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ETHEREUM: A SECURE DECENTRALISED GENERALISED TRANSACTION LEDGER BERLIN VERSION 12 formal model of a virtual state machine, known as the Ethereum Virtual Machine (EVM). It is a quasi-Turing- complete machine; the quasi qualification comes from the fact that the computation is intrinsically bounded through a parameter, gas, which limits the total amount of compu- tation done. 9.1. Basics. The EVM is a simple stack-based architec- ture. The word size of the machine (and thus size of stack items) is 256-bit. This was chosen to facilitate the Keccak- 256 hash scheme and elliptic-curve computations. The memory model is a simple word-addressed byte array. The stack has a maximum size of 1024. The machine also has an independent storage model; this is similar in concept to the memory but rather than a byte array, it is a word- addressable word array. Unlike memory, which is volatile, storage is non volatile and is maintained as part of the system state. All locations in both storage and memory are well-defined initially as zero. The machine does not follow the standard von Neu- mann architecture. Rather than storing program code in generally-accessible memory or storage, it is stored separately in a virtual ROM interactable only through a specialised instruction. The machine can have exceptional execution for several reasons, including stack underflows and invalid instruc- tions. Like the out-of-gas exception, they do not leave state changes intact. Rather, the machine halts immedi- ately and reports the issue to the execution agent (either the transaction processor or, recursively, the spawning execution environment) which will deal with it separately. 9.2. Fees Overview. Fees (denominated in gas) are charged under three distinct circumstances, all three as prerequisite to the execution of an operation. The first and most common is the fee intrinsic to the computation of the operation (see Appendix G). Secondly, gas may be deducted in order to form the payment for a subordinate message call or contract creation; this forms part of the payment for CREATE, CREATE2, CALL and CALLCODE. Finally, gas may be paid due to an increase in the usage of the memory. Over an account’s execution, the total fee for memory- usage payable is proportional to smallest multiple of 32 bytes that are required such that all memory indices (whether for read or write) are included in the range. This is paid for on a just-in-time basis; as such, referencing an area of memory at least 32 bytes greater than any previ- ously indexed memory will certainly result in an additional memory usage fee. Due to this fee it is highly unlikely addresses will ever go above 32-bit bounds. That said, implementations must be able to manage this eventuality. Storage fees have a slightly nuanced behaviour—to in- centivise minimisation of the use of storage (which corre- sponds directly to a larger state database on all nodes), the execution fee for an operation that clears an entry in the storage is not only waived, a qualified refund is given; in fact, this refund is effectively paid up-front since the initial usage of a storage location costs substantially more than normal usage. See Appendix H for a rigorous definition of the EVM gas cost. 9.3. Execution Environment. In addition to the sys- tem state σ, the remaining gas for computation g, and the accrued substate A, there are several pieces of important information used in the execution environment that the execution agent must provide; these are contained in the tuple I: • Ia, the address of the account which owns the code that is executing. • Io, the sender address of the transaction that orig- inated this execution. • Ip, the price of gas in the transaction that origi- nated this execution. • Id, the byte array that is the input data to this execution; if the execution agent is a transaction, this would be the transaction data. • Is, the address of the account which caused the code to be executing; if the execution agent is a transaction, this would be the transaction sender. • Iv, the value, in Wei, passed to this account as part of the same procedure as execution; if the execution agent is a transaction, this would be the transaction value. • Ib, the byte array that is the machine code to be executed. • IH, the block header of the present block. • Ie, the depth of the present message-call or contract-creation (i.e. the number of CALLs or CREATE(2)s being executed at present). • Iw, the permission to make modifications to the state. The execution model defines the function Ξ, which can compute the resultant state σ′, the remaining gas g′, the resultant accrued substate A′ and the resultant output, o, given these definitions. For the present context, we will define it as: (129) (σ′, g′, A′, o) ≡ Ξ(σ, g, A, I) where we will remember that A, the accrued substate, is defined in section 6.1. 9.4. Execution Overview. We must now define the Ξ function. In most practical implementations this will be modelled as an iterative progression of the pair comprising the full system state, σ and the machine state, μ. For- mally, we define it recursively with a function X. This uses an iterator function O (which defines the result of a single cycle of the state machine) together with functions Z which determines if the present state is an exceptional halting state of the machine and H, specifying the output data of the instruction if and only if the present state is a normal halting state of the machine. The empty sequence, denoted (), is not equal to the empty set, denoted ∅; this is important when interpreting the output of H, which evaluates to ∅ when execution is to continue but a series (potentially empty) when executionPDF Image | ETHEREUM: A SECURE DECENTRALISED GENERALISED TRANSACTION
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