ETHEREUM: A SECURE DECENTRALISED GENERALISED TRANSACTION

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ETHEREUM: A SECURE DECENTRALISED GENERALISED TRANSACTION ( ethereum-secure-decentralised-generalised-transaction )

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(320) where: (321) (322) w≡ if otherwise ETHEREUM: A SECURE DECENTRALISED GENERALISED TRANSACTION LEDGER BERLIN VERSION 28 H.1. Gas Cost. The general gas cost function, C, is defined as: (319) CSSTORE(σ, μ, A, I)   G if w = SSTORE if w=EXP∧μ [1]=0 s ×μ [1]+2G s logtopic ×μ [1]+3G s logtopic ×μ [1]+4G C(σ,μ,A,I) ≡ Cmem(μ′i)−Cmem(μi)+CSELFDESTRUCT(σ,μ)   exp  if w=EXP∧μ [1]>0 if w ∈ Wcopy if w = EXTCODECOPY if w ∈ Wextaccount if w=LOG0 if w=LOG1 if w=LOG2 if w=LOG3 if w=LOG4 if w∈W if w = SELFDESTRUCT if w = CREATE if w = CREATE2 if w=SHA3 if w = JUMPDEST if w = SLOAD G +G ×(1+⌊log (μ[1])⌋)  exp expbyte 256s s   Gverylow + Gcopy × ⌈μ [2] ÷ 32⌉ s  160 , A) + Gcopy × ⌈μ [3] ÷ 32⌉ , A)  Caaccess(μ [0] mod 2 ss  160 Caaccess(μ [0] mod 2 s   Glog + Glogdata × μ [1] Glog + Glogdata × μ [1] + Glogtopic  s  G  log   +G logdata +G logdata +G logdata G  log   G  log s logtopic  C (σ, μ, A)  CALL call Gcreate    Gcreate + Gsha3word × ⌈μ [2] ÷ 32⌉  s Gsha3 + Gsha3word × ⌈μ [1] ÷ 32⌉ s Gjumpdest  C (μ,A,I)  SLOAD G  zero G  base  G  verylow     if w∈W if w∈W if w∈W if w∈Wlow if w∈Wmid if w ∈ Whigh if w = BLOCKHASH   zero base verylow Glow   Gmid   Ghigh Gblockhash 􏱏Ib[μpc] STOP  􏱘 a2 􏱙 Cmem(a) ≡ Gmemory · a + 512 Caaccess(x,A) ≡ 􏱏Gwarmaccess x ∈ Aa s μpc < ∥Ib∥ if Gcoldaccountaccess otherwise with CCALL, CSELFDESTRUCT, CSLOAD and CSSTORE as specified in the appropriate section below. We define the following subsets of instructions: Wzero = {STOP, RETURN, REVERT} Wbase = {ADDRESS, ORIGIN, CALLER, CALLVALUE, CALLDATASIZE, CODESIZE, GASPRICE, COINBASE, TIMESTAMP, NUMBER, DIFFICULTY, GASLIMIT, CHAINID, RETURNDATASIZE, POP, PC, MSIZE, GAS} Wverylow = {ADD, SUB, NOT, LT, GT, SLT, SGT, EQ, ISZERO, AND, OR, XOR, BYTE, SHL, SHR, SAR, CALLDATALOAD, MLOAD, MSTORE, MSTORE8, PUSH*, DUP*, SWAP*} Wlow = {MUL, DIV, SDIV, MOD, SMOD, SIGNEXTEND, SELFBALANCE} Wmid = {ADDMOD, MULMOD, JUMP} Whigh = {JUMPI} Wcopy = {CALLDATACOPY, CODECOPY, RETURNDATACOPY} Wcall = {CALL, CALLCODE, DELEGATECALL, STATICCALL} Wextaccount = {BALANCE, EXTCODESIZE, EXTCODEHASH} Note the memory cost component, given as the product of Gmemory and the maximum of 0 & the ceiling of the number of words in size that the memory must be over the current number of words, μi in order that all accesses reference valid memory whether for read or write. Such accesses must be for non-zero number of bytes. Referencing a zero length range (e.g. by attempting to pass it as the input range to a CALL) does not require memory to be extended to the beginning of the range. μ′i is defined as this new maximum number of words of active memory; special-cases are given where these two are not equal.

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