From 42bb1c6e5e5430b30c2fff04c37421b83e74a0f2 Mon Sep 17 00:00:00 2001 From: grants-deployer Date: Mon, 22 Jul 2024 16:07:25 +0000 Subject: [PATCH] Deploy website - based on 43184d2d8330d24de090801eba3f98b8a43e29f5 --- 404.html | 2 +- Implementation Guide.html | 2 +- Implementation Guide/faq.html | 2 +- Polkadot_Protocol_Spec.pdf | Bin 3089930 -> 3089918 bytes Support Docs/privacy_policy.html | 2 +- __docusaurus/debug.html | 2 +- __docusaurus/debug/config.html | 2 +- __docusaurus/debug/content.html | 2 +- __docusaurus/debug/globalData.html | 2 +- __docusaurus/debug/metadata.html | 2 +- __docusaurus/debug/registry.html | 2 +- __docusaurus/debug/routes.html | 2 +- ...Spec-0bddaf1fa3eaf582160860971e8604a3.pdf} | Bin 3089930 -> 3089918 bytes assets/js/1df93b7f.39b1dd24.js | 2 -- assets/js/1df93b7f.5a6ec51a.js | 2 ++ ...E.txt => 1df93b7f.5a6ec51a.js.LICENSE.txt} | 0 assets/js/8806c109.02d0ca5f.js | 1 - assets/js/8806c109.489f5357.js | 1 + ...a5a35.2936fefc.js => fe5a5a35.6d201c2a.js} | 2 +- assets/js/runtime~main.31288950.js | 1 + assets/js/runtime~main.391e1c8f.js | 1 - chap-host-api.html | 2 +- chap-networking.html | 2 +- chap-overview.html | 2 +- chap-runtime-api.html | 2 +- chap-state.html | 2 +- chap-sync.html | 2 +- chapter-anv.html | 2 +- id-consensus.html | 2 +- id-cryptography-encoding.html | 2 +- id-extrinsics.html | 4 ++-- id-glossary.html | 2 +- id-polkadot-protocol.html | 2 +- id-weights.html | 4 ++-- index.html | 4 ++-- part-polkadot-host.html | 2 +- part-polkadot-runtime.html | 2 +- sect-block-production.html | 2 +- sect-finality.html | 2 +- sect-lightclient.html | 2 +- sect-metadata.html | 2 +- 41 files changed, 39 insertions(+), 39 deletions(-) rename assets/files/{Polkadot_Protocol_Spec-7c3af09f94ad223544f5ef459067eaf3.pdf => Polkadot_Protocol_Spec-0bddaf1fa3eaf582160860971e8604a3.pdf} (97%) delete mode 100644 assets/js/1df93b7f.39b1dd24.js create mode 100644 assets/js/1df93b7f.5a6ec51a.js rename assets/js/{1df93b7f.39b1dd24.js.LICENSE.txt => 1df93b7f.5a6ec51a.js.LICENSE.txt} (100%) delete mode 100644 assets/js/8806c109.02d0ca5f.js create mode 100644 assets/js/8806c109.489f5357.js rename assets/js/{fe5a5a35.2936fefc.js => fe5a5a35.6d201c2a.js} (88%) create mode 100644 assets/js/runtime~main.31288950.js delete mode 100644 assets/js/runtime~main.391e1c8f.js diff --git a/404.html b/404.html index 02a80a1ec..f1ce42ee3 100644 --- a/404.html +++ b/404.html @@ -6,7 +6,7 @@ Polkadot Protocol Specification - + diff --git a/Implementation Guide.html b/Implementation Guide.html index 76538ec9f..4f15425f1 100644 --- a/Implementation Guide.html +++ b/Implementation Guide.html @@ -6,7 +6,7 @@ Implementation Guide | Polkadot Protocol Specification - + diff --git a/Implementation Guide/faq.html b/Implementation Guide/faq.html index 36e172e34..a4ae30c0e 100644 --- a/Implementation Guide/faq.html +++ b/Implementation Guide/faq.html @@ -6,7 +6,7 @@ FAQ | Polkadot Protocol Specification - + diff --git a/Polkadot_Protocol_Spec.pdf 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Specification - + diff --git a/__docusaurus/debug.html b/__docusaurus/debug.html index 070bedfbe..9a3cf2373 100644 --- a/__docusaurus/debug.html +++ b/__docusaurus/debug.html @@ -6,7 +6,7 @@ Docusaurus debug panel - + diff --git a/__docusaurus/debug/config.html b/__docusaurus/debug/config.html index 69a9a4f75..3bf9717be 100644 --- a/__docusaurus/debug/config.html +++ b/__docusaurus/debug/config.html @@ -6,7 +6,7 @@ Docusaurus debug panel - + diff --git a/__docusaurus/debug/content.html b/__docusaurus/debug/content.html index 741dcf3e4..990381b65 100644 --- a/__docusaurus/debug/content.html +++ b/__docusaurus/debug/content.html @@ -6,7 +6,7 @@ Docusaurus debug panel - + diff --git a/__docusaurus/debug/globalData.html b/__docusaurus/debug/globalData.html index 3a9283c8f..b5d24c7ae 100644 --- a/__docusaurus/debug/globalData.html +++ b/__docusaurus/debug/globalData.html @@ -6,7 +6,7 @@ Docusaurus debug panel - + diff --git a/__docusaurus/debug/metadata.html 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"}})}},640:(a,e,t)=>{t.r(e),t.d(e,{assets:()=>k,contentTitle:()=>N,default:()=>u,frontMatter:()=>o,metadata:()=>c,toc:()=>h});var n=t(7462),m=(t(7294),t(3905)),s=t(2182);const r='\\begin{algorithm}\n\\caption{"request\\_judgement"` Runtime function benchmark}\n\\begin{algorithmic}\n \\Ensure $\\mathcal{W}$\n \\State \\textbf{init} $collection = \\{\\}$\n \\For{$amount \\leftarrow 1,MaxRegistrars$}\n \\State \\call{Generate-Registrars}{$amount$}\n \\State $caller \\leftarrow$ \\call{Create-Account}{$caller, 1$}\n \\State \\call{Set-Balance}{$caller, 100$}\n \\State $time \\leftarrow$ \\call{Timer}{\\call{Request-Judgement}{\\call{Random}{$amount$}$, 100$}}\n \\State \\call{Add-To}{$collection, time$}\n \\EndFor\n \\State $\\mathcal{W} \\leftarrow$ \\call{Compute-Weight}{$collection$}\n \\Return $\\mathcal{W}$\n\\end{algorithmic}\n\\end{algorithm}',p='\\begin{algorithm}\n\\caption{"payout\\_stakers"` Runtime function benchmark}\n\\begin{algorithmic}\n \\Ensure $\\mathcal{W}$\n \\State \\textbf{init} $collection = \\{\\}$\n \\For{$amount \\leftarrow 1,MaxNominatorRewardedPerValidator$}\n \\For{$era\\_depth \\leftarrow 1,HistoryDepth$}\n \\State $validator \\leftarrow$ \\call{Generate-Validator}{}\n \\State \\call{Validate}{$validator$}\n \\State $nominators \\leftarrow$ \\call{Generate-Nominators}{$amount$}\n \\For{$nominator \\in nominators$}\n \\State \\call{Nominate}{$validator, nominator$}\n \\EndFor\n \\State $era\\_index \\leftarrow$ \\call{Create-Rewards}{$validator, nominators, era\\_depth$}\n \\State $time \\leftarrow$ \\call{Timer}{\\call{Payout-Stakers}{$validator$}$, era\\_index$}\n \\State \\call{Add-To}{$collection, time$}\n \\EndFor\n \\EndFor\n \\State $\\mathcal{W} \\leftarrow$ \\call{Compute-Weight}{$collection$}\n \\Return $\\mathcal{W}$\n\\end{algorithmic}\n\\end{algorithm}',i="\\begin{algorithm}\n\\caption{\"transfer\" Runtime function benchmark}\n\\begin{algorithmic}\n \\Ensure{$collection$: a collection of time measurements of all benchmark iterations}\n \\Function{Main}{}\n \\State \\textbf{init} $collection = \\{ \\}$\n \\State \\textbf{init} $balance = 1'000$\n \\For{$index \\gets 1,1'000$}\n \\State $time \\leftarrow$ \\call{Run-Benchmark}{$index, balance$}\n \\State \\call{Add-To}{$collection, time$}\n \\EndFor\n \\State \\textbf{init} $index = 1'000$\n \\For{$balance \\gets 2,1'000$}\n \\State $time \\leftarrow$ \\call{Run-Benchmark}{$index, balance$}\n \\State \\call{Add-To}{$collection, time$}\n \\EndFor\n \\State $\\mathcal{W} \\leftarrow$ \\call{Compute-Weight}{$collection$}\n \\Return $\\mathcal{W}$\n \\EndFunction\n \\Function{Run-Benchmark}{$index$, $balance$}\n \\State $sender \\leftarrow$ \\call{Create-Account}{$caller, index$}\n \\State $recipient \\leftarrow$ \\call{Create-Accouny}{$recipient, index$}\n \\State \\call{Set-Balance}{$sender, balance$}\n \\State $time \\leftarrow$ \\call{Timer}{\\call{Transfer}{$sender, recipient, balance$}}\n \\Return $time$ \n \\EndFunction\n\\end{algorithmic}\n\\end{algorithm}",l='\\begin{algorithm}\n\\caption{"withdraw\\_unbonded" Runtime function benchmark}\n\\begin{algorithmic}\n \\Ensure $\\mathcal{W}$\n \\Function{Main}{}\n \\State \\textbf{init} $collection = \\{\\}$\n \\For{$balance \\gets 1,100$}\n \\State $stash \\leftarrow$ \\call{Create-Account}{$stash, 1$}\n \\State $controller \\leftarrow$ \\call{Create-Account}{$controller, 1$}\n \\State \\call{Set-Balance}{$stash, 100$}\n \\State \\call{Set-Balance}{$controller, 1$}\n \\State \\call{Bond}{$stash, controller, balance$}\n \\State \\call{Pass-Era}{}\n \\State \\call{UnBond}{$controller, balance$}\n \\State \\call{Pass-Era}{}\n \\State $time \\leftarrow$ \\call{Timer}{\\call{Withdraw-Unbonded}{$controller$}}\n \\State \\call{Add-To}{$collection, time$}\n \\EndFor\n \\State $\\mathcal{W} \\leftarrow$ \\call{Compute-Weight}{$collection$}\n \\Return $\\mathcal{W}$\n \\EndFunction\n\\end{algorithmic}\n\\end{algorithm}',o={title:"10. Weights"},N=void 0,c={unversionedId:"id-weights",id:"id-weights",title:"10. Weights",description:"10.1. Motivation",source:"@site/docs/id-weights.md",sourceDirName:".",slug:"/id-weights",permalink:"/id-weights",draft:!1,unlisted:!1,editUrl:"https://github.com/w3f/polkadot-spec/blob/main/docs/id-weights.md",tags:[],version:"current",frontMatter:{title:"10. Weights"},sidebar:"tutorialSidebar",previous:{title:"9. Extrinsics",permalink:"/id-extrinsics"},next:{title:"11. Consensus",permalink:"/id-consensus"}},k={},h=[{value:"10.1. Motivation",id:"id-motivation",level:2},{value:"10.2. Assumptions",id:"sect-assumptions",level:2},{value:"Definition 160. Block Length",id:"defn-block-length",level:6},{value:"Definition 161. Target Time per Block",id:"defn-target-time-per-block",level:6},{value:"Definition 162. Block Target Time",id:"defn-block-target-time",level:6},{value:"Definition 163. Block Limits",id:"defn-polkadot-block-limits",level:6},{value:"Definition 164. Weight Function",id:"defn-weight-function",level:6},{value:"10.2.1. Limitations",id:"sect-limitations",level:3},{value:"Definition 165. Block Weight",id:"defn-block-weight",level:6},{value:"10.3. Calculation of the weight function",id:"sect-runtime-primitives",level:2},{value:"10.4. Benchmarking",id:"sect-benchmarking",level:2},{value:"10.4.1. Primitive Types",id:"sect-primitive-types",level:3},{value:"10.4.1.1. Considerations",id:"sect-primitive-types-considerations",level:4},{value:"Definition 166. Maximum Value",id:"defn-max-value",level:6},{value:"10.4.2. Parameters",id:"id-parameters",level:3},{value:"10.4.2.1. Weight Refunds",id:"id-weight-refunds",level:4},{value:"10.4.3. Storage I/O cost",id:"id-storage-io-cost",level:3},{value:"10.4.4. Environment",id:"id-environment",level:3},{value:"10.5. Practical examples",id:"sect-practical-examples",level:2},{value:"10.5.1. Practical Example #1: request_judgement",id:"id-practical-example-1-request_judgement",level:3},{value:"10.5.1.1. Analysis",id:"id-analysis",level:4},{value:"10.5.1.2. Considerations",id:"sect-considerations",level:4},{value:"10.5.1.3. Benchmarking Framework",id:"id-benchmarking-framework",level:4},{value:"Algorithm 27. request_judgement Runtime Function Benchmark",id:"algo-benchmark-request-judgement",level:6},{value:"10.5.2. Practical Example #2: payout_stakers",id:"sect-practical-example-payout-stakers",level:3},{value:"10.5.2.1. Analysis",id:"id-analysis-2",level:4},{value:"10.5.2.2. Considerations",id:"considerations-1",level:4},{value:"10.5.2.3. Benchmarking Framework",id:"id-benchmarking-framework-2",level:4},{value:"Definition 167. History Depth",id:"defn-history-depth",level:6},{value:"Definition 168. Maximum Nominator Reward",id:"defn-max-nominator-reward",level:6},{value:"Algorithm 28. payout_stakers Runtime Function Benchmark",id:"algo-benchmark-payout-stakers",level:6},{value:"10.5.3. Practical Example #3: transfer",id:"id-practical-example-3-transfer",level:3},{value:"10.5.3.1. Analysis",id:"id-analysis-3",level:4},{value:"10.5.3.2. Considerations",id:"considerations-2",level:4},{value:"10.5.3.3. Benchmarking Framework",id:"id-benchmarking-framework-3",level:4},{value:"Algorithm 29. transfer Runtime Function Benchmark",id:"algo-benchmark-transfer",level:6},{value:"10.5.4. Practical Example #4: withdraw_unbonded",id:"id-practical-example-4-withdraw_unbonded",level:3},{value:"10.5.4.1. Analysis",id:"id-analysis-4",level:4},{value:"10.5.4.2. Parameters",id:"id-parameters-2",level:4},{value:"10.5.4.3. Considerations",id:"considerations-3",level:4},{value:"10.5.4.4. Benchmarking Framework",id:"id-benchmarking-framework-4",level:4},{value:"Algorithm 30. withdraw_unbonded Runtime Function Benchmark",id:"algo-benchmark-withdraw",level:6},{value:"10.6. Fees",id:"id-fees",level:2},{value:"10.6.1. Fee Calculation",id:"sect-fee-calculation",level:3},{value:"10.6.2. Definitions in Polkadot",id:"id-definitions-in-polkadot",level:3},{value:"10.6.3. Fee Multiplier",id:"id-fee-multiplier",level:3},{value:"10.6.3.1. Update Multiplier",id:"id-update-multiplier",level:4}],d={toc:h},g="wrapper";function u(a){let{components:e,...t}=a;return(0,m.kt)(g,(0,n.Z)({},d,t,{components:e,mdxType:"MDXLayout"}),(0,m.kt)("h2",{id:"id-motivation"},"10.1. Motivation"),(0,m.kt)("p",null,"The Polkadot network, like any other permissionless system, needs to implement a mechanism to measure and limit the usage in order to establish an economic incentive structure, prevent network overload, and mitigate DoS vulnerabilities. In particular, Polkadot enforces a limited time window for block producers to create a block, including limitations on block size, which can make the selection and execution of certain extrinsics too expensive and decelerate the network."),(0,m.kt)("p",null,"In contrast to some other systems, such as Ethereum, which implement fine measurement for each executed low-level operation by smart contracts, known as gas metering, Polkadot takes a more relaxed approach by implementing a measuring system where the cost of the transactions (referred to as \u2019extrinsics\u2019) are determined before execution and are known as the weight system."),(0,m.kt)("p",null,'The Polkadot weight system introduces a mechanism for block producers to measure the cost of running the extrinsics and determine how "heavy" it is in terms of execution time. Within this mechanism, block producers can select a set of extrinsics and saturate the block to its fullest potential without exceeding any limitations (as described in ',(0,m.kt)("a",{parentName:"p",href:"id-weights#sect-limitations"},"Section 10.2.1."),"). Moreover, the weight system can be used to calculate a fee for executing each extrinsics according to its weight (as described in ",(0,m.kt)("a",{parentName:"p",href:"id-weights#sect-fee-calculation"},"Section 10.6.1."),")."),(0,m.kt)("p",null,"Additionally, Polkadot introduces a specified block ratio (as defined in ",(0,m.kt)("a",{parentName:"p",href:"id-weights#sect-limitations"},"Section 10.2.1."),"), ensuring that only a certain portion of the total block size gets used for regular extrinsics. The remaining space is reserved for critical, operational extrinsics required for the functionality of Polkadot itself."),(0,m.kt)("p",null,"To begin, we introduce in ",(0,m.kt)("a",{parentName:"p",href:"id-weights#sect-assumptions"},"Section 10.2.")," the assumption upon which the Polkadot transaction weight system is designed. In ",(0,m.kt)("a",{parentName:"p",href:"id-weights#sect-limitations"},"Section 10.2.1."),", we discuss the limitation Polkadot needs to enforce on the block size. In ",(0,m.kt)("a",{parentName:"p",href:"id-weights#sect-runtime-primitives"},"Section 10.3."),", we describe in detail the procedure upon which the weight of any transaction should be calculated. In ",(0,m.kt)("a",{parentName:"p",href:"id-weights#sect-practical-examples"},"Section 10.5."),", we present how we apply this procedure to compute the weight of particular runtime functions."),(0,m.kt)("h2",{id:"sect-assumptions"},"10.2. Assumptions"),(0,m.kt)("p",null,"In this section, we define the concept of weight, and we discuss the considerations that need to be accounted for when assigning weight to transactions. These considerations are essential in order for the weight system to deliver its fundamental mission, i.e. the fair distribution of network resources and preventing a network overload. In this regard, weights serve as an indicator on whether a block is considered full and how much space is left for remaining, pending extrinsics. Extrinsics that require too many resources are discarded. More formally, the weight system should:"),(0,m.kt)("ul",null,(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},"prevent the block from being filled with too many extrinsics")),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},"avoid extrinsics where its execution takes too long, by assigning a transaction fee to each extrinsic proportional to their resource consumption."))),(0,m.kt)("p",null,"These concepts are formalized in ",(0,m.kt)("a",{parentName:"p",href:"id-weights#defn-block-length"},"Definition 160")," and ",(0,m.kt)("a",{parentName:"p",href:"id-weights#defn-polkadot-block-limits"},"Definition 163"),":"),(0,m.kt)("h6",{id:"defn-block-length"},"Definition 160. 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",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow",mathvariant:"script"},"W"),(0,m.kt)("mrow",{parentName:"mrow"},(0,m.kt)("mo",{parentName:"mrow",fence:"true"},"("),(0,m.kt)("mi",{parentName:"mrow"},"E"),(0,m.kt)("mo",{parentName:"mrow",fence:"true"},")"))),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{\\mathcal{{{W}}}}{\\left({E}\\right)}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathcal",style:{marginRight:"0.08222em"}},"W")))),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"minner"},(0,m.kt)("span",{parentName:"span",className:"mopen delimcenter",style:{top:"0em"}},"("),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05764em"}},"E")),(0,m.kt)("span",{parentName:"span",className:"mclose delimcenter",style:{top:"0em"}},")")))))))," must depend solely on the Runtime function representing ",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow"},"E")),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{E}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6833em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05764em"}},"E"))))))," and its parameters."))),(0,m.kt)("p",{parentName:"admonition"},'Heuristically, "heaviness" corresponds to the execution time of an extrinsic. In that way, the ',(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow",mathvariant:"script"},"W")),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{\\mathcal{{{W}}}}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6833em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathcal",style:{marginRight:"0.08222em"}},"W"))))))))," value for various extrinsics should be proportional to their execution time. For example, if Extrinsic A takes three times longer to execute than Extrinsic B, then Extrinsic A should roughly weighs 3 times of Extrinsic B. 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mathcal",style:{marginRight:"0.08222em"}},"W")))),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"minner"},(0,m.kt)("span",{parentName:"span",className:"mopen delimcenter",style:{top:"0em"}},"("),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05017em"}},"B")),(0,m.kt)("span",{parentName:"span",className:"mclose delimcenter",style:{top:"0em"}},")")))))))),(0,m.kt)("p",{parentName:"admonition"},"Nonetheless, ",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow",mathvariant:"script"},"W"),(0,m.kt)("mrow",{parentName:"mrow"},(0,m.kt)("mo",{parentName:"mrow",fence:"true"},"("),(0,m.kt)("mi",{parentName:"mrow"},"E"),(0,m.kt)("mo",{parentName:"mrow",fence:"true"},")"))),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{\\mathcal{{{W}}}}{\\left({E}\\right)}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord 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as noted by the fundamentals and limitations and can be assigned as the author sees fit. As a simple example, consider a maximum block weight of 1\u2019000\u2019000\u2019000, an available ratio of 75%, and a targeted transaction throughput of 500 transactions. We could assign the (average) weight for each transaction at about 1\u2019500\u2019000. Block producers have an economic incentive to include as many extrinsics as possible (without exceeding limitations) into a block before reaching the targeted block time. Weights give indicators to block producers on which extrinsics to include in order to reach the blocks fullest potential."),(0,m.kt)("h2",{id:"sect-runtime-primitives"},"10.3. Calculation of the weight function"),(0,m.kt)("p",null,"In order to calculate weight of block ",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow"},"B")),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{B}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6833em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05017em"}},"B")))))),", ",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow",mathvariant:"script"},"W"),(0,m.kt)("mrow",{parentName:"mrow"},(0,m.kt)("mo",{parentName:"mrow",fence:"true"},"("),(0,m.kt)("mi",{parentName:"mrow"},"B"),(0,m.kt)("mo",{parentName:"mrow",fence:"true"},")"))),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{\\mathcal{{{W}}}}{\\left({B}\\right)}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathcal",style:{marginRight:"0.08222em"}},"W")))),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"minner"},(0,m.kt)("span",{parentName:"span",className:"mopen delimcenter",style:{top:"0em"}},"("),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05017em"}},"B")),(0,m.kt)("span",{parentName:"span",className:"mclose delimcenter",style:{top:"0em"}},")"))))))),", one needs to evaluate the weight of each transaction included in the block. Each transaction causes the execution of certain Runtime functions. As such, to calculate the weight of a transaction, those functions must be analyzed in order to determine parts of the code which can significantly contribute to the execution time and consume resources such as loops, I/O operations, and data manipulation. Subsequently, the performance and execution time of each part will be evaluated based on variety of input parameters. Based on those observations, weights are assigned Runtime functions or parameters which contribute to long execution times. These sub component of the code are discussed in ",(0,m.kt)("a",{parentName:"p",href:"id-weights#sect-primitive-types"},"Section 10.4.1."),"."),(0,m.kt)("p",null,"The general algorithm to calculate ",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow",mathvariant:"script"},"W"),(0,m.kt)("mrow",{parentName:"mrow"},(0,m.kt)("mo",{parentName:"mrow",fence:"true"},"("),(0,m.kt)("mi",{parentName:"mrow"},"E"),(0,m.kt)("mo",{parentName:"mrow",fence:"true"},")"))),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{\\mathcal{{{W}}}}{\\left({E}\\right)}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathcal",style:{marginRight:"0.08222em"}},"W")))),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"minner"},(0,m.kt)("span",{parentName:"span",className:"mopen delimcenter",style:{top:"0em"}},"("),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05764em"}},"E")),(0,m.kt)("span",{parentName:"span",className:"mclose delimcenter",style:{top:"0em"}},")")))))))," is described in the ",(0,m.kt)("a",{parentName:"p",href:"id-weights#sect-benchmarking"},"Section 10.4."),"."),(0,m.kt)("h2",{id:"sect-benchmarking"},"10.4. Benchmarking"),(0,m.kt)("p",null,"Calculating the extrinsic weight solely based on the theoretical complexity of the underlying implementation proves to be too complicated and unreliable at the same time. Certain decisions in the source code architecture, internal communication within the Runtime or other design choices could add enough overhead to make the asymptotic complexity practically meaningless."),(0,m.kt)("p",null,"On the other hand, benchmarking an extrinsics in a black-box fashion could (using random parameters) most certainly results in missing corner cases and worst case scenarios. Instead, we benchmark all available Runtime functions which are invoked in the course of execution of extrinsics with a large collection of carefully selected input parameters and use the result of the benchmarking process to evaluate ",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow",mathvariant:"script"},"W"),(0,m.kt)("mrow",{parentName:"mrow"},(0,m.kt)("mo",{parentName:"mrow",fence:"true"},"("),(0,m.kt)("mi",{parentName:"mrow"},"E"),(0,m.kt)("mo",{parentName:"mrow",fence:"true"},")"))),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{\\mathcal{{{W}}}}{\\left({E}\\right)}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathcal",style:{marginRight:"0.08222em"}},"W")))),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"minner"},(0,m.kt)("span",{parentName:"span",className:"mopen delimcenter",style:{top:"0em"}},"("),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05764em"}},"E")),(0,m.kt)("span",{parentName:"span",className:"mclose delimcenter",style:{top:"0em"}},")"))))))),"."),(0,m.kt)("p",null,"In order to select useful parameters, the Runtime functions have to be analyzed to fully understand which behaviors or conditions can result in expensive execution times, which is described closer in ",(0,m.kt)("a",{parentName:"p",href:"id-weights#sect-primitive-types"},"Section 10.4.1."),". Not every possible benchmarking outcome can be invoked by varying input parameters of the Runtime function. In some circumstances, preliminary work is required before a specific benchmark can be reliably measured, such as creating certain preexisting entries in the storage or other changes to the environment."),(0,m.kt)("p",null,"The Practical Examples (",(0,m.kt)("a",{parentName:"p",href:"id-weights#sect-practical-examples"},"Section 10.5."),") covers the analysis process and the implementation of preliminary work in more detail."),(0,m.kt)("h3",{id:"sect-primitive-types"},"10.4.1. Primitive Types"),(0,m.kt)("p",null,'The Runtime reuses components, known as "primitives", to interact with the state storage. The execution cost of those primitives can be measured and a weight should be applied for each occurrence within the Runtime code.'),(0,m.kt)("p",null,"For storage, Polkadot uses three different types of storage types across its modules, depending on the context:"),(0,m.kt)("ul",null,(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},(0,m.kt)("strong",{parentName:"p"},"Value"),": Operations on a single value. The final key-value pair is stored under the key:"),(0,m.kt)("pre",{parentName:"li"},(0,m.kt)("code",{parentName:"pre"}," hash(module_prefix) + hash(storage_prefix)\n"))),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},(0,m.kt)("strong",{parentName:"p"},"Map"),": Operations on multiple values, datasets, where each entry has its corresponding, unique key. The final key-value pair is stored under the key:"),(0,m.kt)("pre",{parentName:"li"},(0,m.kt)("code",{parentName:"pre"}," hash(module_prefix) + hash(storage_prefix) + hash(encode(key))\n"))),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},(0,m.kt)("strong",{parentName:"p"},"Double map"),": Just like ",(0,m.kt)("strong",{parentName:"p"},"Map"),', but uses two keys instead of one. This type is also known as "child storage", where the first key is the "parent key" and the second key is the "child key". This is useful in order to scope storage entries (child keys) under a certain ',(0,m.kt)("inlineCode",{parentName:"p"},"context")," (parent key), which is arbitrary. Therefore, one can have separated storage entries based on the context. The final key-value pair is stored under the key:"),(0,m.kt)("pre",{parentName:"li"},(0,m.kt)("code",{parentName:"pre"}," hash(module_prefix) + hash(storage_prefix)\n + hash(encode(key1)) + hash(encode(key2))\n")))),(0,m.kt)("p",null,"It depends on the functionality of the Runtime module (or its sub-processes, rather) which storage type to use. In some cases, only a single value is required. In others, multiple values need to be fetched or inserted from/into the database."),(0,m.kt)("p",null,"Those lower-level types get abstracted over in each individual Runtime module using the ",(0,m.kt)("inlineCode",{parentName:"p"},"decl_storage!")," macro. Therefore, each module specifies its own types that are used as input and output values. The abstractions do give indicators on what operations must be closely observed and where potential performance penalties and attack vectors are possible."),(0,m.kt)("h4",{id:"sect-primitive-types-considerations"},"10.4.1.1. Considerations"),(0,m.kt)("p",null,"The storage layout is mostly the same for every primitive type, primarily differentiated by using special prefixes for the storage key. Big differences arise on how the primitive types are used in the Runtime function, on whether single values or entire datasets are being worked on. Single value operations are generally quite cheap and its execution time does not vary depending on the data that\u2019s being processed. However, excessive overhead can appear when I/O operations are executed repeatedly, such as in loops. Especially, when the amount of loop iterations can be influenced by the caller of the function or by certain conditions in the state storage."),(0,m.kt)("p",null,"Maps, in contrast, have additional overhead when inserting or retrieving datasets, which vary in sizes. Additionally, the Runtime function has to process each item inside that list."),(0,m.kt)("p",null,"Indicators for performance penalties:"),(0,m.kt)("ul",null,(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},(0,m.kt)("strong",{parentName:"p"},"Fixed iterations and datasets")," - Fixed iterations and datasets can increase the overall cost of the Runtime functions, but the execution time does not vary depending on the input parameters or storage entries. A base Weight is appropriate in this case.")),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},(0,m.kt)("strong",{parentName:"p"},"Adjustable iterations and datasets")," - If the amount of iterations or datasets depends on the input parameters of the caller or specific entries in storage, then a certain weight should be applied for each (additional) iteration or item. The Runtime defines the maximum value for such cases. If it doesn\u2019t, it unconditionally has to and the Runtime module must be adjusted. When selecting parameters for benchmarking, the benchmarks should range from the minimum value to the maximum value, as described in ",(0,m.kt)("a",{parentName:"p",href:"id-weights#defn-max-value"},"Definition 166"),".")),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},(0,m.kt)("strong",{parentName:"p"},"Input parameters")," - Input parameters that users pass on to the Runtime function can result in expensive operations. Depending on the data type, it can be appropriate to add additional weights based on certain properties, such as data size, assuming the data type allows varying sizes. The Runtime must define limits on those properties. If it doesn\u2019t, it unconditionally has to, and the Runtime module must be adjusted. When selecting parameters for benchmarking, the benchmarks should range from the minimum values to the maximum value, as described in paragraph ",(0,m.kt)("a",{parentName:"p",href:"id-weights#defn-max-value"},"Definition 166"),"."))),(0,m.kt)("h6",{id:"defn-max-value"},"Definition 166. Maximum Value"),(0,m.kt)("admonition",{type:"definition"},(0,m.kt)("p",{parentName:"admonition"},"What the maximum value should be really depends on the functionality that the Runtime function is trying to provide. If the choice for that value is not obvious, then it\u2019s advised to run benchmarks on a big range of values and pick a conservative value below the ",(0,m.kt)("inlineCode",{parentName:"p"},"targeted time per block")," limit as described in section ",(0,m.kt)("a",{parentName:"p",href:"id-weights#sect-limitations"},"Section 10.2.1."),".")),(0,m.kt)("h3",{id:"id-parameters"},"10.4.2. Parameters"),(0,m.kt)("p",null,"The input parameters highly vary depending on the Runtime function and must therefore be carefully selected. The benchmarks should use input parameters which will most likely be used in regular cases, as intended by the authors, but must also consider worst-case scenarios and inputs that might decelerate or heavily impact the performance of the function. The input parameters should be randomized in order to cause various effects in behaviors on certain values, such as memory relocations and other outcomes that can impact performance."),(0,m.kt)("p",null,"It\u2019s not possible to benchmark every single value. However, one should select a range of inputs to benchmark, spanning from the minimum value to the maximum value, which will most likely exceed the expected usage of that function. This is described in more detail in ",(0,m.kt)("a",{parentName:"p",href:"id-weights#sect-primitive-types-considerations"},"Section 10.4.1.1."),". The benchmarks should run individual executions/iterations within that range, where the chosen parameters should give insight on the execution time. Selecting imprecise parameters or too extreme ranges might indicate an inaccurate result of the function as it will be used in production. Therefore, when a range of input parameters gets benchmarked, the result of each individual parameter should be recorded and optionally visualized, then the necessary adjustment can be made. Generally, the worst-case scenario should be assigned as the weight value for the corresponding runtime function."),(0,m.kt)("p",null,"Additionally, given the distinction between theoretical and practical usage, the author reserves the right to make adjustments to the input parameters and assign weights according to the observed behavior of the actual, real-world network."),(0,m.kt)("h4",{id:"id-weight-refunds"},"10.4.2.1. Weight Refunds"),(0,m.kt)("p",null,'When assigning the final weight, the worst-case scenario of each runtime function should be used. The runtime can then additional "refund" the amount of weights which were overestimated once the runtime function is actually executed.'),(0,m.kt)("p",null,"The Polkadot runtime only returns weights if the difference between the assigned weight and the actual weight calculated during execution is greater than 20%."),(0,m.kt)("h3",{id:"id-storage-io-cost"},"10.4.3. Storage I/O cost"),(0,m.kt)("p",null,'It is advised to benchmark the raw I/O operations of the database and assign "base weights" for each I/O operation type, such as insertion, deletion, querying, etc. When a runtime function is executed, the runtime can then add those base weights of each used operation in order to calculate the final weight.'),(0,m.kt)("h3",{id:"id-environment"},"10.4.4. Environment"),(0,m.kt)("p",null,"The benchmarks should be executed on clean systems without interference of other processes or software. Additionally, the benchmarks should be executed on multiple machines with different system resources, such as CPU performance, CPU cores, RAM, and storage speed."),(0,m.kt)("h2",{id:"sect-practical-examples"},"10.5. Practical examples"),(0,m.kt)("p",null,"This section walks through Runtime functions available in the Polkadot Runtime to demonstrate the analysis process as described in ",(0,m.kt)("a",{parentName:"p",href:"id-weights#sect-primitive-types"},"Section 10.4.1."),"."),(0,m.kt)("p",null,"In order for certain benchmarks to produce conditions where resource heavy computation or excessive I/O can be observed, the benchmarks might require some preliminary work on the environment, since those conditions cannot be created with simply selected parameters. The analysis process shows indicators on how the preliminary work should be implemented."),(0,m.kt)("h3",{id:"id-practical-example-1-request_judgement"},"10.5.1. Practical Example ","#","1: ",(0,m.kt)("inlineCode",{parentName:"h3"},"request_judgement")),(0,m.kt)("p",null,'In Polkadot, accounts can save information about themselves on-chain, known as the "Identity Info". This includes information such as display name, legal name, email address and so on. Polkadot offers a set of trusted registrars, entities elected by a Polkadot public referendum, which can verify the specified contact addresses of the identities, such as Email, and vouch on whether the identity actually owns those accounts. This can be achieved, for example, by sending a challenge to the specified address and requesting a signature as a response. The verification is done off-chain, while the final judgement is saved on-chain, directly in the corresponding Identity Info. It\u2019s also noteworthy that Identity Info can contain additional fields, set manually by the corresponding account holder.'),(0,m.kt)("p",null,"Information such as legal name must be verified by ID card or passport submission."),(0,m.kt)("p",null,"The function ",(0,m.kt)("inlineCode",{parentName:"p"},"request_judgement")," from the ",(0,m.kt)("inlineCode",{parentName:"p"},"identity")," pallet allows users to request judgment from a specific registrar."),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre"},"(func $request_judgement (param $req_index int) (param $max_fee int))\n")),(0,m.kt)("ul",null,(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},(0,m.kt)("inlineCode",{parentName:"p"},"req_index"),": the index which is assigned to the registrar.")),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},(0,m.kt)("inlineCode",{parentName:"p"},"max_fee"),": the maximum fee the requester is willing to pay. The judgment fee varies for each registrar."))),(0,m.kt)("p",null,"Studying this function reveals multiple design choices that can impact performance, as it will be revealed by this analysis."),(0,m.kt)("h4",{id:"id-analysis"},"10.5.1.1. Analysis"),(0,m.kt)("p",null,"First, it fetches a list of current registrars from storage and then searches that list for the specified registrar index."),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"let registrars = >::get();\nlet registrar = registrars.get(reg_index as usize).and_then(Option::as_ref)\n .ok_or(Error::::EmptyIndex)?;\n")),(0,m.kt)("p",null,"Then, it searches for the Identity Info from storage, based on the sender of the transaction."),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"let mut id = >::get(&sender).ok_or(Error::::NoIdentity)?;\n")),(0,m.kt)("p",null,'The Identity Info contains all fields that have a data in them, set by the corresponding owner of the identity, in an ordered form. It then proceeds to search for the specific field type that will be inserted or updated, such as email address. If the entry can be found, the corresponding value is to the value passed on as the function parameters (assuming the registrar is not "stickied", which implies it cannot be changed). If the entry cannot be found, the value is inserted into the index where a matching element can be inserted while maintaining sorted order. This results in memory reallocation, which increases resource consumption.'),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"match id.judgements.binary_search_by_key(®_index, |x| x.0) {\n Ok(i) => if id.judgements[i].1.is_sticky() {\n Err(Error::::StickyJudgement)?\n } else {\n id.judgements[i] = item\n },\n Err(i) => id.judgements.insert(i, item),\n}\n")),(0,m.kt)("p",null,"In the end, the function deposits the specified ",(0,m.kt)("inlineCode",{parentName:"p"},"max_fee")," balance, which can later be redeemed by the registrar. Then, an event is created to insert the Identity Info into storage. The creation of events is lightweight, but its execution is what will actually commit the state changes."),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"T::Currency::reserve(&sender, registrar.fee)?;\n>::insert(&sender, id);\nSelf::deposit_event(RawEvent::JudgementRequested(sender, reg_index));\n")),(0,m.kt)("h4",{id:"sect-considerations"},"10.5.1.2. Considerations"),(0,m.kt)("p",null,"The following points must be considered:"),(0,m.kt)("ul",null,(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},"Varying count of registrars.")),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},"Varying count of preexisting accounts in storage.")),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},"The specified registrar is searched for in the Identity Info. An identity can be judged by as many registrars as the identity owner issues requests, therefore increasing its footprint in the state storage. Additionally, if a new value gets inserted into the byte array, memory gets reallocated. Depending on the size of the Identity Info, the execution time can vary.")),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},"The Identity-Info can contain only a few fields or many. It is legitimate to introduce additional weights for changes the owner/sender has influence over, such as the additional fields in the Identity-Info."))),(0,m.kt)("h4",{id:"id-benchmarking-framework"},"10.5.1.3. Benchmarking Framework"),(0,m.kt)("p",null,"The Polkadot Runtime specifies the ",(0,m.kt)("inlineCode",{parentName:"p"},"MaxRegistrars")," constant, which will prevent the list of registrars of reaching an undesired length. 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This should be used when the benchmark should account for unpredictable values.")),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},"Add-To(",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow"},"c"),(0,m.kt)("mi",{parentName:"mrow"},"o"),(0,m.kt)("mi",{parentName:"mrow"},"l"),(0,m.kt)("mi",{parentName:"mrow"},"l"),(0,m.kt)("mi",{parentName:"mrow"},"e"),(0,m.kt)("mi",{parentName:"mrow"},"c"),(0,m.kt)("mi",{parentName:"mrow"},"t"),(0,m.kt)("mi",{parentName:"mrow"},"i"),(0,m.kt)("mi",{parentName:"mrow"},"o"),(0,m.kt)("mi",{parentName:"mrow"},"n")),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{collection}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6944em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"co"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.01968em"}},"ll"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"ec"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"t"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"i"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"o"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"n")))))),", ",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow"},"t"),(0,m.kt)("mi",{parentName:"mrow"},"i"),(0,m.kt)("mi",{parentName:"mrow"},"m"),(0,m.kt)("mi",{parentName:"mrow"},"e")),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{time}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6595em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"t"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"im"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"e")))))),")"),(0,m.kt)("p",{parentName:"li"},"Adds a returned time measurement (time) to collection.")),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},"Compute-Weight(",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow"},"c"),(0,m.kt)("mi",{parentName:"mrow"},"o"),(0,m.kt)("mi",{parentName:"mrow"},"l"),(0,m.kt)("mi",{parentName:"mrow"},"l"),(0,m.kt)("mi",{parentName:"mrow"},"e"),(0,m.kt)("mi",{parentName:"mrow"},"c"),(0,m.kt)("mi",{parentName:"mrow"},"t"),(0,m.kt)("mi",{parentName:"mrow"},"i"),(0,m.kt)("mi",{parentName:"mrow"},"o"),(0,m.kt)("mi",{parentName:"mrow"},"n")),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{collection}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6944em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"co"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.01968em"}},"ll"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"ec"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"t"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"i"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"o"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"n")))))),")"),(0,m.kt)("p",{parentName:"li"},"Computes the resulting weight based on the time measurements in the collection. The worst-case scenario should be chosen (the highest value).")))),(0,m.kt)("h3",{id:"sect-practical-example-payout-stakers"},"10.5.2. Practical Example ","#","2: ",(0,m.kt)("inlineCode",{parentName:"h3"},"payout_stakers")),(0,m.kt)("h4",{id:"id-analysis-2"},"10.5.2.1. Analysis"),(0,m.kt)("p",null,"The function ",(0,m.kt)("inlineCode",{parentName:"p"},"payout_stakers")," from the ",(0,m.kt)("inlineCode",{parentName:"p"},"staking")," Pallet can be called by a single account in order to payout the reward for all nominators who back a particular validator. The reward also covers the validator\u2019s share. This function is interesting because it iterates over a range of nominators, which varies, and does I/O operations for each of them."),(0,m.kt)("p",null,'First, this function makes a few basic checks to verify if the specified era is not higher then the current era (as it is not in the future) and is within the allowed range also known as "history depth", as specified by the Runtime. After that, it fetches the era payout from storage and additionally verifies whether the specified account is indeed a validator and receives the corresponding "Ledger". The Ledger keeps information about the stash key, controller key, and other information such as actively bonded balance and a list of tracked rewards. The function only retains the entries of the history depth and conducts a binary search for the specified era.'),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"let era_payout = >::get(&era)\n .ok_or_else(|| Error::::InvalidEraToReward)?;\n\nlet controller = Self::bonded(&validator_stash).ok_or(Error::::NotStash)?;\nlet mut ledger = >::get(&controller).ok_or_else(|| Error::::NotController)?;\n")),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"ledger.claimed_rewards.retain(|&x| x >= current_era.saturating_sub(history_depth));\nmatch ledger.claimed_rewards.binary_search(&era) {\n Ok(_) => Err(Error::::AlreadyClaimed)?,\n Err(pos) => ledger.claimed_rewards.insert(pos, era),\n}\n")),(0,m.kt)("p",null,"The retained claimed rewards are inserted back into storage."),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},">::insert(&controller, &ledger);\n")),(0,m.kt)("p",null,"As an optimization, Runtime only fetches a list of the 64 highest-staked nominators, although this might be changed in the future. Accordingly, any lower-staked nominator gets no reward."),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"let exposure = >::get(&era, &ledger.stash);\n")),(0,m.kt)("p",null,"Next, the function gets the era reward points from storage."),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"let era_reward_points = >::get(&era);\n")),(0,m.kt)("p",null,"After that, the payout is split among the validator and its nominators. The validators receive the payment first, creating an insertion into storage and sending a deposit event to the scheduler."),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"if let Some(imbalance) = Self::make_payout(\n &ledger.stash,\n validator_staking_payout + validator_commission_payout\n) {\n Self::deposit_event(RawEvent::Reward(ledger.stash, imbalance.peek()));\n}\n")),(0,m.kt)("p",null,"Then, the nominators receive their payout rewards. The functions loop over the nominator list, conducting an insertion into storage and a creation of a deposit event for each of the nominators."),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"for nominator in exposure.others.iter() {\n let nominator_exposure_part = Perbill::from_rational_approximation(\n nominator.value,\n exposure.total,\n );\n\n let nominator_reward: BalanceOf = nominator_exposure_part * validator_leftover_payout;\n // We can now make nominator payout:\n if let Some(imbalance) = Self::make_payout(&nominator.who, nominator_reward) {\n Self::deposit_event(RawEvent::Reward(nominator.who.clone(), imbalance.peek()));\n }\n}\n")),(0,m.kt)("h4",{id:"considerations-1"},"10.5.2.2. Considerations"),(0,m.kt)("p",null,"The following points must be considered:"),(0,m.kt)("ul",null,(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},"The Ledger contains a varying list of claimed rewards. Fetching, retaining, and searching through it can affect execution time. The retained list is inserted back into storage.")),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},"Looping through a list of nominators and creating I/O operations for each increases execution time. The Runtime fetches up to 64 nominators."))),(0,m.kt)("h4",{id:"id-benchmarking-framework-2"},"10.5.2.3. Benchmarking Framework"),(0,m.kt)("h6",{id:"defn-history-depth"},"Definition 167. History Depth"),(0,m.kt)("admonition",{type:"definition"},(0,m.kt)("p",{parentName:"admonition"},"H\u0331istory Depth indicated as ",(0,m.kt)("inlineCode",{parentName:"p"},"MaxNominatorRewardedPerValidator")," is a fixed constant specified by the Polkadot Runtime which dictates the number of Eras the Runtime will reward nominators and validators for.")),(0,m.kt)("h6",{id:"defn-max-nominator-reward"},"Definition 168. Maximum Nominator Reward"),(0,m.kt)("admonition",{type:"definition"},(0,m.kt)("p",{parentName:"admonition"},"M\u0331aximum Nominator Rewarded Per Validator indicated as ",(0,m.kt)("inlineCode",{parentName:"p"},"MaxNominatorRewardedPerValidator"),", specifies the maximum amount of the highest-staked nominators which will get a reward. Those values should have some influence in the benchmarking process.")),(0,m.kt)("p",null,"The benchmarking implementation for the function ",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow"},"p"),(0,m.kt)("mi",{parentName:"mrow"},"a"),(0,m.kt)("mi",{parentName:"mrow"},"y"),(0,m.kt)("mi",{parentName:"mrow"},"o"),(0,m.kt)("mi",{parentName:"mrow"},"u"),(0,m.kt)("mi",{parentName:"mrow"},"t")),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{payout}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"0.8095em",verticalAlign:"-0.1944em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"p"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"a"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"yo"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"u"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"t"))))))," ",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow"},"s"),(0,m.kt)("mi",{parentName:"mrow"},"t"),(0,m.kt)("mi",{parentName:"mrow"},"a"),(0,m.kt)("mi",{parentName:"mrow"},"k"),(0,m.kt)("mi",{parentName:"mrow"},"e"),(0,m.kt)("mi",{parentName:"mrow"},"r"),(0,m.kt)("mi",{parentName:"mrow"},"s")),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{stakers}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6944em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"s"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"t"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03148em"}},"ak"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"ers"))))))," can be defined as follows:"),(0,m.kt)("h6",{id:"algo-benchmark-payout-stakers"},"Algorithm 28. ",(0,m.kt)("inlineCode",{parentName:"h6"},"payout_stakers")," Runtime Function Benchmark"),(0,m.kt)("admonition",{type:"algorithm"},(0,m.kt)(s.Z,{content:p,algID:"{payoutStakersRuntimeFunctionBenchmark",options:{lineNumber:!0},mdxType:"Pseudocode"}),(0,m.kt)("p",{parentName:"admonition"},(0,m.kt)("strong",{parentName:"p"},"where")," "),(0,m.kt)("ul",{parentName:"admonition"},(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},"Generate-Validator()"),(0,m.kt)("p",{parentName:"li"},"Creates a validator with some unbonded balances.")),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},"Validate(",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow"},"v"),(0,m.kt)("mi",{parentName:"mrow"},"a"),(0,m.kt)("mi",{parentName:"mrow"},"l"),(0,m.kt)("mi",{parentName:"mrow"},"i"),(0,m.kt)("mi",{parentName:"mrow"},"d"),(0,m.kt)("mi",{parentName:"mrow"},"a"),(0,m.kt)("mi",{parentName:"mrow"},"t"),(0,m.kt)("mi",{parentName:"mrow"},"o"),(0,m.kt)("mi",{parentName:"mrow"},"r")),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{validator}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6944em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03588em"}},"v"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"a"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.01968em"}},"l"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"i"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"d"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"a"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"t"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.02778em"}},"or")))))),")"),(0,m.kt)("p",{parentName:"li"},"Bonds balances of validator and bonds balances.")),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},"Generate-Nominators(",(0,m.kt)("span",{parentName:"p",className:"math 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Therefore, this benchmark is configured to first set the balance at value 1\u2019000 and then to iterate from 1 to 1\u2019000 for the index value. 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The ",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow"},"t"),(0,m.kt)("mi",{parentName:"mrow"},"r"),(0,m.kt)("mi",{parentName:"mrow"},"a"),(0,m.kt)("mi",{parentName:"mrow"},"n"),(0,m.kt)("mi",{parentName:"mrow"},"s"),(0,m.kt)("mi",{parentName:"mrow"},"f"),(0,m.kt)("mi",{parentName:"mrow"},"e"),(0,m.kt)("mi",{parentName:"mrow"},"r")),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{transfer}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"0.8889em",verticalAlign:"-0.1944em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"t"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.02778em"}},"r"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"an"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"s"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.10764em"}},"f"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.02778em"}},"er"))))))," benchmark is implemented as defined in ",(0,m.kt)("a",{parentName:"p",href:"id-weights#algo-benchmark-transfer"},'"transfer" Runtime function benchmark'),"."),(0,m.kt)("h4",{id:"id-benchmarking-framework-3"},"10.5.3.3. 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The worst case scenario should be chosen (the highest value).")))),(0,m.kt)("h3",{id:"id-practical-example-4-withdraw_unbonded"},"10.5.4. Practical Example ","#","4: ",(0,m.kt)("inlineCode",{parentName:"h3"},"withdraw_unbonded")),(0,m.kt)("p",null,"The ",(0,m.kt)("inlineCode",{parentName:"p"},"withdraw_unbonded")," function of the ",(0,m.kt)("inlineCode",{parentName:"p"},"staking")," module is designed to move any unlocked funds from the staking management system to be ready for transfer. It contains some operations which have some I/O overhead."),(0,m.kt)("h4",{id:"id-analysis-4"},"10.5.4.1. Analysis"),(0,m.kt)("p",null,"Similarly to the ",(0,m.kt)("inlineCode",{parentName:"p"},"payout_stakers")," function (",(0,m.kt)("a",{parentName:"p",href:"id-weights#sect-practical-example-payout-stakers"},"Section 10.5.2."),"), this function fetches the Ledger which contains information about the stash, such as bonded balance and unlocking balance (balance that will eventually be freed and can be withdrawn)."),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"if let Some(current_era) = Self::current_era() {\n ledger = ledger.consolidate_unlocked(current_era)\n}\n")),(0,m.kt)("p",null,"The function ",(0,m.kt)("inlineCode",{parentName:"p"},"consolidate_unlocked")," does some cleaning up on the ledger, where it removes outdated entries from the unlocking balance (which implies that balance is now free and is no longer awaiting unlock)."),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"let mut total = self.total;\nlet unlocking = self.unlocking.into_iter()\n .filter(|chunk| if chunk.era > current_era {\n true\n } else {\n total = total.saturating_sub(chunk.value);\n false\n })\n .collect();\n")),(0,m.kt)("p",null,"This function does a check on wether the updated ledger has any balance left in regards to staking, both in terms of locked, staking balance and unlocking balance. If not amount is left, the all information related to the stash will be deleted. This results in multiple I/O calls."),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"if ledger.unlocking.is_empty() && ledger.active.is_zero() {\n // This account must have called `unbond()` with some value that caused the active\n // portion to fall below existential deposit + will have no more unlocking chunks\n // left. We can now safely remove all staking-related information.\n Self::kill_stash(&stash, num_slashing_spans)?;\n // remove the lock.\n T::Currency::remove_lock(STAKING_ID, &stash);\n // This is worst case scenario, so we use the full weight and return None\n None\n}\n")),(0,m.kt)("p",null,"The resulting call to ",(0,m.kt)("inlineCode",{parentName:"p"},"Self::kill_stash()")," triggers:"),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"slashing::clear_stash_metadata::(stash, num_slashing_spans)?;\n>::remove(stash);\n>::remove(&controller);\n>::remove(stash);\n>::remove(stash);\n>::remove(stash);\n")),(0,m.kt)("p",null,"Alternatively, if there\u2019s some balance left, the adjusted ledger simply gets updated back into storage."),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"// This was the consequence of a partial unbond. just update the ledger and move on.\nSelf::update_ledger(&controller, &ledger);\n")),(0,m.kt)("p",null,"Finally, it withdraws the unlocked balance, making it ready for transfer:"),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"let value = old_total - ledger.total;\nSelf::deposit_event(RawEvent::Withdrawn(stash, value));\n")),(0,m.kt)("h4",{id:"id-parameters-2"},"10.5.4.2. Parameters"),(0,m.kt)("p",null,"The following parameters are selected:"),(0,m.kt)("table",null,(0,m.kt)("thead",{parentName:"table"},(0,m.kt)("tr",{parentName:"thead"},(0,m.kt)("th",{parentName:"tr",align:null},(0,m.kt)("strong",{parentName:"th"},"Type")),(0,m.kt)("th",{parentName:"tr",align:null}),(0,m.kt)("th",{parentName:"tr",align:null},(0,m.kt)("strong",{parentName:"th"},"From")),(0,m.kt)("th",{parentName:"tr",align:null},(0,m.kt)("strong",{parentName:"th"},"To")),(0,m.kt)("th",{parentName:"tr",align:null},(0,m.kt)("strong",{parentName:"th"},"Description")))),(0,m.kt)("tbody",{parentName:"table"},(0,m.kt)("tr",{parentName:"tbody"},(0,m.kt)("td",{parentName:"tr",align:null},"Account index"),(0,m.kt)("td",{parentName:"tr",align:null},(0,m.kt)("inlineCode",{parentName:"td"},"index")," in\u2026\u200b"),(0,m.kt)("td",{parentName:"tr",align:null},"0"),(0,m.kt)("td",{parentName:"tr",align:null},"1000"),(0,m.kt)("td",{parentName:"tr",align:null},"Used as a seed for account creation")))),(0,m.kt)("p",null,"This benchmark does not require complex parameters. 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vlist-t2"},(0,m.kt)("span",{parentName:"span",className:"vlist-r"},(0,m.kt)("span",{parentName:"span",className:"vlist",style:{height:"2.5em"}},(0,m.kt)("span",{parentName:"span",style:{top:"-4.66em"}},(0,m.kt)("span",{parentName:"span",className:"pstrut",style:{height:"3em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord"}),(0,m.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}}),(0,m.kt)("span",{parentName:"span",className:"mrel"},"="),(0,m.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}}),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"ba"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"se"),(0,m.kt)("span",{parentName:"span",className:"mspace"},"\xa0"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.10764em"}},"f"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"ee"))),(0,m.kt)("span",{parentName:"span",style:{top:"-3.16em"}},(0,m.kt)("span",{parentName:"span",className:"pstrut",style:{height:"3em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord"}),(0,m.kt)("span",{parentName:"span",className:"mord"}),(0,m.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}}),(0,m.kt)("span",{parentName:"span",className:"mbin"},"+"),(0,m.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}}),(0,m.kt)("span",{parentName:"span",className:"mord text"},(0,m.kt)("span",{parentName:"span",className:"mord"},"length\xa0of\xa0transaction\xa0in\xa0bytes")),(0,m.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}}),(0,m.kt)("span",{parentName:"span",className:"mbin"},"\xd7"),(0,m.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}}),(0,m.kt)("span",{parentName:"span",className:"mord text"},(0,m.kt)("span",{parentName:"span",className:"mord"},"length\xa0fee")))),(0,m.kt)("span",{parentName:"span",style:{top:"-1.66em"}},(0,m.kt)("span",{parentName:"span",className:"pstrut",style:{height:"3em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord"}),(0,m.kt)("span",{parentName:"span",className:"mord"}),(0,m.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}}),(0,m.kt)("span",{parentName:"span",className:"mbin"},"+"),(0,m.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}}),(0,m.kt)("span",{parentName:"span",className:"mord text"},(0,m.kt)("span",{parentName:"span",className:"mord"},"weight\xa0to\xa0fee"))))),(0,m.kt)("span",{parentName:"span",className:"vlist-s"},"\u200b")),(0,m.kt)("span",{parentName:"span",className:"vlist-r"},(0,m.kt)("span",{parentName:"span",className:"vlist",style:{height:"2em"}},(0,m.kt)("span",{parentName:"span"})))))))))))),(0,m.kt)("h3",{id:"id-definitions-in-polkadot"},"10.6.2. Definitions in Polkadot"),(0,m.kt)("p",null,"The Polkadot Runtime defines the following values:"),(0,m.kt)("ul",null,(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},"Base fee: 100 uDOTs")),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},"Length fee: 0.1 uDOTs")),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},"Weight to fee conversion:"),(0,m.kt)("p",{parentName:"li"},(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow"},"w"),(0,m.kt)("mi",{parentName:"mrow"},"e"),(0,m.kt)("mi",{parentName:"mrow"},"i"),(0,m.kt)("mi",{parentName:"mrow"},"g"),(0,m.kt)("mi",{parentName:"mrow"},"h"),(0,m.kt)("mi",{parentName:"mrow"},"t")),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{weight}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"0.8889em",verticalAlign:"-0.1944em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.02691em"}},"w"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"e"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"i"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03588em"}},"g"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"h"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"t"))))))," fee = weight \\times (100",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow"},"u"),(0,m.kt)("mi",{parentName:"mrow"},"D"),(0,m.kt)("mi",{parentName:"mrow"},"O"),(0,m.kt)("mi",{parentName:"mrow"},"T"),(0,m.kt)("mi",{parentName:"mrow"},"s"),(0,m.kt)("mo",{parentName:"mrow"},"\xf7"),(0,m.kt)("mrow",{parentName:"mrow"},(0,m.kt)("mo",{parentName:"mrow",fence:"true"},"("),(0,m.kt)("mn",{parentName:"mrow"},"10"),(0,m.kt)("mo",{parentName:"mrow"},"\xd7"),(0,m.kt)("msup",{parentName:"mrow"},(0,m.kt)("mn",{parentName:"msup"},"10"),(0,m.kt)("mo",{parentName:"msup",mathvariant:"normal",lspace:"0em",rspace:"0em"},"\u2032")),(0,m.kt)("mn",{parentName:"mrow"},"000"),(0,m.kt)("mo",{parentName:"mrow",fence:"true"},")")),(0,m.kt)("mo",{parentName:"mrow",stretchy:"false",lspace:"0em",rspace:"0em"},")")),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{u}{D}{O}{T}{s}\\div{\\left({10}\\times{10}'{000}\\right)}{)}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"0.7667em",verticalAlign:"-0.0833em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"u")),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.02778em"}},"D")),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.02778em"}},"O")),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.13889em"}},"T")),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"s")),(0,m.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}}),(0,m.kt)("span",{parentName:"span",className:"mbin"},"\xf7"),(0,m.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}})),(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"1.0362em",verticalAlign:"-0.25em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"minner"},(0,m.kt)("span",{parentName:"span",className:"mopen 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reset-size6 size3 mtight"},(0,m.kt)("span",{parentName:"span",className:"mord mtight"},(0,m.kt)("span",{parentName:"span",className:"mord mtight"},"\u2032"))))))))),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord"},"000")),(0,m.kt)("span",{parentName:"span",className:"mclose delimcenter",style:{top:"0em"}},")"))),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mclose"},")"))))))),(0,m.kt)("p",{parentName:"li"},"A weight of 10\u2019000 (the smallest non-zero weight) is mapped to ",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mfrac",{parentName:"mrow"},(0,m.kt)("mn",{parentName:"mfrac"},"1"),(0,m.kt)("mn",{parentName:"mfrac"},"10"))),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{\\frac{{{1}}}{{{10}}}}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"1.1901em",verticalAlign:"-0.345em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mopen 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mtight"},"10")))))),(0,m.kt)("span",{parentName:"span",style:{top:"-3.23em"}},(0,m.kt)("span",{parentName:"span",className:"pstrut",style:{height:"3em"}}),(0,m.kt)("span",{parentName:"span",className:"frac-line",style:{borderBottomWidth:"0.04em"}})),(0,m.kt)("span",{parentName:"span",style:{top:"-3.394em"}},(0,m.kt)("span",{parentName:"span",className:"pstrut",style:{height:"3em"}}),(0,m.kt)("span",{parentName:"span",className:"sizing reset-size6 size3 mtight"},(0,m.kt)("span",{parentName:"span",className:"mord mtight"},(0,m.kt)("span",{parentName:"span",className:"mord mtight"},(0,m.kt)("span",{parentName:"span",className:"mord mtight"},(0,m.kt)("span",{parentName:"span",className:"mord mtight"},"1"))))))),(0,m.kt)("span",{parentName:"span",className:"vlist-s"},"\u200b")),(0,m.kt)("span",{parentName:"span",className:"vlist-r"},(0,m.kt)("span",{parentName:"span",className:"vlist",style:{height:"0.345em"}},(0,m.kt)("span",{parentName:"span"}))))),(0,m.kt)("span",{parentName:"span",className:"mclose nulldelimiter"})))))))," of 100 uDOT. This fee will never exceed the max size of an unsigned 128 bit integer."))),(0,m.kt)("h3",{id:"id-fee-multiplier"},"10.6.3. Fee Multiplier"),(0,m.kt)("p",null,"Polkadot can add a additional fee to transactions if the network becomes too busy and starts to decelerate the system. This fee can create an incentive to avoid the production of low priority or insignificant transactions. In contrast, those additional fees will decrease if the network calms down and it can execute transactions without much difficulties."),(0,m.kt)("p",null,"That additional fee is known as the ",(0,m.kt)("inlineCode",{parentName:"p"},"Fee Multiplier")," and its value is defined by the Polkadot Runtime. The multiplier works by comparing the saturation of blocks; if the previous block is less saturated than the current block (implying an uptrend), the fee is slightly increased. 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Fee Multiplier",id:"id-fee-multiplier",level:3},{value:"10.6.3.1. Update Multiplier",id:"id-update-multiplier",level:4}],d={toc:h},w="wrapper";function g(a){let{components:e,...t}=a;return(0,m.kt)(w,(0,n.Z)({},d,t,{components:e,mdxType:"MDXLayout"}),(0,m.kt)("h2",{id:"id-motivation"},"10.1. Motivation"),(0,m.kt)("p",null,"The Polkadot network, like any other permissionless system, needs to implement a mechanism to measure and limit the usage in order to establish an economic incentive structure, prevent network overload, and mitigate DoS vulnerabilities. In particular, Polkadot enforces a limited time window for block producers to create a block, including limitations on block size, which can make the selection and execution of certain extrinsics too expensive and decelerate the network."),(0,m.kt)("p",null,"In contrast to some other systems, such as Ethereum, which implement fine measurement for each executed low-level operation by smart contracts, known as gas metering, Polkadot takes a more relaxed approach by implementing a measuring system where the cost of the transactions (referred to as \u2019extrinsics\u2019) are determined before execution and are known as the weight system."),(0,m.kt)("p",null,'The Polkadot weight system introduces a mechanism for block producers to measure the cost of running the extrinsics and determine how "heavy" it is in terms of execution time. Within this mechanism, block producers can select a set of extrinsics and saturate the block to its fullest potential without exceeding any limitations (as described in ',(0,m.kt)("a",{parentName:"p",href:"id-weights#sect-limitations"},"Section 10.2.1."),"). Moreover, the weight system can be used to calculate a fee for executing each extrinsics according to its weight (as described in ",(0,m.kt)("a",{parentName:"p",href:"id-weights#sect-fee-calculation"},"Section 10.6.1."),")."),(0,m.kt)("p",null,"Additionally, Polkadot introduces a specified block ratio (as defined in ",(0,m.kt)("a",{parentName:"p",href:"id-weights#sect-limitations"},"Section 10.2.1."),"), ensuring that only a certain portion of the total block size gets used for regular extrinsics. The remaining space is reserved for critical, operational extrinsics required for the functionality of Polkadot itself."),(0,m.kt)("p",null,"To begin, we introduce in ",(0,m.kt)("a",{parentName:"p",href:"id-weights#sect-assumptions"},"Section 10.2.")," the assumption upon which the Polkadot transaction weight system is designed. In ",(0,m.kt)("a",{parentName:"p",href:"id-weights#sect-limitations"},"Section 10.2.1."),", we discuss the limitation Polkadot needs to enforce on the block size. In ",(0,m.kt)("a",{parentName:"p",href:"id-weights#sect-runtime-primitives"},"Section 10.3."),", we describe in detail the procedure upon which the weight of any transaction should be calculated. In ",(0,m.kt)("a",{parentName:"p",href:"id-weights#sect-practical-examples"},"Section 10.5."),", we present how we apply this procedure to compute the weight of particular runtime functions."),(0,m.kt)("h2",{id:"sect-assumptions"},"10.2. Assumptions"),(0,m.kt)("p",null,"In this section, we define the concept of weight, and we discuss the considerations that need to be accounted for when assigning weight to transactions. These considerations are essential in order for the weight system to deliver its fundamental mission, i.e. the fair distribution of network resources and preventing a network overload. In this regard, weights serve as an indicator on whether a block is considered full and how much space is left for remaining, pending extrinsics. Extrinsics that require too many resources are discarded. 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as noted by the fundamentals and limitations and can be assigned as the author sees fit. As a simple example, consider a maximum block weight of 1\u2019000\u2019000\u2019000, an available ratio of 75%, and a targeted transaction throughput of 500 transactions. We could assign the (average) weight for each transaction at about 1\u2019500\u2019000. Block producers have an economic incentive to include as many extrinsics as possible (without exceeding limitations) into a block before reaching the targeted block time. Weights give indicators to block producers on which extrinsics to include in order to reach the blocks fullest potential."),(0,m.kt)("h2",{id:"sect-runtime-primitives"},"10.3. Calculation of the weight function"),(0,m.kt)("p",null,"In order to calculate weight of block ",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow"},"B")),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{B}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6833em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05017em"}},"B")))))),", ",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow",mathvariant:"script"},"W"),(0,m.kt)("mrow",{parentName:"mrow"},(0,m.kt)("mo",{parentName:"mrow",fence:"true"},"("),(0,m.kt)("mi",{parentName:"mrow"},"B"),(0,m.kt)("mo",{parentName:"mrow",fence:"true"},")"))),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{\\mathcal{{{W}}}}{\\left({B}\\right)}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathcal",style:{marginRight:"0.08222em"}},"W")))),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"minner"},(0,m.kt)("span",{parentName:"span",className:"mopen delimcenter",style:{top:"0em"}},"("),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05017em"}},"B")),(0,m.kt)("span",{parentName:"span",className:"mclose delimcenter",style:{top:"0em"}},")"))))))),", one needs to evaluate the weight of each transaction included in the block. Each transaction causes the execution of certain Runtime functions. As such, to calculate the weight of a transaction, those functions must be analyzed in order to determine parts of the code which can significantly contribute to the execution time and consume resources such as loops, I/O operations, and data manipulation. Subsequently, the performance and execution time of each part will be evaluated based on variety of input parameters. Based on those observations, weights are assigned Runtime functions or parameters which contribute to long execution times. These sub component of the code are discussed in ",(0,m.kt)("a",{parentName:"p",href:"id-weights#sect-primitive-types"},"Section 10.4.1."),"."),(0,m.kt)("p",null,"The general algorithm to calculate ",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow",mathvariant:"script"},"W"),(0,m.kt)("mrow",{parentName:"mrow"},(0,m.kt)("mo",{parentName:"mrow",fence:"true"},"("),(0,m.kt)("mi",{parentName:"mrow"},"E"),(0,m.kt)("mo",{parentName:"mrow",fence:"true"},")"))),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{\\mathcal{{{W}}}}{\\left({E}\\right)}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathcal",style:{marginRight:"0.08222em"}},"W")))),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"minner"},(0,m.kt)("span",{parentName:"span",className:"mopen delimcenter",style:{top:"0em"}},"("),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05764em"}},"E")),(0,m.kt)("span",{parentName:"span",className:"mclose delimcenter",style:{top:"0em"}},")")))))))," is described in the ",(0,m.kt)("a",{parentName:"p",href:"id-weights#sect-benchmarking"},"Section 10.4."),"."),(0,m.kt)("h2",{id:"sect-benchmarking"},"10.4. Benchmarking"),(0,m.kt)("p",null,"Calculating the extrinsic weight solely based on the theoretical complexity of the underlying implementation proves to be too complicated and unreliable at the same time. Certain decisions in the source code architecture, internal communication within the Runtime or other design choices could add enough overhead to make the asymptotic complexity practically meaningless."),(0,m.kt)("p",null,"On the other hand, benchmarking an extrinsics in a black-box fashion could (using random parameters) most certainly results in missing corner cases and worst case scenarios. Instead, we benchmark all available Runtime functions which are invoked in the course of execution of extrinsics with a large collection of carefully selected input parameters and use the result of the benchmarking process to evaluate ",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow",mathvariant:"script"},"W"),(0,m.kt)("mrow",{parentName:"mrow"},(0,m.kt)("mo",{parentName:"mrow",fence:"true"},"("),(0,m.kt)("mi",{parentName:"mrow"},"E"),(0,m.kt)("mo",{parentName:"mrow",fence:"true"},")"))),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{\\mathcal{{{W}}}}{\\left({E}\\right)}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathcal",style:{marginRight:"0.08222em"}},"W")))),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"minner"},(0,m.kt)("span",{parentName:"span",className:"mopen delimcenter",style:{top:"0em"}},"("),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05764em"}},"E")),(0,m.kt)("span",{parentName:"span",className:"mclose delimcenter",style:{top:"0em"}},")"))))))),"."),(0,m.kt)("p",null,"In order to select useful parameters, the Runtime functions have to be analyzed to fully understand which behaviors or conditions can result in expensive execution times, which is described closer in ",(0,m.kt)("a",{parentName:"p",href:"id-weights#sect-primitive-types"},"Section 10.4.1."),". Not every possible benchmarking outcome can be invoked by varying input parameters of the Runtime function. In some circumstances, preliminary work is required before a specific benchmark can be reliably measured, such as creating certain preexisting entries in the storage or other changes to the environment."),(0,m.kt)("p",null,"The Practical Examples (",(0,m.kt)("a",{parentName:"p",href:"id-weights#sect-practical-examples"},"Section 10.5."),") covers the analysis process and the implementation of preliminary work in more detail."),(0,m.kt)("h3",{id:"sect-primitive-types"},"10.4.1. Primitive Types"),(0,m.kt)("p",null,'The Runtime reuses components, known as "primitives", to interact with the state storage. The execution cost of those primitives can be measured and a weight should be applied for each occurrence within the Runtime code.'),(0,m.kt)("p",null,"For storage, Polkadot uses three different types of storage types across its modules, depending on the context:"),(0,m.kt)("ul",null,(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},(0,m.kt)("strong",{parentName:"p"},"Value"),": Operations on a single value. The final key-value pair is stored under the key:"),(0,m.kt)("pre",{parentName:"li"},(0,m.kt)("code",{parentName:"pre"}," hash(module_prefix) + hash(storage_prefix)\n"))),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},(0,m.kt)("strong",{parentName:"p"},"Map"),": Operations on multiple values, datasets, where each entry has its corresponding, unique key. The final key-value pair is stored under the key:"),(0,m.kt)("pre",{parentName:"li"},(0,m.kt)("code",{parentName:"pre"}," hash(module_prefix) + hash(storage_prefix) + hash(encode(key))\n"))),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},(0,m.kt)("strong",{parentName:"p"},"Double map"),": Just like ",(0,m.kt)("strong",{parentName:"p"},"Map"),', but uses two keys instead of one. This type is also known as "child storage", where the first key is the "parent key" and the second key is the "child key". This is useful in order to scope storage entries (child keys) under a certain ',(0,m.kt)("inlineCode",{parentName:"p"},"context")," (parent key), which is arbitrary. Therefore, one can have separated storage entries based on the context. The final key-value pair is stored under the key:"),(0,m.kt)("pre",{parentName:"li"},(0,m.kt)("code",{parentName:"pre"}," hash(module_prefix) + hash(storage_prefix)\n + hash(encode(key1)) + hash(encode(key2))\n")))),(0,m.kt)("p",null,"It depends on the functionality of the Runtime module (or its sub-processes, rather) which storage type to use. In some cases, only a single value is required. In others, multiple values need to be fetched or inserted from/into the database."),(0,m.kt)("p",null,"Those lower-level types get abstracted over in each individual Runtime module using the ",(0,m.kt)("inlineCode",{parentName:"p"},"decl_storage!")," macro. Therefore, each module specifies its own types that are used as input and output values. The abstractions do give indicators on what operations must be closely observed and where potential performance penalties and attack vectors are possible."),(0,m.kt)("h4",{id:"sect-primitive-types-considerations"},"10.4.1.1. Considerations"),(0,m.kt)("p",null,"The storage layout is mostly the same for every primitive type, primarily differentiated by using special prefixes for the storage key. Big differences arise on how the primitive types are used in the Runtime function, on whether single values or entire datasets are being worked on. Single value operations are generally quite cheap and its execution time does not vary depending on the data that\u2019s being processed. However, excessive overhead can appear when I/O operations are executed repeatedly, such as in loops. Especially, when the amount of loop iterations can be influenced by the caller of the function or by certain conditions in the state storage."),(0,m.kt)("p",null,"Maps, in contrast, have additional overhead when inserting or retrieving datasets, which vary in sizes. Additionally, the Runtime function has to process each item inside that list."),(0,m.kt)("p",null,"Indicators for performance penalties:"),(0,m.kt)("ul",null,(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},(0,m.kt)("strong",{parentName:"p"},"Fixed iterations and datasets")," - Fixed iterations and datasets can increase the overall cost of the Runtime functions, but the execution time does not vary depending on the input parameters or storage entries. A base Weight is appropriate in this case.")),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},(0,m.kt)("strong",{parentName:"p"},"Adjustable iterations and datasets")," - If the amount of iterations or datasets depends on the input parameters of the caller or specific entries in storage, then a certain weight should be applied for each (additional) iteration or item. The Runtime defines the maximum value for such cases. If it doesn\u2019t, it unconditionally has to and the Runtime module must be adjusted. When selecting parameters for benchmarking, the benchmarks should range from the minimum value to the maximum value, as described in ",(0,m.kt)("a",{parentName:"p",href:"id-weights#defn-max-value"},"Definition 166"),".")),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},(0,m.kt)("strong",{parentName:"p"},"Input parameters")," - Input parameters that users pass on to the Runtime function can result in expensive operations. Depending on the data type, it can be appropriate to add additional weights based on certain properties, such as data size, assuming the data type allows varying sizes. The Runtime must define limits on those properties. If it doesn\u2019t, it unconditionally has to, and the Runtime module must be adjusted. When selecting parameters for benchmarking, the benchmarks should range from the minimum values to the maximum value, as described in paragraph ",(0,m.kt)("a",{parentName:"p",href:"id-weights#defn-max-value"},"Definition 166"),"."))),(0,m.kt)("h6",{id:"defn-max-value"},"Definition 166. Maximum Value"),(0,m.kt)("admonition",{type:"definition"},(0,m.kt)("p",{parentName:"admonition"},"What the maximum value should be really depends on the functionality that the Runtime function is trying to provide. If the choice for that value is not obvious, then it\u2019s advised to run benchmarks on a big range of values and pick a conservative value below the ",(0,m.kt)("inlineCode",{parentName:"p"},"targeted time per block")," limit as described in section ",(0,m.kt)("a",{parentName:"p",href:"id-weights#sect-limitations"},"Section 10.2.1."),".")),(0,m.kt)("h3",{id:"id-parameters"},"10.4.2. Parameters"),(0,m.kt)("p",null,"The input parameters highly vary depending on the Runtime function and must therefore be carefully selected. The benchmarks should use input parameters which will most likely be used in regular cases, as intended by the authors, but must also consider worst-case scenarios and inputs that might decelerate or heavily impact the performance of the function. The input parameters should be randomized in order to cause various effects in behaviors on certain values, such as memory relocations and other outcomes that can impact performance."),(0,m.kt)("p",null,"It\u2019s not possible to benchmark every single value. However, one should select a range of inputs to benchmark, spanning from the minimum value to the maximum value, which will most likely exceed the expected usage of that function. This is described in more detail in ",(0,m.kt)("a",{parentName:"p",href:"id-weights#sect-primitive-types-considerations"},"Section 10.4.1.1."),". The benchmarks should run individual executions/iterations within that range, where the chosen parameters should give insight on the execution time. Selecting imprecise parameters or too extreme ranges might indicate an inaccurate result of the function as it will be used in production. Therefore, when a range of input parameters gets benchmarked, the result of each individual parameter should be recorded and optionally visualized, then the necessary adjustment can be made. Generally, the worst-case scenario should be assigned as the weight value for the corresponding runtime function."),(0,m.kt)("p",null,"Additionally, given the distinction between theoretical and practical usage, the author reserves the right to make adjustments to the input parameters and assign weights according to the observed behavior of the actual, real-world network."),(0,m.kt)("h4",{id:"id-weight-refunds"},"10.4.2.1. Weight Refunds"),(0,m.kt)("p",null,'When assigning the final weight, the worst-case scenario of each runtime function should be used. The runtime can then additional "refund" the amount of weights which were overestimated once the runtime function is actually executed.'),(0,m.kt)("p",null,"The Polkadot runtime only returns weights if the difference between the assigned weight and the actual weight calculated during execution is greater than 20%."),(0,m.kt)("h3",{id:"id-storage-io-cost"},"10.4.3. Storage I/O cost"),(0,m.kt)("p",null,'It is advised to benchmark the raw I/O operations of the database and assign "base weights" for each I/O operation type, such as insertion, deletion, querying, etc. When a runtime function is executed, the runtime can then add those base weights of each used operation in order to calculate the final weight.'),(0,m.kt)("h3",{id:"id-environment"},"10.4.4. Environment"),(0,m.kt)("p",null,"The benchmarks should be executed on clean systems without interference of other processes or software. Additionally, the benchmarks should be executed on multiple machines with different system resources, such as CPU performance, CPU cores, RAM, and storage speed."),(0,m.kt)("h2",{id:"sect-practical-examples"},"10.5. Practical examples"),(0,m.kt)("p",null,"This section walks through Runtime functions available in the Polkadot Runtime to demonstrate the analysis process as described in ",(0,m.kt)("a",{parentName:"p",href:"id-weights#sect-primitive-types"},"Section 10.4.1."),"."),(0,m.kt)("p",null,"In order for certain benchmarks to produce conditions where resource heavy computation or excessive I/O can be observed, the benchmarks might require some preliminary work on the environment, since those conditions cannot be created with simply selected parameters. The analysis process shows indicators on how the preliminary work should be implemented."),(0,m.kt)("h3",{id:"id-practical-example-1-request_judgement"},"10.5.1. Practical Example ","#","1: ",(0,m.kt)("inlineCode",{parentName:"h3"},"request_judgement")),(0,m.kt)("p",null,'In Polkadot, accounts can save information about themselves on-chain, known as the "Identity Info". This includes information such as display name, legal name, email address and so on. Polkadot offers a set of trusted registrars, entities elected by a Polkadot public referendum, which can verify the specified contact addresses of the identities, such as Email, and vouch on whether the identity actually owns those accounts. This can be achieved, for example, by sending a challenge to the specified address and requesting a signature as a response. The verification is done off-chain, while the final judgement is saved on-chain, directly in the corresponding Identity Info. It\u2019s also noteworthy that Identity Info can contain additional fields, set manually by the corresponding account holder.'),(0,m.kt)("p",null,"Information such as legal name must be verified by ID card or passport submission."),(0,m.kt)("p",null,"The function ",(0,m.kt)("inlineCode",{parentName:"p"},"request_judgement")," from the ",(0,m.kt)("inlineCode",{parentName:"p"},"identity")," pallet allows users to request judgment from a specific registrar."),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre"},"(func $request_judgement (param $req_index int) (param $max_fee int))\n")),(0,m.kt)("ul",null,(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},(0,m.kt)("inlineCode",{parentName:"p"},"req_index"),": the index which is assigned to the registrar.")),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},(0,m.kt)("inlineCode",{parentName:"p"},"max_fee"),": the maximum fee the requester is willing to pay. The judgment fee varies for each registrar."))),(0,m.kt)("p",null,"Studying this function reveals multiple design choices that can impact performance, as it will be revealed by this analysis."),(0,m.kt)("h4",{id:"id-analysis"},"10.5.1.1. Analysis"),(0,m.kt)("p",null,"First, it fetches a list of current registrars from storage and then searches that list for the specified registrar index."),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"let registrars = >::get();\nlet registrar = registrars.get(reg_index as usize).and_then(Option::as_ref)\n .ok_or(Error::::EmptyIndex)?;\n")),(0,m.kt)("p",null,"Then, it searches for the Identity Info from storage, based on the sender of the transaction."),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"let mut id = >::get(&sender).ok_or(Error::::NoIdentity)?;\n")),(0,m.kt)("p",null,'The Identity Info contains all fields that have a data in them, set by the corresponding owner of the identity, in an ordered form. It then proceeds to search for the specific field type that will be inserted or updated, such as email address. If the entry can be found, the corresponding value is to the value passed on as the function parameters (assuming the registrar is not "stickied", which implies it cannot be changed). If the entry cannot be found, the value is inserted into the index where a matching element can be inserted while maintaining sorted order. This results in memory reallocation, which increases resource consumption.'),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"match id.judgements.binary_search_by_key(®_index, |x| x.0) {\n Ok(i) => if id.judgements[i].1.is_sticky() {\n Err(Error::::StickyJudgement)?\n } else {\n id.judgements[i] = item\n },\n Err(i) => id.judgements.insert(i, item),\n}\n")),(0,m.kt)("p",null,"In the end, the function deposits the specified ",(0,m.kt)("inlineCode",{parentName:"p"},"max_fee")," balance, which can later be redeemed by the registrar. Then, an event is created to insert the Identity Info into storage. The creation of events is lightweight, but its execution is what will actually commit the state changes."),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"T::Currency::reserve(&sender, registrar.fee)?;\n>::insert(&sender, id);\nSelf::deposit_event(RawEvent::JudgementRequested(sender, reg_index));\n")),(0,m.kt)("h4",{id:"sect-considerations"},"10.5.1.2. Considerations"),(0,m.kt)("p",null,"The following points must be considered:"),(0,m.kt)("ul",null,(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},"Varying count of registrars.")),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},"Varying count of preexisting accounts in storage.")),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},"The specified registrar is searched for in the Identity Info. An identity can be judged by as many registrars as the identity owner issues requests, therefore increasing its footprint in the state storage. Additionally, if a new value gets inserted into the byte array, memory gets reallocated. Depending on the size of the Identity Info, the execution time can vary.")),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},"The Identity-Info can contain only a few fields or many. It is legitimate to introduce additional weights for changes the owner/sender has influence over, such as the additional fields in the Identity-Info."))),(0,m.kt)("h4",{id:"id-benchmarking-framework"},"10.5.1.3. Benchmarking Framework"),(0,m.kt)("p",null,"The Polkadot Runtime specifies the ",(0,m.kt)("inlineCode",{parentName:"p"},"MaxRegistrars")," constant, which will prevent the list of registrars of reaching an undesired length. This value should have some influence on the benchmarking process."),(0,m.kt)("p",null,"The benchmarking implementation of for the function ",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow"},"r"),(0,m.kt)("mi",{parentName:"mrow"},"e"),(0,m.kt)("mi",{parentName:"mrow"},"q"),(0,m.kt)("mi",{parentName:"mrow"},"u"),(0,m.kt)("mi",{parentName:"mrow"},"e"),(0,m.kt)("mi",{parentName:"mrow"},"s"),(0,m.kt)("mi",{parentName:"mrow"},"t")),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{request}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"0.8095em",verticalAlign:"-0.1944em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"re"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03588em"}},"q"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"u"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"es"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"t"))))))," ",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow"},"j"),(0,m.kt)("mi",{parentName:"mrow"},"u"),(0,m.kt)("mi",{parentName:"mrow"},"d"),(0,m.kt)("mi",{parentName:"mrow"},"g"),(0,m.kt)("mi",{parentName:"mrow"},"e"),(0,m.kt)("mi",{parentName:"mrow"},"m"),(0,m.kt)("mi",{parentName:"mrow"},"e"),(0,m.kt)("mi",{parentName:"mrow"},"n"),(0,m.kt)("mi",{parentName:"mrow"},"t")),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{judgement}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"0.8889em",verticalAlign:"-0.1944em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05724em"}},"j"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"u"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"d"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03588em"}},"g"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"e"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"m"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"e"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"n"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"t"))))))," can be defined as follows:"),(0,m.kt)("h6",{id:"algo-benchmark-request-judgement"},"Algorithm 27. 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This should be used when the benchmark should account for unpredictable values.")),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},"Add-To(",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow"},"c"),(0,m.kt)("mi",{parentName:"mrow"},"o"),(0,m.kt)("mi",{parentName:"mrow"},"l"),(0,m.kt)("mi",{parentName:"mrow"},"l"),(0,m.kt)("mi",{parentName:"mrow"},"e"),(0,m.kt)("mi",{parentName:"mrow"},"c"),(0,m.kt)("mi",{parentName:"mrow"},"t"),(0,m.kt)("mi",{parentName:"mrow"},"i"),(0,m.kt)("mi",{parentName:"mrow"},"o"),(0,m.kt)("mi",{parentName:"mrow"},"n")),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{collection}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6944em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"co"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.01968em"}},"ll"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"ec"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"t"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"i"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"o"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"n")))))),", ",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow"},"t"),(0,m.kt)("mi",{parentName:"mrow"},"i"),(0,m.kt)("mi",{parentName:"mrow"},"m"),(0,m.kt)("mi",{parentName:"mrow"},"e")),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{time}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6595em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"t"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"im"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"e")))))),")"),(0,m.kt)("p",{parentName:"li"},"Adds a returned time measurement (time) to collection.")),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},"Compute-Weight(",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow"},"c"),(0,m.kt)("mi",{parentName:"mrow"},"o"),(0,m.kt)("mi",{parentName:"mrow"},"l"),(0,m.kt)("mi",{parentName:"mrow"},"l"),(0,m.kt)("mi",{parentName:"mrow"},"e"),(0,m.kt)("mi",{parentName:"mrow"},"c"),(0,m.kt)("mi",{parentName:"mrow"},"t"),(0,m.kt)("mi",{parentName:"mrow"},"i"),(0,m.kt)("mi",{parentName:"mrow"},"o"),(0,m.kt)("mi",{parentName:"mrow"},"n")),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{collection}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6944em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"co"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.01968em"}},"ll"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"ec"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"t"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"i"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"o"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"n")))))),")"),(0,m.kt)("p",{parentName:"li"},"Computes the resulting weight based on the time measurements in the collection. The worst-case scenario should be chosen (the highest value).")))),(0,m.kt)("h3",{id:"sect-practical-example-payout-stakers"},"10.5.2. Practical Example ","#","2: ",(0,m.kt)("inlineCode",{parentName:"h3"},"payout_stakers")),(0,m.kt)("h4",{id:"id-analysis-2"},"10.5.2.1. Analysis"),(0,m.kt)("p",null,"The function ",(0,m.kt)("inlineCode",{parentName:"p"},"payout_stakers")," from the ",(0,m.kt)("inlineCode",{parentName:"p"},"staking")," Pallet can be called by a single account in order to payout the reward for all nominators who back a particular validator. The reward also covers the validator\u2019s share. This function is interesting because it iterates over a range of nominators, which varies, and does I/O operations for each of them."),(0,m.kt)("p",null,'First, this function makes a few basic checks to verify if the specified era is not higher then the current era (as it is not in the future) and is within the allowed range also known as "history depth", as specified by the Runtime. After that, it fetches the era payout from storage and additionally verifies whether the specified account is indeed a validator and receives the corresponding "Ledger". The Ledger keeps information about the stash key, controller key, and other information such as actively bonded balance and a list of tracked rewards. The function only retains the entries of the history depth and conducts a binary search for the specified era.'),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"let era_payout = >::get(&era)\n .ok_or_else(|| Error::::InvalidEraToReward)?;\n\nlet controller = Self::bonded(&validator_stash).ok_or(Error::::NotStash)?;\nlet mut ledger = >::get(&controller).ok_or_else(|| Error::::NotController)?;\n")),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"ledger.claimed_rewards.retain(|&x| x >= current_era.saturating_sub(history_depth));\nmatch ledger.claimed_rewards.binary_search(&era) {\n Ok(_) => Err(Error::::AlreadyClaimed)?,\n Err(pos) => ledger.claimed_rewards.insert(pos, era),\n}\n")),(0,m.kt)("p",null,"The retained claimed rewards are inserted back into storage."),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},">::insert(&controller, &ledger);\n")),(0,m.kt)("p",null,"As an optimization, Runtime only fetches a list of the 64 highest-staked nominators, although this might be changed in the future. Accordingly, any lower-staked nominator gets no reward."),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"let exposure = >::get(&era, &ledger.stash);\n")),(0,m.kt)("p",null,"Next, the function gets the era reward points from storage."),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"let era_reward_points = >::get(&era);\n")),(0,m.kt)("p",null,"After that, the payout is split among the validator and its nominators. The validators receive the payment first, creating an insertion into storage and sending a deposit event to the scheduler."),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"if let Some(imbalance) = Self::make_payout(\n &ledger.stash,\n validator_staking_payout + validator_commission_payout\n) {\n Self::deposit_event(RawEvent::Reward(ledger.stash, imbalance.peek()));\n}\n")),(0,m.kt)("p",null,"Then, the nominators receive their payout rewards. The functions loop over the nominator list, conducting an insertion into storage and a creation of a deposit event for each of the nominators."),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"for nominator in exposure.others.iter() {\n let nominator_exposure_part = Perbill::from_rational_approximation(\n nominator.value,\n exposure.total,\n );\n\n let nominator_reward: BalanceOf = nominator_exposure_part * validator_leftover_payout;\n // We can now make nominator payout:\n if let Some(imbalance) = Self::make_payout(&nominator.who, nominator_reward) {\n Self::deposit_event(RawEvent::Reward(nominator.who.clone(), imbalance.peek()));\n }\n}\n")),(0,m.kt)("h4",{id:"considerations-1"},"10.5.2.2. Considerations"),(0,m.kt)("p",null,"The following points must be considered:"),(0,m.kt)("ul",null,(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},"The Ledger contains a varying list of claimed rewards. Fetching, retaining, and searching through it can affect execution time. The retained list is inserted back into storage.")),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},"Looping through a list of nominators and creating I/O operations for each increases execution time. The Runtime fetches up to 64 nominators."))),(0,m.kt)("h4",{id:"id-benchmarking-framework-2"},"10.5.2.3. Benchmarking Framework"),(0,m.kt)("h6",{id:"defn-history-depth"},"Definition 167. History Depth"),(0,m.kt)("admonition",{type:"definition"},(0,m.kt)("p",{parentName:"admonition"},"H\u0331istory Depth indicated as ",(0,m.kt)("inlineCode",{parentName:"p"},"MaxNominatorRewardedPerValidator")," is a fixed constant specified by the Polkadot Runtime which dictates the number of Eras the Runtime will reward nominators and validators for.")),(0,m.kt)("h6",{id:"defn-max-nominator-reward"},"Definition 168. Maximum Nominator Reward"),(0,m.kt)("admonition",{type:"definition"},(0,m.kt)("p",{parentName:"admonition"},"M\u0331aximum Nominator Rewarded Per Validator indicated as ",(0,m.kt)("inlineCode",{parentName:"p"},"MaxNominatorRewardedPerValidator"),", specifies the maximum amount of the highest-staked nominators which will get a reward. Those values should have some influence in the benchmarking process.")),(0,m.kt)("p",null,"The benchmarking implementation for the function ",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow"},"p"),(0,m.kt)("mi",{parentName:"mrow"},"a"),(0,m.kt)("mi",{parentName:"mrow"},"y"),(0,m.kt)("mi",{parentName:"mrow"},"o"),(0,m.kt)("mi",{parentName:"mrow"},"u"),(0,m.kt)("mi",{parentName:"mrow"},"t")),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{payout}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"0.8095em",verticalAlign:"-0.1944em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"p"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"a"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"yo"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"u"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"t"))))))," ",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow"},"s"),(0,m.kt)("mi",{parentName:"mrow"},"t"),(0,m.kt)("mi",{parentName:"mrow"},"a"),(0,m.kt)("mi",{parentName:"mrow"},"k"),(0,m.kt)("mi",{parentName:"mrow"},"e"),(0,m.kt)("mi",{parentName:"mrow"},"r"),(0,m.kt)("mi",{parentName:"mrow"},"s")),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{stakers}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6944em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"s"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"t"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03148em"}},"ak"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"ers"))))))," can be defined as follows:"),(0,m.kt)("h6",{id:"algo-benchmark-payout-stakers"},"Algorithm 28. ",(0,m.kt)("inlineCode",{parentName:"h6"},"payout_stakers")," Runtime Function Benchmark"),(0,m.kt)("admonition",{type:"algorithm"},(0,m.kt)(s.Z,{content:p,algID:"{payoutStakersRuntimeFunctionBenchmark",options:{lineNumber:!0},mdxType:"Pseudocode"}),(0,m.kt)("p",{parentName:"admonition"},(0,m.kt)("strong",{parentName:"p"},"where")," "),(0,m.kt)("ul",{parentName:"admonition"},(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},"Generate-Validator()"),(0,m.kt)("p",{parentName:"li"},"Creates a validator with some unbonded balances.")),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},"Validate(",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow"},"v"),(0,m.kt)("mi",{parentName:"mrow"},"a"),(0,m.kt)("mi",{parentName:"mrow"},"l"),(0,m.kt)("mi",{parentName:"mrow"},"i"),(0,m.kt)("mi",{parentName:"mrow"},"d"),(0,m.kt)("mi",{parentName:"mrow"},"a"),(0,m.kt)("mi",{parentName:"mrow"},"t"),(0,m.kt)("mi",{parentName:"mrow"},"o"),(0,m.kt)("mi",{parentName:"mrow"},"r")),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{validator}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6944em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03588em"}},"v"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"a"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.01968em"}},"l"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"i"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"d"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"a"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"t"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.02778em"}},"or")))))),")"),(0,m.kt)("p",{parentName:"li"},"Bonds balances of validator and bonds balances.")),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},"Generate-Nominators(",(0,m.kt)("span",{parentName:"p",className:"math 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Therefore, this benchmark is configured to first set the balance at value 1\u2019000 and then to iterate from 1 to 1\u2019000 for the index value. 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The ",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow"},"t"),(0,m.kt)("mi",{parentName:"mrow"},"r"),(0,m.kt)("mi",{parentName:"mrow"},"a"),(0,m.kt)("mi",{parentName:"mrow"},"n"),(0,m.kt)("mi",{parentName:"mrow"},"s"),(0,m.kt)("mi",{parentName:"mrow"},"f"),(0,m.kt)("mi",{parentName:"mrow"},"e"),(0,m.kt)("mi",{parentName:"mrow"},"r")),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{transfer}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"0.8889em",verticalAlign:"-0.1944em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"t"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.02778em"}},"r"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"an"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"s"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.10764em"}},"f"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.02778em"}},"er"))))))," benchmark is implemented as defined in ",(0,m.kt)("a",{parentName:"p",href:"id-weights#algo-benchmark-transfer"},'"transfer" Runtime function benchmark'),"."),(0,m.kt)("h4",{id:"id-benchmarking-framework-3"},"10.5.3.3. 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The worst case scenario should be chosen (the highest value).")))),(0,m.kt)("h3",{id:"id-practical-example-4-withdraw_unbonded"},"10.5.4. Practical Example ","#","4: ",(0,m.kt)("inlineCode",{parentName:"h3"},"withdraw_unbonded")),(0,m.kt)("p",null,"The ",(0,m.kt)("inlineCode",{parentName:"p"},"withdraw_unbonded")," function of the ",(0,m.kt)("inlineCode",{parentName:"p"},"staking")," module is designed to move any unlocked funds from the staking management system to be ready for transfer. It contains some operations which have some I/O overhead."),(0,m.kt)("h4",{id:"id-analysis-4"},"10.5.4.1. Analysis"),(0,m.kt)("p",null,"Similarly to the ",(0,m.kt)("inlineCode",{parentName:"p"},"payout_stakers")," function (",(0,m.kt)("a",{parentName:"p",href:"id-weights#sect-practical-example-payout-stakers"},"Section 10.5.2."),"), this function fetches the Ledger which contains information about the stash, such as bonded balance and unlocking balance (balance that will eventually be freed and can be withdrawn)."),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"if let Some(current_era) = Self::current_era() {\n ledger = ledger.consolidate_unlocked(current_era)\n}\n")),(0,m.kt)("p",null,"The function ",(0,m.kt)("inlineCode",{parentName:"p"},"consolidate_unlocked")," does some cleaning up on the ledger, where it removes outdated entries from the unlocking balance (which implies that balance is now free and is no longer awaiting unlock)."),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"let mut total = self.total;\nlet unlocking = self.unlocking.into_iter()\n .filter(|chunk| if chunk.era > current_era {\n true\n } else {\n total = total.saturating_sub(chunk.value);\n false\n })\n .collect();\n")),(0,m.kt)("p",null,"This function does a check on wether the updated ledger has any balance left in regards to staking, both in terms of locked, staking balance and unlocking balance. If not amount is left, the all information related to the stash will be deleted. This results in multiple I/O calls."),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"if ledger.unlocking.is_empty() && ledger.active.is_zero() {\n // This account must have called `unbond()` with some value that caused the active\n // portion to fall below existential deposit + will have no more unlocking chunks\n // left. We can now safely remove all staking-related information.\n Self::kill_stash(&stash, num_slashing_spans)?;\n // remove the lock.\n T::Currency::remove_lock(STAKING_ID, &stash);\n // This is worst case scenario, so we use the full weight and return None\n None\n}\n")),(0,m.kt)("p",null,"The resulting call to ",(0,m.kt)("inlineCode",{parentName:"p"},"Self::kill_stash()")," triggers:"),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"slashing::clear_stash_metadata::(stash, num_slashing_spans)?;\n>::remove(stash);\n>::remove(&controller);\n>::remove(stash);\n>::remove(stash);\n>::remove(stash);\n")),(0,m.kt)("p",null,"Alternatively, if there\u2019s some balance left, the adjusted ledger simply gets updated back into storage."),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"// This was the consequence of a partial unbond. just update the ledger and move on.\nSelf::update_ledger(&controller, &ledger);\n")),(0,m.kt)("p",null,"Finally, it withdraws the unlocked balance, making it ready for transfer:"),(0,m.kt)("pre",null,(0,m.kt)("code",{parentName:"pre",className:"language-rust"},"let value = old_total - ledger.total;\nSelf::deposit_event(RawEvent::Withdrawn(stash, value));\n")),(0,m.kt)("h4",{id:"id-parameters-2"},"10.5.4.2. Parameters"),(0,m.kt)("p",null,"The following parameters are selected:"),(0,m.kt)("table",null,(0,m.kt)("thead",{parentName:"table"},(0,m.kt)("tr",{parentName:"thead"},(0,m.kt)("th",{parentName:"tr",align:null},(0,m.kt)("strong",{parentName:"th"},"Type")),(0,m.kt)("th",{parentName:"tr",align:null}),(0,m.kt)("th",{parentName:"tr",align:null},(0,m.kt)("strong",{parentName:"th"},"From")),(0,m.kt)("th",{parentName:"tr",align:null},(0,m.kt)("strong",{parentName:"th"},"To")),(0,m.kt)("th",{parentName:"tr",align:null},(0,m.kt)("strong",{parentName:"th"},"Description")))),(0,m.kt)("tbody",{parentName:"table"},(0,m.kt)("tr",{parentName:"tbody"},(0,m.kt)("td",{parentName:"tr",align:null},"Account index"),(0,m.kt)("td",{parentName:"tr",align:null},(0,m.kt)("inlineCode",{parentName:"td"},"index")," in\u2026\u200b"),(0,m.kt)("td",{parentName:"tr",align:null},"0"),(0,m.kt)("td",{parentName:"tr",align:null},"1000"),(0,m.kt)("td",{parentName:"tr",align:null},"Used as a seed for account creation")))),(0,m.kt)("p",null,"This benchmark does not require complex parameters. 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vlist-t2"},(0,m.kt)("span",{parentName:"span",className:"vlist-r"},(0,m.kt)("span",{parentName:"span",className:"vlist",style:{height:"2.5em"}},(0,m.kt)("span",{parentName:"span",style:{top:"-4.66em"}},(0,m.kt)("span",{parentName:"span",className:"pstrut",style:{height:"3em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord"}),(0,m.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}}),(0,m.kt)("span",{parentName:"span",className:"mrel"},"="),(0,m.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}}),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"ba"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"se"),(0,m.kt)("span",{parentName:"span",className:"mspace"},"\xa0"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.10764em"}},"f"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"ee"))),(0,m.kt)("span",{parentName:"span",style:{top:"-3.16em"}},(0,m.kt)("span",{parentName:"span",className:"pstrut",style:{height:"3em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord"}),(0,m.kt)("span",{parentName:"span",className:"mord"}),(0,m.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}}),(0,m.kt)("span",{parentName:"span",className:"mbin"},"+"),(0,m.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}}),(0,m.kt)("span",{parentName:"span",className:"mord text"},(0,m.kt)("span",{parentName:"span",className:"mord"},"length\xa0of\xa0transaction\xa0in\xa0bytes")),(0,m.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}}),(0,m.kt)("span",{parentName:"span",className:"mbin"},"\xd7"),(0,m.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}}),(0,m.kt)("span",{parentName:"span",className:"mord text"},(0,m.kt)("span",{parentName:"span",className:"mord"},"length\xa0fee")))),(0,m.kt)("span",{parentName:"span",style:{top:"-1.66em"}},(0,m.kt)("span",{parentName:"span",className:"pstrut",style:{height:"3em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord"}),(0,m.kt)("span",{parentName:"span",className:"mord"}),(0,m.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}}),(0,m.kt)("span",{parentName:"span",className:"mbin"},"+"),(0,m.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}}),(0,m.kt)("span",{parentName:"span",className:"mord text"},(0,m.kt)("span",{parentName:"span",className:"mord"},"weight\xa0to\xa0fee"))))),(0,m.kt)("span",{parentName:"span",className:"vlist-s"},"\u200b")),(0,m.kt)("span",{parentName:"span",className:"vlist-r"},(0,m.kt)("span",{parentName:"span",className:"vlist",style:{height:"2em"}},(0,m.kt)("span",{parentName:"span"})))))))))))),(0,m.kt)("h3",{id:"id-definitions-in-polkadot"},"10.6.2. Definitions in Polkadot"),(0,m.kt)("p",null,"The Polkadot Runtime defines the following values:"),(0,m.kt)("ul",null,(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},"Base fee: 1 mDOTs ",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mo",{parentName:"mrow",stretchy:"false"},"("),(0,m.kt)("mn",{parentName:"mrow"},"1"),(0,m.kt)("msup",{parentName:"mrow"},(0,m.kt)("mn",{parentName:"msup"},"0"),(0,m.kt)("mrow",{parentName:"msup"},(0,m.kt)("mo",{parentName:"mrow"},"\u2212"),(0,m.kt)("mn",{parentName:"mrow"},"3"))),(0,m.kt)("mi",{parentName:"mrow"},"D"),(0,m.kt)("mi",{parentName:"mrow"},"O"),(0,m.kt)("mi",{parentName:"mrow"},"T"),(0,m.kt)("mo",{parentName:"mrow",stretchy:"false"},")")),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"(10^{-3}DOT)")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"1.0641em",verticalAlign:"-0.25em"}}),(0,m.kt)("span",{parentName:"span",className:"mopen"},"("),(0,m.kt)("span",{parentName:"span",className:"mord"},"1"),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord"},"0"),(0,m.kt)("span",{parentName:"span",className:"msupsub"},(0,m.kt)("span",{parentName:"span",className:"vlist-t"},(0,m.kt)("span",{parentName:"span",className:"vlist-r"},(0,m.kt)("span",{parentName:"span",className:"vlist",style:{height:"0.8141em"}},(0,m.kt)("span",{parentName:"span",style:{top:"-3.063em",marginRight:"0.05em"}},(0,m.kt)("span",{parentName:"span",className:"pstrut",style:{height:"2.7em"}}),(0,m.kt)("span",{parentName:"span",className:"sizing reset-size6 size3 mtight"},(0,m.kt)("span",{parentName:"span",className:"mord mtight"},(0,m.kt)("span",{parentName:"span",className:"mord mtight"},"\u2212"),(0,m.kt)("span",{parentName:"span",className:"mord mtight"},"3"))))))))),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.02778em"}},"D"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.13889em"}},"OT"),(0,m.kt)("span",{parentName:"span",className:"mclose"},")"))))),". Base Fee is defined as the fee for a No-op extrinsic (for e.g., an empty System::Remark call, currently with a weight of 126 micro Seconds). ")),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},"Length fee: 0.1 uDOTs")),(0,m.kt)("li",{parentName:"ul"},(0,m.kt)("p",{parentName:"li"},"Weight to fee conversion:"),(0,m.kt)("p",{parentName:"li"},(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow"},"w"),(0,m.kt)("mi",{parentName:"mrow"},"e"),(0,m.kt)("mi",{parentName:"mrow"},"i"),(0,m.kt)("mi",{parentName:"mrow"},"g"),(0,m.kt)("mi",{parentName:"mrow"},"h"),(0,m.kt)("mi",{parentName:"mrow"},"t")),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"{weight}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"0.8889em",verticalAlign:"-0.1944em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.02691em"}},"w"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"e"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"i"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03588em"}},"g"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"h"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"t"))))))," fee = ",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow"},"w"),(0,m.kt)("mi",{parentName:"mrow"},"e"),(0,m.kt)("mi",{parentName:"mrow"},"i"),(0,m.kt)("mi",{parentName:"mrow"},"g"),(0,m.kt)("mi",{parentName:"mrow"},"h"),(0,m.kt)("mi",{parentName:"mrow"},"t"),(0,m.kt)("mi",{parentName:"mrow",mathvariant:"normal"},"/"),(0,m.kt)("mn",{parentName:"mrow"},"1.26"),(0,m.kt)("mo",{parentName:"mrow"},"\u2217"),(0,m.kt)("mo",{parentName:"mrow",stretchy:"false"},"("),(0,m.kt)("mn",{parentName:"mrow"},"1"),(0,m.kt)("msup",{parentName:"mrow"},(0,m.kt)("mn",{parentName:"msup"},"0"),(0,m.kt)("mrow",{parentName:"msup"},(0,m.kt)("mo",{parentName:"mrow"},"\u2212"),(0,m.kt)("mn",{parentName:"mrow"},"8"))),(0,m.kt)("mo",{parentName:"mrow",stretchy:"false"},")")),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"weight/1.26 * (10^{-8})")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.02691em"}},"w"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"e"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"i"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03588em"}},"g"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"h"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"t"),(0,m.kt)("span",{parentName:"span",className:"mord"},"/1.26"),(0,m.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}}),(0,m.kt)("span",{parentName:"span",className:"mbin"},"\u2217"),(0,m.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}})),(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"1.0641em",verticalAlign:"-0.25em"}}),(0,m.kt)("span",{parentName:"span",className:"mopen"},"("),(0,m.kt)("span",{parentName:"span",className:"mord"},"1"),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mord"},"0"),(0,m.kt)("span",{parentName:"span",className:"msupsub"},(0,m.kt)("span",{parentName:"span",className:"vlist-t"},(0,m.kt)("span",{parentName:"span",className:"vlist-r"},(0,m.kt)("span",{parentName:"span",className:"vlist",style:{height:"0.8141em"}},(0,m.kt)("span",{parentName:"span",style:{top:"-3.063em",marginRight:"0.05em"}},(0,m.kt)("span",{parentName:"span",className:"pstrut",style:{height:"2.7em"}}),(0,m.kt)("span",{parentName:"span",className:"sizing reset-size6 size3 mtight"},(0,m.kt)("span",{parentName:"span",className:"mord mtight"},(0,m.kt)("span",{parentName:"span",className:"mord mtight"},"\u2212"),(0,m.kt)("span",{parentName:"span",className:"mord mtight"},"8"))))))))),(0,m.kt)("span",{parentName:"span",className:"mclose"},")")))))," where ",(0,m.kt)("span",{parentName:"p",className:"math math-inline"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow"},"w"),(0,m.kt)("mi",{parentName:"mrow"},"e"),(0,m.kt)("mi",{parentName:"mrow"},"i"),(0,m.kt)("mi",{parentName:"mrow"},"g"),(0,m.kt)("mi",{parentName:"mrow"},"h"),(0,m.kt)("mi",{parentName:"mrow"},"t")),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"weight")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"0.8889em",verticalAlign:"-0.1944em"}}),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.02691em"}},"w"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"e"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"i"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03588em"}},"g"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"h"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"t")))))," is in nS."),(0,m.kt)("p",{parentName:"li"},"A weight of 126\u2019000 nS is mapped to 1 mDOT. This fee will never exceed the max size of an unsigned 128 bit integer."))),(0,m.kt)("h3",{id:"id-fee-multiplier"},"10.6.3. Fee Multiplier"),(0,m.kt)("p",null,"Polkadot can add a additional fee to transactions if the network becomes too busy and starts to decelerate the system. This fee can create an incentive to avoid the production of low priority or insignificant transactions. In contrast, those additional fees will decrease if the network calms down and it can execute transactions without much difficulties."),(0,m.kt)("p",null,"That additional fee is known as the ",(0,m.kt)("inlineCode",{parentName:"p"},"Fee Multiplier")," and its value is defined by the Polkadot Runtime. The multiplier works by comparing the saturation of blocks; if the previous block is less saturated than the current block (implying an uptrend), the fee is slightly increased. Similarly, if the previous block is more saturated than the current block (implying a downtrend), the fee is slightly decreased."),(0,m.kt)("p",null,"The final fee is calculated as:"),(0,m.kt)("div",{className:"math math-display"},(0,m.kt)("span",{parentName:"div",className:"katex-display"},(0,m.kt)("span",{parentName:"span",className:"katex"},(0,m.kt)("span",{parentName:"span",className:"katex-mathml"},(0,m.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},(0,m.kt)("semantics",{parentName:"math"},(0,m.kt)("mrow",{parentName:"semantics"},(0,m.kt)("mi",{parentName:"mrow"},"f"),(0,m.kt)("mi",{parentName:"mrow"},"i"),(0,m.kt)("mi",{parentName:"mrow"},"n"),(0,m.kt)("mi",{parentName:"mrow"},"a"),(0,m.kt)("mi",{parentName:"mrow"},"l"),(0,m.kt)("mi",{parentName:"mrow"},"f"),(0,m.kt)("mi",{parentName:"mrow"},"e"),(0,m.kt)("mi",{parentName:"mrow"},"e"),(0,m.kt)("mo",{parentName:"mrow"},"="),(0,m.kt)("mi",{parentName:"mrow"},"f"),(0,m.kt)("mi",{parentName:"mrow"},"e"),(0,m.kt)("mi",{parentName:"mrow"},"e"),(0,m.kt)("mo",{parentName:"mrow"},"\xd7"),(0,m.kt)("mi",{parentName:"mrow"},"F"),(0,m.kt)("mi",{parentName:"mrow"},"e"),(0,m.kt)("mi",{parentName:"mrow"},"e"),(0,m.kt)("mi",{parentName:"mrow"},"M"),(0,m.kt)("mi",{parentName:"mrow"},"u"),(0,m.kt)("mi",{parentName:"mrow"},"l"),(0,m.kt)("mi",{parentName:"mrow"},"t"),(0,m.kt)("mi",{parentName:"mrow"},"i"),(0,m.kt)("mi",{parentName:"mrow"},"p"),(0,m.kt)("mi",{parentName:"mrow"},"l"),(0,m.kt)("mi",{parentName:"mrow"},"i"),(0,m.kt)("mi",{parentName:"mrow"},"e"),(0,m.kt)("mi",{parentName:"mrow"},"r")),(0,m.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"final fee = fee \\times Fee Multiplier")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"0.8889em",verticalAlign:"-0.1944em"}}),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.10764em"}},"f"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"ina"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.01968em"}},"l"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.10764em"}},"f"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"ee"),(0,m.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}}),(0,m.kt)("span",{parentName:"span",className:"mrel"},"="),(0,m.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}})),(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"0.8889em",verticalAlign:"-0.1944em"}}),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.10764em"}},"f"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"ee"),(0,m.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}}),(0,m.kt)("span",{parentName:"span",className:"mbin"},"\xd7"),(0,m.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}})),(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"0.8889em",verticalAlign:"-0.1944em"}}),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.13889em"}},"F"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"ee"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.10903em"}},"M"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"u"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"lt"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"i"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.01968em"}},"pl"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal"},"i"),(0,m.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.02778em"}},"er")))))),(0,m.kt)("h4",{id:"id-update-multiplier"},"10.6.3.1. Update Multiplier"),(0,m.kt)("p",null,"The ",(0,m.kt)("inlineCode",{parentName:"p"},"Update Multiplier")," defines how the multiplier can change. 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diff &=& (target\\ weight - previous\\ block\\ weight) \\\\ v &=& 0.00004 \\\\ next\\ weight &=& weight \\times (1 + (v \\times diff) + (v \\times diff)^2 / 2) \\end{aligned}")))),(0,m.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,m.kt)("span",{parentName:"span",className:"base"},(0,m.kt)("span",{parentName:"span",className:"strut",style:{height:"4.5241em",verticalAlign:"-2.0121em"}}),(0,m.kt)("span",{parentName:"span",className:"mord"},(0,m.kt)("span",{parentName:"span",className:"mtable"},(0,m.kt)("span",{parentName:"span",className:"col-align-r"},(0,m.kt)("span",{parentName:"span",className:"vlist-t 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Networking | Polkadot Protocol Specification - + diff --git a/chap-overview.html b/chap-overview.html index 72e66f1c7..54e83e64e 100644 --- a/chap-overview.html +++ b/chap-overview.html @@ -6,7 +6,7 @@ 1. Overview | Polkadot Protocol Specification - + diff --git a/chap-runtime-api.html b/chap-runtime-api.html index 6c28b0b2e..a682d929c 100644 --- a/chap-runtime-api.html +++ b/chap-runtime-api.html @@ -6,7 +6,7 @@ Appendix C: Runtime API | Polkadot Protocol Specification - + diff --git a/chap-state.html b/chap-state.html index 39a2100eb..2410efa94 100644 --- a/chap-state.html +++ b/chap-state.html @@ -6,7 +6,7 @@ 2. States and Transitions | Polkadot Protocol Specification - + diff --git a/chap-sync.html b/chap-sync.html index 2ba411796..49f15826f 100644 --- a/chap-sync.html +++ b/chap-sync.html @@ -6,7 +6,7 @@ 3. Synchronization | Polkadot Protocol Specification - + diff --git a/chapter-anv.html b/chapter-anv.html index e1f05bc6f..f8d22ca3f 100644 --- a/chapter-anv.html +++ b/chapter-anv.html @@ -6,7 +6,7 @@ 8. Availability & Validity | Polkadot Protocol Specification - + diff --git a/id-consensus.html b/id-consensus.html index cc70f0aee..c34e924f2 100644 --- a/id-consensus.html +++ b/id-consensus.html @@ -6,7 +6,7 @@ 11. Consensus | Polkadot Protocol Specification - + diff --git a/id-cryptography-encoding.html b/id-cryptography-encoding.html index b446851ab..49f0ba304 100644 --- a/id-cryptography-encoding.html +++ b/id-cryptography-encoding.html @@ -6,7 +6,7 @@ Appendix A: Cryptography & Encoding | Polkadot Protocol Specification - + diff --git a/id-extrinsics.html b/id-extrinsics.html index ccfdb5003..20b5c215b 100644 --- a/id-extrinsics.html +++ b/id-extrinsics.html @@ -6,12 +6,12 @@ 9. Extrinsics | Polkadot Protocol Specification - +
-

9. Extrinsics

9.1. Introduction​

An extrinsic is a SCALE encoded array consisting of a version number, signature, and varying data types indicating the resulting Runtime function to be called, including the parameters required for that function to be executed.

9.2. Preliminaries​

Definition 152. Extrinsic​

An extrinsic , tx{t}{x}, is a tuple consisting of the extrinsic version, Tv{T}_{{v}} (Definition 153), and the body of the extrinsic, Tb{T}_{{b}}.

tx =(Tv,Tb){t}{x}\:={\left({T}_{{v}},{T}_{{b}}\right)}

The value of Tb{T}_{{b}} varies for each version. The current version 4 is described in Section 9.3.1..

Definition 153. Extrinsic Version​

Tv{T}_{{v}} is a 8-bit bitfield and defines the extrinsic version. The required format of an extrinsic body, Tb{T}_{{b}}, is dictated by the Runtime. Older or unsupported versions are rejected.

The most significant bit of Tv{T}_{{v}} indicates whether the transaction is signed (1{1}) or unsigned (0{0}). The remaining 7-bits represent the version number. As an example, for extrinsic format version 4, a signed extrinsic represents Tv{T}_{{v}} as 132 while an unsigned extrinsic represents it as 4.

9.3. Extrinsics Body​

9.3.1. Version 4​

Version 4 of the Polkadot extrinsic format is defined as follows:

Tb =(Ai,Sig,E,Mi,Fi(m)){T}_{{b}}\:={\left({A}_{{i}},{Sig},{E},{M}_{{i}},{F}_{{i}}{\left({m}\right)}\right)}

where

  • Ai{A}_{{i}}: the 32-byte address of the sender (Definition 154).

  • Sig{Sig}: the signature of the sender (Definition 155).

  • E{E}: the extra data for the extrinsic (Definition 156).

  • Mi{M}_{{i}}: the indicator of the Polkadot module (Definition 157).

  • Fi(m){F}_{{i}}{\left({m}\right)}: the indicator of the function of the Polkadot module (Definition 158).

Definition 154. Extrinsic Address​

Account Id, Ai{A}_{{i}}, is the 32-byte address of the sender of the extrinsic as described in the external SS58 address format.

Definition 155. Extrinsic Signature​

The signature, Sig{Sig}, is a varying data type indicating the used signature type, followed by the signature created by the extrinsic author. The following types are supported:

Sig:={0,Ed25519, followed by: (b0,…,b63)1,Sr25519, followed by: (b0,…,b63)2,Ecdsa, followed by: (b0,…,b64)Sig := \begin{cases} 0, & \text{Ed25519, followed by: } (b_0, \ldots,b_{63}) \\ 1, & \text{Sr25519, followed by: } (b_0, \ldots,b_{63}) \\ 2, & \text{Ecdsa, followed by: } (b_0, \ldots,b_{64}) \end{cases}

Signature types vary in size, but each individual type is always fixed-size and therefore does not contain a length prefix. Ed25519 and Sr25519 signatures are 512-bit while Ecdsa is 520-bit, where the last 8 bits are the recovery ID.

The signature is created by signing payload P{P}.

P:={Raw,if ∥Raw∥≤256Blake2(Raw),if ∥Raw∥>256Raw:=(Mi,Fi(m),E,Rv,Fv,Hh(G),Hh(B))\begin{aligned} P &:= \begin{cases} Raw, & \text{if } \|Raw\| \leq 256 \\ \text{Blake2}(Raw), & \text{if } \|Raw\| > 256 \\ \end{cases} \\ Raw &:= (M_i, F_i(m), E, R_v, F_v, H_h(G), H_h(B)) \end{aligned}

where

  • Mi{M}_{{i}}: the module indicator (Definition 157).

  • Fi(m){F}_{{i}}{\left({m}\right)}: the function indicator of the module (Definition 158).

  • E{E}: the extra data (Definition 156).

  • Rv{R}_{{v}}: a UINT32 containing the specification version (spec_version) of the Runtime (Section C.4.1.), which can be updated and is therefore subject to change.

  • Fv{F}_{{v}}: a UINT32 containing the transaction version (transaction_version) of the Runtime (Section C.4.1.), which can be updated and is therefore subject to change.

  • Hh(G){H}_{{h}}{\left({G}\right)}: a 32-byte array containing the genesis hash.

  • Hh(B){H}_{{h}}{\left({B}\right)}: a 32-byte array containing the hash of the block which starts the mortality period, as described in Definition 159.

Definition 156. Extra Data​

Extra data, E{E}, is a tuple containing additional metadata about the extrinsic and the system it is meant to be executed in.

E =(Tmor,N,Pt){E}\:={\left({T}_{mor},{N},{P}_{{t}}\right)}

where

  • Tmor{T}_{mor}: contains the SCALE encoded mortality of the extrinsic (Definition 159).

  • N{N}: a compact integer containing the nonce of the sender. The nonce must be incremented by one for each extrinsic created, otherwise, the Polkadot network will reject the extrinsic.

  • Pt{P}_{{t}}: a compact integer containing the transactor pay including tip.

Definition 157. Module Indicator​

Mi{M}_{{i}} is an indicator for the Runtime to which Polkadot module, m{m}, the extrinsic should be forwarded to.

Mi{M}_{{i}} is a varying data type pointing to every module exposed to the network.

Mi:={0,System1,Utility…7,Balances…M_i := \begin{cases} 0, & \text{System} \\ 1, & \text{Utility} \\ \ldots & \\ 7, & \text{Balances} \\ \ldots & \end{cases}
Definition 158. Function Indicator​

Fi(m){F}_{{i}}{\left({m}\right)} is a tuple which contains an indicator, mi{m}_{{i}}, for the Runtime to which function within the Polkadot module, m{m}, the extrinsic should be forwarded to. This indicator is followed by the concatenated and SCALE encoded parameters of the corresponding function, params{p}{a}{r}{a}{m}{s}.

Fi(m) =(mi,params){F}_{{i}}{\left({m}\right)}\:={\left({m}_{{i}},{p}{a}{r}{a}{m}{s}\right)}

The value of mi{m}_{{i}} varies for each Polkadot module since every module offers different functions. As an example, the Balances module has the following functions:

Balancesi:={0,transfer1,set_balance2,force_transfer3,transfer_keep_alive…Balances_i := \begin{cases} 0, & \text{transfer} \\ 1, & \text{set\_balance} \\ 2, & \text{force\_transfer} \\ 3, & \text{transfer\_keep\_alive} \\ \ldots & \end{cases}

9.3.2. Mortality​

Definition 159. Extrinsic Mortality​

Extrinsic mortality is a mechanism which ensures that an extrinsic is only valid within a certain period of the ongoing Polkadot lifetime. Extrinsics can also be immortal, as clarified in Section 9.3.2.2..

The mortality mechanism works with two related values:

  • Mper{M}_{{{per}}}: the period of validity in terms of block numbers from the block hash specified as Hh(B){H}_{{h}}{\left({B}\right)} in the payload (Definition 155). The requirement is Mper≥4{M}_{{{per}}}\geq{4} and Mper{M}_{{{per}}} must be the power of two, such as 32, 64, 128, etc.

  • Mpha{M}_{{{pha}}}: the phase in the period that this extrinsic’s lifetime begins. This value is calculated with a formula, and validators can use this value in order to determine which block hash is included in the payload. The requirement is Mpha<Mper{M}_{{{pha}}}<{M}_{{{per}}}.

In order to tie a transaction’s lifetime to a certain block (Hi(B){H}_{{i}}{\left({B}\right)}) after it was issued, without wasting precious space for block hashes, block numbers are divided into regular periods and the lifetime is instead expressed as a "phase" (Mpha{M}_{{{pha}}}) from these regular boundaries:

Mpha=Hi(B)  mod  Mper{M}_{pha}={H}_{{i}}{\left({B}\right)} \; mod \; {M}_{{{per}}}

Mper{M}_{{{per}}} and Mpha{M}_{{{pha}}} are then included in the extrinsic, as clarified in Definition 156, in the SCALE encoded form of Tmor{T}_{mor} (Section 9.3.2.2.). Polkadot validators can use Mpha{M}_{{{pha}}} to figure out the block hash included in the payload, which will therefore result in a valid signature if the extrinsic is within the specified period or an invalid signature if the extrinsic "died".

9.3.2.1. Example​

The extrinsic author choses Mper=256{M}_{{{per}}}={256} at block 10'000, resulting with Mpha=16{M}_{{{pha}}}={16}. The extrinsic is then valid for blocks ranging from 10'000 to 10'256.

9.3.2.2. Encoding​

Tmor{T}_{mor} refers to the SCALE encoded form of type Mper{M}_{{{per}}} and Mpha{M}_{{{pha}}}. Tmor{T}_{mor} is the size of two bytes if the extrinsic is considered mortal, or simply one bytes with a value equal to zero if the extrinsic is considered immortal.

Tmor =EncSC(Mper,Mpha){T}_{mor}\:={E}{n}{c}_{{{S}{C}}}{\left({M}_{{{per}}},{M}_{{{pha}}}\right)}

The SCALE encoded representation of mortality Tmor{T}_{mor} deviates from most other types, as it’s specialized to be the smallest possible value, as described in Encode Mortality and Decode Mortality.

If the extrinsic is immortal, specify a single byte with a value equal to zero.

Algorithm 25. Encode Mortality​
\begin{algorithm}
+
9. Extrinsics
9.1. Introduction​
An extrinsic is a SCALE encoded array consisting of a version number, signature, and varying data types indicating the resulting Runtime function to be called, including the parameters required for that function to be executed.
9.2. Preliminaries​
Definition 152. Extrinsic​
An extrinsic , tx{t}{x}, is a tuple consisting of the extrinsic version, Tv{T}_{{v}} (Definition 153), and the body of the extrinsic, Tb{T}_{{b}}.
tx =(Tv,Tb){t}{x}\:={\left({T}_{{v}},{T}_{{b}}\right)}
The value of Tb{T}_{{b}} varies for each version. The current version 4 is described in Section 9.3.1..
Definition 153. Extrinsic Version​
Tv{T}_{{v}} is a 8-bit bitfield and defines the extrinsic version. The required format of an extrinsic body, Tb{T}_{{b}}, is dictated by the Runtime. Older or unsupported versions are rejected.
The most significant bit of Tv{T}_{{v}} indicates whether the transaction is signed (1{1}) or unsigned (0{0}). The remaining 7-bits represent the version number. As an example, for extrinsic format version 4, a signed extrinsic represents Tv{T}_{{v}} as 132 while an unsigned extrinsic represents it as 4.
9.3. Extrinsics Body​
9.3.1. Version 4​
Version 4 of the Polkadot extrinsic format is defined as follows:
Tb =(Ai,Sig,E,Mi,Fi(m)){T}_{{b}}\:={\left({A}_{{i}},{Sig},{E},{M}_{{i}},{F}_{{i}}{\left({m}\right)}\right)}
where  
  • Ai{A}_{{i}} is the multi-address of the sender defined in Definition 154.
  • Sig{Sig}: the signature of the sender (Definition 155).
  • E{E}: the extra data for the extrinsic (Definition 156).
  • Mi{M}_{{i}}: the indicator of the Polkadot module (Definition 157).
  • Fi(m){F}_{{i}}{\left({m}\right)}: the indicator of the function of the Polkadot module (Definition 158).
Definition 154. Extrinsic Address​
Account Id, Ai{A}_{{i}}, is the 32-byte address of the sender of the extrinsic as described in the external SS58 address format.
Definition 155. Extrinsic Signature​
The signature, Sig{Sig}, is a varying data type indicating the used signature type, followed by the signature created by the extrinsic author. The following types are supported:
Sig:={0,Ed25519, followed by: (b0,…,b63)1,Sr25519, followed by: (b0,…,b63)2,Ecdsa, followed by: (b0,…,b64)Sig := \begin{cases} 0, & \text{Ed25519, followed by: } (b_0, \ldots,b_{63}) \\ 1, & \text{Sr25519, followed by: } (b_0, \ldots,b_{63}) \\ 2, & \text{Ecdsa, followed by: } (b_0, \ldots,b_{64}) \end{cases}
Signature types vary in size, but each individual type is always fixed-size and therefore does not contain a length prefix. Ed25519 and Sr25519 signatures are 512-bit while Ecdsa is 520-bit, where the last 8 bits are the recovery ID.
The signature is created by signing payload P{P}.
P:={Raw,if ∥Raw∥≤256Blake2(Raw),if ∥Raw∥>256Raw:=(Mi,Fi(m),E,Rv,Fv,Hh(G),Hh(B))\begin{aligned} P &:= \begin{cases} Raw, & \text{if } \|Raw\| \leq 256 \\ \text{Blake2}(Raw), & \text{if } \|Raw\| > 256 \\ \end{cases} \\ Raw &:= (M_i, F_i(m), E, R_v, F_v, H_h(G), H_h(B)) \end{aligned}
where  
  • Mi{M}_{{i}}: the module indicator (Definition 157).
  • Fi(m){F}_{{i}}{\left({m}\right)}: the function indicator of the module (Definition 158).
  • E{E}: the extra data (Definition 156).
  • Rv{R}_{{v}}: a UINT32 containing the specification version (spec_version) of the Runtime (Section C.4.1.), which can be updated and is therefore subject to change.
  • Fv{F}_{{v}}: a UINT32 containing the transaction version (transaction_version) of the Runtime (Section C.4.1.), which can be updated and is therefore subject to change.
  • Hh(G){H}_{{h}}{\left({G}\right)}: a 32-byte array containing the genesis hash.
  • Hh(B){H}_{{h}}{\left({B}\right)}: a 32-byte array containing the hash of the block which starts the mortality period, as described in Definition 159.
Definition 156. Extra Data​
Extra data, E{E}, is a tuple containing additional metadata about the extrinsic and the system it is meant to be executed in.
E =(Tmor,N,Pt){E}\:={\left({T}_{mor},{N},{P}_{{t}}\right)}
where  
  • Tmor{T}_{mor}: contains the SCALE encoded mortality of the extrinsic (Definition 159).
  • N{N}: a compact integer containing the nonce of the sender. The nonce must be incremented by one for each extrinsic created, otherwise, the Polkadot network will reject the extrinsic.
  • Pt{P}_{{t}}: a compact integer containing the transactor pay including tip.
Definition 157. Module Indicator​
Mi{M}_{{i}} is an indicator for the Runtime to which Polkadot module, m{m}, the extrinsic should be forwarded to.
Mi{M}_{{i}} is a varying data type pointing to every module exposed to the network.
Mi:={0,System1,Utility…7,Balances…M_i := \begin{cases} 0, & \text{System} \\ 1, & \text{Utility} \\ \ldots & \\ 7, & \text{Balances} \\ \ldots & \end{cases}
Definition 158. Function Indicator​
Fi(m){F}_{{i}}{\left({m}\right)} is a tuple which contains an indicator, mi{m}_{{i}}, for the Runtime to which function within the Polkadot module, m{m}, the extrinsic should be forwarded to. This indicator is followed by the concatenated and SCALE encoded parameters of the corresponding function, params{p}{a}{r}{a}{m}{s}.
Fi(m) =(mi,params){F}_{{i}}{\left({m}\right)}\:={\left({m}_{{i}},{p}{a}{r}{a}{m}{s}\right)}
The value of mi{m}_{{i}} varies for each Polkadot module since every module offers different functions. As an example, the Balances module has the following functions:
Balancesi:={0,transfer1,set_balance2,force_transfer3,transfer_keep_alive…Balances_i := \begin{cases} 0, & \text{transfer} \\ 1, & \text{set\_balance} \\ 2, & \text{force\_transfer} \\ 3, & \text{transfer\_keep\_alive} \\ \ldots & \end{cases}
9.3.2. Mortality​
Definition 159. Extrinsic Mortality​
Extrinsic mortality is a mechanism which ensures that an extrinsic is only valid within a certain period of the ongoing Polkadot lifetime. Extrinsics can also be immortal, as clarified in Section 9.3.2.2..
The mortality mechanism works with two related values:
  • Mper{M}_{{{per}}}: the period of validity in terms of block numbers from the block hash specified as Hh(B){H}_{{h}}{\left({B}\right)} in the payload (Definition 155). The requirement is Mper≥4{M}_{{{per}}}\geq{4} and Mper{M}_{{{per}}} must be the power of two, such as 32, 64, 128, etc.
  • Mpha{M}_{{{pha}}}: the phase in the period that this extrinsic’s lifetime begins. This value is calculated with a formula, and validators can use this value in order to determine which block hash is included in the payload. The requirement is Mpha<Mper{M}_{{{pha}}}<{M}_{{{per}}}.
In order to tie a transaction’s lifetime to a certain block (Hi(B){H}_{{i}}{\left({B}\right)}) after it was issued, without wasting precious space for block hashes, block numbers are divided into regular periods and the lifetime is instead expressed as a "phase" (Mpha{M}_{{{pha}}}) from these regular boundaries:
Mpha=Hi(B)  mod  Mper{M}_{pha}={H}_{{i}}{\left({B}\right)} \; mod \; {M}_{{{per}}}
Mper{M}_{{{per}}} and Mpha{M}_{{{pha}}} are then included in the extrinsic, as clarified in Definition 156, in the SCALE encoded form of Tmor{T}_{mor} (Section 9.3.2.2.). Polkadot validators can use Mpha{M}_{{{pha}}} to figure out the block hash included in the payload, which will therefore result in a valid signature if the extrinsic is within the specified period or an invalid signature if the extrinsic "died".
9.3.2.1. Example​
The extrinsic author choses Mper=256{M}_{{{per}}}={256} at block 10'000, resulting with Mpha=16{M}_{{{pha}}}={16}. The extrinsic is then valid for blocks ranging from 10'000 to 10'256.
9.3.2.2. Encoding​
Tmor{T}_{mor} refers to the SCALE encoded form of type Mper{M}_{{{per}}} and Mpha{M}_{{{pha}}}. Tmor{T}_{mor} is the size of two bytes if the extrinsic is considered mortal, or simply one bytes with a value equal to zero if the extrinsic is considered immortal.
Tmor =EncSC(Mper,Mpha){T}_{mor}\:={E}{n}{c}_{{{S}{C}}}{\left({M}_{{{per}}},{M}_{{{pha}}}\right)}
The SCALE encoded representation of mortality Tmor{T}_{mor} deviates from most other types, as it’s specialized to be the smallest possible value, as described in Encode Mortality and Decode Mortality.
If the extrinsic is immortal, specify a single byte with a value equal to zero.
Algorithm 25. Encode Mortality​
\begin{algorithm}
 \caption{Encode Mortality}
 \begin{algorithmic}
     \Require{$M_{per}, M_{pha}$}
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 Glossary | Polkadot Protocol Specification
 
 
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 Polkadot Protocol | Polkadot Protocol Specification
 
 
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 10. Weights | Polkadot Protocol Specification
 
 
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@@ -96,7 +96,7 @@
         \Return $\mathcal{W}$
     \EndFunction
 \end{algorithmic}
-\end{algorithm}
where  
  • Create-Account(name{name}, indexindex)
    Creates a Blake2 hash of the concatenated input of name and index representing the address of a account. This function only creates an address and does not conduct any I/O.
  • Set-Balance(amount{amount}, balance{balance})
    Sets a initial balance for the specified account in the storage state.
  • Bond(stash{stash}, controller{controller}, amount{amount})
    Bonds the specified amount for the stash and controller pair.
  • UnBond(account{account}, amount{amount})
    Unbonds the specified amount for the given account.
  • Pass-Era()
    Pass one era. Forces the function withdraw_unbonded to update the ledger and eventually delete information.
  • Withdraw-Unbonded(controller{controller})
    Withdraws the the full unbonded amount of the specified controller account. This represents the target Runtime function to be benchmarked.
  • Add-To(collection{collection}, time{time})
    Adds a returned time measurement (time) to collection.
  • Timer(function{function})
    Measures the time from the start of the specified f unction to its completion.
  • Compute-Weight(collection{collection})
    Computes the resulting weight based on the time measurements in the collection. The worst case scenario should be chosen (the highest value).
10.6. Fees​
Block producers charge a fee in order to be economically sustainable. That fee must always be covered by the sender of the transaction. Polkadot has a flexible mechanism to determine the minimum cost to include transactions in a block.
10.6.1. Fee Calculation​
Polkadot fees consists of three parts:
  • Base fee: a fixed fee that is applied to every transaction and set by the Runtime.
  • Length fee: a fee that gets multiplied by the length of the transaction, in bytes.
  • Weight fee: a fee for each, varying Runtime function. Runtime implementers need to implement a conversion mechanism which determines the corresponding currency amount for the calculated weight.
The final fee can be summarized as:
fee=base fee+length of transaction in bytes×length fee+weight to fee\begin{aligned} fee &= base\ fee \\ &{} + \text{length of transaction in bytes} \times \text{length fee} \\ &{} + \text{weight to fee} \end{aligned}
10.6.2. Definitions in Polkadot​
The Polkadot Runtime defines the following values:
  • Base fee: 100 uDOTs
  • Length fee: 0.1 uDOTs
  • Weight to fee conversion:
    weight{weight} fee = weight \times (100uDOTs÷(10×10′000)){u}{D}{O}{T}{s}\div{\left({10}\times{10}'{000}\right)}{)}
    A weight of 10’000 (the smallest non-zero weight) is mapped to 110{\frac{{{1}}}{{{10}}}} of 100 uDOT. This fee will never exceed the max size of an unsigned 128 bit integer.
10.6.3. Fee Multiplier​
Polkadot can add a additional fee to transactions if the network becomes too busy and starts to decelerate the system. This fee can create an incentive to avoid the production of low priority or insignificant transactions. In contrast, those additional fees will decrease if the network calms down and it can execute transactions without much difficulties.
That additional fee is known as the Fee Multiplier and its value is defined by the Polkadot Runtime. The multiplier works by comparing the saturation of blocks; if the previous block is less saturated than the current block (implying an uptrend), the fee is slightly increased. Similarly, if the previous block is more saturated than the current block (implying a downtrend), the fee is slightly decreased.
The final fee is calculated as:
finalfee=fee×FeeMultiplierfinal fee = fee \times Fee Multiplier
10.6.3.1. Update Multiplier​
The Update Multiplier defines how the multiplier can change. The Polkadot Runtime internally updates the multiplier after each block according the following formula:
diff=(target weight−previous block weight)v=0.00004next weight=weight×(1+(v×diff)+(v×diff)2/2)\begin{aligned} diff &=& (target\ weight - previous\ block\ weight) \\ v &=& 0.00004 \\ next\ weight &=& weight \times (1 + (v \times diff) + (v \times diff)^2 / 2) \end{aligned}
Polkadot defines the target_weight as 0.25 (25%). More information about this algorithm is described in the Web3 Foundation research paper.
+\end{algorithm}

where

  • Create-Account(name{name}, indexindex)

    Creates a Blake2 hash of the concatenated input of name and index representing the address of a account. This function only creates an address and does not conduct any I/O.

  • Set-Balance(amount{amount}, balance{balance})

    Sets a initial balance for the specified account in the storage state.

  • Bond(stash{stash}, controller{controller}, amount{amount})

    Bonds the specified amount for the stash and controller pair.

  • UnBond(account{account}, amount{amount})

    Unbonds the specified amount for the given account.

  • Pass-Era()

    Pass one era. Forces the function withdraw_unbonded to update the ledger and eventually delete information.

  • Withdraw-Unbonded(controller{controller})

    Withdraws the the full unbonded amount of the specified controller account. This represents the target Runtime function to be benchmarked.

  • Add-To(collection{collection}, time{time})

    Adds a returned time measurement (time) to collection.

  • Timer(function{function})

    Measures the time from the start of the specified f unction to its completion.

  • Compute-Weight(collection{collection})

    Computes the resulting weight based on the time measurements in the collection. The worst case scenario should be chosen (the highest value).

10.6. Fees​

Block producers charge a fee in order to be economically sustainable. That fee must always be covered by the sender of the transaction. Polkadot has a flexible mechanism to determine the minimum cost to include transactions in a block.

10.6.1. Fee Calculation​

Polkadot fees consists of three parts:

  • Base fee: a fixed fee that is applied to every transaction and set by the Runtime.

  • Length fee: a fee that gets multiplied by the length of the transaction, in bytes.

  • Weight fee: a fee for each, varying Runtime function. Runtime implementers need to implement a conversion mechanism which determines the corresponding currency amount for the calculated weight.

The final fee can be summarized as:

fee=base fee+length of transaction in bytes×length fee+weight to fee\begin{aligned} fee &= base\ fee \\ &{} + \text{length of transaction in bytes} \times \text{length fee} \\ &{} + \text{weight to fee} \end{aligned}

10.6.2. Definitions in Polkadot​

The Polkadot Runtime defines the following values:

  • Base fee: 1 mDOTs (10−3DOT)(10^{-3}DOT). Base Fee is defined as the fee for a No-op extrinsic (for e.g., an empty System::Remark call, currently with a weight of 126 micro Seconds).

  • Length fee: 0.1 uDOTs

  • Weight to fee conversion:

    weight{weight} fee = weight/1.26∗(10−8)weight/1.26 * (10^{-8}) where weightweight is in nS.

    A weight of 126’000 nS is mapped to 1 mDOT. This fee will never exceed the max size of an unsigned 128 bit integer.

10.6.3. Fee Multiplier​

Polkadot can add a additional fee to transactions if the network becomes too busy and starts to decelerate the system. This fee can create an incentive to avoid the production of low priority or insignificant transactions. In contrast, those additional fees will decrease if the network calms down and it can execute transactions without much difficulties.

That additional fee is known as the Fee Multiplier and its value is defined by the Polkadot Runtime. The multiplier works by comparing the saturation of blocks; if the previous block is less saturated than the current block (implying an uptrend), the fee is slightly increased. Similarly, if the previous block is more saturated than the current block (implying a downtrend), the fee is slightly decreased.

The final fee is calculated as:

finalfee=fee×FeeMultiplierfinal fee = fee \times Fee Multiplier

10.6.3.1. Update Multiplier​

The Update Multiplier defines how the multiplier can change. The Polkadot Runtime internally updates the multiplier after each block according the following formula:

diff=(target weight−previous block weight)v=0.00004next weight=weight×(1+(v×diff)+(v×diff)2/2)\begin{aligned} diff &=& (target\ weight - previous\ block\ weight) \\ v &=& 0.00004 \\ next\ weight &=& weight \times (1 + (v \times diff) + (v \times diff)^2 / 2) \end{aligned}

Polkadot defines the target_weight as 0.25 (25%). More information about this algorithm is described in the Web3 Foundation research paper.

diff --git a/index.html b/index.html index 061918822..216fcb180 100644 --- a/index.html +++ b/index.html @@ -6,12 +6,12 @@ Polkadot Protocol Specification | Polkadot Protocol Specification - +
-

Polkadot

Enabling Implementers - Version 0.3.1-beta

Read the SpecDownload PDF

Rust

See Node Implementation by Parity and smoldot

Go

See Gossamer by Chainsafe

C++

See Kagome by Soramitsu

+

Polkadot

Enabling Implementers - Version 0.3.1-beta

Read the SpecDownload PDF

Rust

See Node Implementation by Parity and smoldot

Go

See Gossamer by Chainsafe

C++

See Kagome by Soramitsu

diff --git a/part-polkadot-host.html b/part-polkadot-host.html index 9f241845b..da96ba470 100644 --- a/part-polkadot-host.html +++ b/part-polkadot-host.html @@ -6,7 +6,7 @@ Polkadot Host | Polkadot Protocol Specification - + diff --git a/part-polkadot-runtime.html b/part-polkadot-runtime.html index c7414aa18..d5ee08088 100644 --- a/part-polkadot-runtime.html +++ b/part-polkadot-runtime.html @@ -6,7 +6,7 @@ Polkadot Runtime | Polkadot Protocol Specification - + diff --git a/sect-block-production.html b/sect-block-production.html index 9c1d5d37e..cd7095222 100644 --- a/sect-block-production.html +++ b/sect-block-production.html @@ -6,7 +6,7 @@ 5. Block Production | Polkadot Protocol Specification - + diff --git a/sect-finality.html b/sect-finality.html index a8f0b3ccf..b9888de16 100644 --- a/sect-finality.html +++ b/sect-finality.html @@ -6,7 +6,7 @@ 6. Finality | Polkadot Protocol Specification - + diff --git a/sect-lightclient.html b/sect-lightclient.html index 9840b4344..1c175e8f4 100644 --- a/sect-lightclient.html +++ b/sect-lightclient.html @@ -6,7 +6,7 @@ 7. Light Clients | Polkadot Protocol Specification - + diff --git a/sect-metadata.html b/sect-metadata.html index e6155538e..fb54b732d 100644 --- a/sect-metadata.html +++ b/sect-metadata.html @@ -6,7 +6,7 @@ 12. Metadata | Polkadot Protocol Specification - +