0.001405
0.00%
0.2461
-0.28%
0.000483
5.69%
0.000902
0.00%
0.0001
0.00%
0.0009
0.00%
0.0560
0.00%
0.004025
0.00%
0.00000100
0.00%
0.0000000104
0.00%
0.000685
0.00%
0.00000006
0.00%
0.001000
0.00%
0.0000000053
0.00%
0.0000000039
0.00%
0.00001626
0.00%
0.000423
0.00%
0.0065
0.00%
0.000310
0.00%
0.3284
0.00%
0.9500
0.00%
0.0057
0.00%
0.000405
0.00%
----
0.001290
0.00%
0.00000011
0.00%
0.00023846
0.00%
0.000758
0.00%
0.001000
0.00%
0.000058
0.00%
1.6799
0.00%
0.0920
0.00%
0.000098
0.00%
0.00000000002387
0.00%
0.00425
0.00%
0.00001
0.00%
0.000118
0.00%
0.0010
0.00%
0.00037
0.00%
0.001963
0.00%
0.00000055
0.00%
0.00006767
0.00%
0.00005458
0.00%
0.001263
0.00%
0.001210
0.00%
0.00171
0.00%
0.0072
0.00%
0.0001000
0.00%
0.05056
0.00%
1.3575
0.00%
0.00136
0.00%
0.00007
0.00%
0.001234
0.00%
0.000449
0.00%
0.0066
0.00%
0.0004
0.00%
0.0007
0.00%
0.0240
0.00%
0.000522
0.00%
0.020562
0.00%
0.9990
0.00%
0.0000111
0.00%
0.007000
0.00%
0.000363
0.00%
0.0012
0.00%
0.000792
0.00%
0.001200
0.00%
0.000331
0.00%
0.001050
0.00%
0.000383
0.00%
0.01595
0.00%
0.001000
0.00%
50.0000
0.00%
0.0006
0.00%
0.0786
0.00%
0.001563
0.00%
1.6349
0.00%
0.00000000000540
0.00%
0.000028
0.00%
0.000999
0.00%
0.001801
0.00%
0.0200
0.00%
0.0093
0.00%
0.0006
0.00%
65.1101
0.00%
1.418
-0.07%
3.7189
0.00%
0.000082
0.00%
0.0071
0.00%
0.016111
0.00%
4.1000
0.00%
0.0489
0.00%
0.00008997
0.00%
0.0131
0.00%
0.0013
0.00%
0.1078
0.00%
4.4022
0.00%
0.0745
0.00%
0.002461
0.00%
0.001160
0.00%
0.3882
0.00%
0.001000
0.00%
0.076250
0.00%
0.020595
0.00%
0.0150
0.00%
0.0036
0.00%
0.1769
0.00%
2.2915
0.00%
0.000257
0.00%
0.000620
0.00%
0.000946
0.00%
0.022345
0.00%
0.4820
0.00%
0.0490
0.00%
0.0096
0.00%
1.76670591
0.00%
0.0024
0.00%
0.000399
0.00%
0.0000000000270
0.00%
0.0000002850
0.00%
0.6700
0.00%
0.0102
0.00%
0.00007
0.00%
0.01989
0.00%
0.2888
0.00%
0.00501
0.00%
0.02700
0.00%
0.0650
0.00%
0.3515
0.00%
0.00125
0.00%
0.000446
0.00%
0.4900
0.00%
1.0100
0.00%
0.5000
0.00%
0.010100
0.00%
0.0069
0.00%
0.88686
0.00%
0.05578
0.00%
1.1760
0.00%
0.000561
0.00%
0.1725
0.00%
0.01463
0.00%
0.01451
0.48%
0.00614
0.00%
0.4606
0.00%
0.001800
0.00%
0.000001000
0.00%
0.0000008
0.00%
1.3224
-1.74%
0.00390
0.00%
0.0000325
0.00%
0.00000326
0.00%
1.0000
0.00%
0.00455
0.00%
0.34211
0.00%
0.00132
0.00%
0.0000077
0.00%
0.0005
0.00%
0.00146
0.00%
0.001277
0.00%
0.03520
0.00%
0.0000023
0.00%
0.000000005
0.00%
0.000514
0.00%
0.001987
0.00%
0.0000061
0.00%
0.000313
0.00%
0.0000029
0.00%
0.0007000
0.00%
0.00200
0.00%
0.03455
0.00%
0.0032
0.00%
0.000495
0.00%
0.00049
0.00%
0.00041
0.00%
0.00017800
0.00%
0.007210
0.00%
0.00635
0.00%
0.0900
0.00%
0.00006
0.00%
0.000000000009
0.00%
0.01030
0.00%
0.00240
0.00%
0.00070
0.00%
0.003000
0.00%
0.000310
0.00%
0.0000269
0.00%
0.0000000500
0.00%
0.0000001300
0.00%
0.000996
0.00%
0.7997
0.00%
0.0001543
0.00%
0.000426832
0.00%
0.00002805
0.00%
0.00776
0.00%
0.1600
0.00%
0.0000245
0.00%
0.1197
0.00%
0.00056
0.00%
0.000510
0.00%
0.00218
0.00%
0.002100
0.00%
0.000270
0.00%
0.0668
0.00%
0.000055
0.00%
0.3101
0.00%
0.00639
0.00%
0.4400
0.00%
1.4371
0.00%
0.002579
0.00%
0.250
0.00%
0.4389
2.12%
0.3771
-3.97%
0.001106
0.00%
0.0249
0.00%
0.6608
0.00%
0.0614
0.33%
0.5235
-1.51%
0.0922
-4.85%
0.00500
0.00%
3.58
0.00%
0.01138
-1.47%
0.0020
0.00%
0.00538
0.00%
0.4501
1.40%
5155.00
0.00%
2.195
-1.79%
1.475
-4.47%
0.0091
0.00%