Klaytn Virtual Machine

NOTE: KLVM has changed with the Kore hardfork. If you want the previous document, please refer to previous document.

Kore hardfork block numbers are as follows.

• Baobab Testnet: #111736800

• Cypress Mainnet: #119750400

Overview

The current version of the Klaytn Virtual Machine (KLVM) is derived from the Ethereum Virtual Machine (EVM). The content of this chapter is based primarily on the Ethereum Yellow Paper. KLVM is continuously being improved by the Klaytn team, thus this document could be updated frequently. Please do not regard this document as the final version of the KLVM specification. As described in the Klaytn position paper, the Klaytn team also plans to adopt other virtual machines or execution environments in order to strengthen the capability and performance of the Klaytn platform. This chapter presents a specification of KLVM and the differences between KLVM and EVM.

KLVM is a virtual state machine that formally specifies Klaytn's execution model. The execution model specifies how the system state is altered given a series of bytecode instructions and a small tuple of environmental data. KLVM is a quasi-Turing-complete machine; the quasi qualification stems from the fact that the computation is intrinsically bounded through a parameter, gas, which limits the total amount of computation performed.

KLVM executes Klaytn virtual machine code (or Klaytn bytecode) which consists of a sequence of KLVM instructions. The KLVM code is the programming language used for accounts on the Klaytn blockchain that contain code. The KLVM code associated with an account is executed every time a message is sent to that account; this code has the ability to read/write from/to storage and send messages.

KLVM Specification

Conventions

We use the following notations and conventions in this document.

• A := B

  • := is used to define A as B.

• We use the terms "smart contract" and "contract" interchangeably.

• We use the terms "opcode" as the "operation code/operation"

Symbols

The following tables summarize the symbols used in the KLVM specification.

Blockchain-Related Symbols

Symbol	Description
BC	Blockchain
B	Block
B_header	The block header of the present block

State-Related Symbols

Symbol	Description
S	State
S_system	System state
S_machine	Machine state
P_modify_state	The permission to make state modifications

Transaction-Related Symbols

Symbol	Description
T	Transaction
T_code	A byte array containing machine code to be executed
T_data	A byte array containing the input data to the execution; if the execution agent is a transaction, this would be the transaction data.
T_value	A value, in peb, passed to the account as part of the execution procedure; if the execution agent is a transaction, this would be the transaction value.
T_depth	The depth of the present message-call or contract-creation stack (i.e., the number of CALLs or CREATEs being executed at present)

Gas-Related Symbols

Symbol	Description
G	Gas
G_rem	Remaining gas for computation
G_price	The price of gas in the transaction that originated the execution

Address-Related Symbols

Symbol	Description
A	Address
A_code_owner	The address of the account that owns the executing code
A_tx_sender	The sender address of the transaction that originated the current execution
A_code_executor	the address of the account that initiated code execution; if the execution agent is a transaction, this would be the transaction sender.

Functions

Symbol	Description
F_apply	A function that applies a transaction with input to a given state and returns the resultant state and outputs

Basics

KLVM is a simple stack-based architecture. The word size of the machine (and thus the size of stack items) is 256-bit. This was chosen to facilitate the Keccak-256 hash scheme and the 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 nonvolatile and is maintained as part of the system state. All locations in both storage and memory are initially well-defined as zero.

The machine does not follow the standard von Neumann architecture. Rather than storing program code in generally accessible memory or storage, code is stored separately in virtual read-only memory and can be interacted with only through specialized instructions.

The machine can execute exception code for several reasons, including stack underflows and invalid instructions. Similar to an out-of-gas exception, these exceptions do not leave state changes intact. Rather, the virtual machine halts immediately and reports the issue to the execution agent (either the transaction processor or, recursively, the spawning execution environment), which will be addressed separately.

Fees Overview

Fees (denominated in gas) are charged under three distinct circumstances. Sometimes, some policies may be omitted.

• The first and most common is the constantGas. It's a fee intrinsic to the computation of the operation.

• Second, gas may be deducted to form the payment for a subordinate message call or contract creation; this forms part of the payment for CREATE, CALL and CALLCODE.

• Finally, gas may be charged due to an increase in memory usage.

Over an account's execution, the total fee payable for memory-usage payable is proportional to the smallest multiple of 32 bytes that are required to include all memory indices (whether for read or write) in the range. This fee is paid on a just-in-time basis; consequently, referencing an area of memory at least 32 bytes greater than any previously indexed memory will result in an additional memory usage fee. Due to this fee, it is highly unlikely that addresses will ever exceed the 32-bit bounds. That said, implementations must be able to manage this eventuality.

Storage fees have a slightly nuanced behavior. To incentivize minimization of the use of storage (which corresponds directly to a larger state database on all nodes), the execution fee for an operation that clears an entry from storage is not only waived but also elicits a qualified refund; in fact, this refund is effectively paid in advance because the initial usage of a storage location costs substantially more than normal usage.

Fee Schedule

The fee schedule G is a tuple of 37 scalar values corresponding to the relative costs, in gas, of a number of abstract operations that a transaction may incur. Also, there's gas items to calculate the gas of the precompiled contracts called by CALL_* opcodes. For other tables such as intrinsic gas cost or key validation gas cost, please refer to this document

Scalar values representing constantGas of an opcode

Name	Value	Name in code	Opcodes
G_base	2	GasQuickStep	ADDRESS, ORIGIN, CALLER, CALLVALUE, CALLDATASIZE, CODESIZE, GASPRICE, COINBASE, TIMESTAMP, NUMBER, PREVRANDAO(originally it was difficulty), GASLIMIT, RETURNDATASIZE, POP, PC, MSIZE, GAS, CHAINID(added at istanbul hardfork), BASEFEE(added at london Hardfork), PUSH0(added at shanghai Hardfork)
G_verylow	3	GasFastestStep	ADD, SUB, LT, GT, SLT, SGT, EQ, ISZERO, AND, OR, XOR, NOT, BYTE, CALLDATALOAD, MLOAD, MSTORE, MSTORE8, PUSH, DUP, SWAP
G_low	5	GasFastStep	MUL, DIV, SDIV, MOD, SMOD, SIGNEXTEND, SELFBALANCE(added at istanbul hardfork)
G_mid	8	GasMidStep	ADDMOD, MULMOD, JUMP
G_high	10	GasSlowStep	JUMPI
G_selfdestruct	5000	SelfdestructGas	SELFDESTRUCT
G_warmStorageReadCost	100	WarmStorageReadCostEIP2929 (newly added at Kore hardfork)	EXTCODECOPY, EXTCODESIZE, EXTCODEHASH, BALANCE, CALL, CALLCODE, STATICCALL, DELEGATECALL
G_blockhash	20	GasExtStep	BLOCKHASH
G_jumpdest	1	JumpdestGas	JUMPDEST
G_sha3	30	Sha3Gas	SHA3
G_create	32000	CreateGas	CREATE, CREATE2

Scalar values used to calculate the gas based on memory and log usage

Name	Value	Name in Code	Description
G_memory	3	MemoryGas	Amount of gas paid for every additional word when expanding memory
G_copy	3	CopyGas	Partial payment for COPY operations, multiplied by words copied, rounded up
G_log	375	LogGas	Partial payment for a LOG operation
G_logdata	8	LogDataGas	Amount of gas paid for each byte in a LOG operation's data
G_logtopic	375	LogTopicGas	Amount of gas paid for each topic of a LOG operation

Scalar values used to calculate the gas of the particular opcode

Name	Value	Name in Code	Description
G_sset	20000	SstoreSetGas	Amount of gas paid when the storage value when set storage
G_sreset	5000	SstoreResetGas	Amount of gas paid when the storage value remains unchanged at zero or is set to zero
G_coldSloadCost	2100	ColdSloadCostEIP2929	Amount of gas paid when the storage value is not in accessList
R_sclear	15000	SstoreClearsScheduleRefundEIP3529	G_sreset - G_coldSloadCost + TxAccessListStorageKeyGas (1900)
G_exp	10	ExpGas	Partial payment
G_expbyte	50	ExpByte	Partial payment when multiplied by ceil(log_256(exponent))
G_selfdestruct	5000	SelfdestructGas	Amount of gas paid for a SELFDESTRUCT operation
G_callvalue	9000	CallValueTransferGas	Amount of gas paid for a nonzero value transfer
G_callstipend	2300	CallStipend	Free gas given at beginning of call for a nonzero value transfer
G_newaccount	25000	CallNewAccountGas	Amount of gas paid when creating an account. It is also be defined as CreateBySelfdestructGas with SELFDESTRUCT operation.
G_codedeposit	200	CreateDataGas	Amount of gas paid per byte for a creating a contract that succeeds in placing code into state
G_sha3word	6	Sha3WordGas	Amount of gas paid for each word (rounded up) for an SHA3 input data

Items to calculate the precompiled contracts gas

Precompiled contracts are special kind of contracts which usually perform complex cryptographic computations and are initiated by other contracts.

For example, gas cost can be calculated simply like below, but some gas cost calculation functions are very complex. So I would not explain the exact gas cost calculation function here.

# ecrecover, sha256hash, ripemd160hash, dataCopy
Gas = XXXBaseGas + (number of words * XXXPerWordGas)

# validateSender
Gas = number of signatures * ValidateSenderGas

Address	Precompiled contracts	Item	Value
0x01	ecrecover	EcrecoverGas	3000
0x02	sha256hash	Sha256BaseGas, Sha256PerWordGas	60, 12
0x03	ripemd160hash	Ripemd160BaseGas, Ripemd160PerWordGas	600, 120
0x04	dataCopy	IdentityBaseGas, IdentityPerWordGas	15, 3
0x05	bigModExp	ModExpQuadCoeffDiv	20
0x06	bn256Add	Bn256AddGas	150
0x07	bn256ScalarMul	Bn256ScalarMulGas	6000
0x08	bn256Pairing	Bn256PairingBaseGas, Bn256PairingPerPointGas	45000, 34000
0x09	blake2f	-	-
0xFD	vmLog	VMLogBaseGas, VMLogPerByteGas	100, 20
0xFE	feePayer	FeePayerGas	300
0xFF	validateSender	ValidateSenderGas	5000

Gas calculation during contract execution

The gas cost of one transaction is calculated through the methods described below. First, gas is added according to the transaction type and input. Then, if the contract is executed, opcodes are executed one by one until the execution ends or STOP operation appears. In the process, the cost is charged according to the constantGas defined for each opcode and the additionally defined gas calculation method.

Here, I will briefly explain the gas calculation logic during contract execution using the fee schedule variables defined above. As this explanation assumes a general situation, the unusual situations such as revert appears is not considered.

• add constantGas defined in each opcode to gas

  • e.g. if an opcode is MUL, add G_low to gas

  • e.g. if an opcode is CREATE2, add G_create to gas

• add the gas which is calculated through additionally defined gas calculation method

  • For LOG'N', where N is [0,1,2,3,4], add G_log + memoryGasCost * g_logdata + N x G_logtopic to gas

  • For EXP, add G_exp + byteSize(stack.back(1)) x G_expbyte to gas

  • For CALLDATACOPY or CODECOPY or RETURNDATACOPY, add wordSize(stack.back(2)) x G_copy to gas

  • For EXTCODECOPY,

    • add wordSize(stack.back(3)) x G_copy to gas

    • [eip2929] If an address is not in AccessList, add it to accessList and add G_coldSloadCost - G_warmStorageReadCost to gas

  • For EXTCODESIZE or EXTCODEHASH or BALANCE,

    • [eip2929] If an address is not in AccessList, add it to accessList and add G_coldSloadCost - G_warmStorageReadCost to gas

  • For SHA3, add G_sha3 + wordSize(stack.back(1)) x G_sha3word to gas

  • For RETURN, REVERT, MLoad, MStore8, MStore, add memoryGasCost to gas

  • For CREATE, add memoryGasCost + size(contract.code) x G_codedeposit to gas

  • For CREATE2, add memoryGasCost + size(data) x G_sha3word + size(contract.code) x G_codedeposit to gas

  • For SSTORE,

    • [eip2929] If a slot(contractAddr, slot) is not in AccessList, add it to accessList and add G_coldSloadCost to gas

    • If it just reads the slot (no-op), add G_warmStorageReadCost to gas

    • If it creates a new slot, add G_sset to gas

    • If it deletes the slot, add G_sreset-G_coldSloadCost to gas and add R_sclear to refund

    • If it recreates the slot once exists before, add G_warmStorageReadCost to gas and subtract R_sclear from refund

    • If it deletes the slot once exists before, add R_sclear to refund

    • If it resets to the original inexistent slot, add G_warmStorageReadCost to gas and add G_sset - G_warmStorageReadCost to refund

    • IF it resets to the original existing slot, add G_warmStorageReadCost to gas and add G_sreset - G_coldSloadCost - G_warmStorageReadCost to refund

  • For SLOAD,

    • [eip2929] If a slot(contractAddr, slot) is not in AccessList, add it to accessList and add G_coldSloadCost to gas

    • [eip2929] If a slot(contractAddr, slot) is in AccessList, add G_warmStorageReadCost to gas

  • For CALL, CALLCODE, DELEGATECALL, STATICCALL,

    • [eip2929] If an address is not in AccessList, add it to accessList and add G_coldSloadCost to gas

    • if it is CALL and CALLCODE and if it transfers value, add G_callvalue to gas

    • if it is CALL and if it transfers value and if it is a new account, add G_newaccount to gas

    • if the callee contract is precompiled contracts, calculate precompiled contract gas cost and add it to gas

    • add memoryGasCost + availableGas - availableGas/64, where availableGas = contract.Gas - gas to gas

  • For SELFDESTRUCT,

    • [eip2929] If an address is not in AccessList, add it to accessList and add G_coldSloadCost to gas

    • if it transfers value and if is a new account, add G_newaccount to gas

Execution Environment

The execution environment consists of the system state S_system, the remaining gas for computation G_rem, and the information I that the execution agent provides. I is a tuple defined as shown below:

I := (B_header, T_code, T_depth, T_value, T_data, A_tx_sender, A_code_executor, A_code_owner, G_price, P_modify_state)

The execution model defines the function F_apply, which can compute the resultant state S_system', the remaining gas G_rem', the accrued substate A and the resultant output O_result when given these definitions. For the present context, we will define it as follows:

(S_system', G_rem', A, O_result) = F_apply(S_system, G_rem, I)

where we must remember that A, the accrued substate, is defined as the tuple of the suicides set Set_suicide, the log series L, the touched accounts Set_touched_accounts and the refunds G_refund:

A := (Set_suicide, L, Set_touched_accounts, G_refund)

Execution Overview

In most practical implementations, F_apply will be modeled as an iterative progression of the pair comprising the full system state S_system and the machine state S_machine. Formally, we define it recursively with a function X that 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 halted machine state, and H, which specifies the output data of an instruction if and only if the present state is a normal halted machine state.

The empty sequence, denoted as (), is not equal to the empty set, denoted as Set_empty; this is important when interpreting the output of H, which evaluates to Set_empty when execution is to continue but to a series (potentially empty) when execution should halt.

F_apply(S_machine, G_rem, I, T) := (S_system', S_machine,g', A, o)

• (S_system', S_machine,g', A, ..., o) := X((S_system, S_machine, A^0, I))

• S_machine,g := G_rem

• S_machine,pc := 0

• S_machine,memory := (0, 0, ...)

• S_machine,i := 0

• S_machine,stack := ()

• S_machine,o := ()

• X((S_system, S_machine, A, I)) :=

  • (Set_empty, S_machine, A^0, I, Set_empty) if Z(S_system, S_machine, I)

  • (Set_empty, S_machine', A^0, I, o) if w = REVERT

  • O(S_system, S_machine, A, I) · o if o != Set_empty

  • X(O(S_system, S_machine, A, I)) otherwise

where

• o := H(S_machine, I)

• (a, b, c, d) · e := (a, b, c, d, e)

• S_machine' := S_machine except

  S_machine,g' := S_machine,g - C(S_system, S_machine, I)

  • This means that when we evaluate F_apply, we

    extract the remaining gas S_machine,g' from the

    resultant machine state S_machine'.

X is thus cycled (recursively here, but implementations are generally expected to use a simple iterative loop) until either Z becomes true, indicating that the present state is exceptional and that the machine must be halted and any changes are discarded, or until H becomes a series (rather than the empty set), indicating that the machine has reached a controlled halt.

Machine State

The machine state S_machine is defined as a tuple (g, pc, memory, i, stack), which represent the available gas, the program counter pc (64-bit unsigned integer), the memory contents, the active number of words in memory (counting continuously from position 0), and the stack contents. The memory contents S_machine,memory are a series of zeroes of size 2^256.

For ease of reading, the instruction mnemonics written in small-caps (e.g., ADD) should be interpreted as their numeric equivalents; the full table of instructions and their specifics is given in the Instruction Set section.

To define Z, H and O, we define w as the current operation to be executed:

• w := T_code[S_machine,pc] if S_machine,pc < len(T_code)

• w :=STOP otherwise

Instruction Set

NOTE: This section will be filled in the future.

How KLVM Differs From EVM

As mentioned earlier, the current KLVM is based on EVM; thus, its specification currently is very similar to that of EVM. Some differences between KLVM and EVM are listed below.

• KLVM uses Klaytn's gas units, such as peb, ston, or KLAY.

• KLVM does not accept a gas price from the user; instead, it uses a platform-defined value as the gas price.

The Klaytn team will try to maintain compatibility between KLVM and EVM, but as Klaytn becomes increasingly implemented and evolves, the KLVM specification will be updated, and there will probably be more differences compared to EVM.

NOTE: This section will be updated in the future.