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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.
Symbol
Description
BC
Blockchain
B
Block
B_header
The block header of the present block
Symbol
Description
S
State
S_system
System state
S_machine
Machine state
P_modify_state
The permission to make state modifications
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)
Symbol
Description
G
Gas
G_rem
Remaining gas for computation
G_price
The price of gas in the transaction that originated the execution
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.
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