đ§ Stagnant Standards Track: Core

# EIP-6888: Math checking in EVM

### Check for math underflows overflows and division by zero at EVM level

Authors Renan Rodrigues de Souza (@RenanSouza2) 2023-04-16 https://ethereum-magicians.org/t/eip-math-checking/13846

## Abstract

This EIP adds many checks to EVM arithmetic and a new opcode to get the corresponding flags and clear them. The list of check includes underflows, overflows, division by zero.

## Motivation

The importance of math checks in smart contract projects is very clear. It was an OpenZeppelin library and then incorporated in Solidityâs default behavior. Bringing this to EVM level can combine both gas efficiency and safety.

## Specification

The key words âMUSTâ, âMUST NOTâ, âREQUIREDâ, âSHALLâ, âSHALL NOTâ, âSHOULDâ, âSHOULD NOTâ, âRECOMMENDEDâ, âNOT RECOMMENDEDâ, âMAYâ, and âOPTIONALâ in this document are to be interpreted as described in RFC 2119 and RFC 8174.

Starting from BLOCK_TIMESAMP >= HARDFORK_TIMESTAMP

### Constants

Constant Type Value
INT_MIN int -(2**255)
UINT_MAX uint 2 ** 256

### Flags

Variable Type Initial Value
carry bool false
overflow bool false

Two new flags are added to the EVM state: unsigned error (carry) and signed error (overflow). The scope of those flags are the same as the program counter. Each frame of execution has their own flags. At the frame creation they are unset and they are updated in call.

From this point forward a, b and c references the arguments in a math operation and res the output. c is only used if the operation takes 3 inputs.

The carry flag MUST be set in the following circumstances:

• When opcode is ADD (0x01) and res < a
• When opcode is MUL (0x02) and a != 0 â§ res / a != b
• When opcode is SUB (0x03) and b > a
• When opcode is DIV (0x04) or MOD (0x06); and b == 0
• When opcode is ADDMOD (0x08) and c == 0 â¨ ((a + b) / UINT_MAX > c)
• When opcode is MULMOD (0x08) and c == 0 â¨ ((a * b) / UINT_MAX > c)
• When opcode is EXP (0x0A) and ideal a ** b > UINT_MAX
• When opcode is SHL (0x1b) and res >> a != b

The overflow flag is MUST set in the following circumstances:

• When opcode is SUB (0x03) and a != 0 â§ sgn(a) != sgn(b) â§ sgn(b) == sgn(res)
• When opcode is ADD (0x01) and a != 0 â§ sgn(a) == sgn(b) â§ sgn(a) != sgn(res)
• When opcode is MUL (0x02) and (a == -1 â§ b == INT_MIN) â¨ (a == INT_MIN â§ b == -1) â¨ (a != 0 â§ (res / a != b)) (this / represents SDIV)
• When opcode is SDIV (0x05) or SMOD (0x06); and b == 0 â¨ (a == INT_MIN â§ b == -1)
• When opcode is SHL (0x1b) and res >> a != b (this >> represents SAR)

The function sgn(num) returns the sign of the number, it can be negative, zero or positive.

Value Mnemonic Î´ Îą Description
JUMPC 0x5B 1 0 Conditionally alter the program counter.
Â  Â  Â  Â  J_JUMPC = carry ? Âľ_s[0] : Âľ_pc + 1
Â  Â  Â  Â  carry = overflow = false
JUMPO 0x5C 1 0 Conditionally alter the program counter.
Â  Â  Â  Â  J_JUMPO = ovewrflow ? Âľ_s[0] : Âľ_pc + 1
Â  Â  Â  Â  carry = overflow = false

### gas

The gas cost for both instructions is G_high, the same as JUMPI.

## Rationale

EVM uses twoâs complement for negative numbers. The opcodes listed above triggers one or two flags depending if they are used for signed and unsigned numbers.

The conditions described for each opcode is made with implementation friendliness in mind. The only exception is EXP as it is hard to give a concise test as most of the others relied on the inverse operation and there is no native LOG. Most EXP implementations will internally use MUL so the flag carry can be drawn from that instruction, not the overflow.

The divisions by UINT_MAX used in the ADDMOD and MULMOD is another way to represent the higher 256 bits of the internal 512 number representation.

Both flags are cleaned at the same time because the instructions are expected to be used when transitioning between codes where numbers are treated as signed or unsigned.

## Backwards Compatibility

This EIP introduces a new opcode and changes int EVM behavior.

TBD

TBD

## Security Considerations

This is a new EVM behavior but each code will decide how to interact with it.

Copyright and related rights waived via CC0.