Klaytn Virtual Machine

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.

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, all three are prerequisite to operation execution. The first and most common is the 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. For other tables such as Precompiled contracts and accounts, please refer to this document

Name	Value	Description
G_zero	0	Nothing paid for operations of the set W_zero
G_base	2	Amount of gas paid for operations of the set W_base
G_verylow	3	Amount of gas paid for operations of the set W_verylow
G_low	5	Amount of gas paid for operations of the set W_low
G_mid	8	Amount of gas paid for operations of the set W_mid
G_high	10	Amount of gas paid for operations of the set W_high
G_blockhash	20	Payment for a BLOCKHASH operation
G_extcode	700	Amount of gas paid for operations of the set W_extcode
G_balance	400	Amount of gas paid for a BALANCE operation
G_sload	200	Amount of gas paid for an SLOAD operation
G_jumpdest	1	Amount of gas paid for a JUMPDEST operation
G_sset	20000	Amount of gas paid for an SSTORE operation when the storage value is set to nonzero from zero
G_sreset	5000	Amount of gas paid for an SSTORE operation when the storage value remains unchanged at zero or is set to zero
R_sclear	15000	Refund given (added to the refund counter) when the storage value is set to zero from nonzero
R_selfdestruct	24000	Refund given (added to the refund counter) for self-destructing an account
G_selfdestruct	5000	Amount of gas paid for a SELFDESTRUCT operation
G_create	32000	Amount of gas paid for a CREATE operation
G_codedeposit	200	Amount of gas paid per byte for a CREATE operation that succeeds in placing code into state
G_call	700	Amount of gas paid for a CALL operation
G_callvalue	9000	Amount of gas paid for a nonzero value transfer as part of a CALL operation
G_callstipend	2300	A stipend for the called contract subtracted from G_callvalue for a nonzero value transfer
G_newaccount	25000	Amount of gas paid for a CALL or SELFDESTRUCT operation that creates an account
G_exp	10	Partial payment for an EXP operation
G_expbyte	50	Partial payment when multiplied by ceil(log_256(exponent)) for an EXP operation
G_memory	3	Amount of gas paid for every additional word when expanding memory
G_txcreate	32000	Amount of gas paid by all contract-creating transactions
G_txdatazero	4	Amount of gas paid for every zero byte of data or code for a transaction
G_txdatanonzero	68	Amount of gas paid for every nonzero byte of data or code for a transaction
G_transaction	21000	Amount of gas paid for every transaction
G_log	375	Partial payment for a LOG operation
G_logdata	8	Amount of gas paid for each byte in a LOG operation's data
G_logtopic	375	Amount of gas paid for each topic of a LOG operation
G_sha3	30	Amount of gas paid for each SHA3 operation
G_sha3word	6	Amount of gas paid for each word (rounded up) for input data to a SHA3 operation
G_copy	3	Partial payment for COPY operations, multiplied by words copied, rounded up
G_extcodehash	400	Paid for getting keccak256 hash of a contract's code
G_create2	32000	Paid for opcode CREATE2 which bahaves identically with CREATE but use different arguments

We define the following subsets of instructions:

• W_zero = {STOP, RETURN, REVERT}

• W_base = {ADDRESS, ORIGIN, CALLER, CALLVALUE, CALLDATASIZE, CODESIZE, GASPRICE, COINBASE, TIMESTAMP, NUMBER, DIFFICULTY, GASLIMIT, RETURNDATASIZE, POP, PC, MSIZE, GAS}

• W_verylow = {ADD, SUB, LT, GT, SLT, SGT, EQ, ISZERO, AND, OR, XOR, NOT, BYTE, CALLDATALOAD, MLOAD, MSTORE, MSTORE8, PUSH, DUP, SWAP}

• W_low = {MUL, DIV, SDIV, MOD, SMOD, SIGNEXTEND}

• W_mid = {ADDMOD, MULMOD, JUMP}

• W_high = {JUMPI}

• W_extcode = {EXTCODESIZE}

Gas Cost

The general gas cost function, C, is defined as follows:

C(S_system, S_machine, I) := C_mem(S_machine,i') - C_mem(S_machine, i) +

• C_SSTORE(S_system, S_machine), if w == SSTORE

• G_exp, if (w == EXP) && (S_machine[1] == 0)

• G_exp + G_expbyte x (1 + floor(log_256(S_machine,sp[1]))),

  if (w == EXP) && (S_machine,sp[1] > 0)

• G_verylow + G_copy x ceil(S_machine,sp[2] / 32),

  if w == CALLDATACOPY || CODECOPY || RETURNDATACOPY

• G_extcode + G_copy x ceil(S_machine,sp[3] / 32),

  if w == EXTCODECOPY

• G_log + G_logdata x S_machine,sp[1],

  if w == LOG0

• G_log + G_logdata x S_machine,sp[1] + G_logtopic,

  if w == LOG1

• G_log + G_logdata x S_machine,sp[1] + 2 x G_logtopic,

  if w == LOG2

• G_log + G_logdata x S_machine,sp[1] + 3 x G_logtopic,

  if w == LOG3

• G_log + G_logdata x S_machine,sp[1] + 4 x G_logtopic,

  if w == LOG4

• C_CALL(S_system, S_machine),

  if w == CALL || CALLCODE || DELEGATECALL

• C_SELFDESTRUCT(S_system, S_machine),

  if w == SELFDESTRUCT

• G_create, if w == CREATE

• G_sha3 + G_sha3word x ceil(s[1] / 32),

  if w == SHA3

• G_jumpdest, if w == JUMPDEST

• G_sload, if w == SLOAD

• G_zero, if w in W_zero

• G_base, if w in W_base

• G_verylow, if w in W_verylow

• G_low, if w in W_low

• G_mid, if w in W_mid

• G__high</sub>, if w in W_high

• G_extcode, if w in W_extcode

• G_balance, if w == BALANCE

• G_blockhash, if w == BLOCKHASH

• where w is

  • T_code[S_machine,pc],

    if S_machine,pc < length(T_code)

  • STOP, otherwise

• where C_mem(a) := G_memory x a + floor(a^2 / 512)

with C_CALL, C_SELFDESTRUCT and C_SSTORE which will be described in the future.

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.