LT (0x10) - Voltaire

This page is a placeholder. All examples on this page are currently AI-generated and are not correct. This documentation will be completed in the future with accurate, tested examples.

Overview

Opcode: 0x10 Introduced: Frontier (EVM genesis) LT performs unsigned less than comparison on two 256-bit integers. Returns 1 if the first value is strictly less than the second, 0 otherwise. All values are treated as unsigned integers in the range 0 to 2^256 - 1. This is the fundamental comparison operation for implementing conditional logic and bounds checking in smart contracts.

Specification

Stack Input:

a (top)
b

Stack Output:

a < b ? 1 : 0

Gas Cost: 3 (GasFastestStep) Operation:

result = (a < b) ? 1 : 0

Behavior

LT pops two values from the stack, compares them as unsigned 256-bit integers, and pushes 1 if a < b, otherwise 0:

If a < b: Result is 1 (true)
If a >= b: Result is 0 (false)

All comparisons are unsigned. Values with bit 255 set are treated as large positive numbers, not negative values.

Examples

Basic Comparison

import { lt } from '@tevm/voltaire/evm/comparison';
import { createFrame } from '@tevm/voltaire/evm/Frame';

// 5 < 10 = 1 (true)
const frame = createFrame({ stack: [5n, 10n] });
const err = lt(frame);

console.log(frame.stack); // [1n]
console.log(frame.gasRemaining); // Original - 3

Equal Values

// 20 < 20 = 0 (false)
const frame = createFrame({ stack: [20n, 20n] });
const err = lt(frame);

console.log(frame.stack); // [0n]

Greater Value

// 30 < 20 = 0 (false)
const frame = createFrame({ stack: [30n, 20n] });
const err = lt(frame);

console.log(frame.stack); // [0n]

Zero Comparison

// 0 < 1 = 1 (true)
const frame = createFrame({ stack: [0n, 1n] });
lt(frame);
console.log(frame.stack); // [1n]

// 1 < 0 = 0 (false)
const frame2 = createFrame({ stack: [1n, 0n] });
lt(frame2);
console.log(frame2.stack); // [0n]

Maximum Values

// (2^256 - 2) < (2^256 - 1) = 1 (true)
const MAX = (1n << 256n) - 1n;
const frame = createFrame({ stack: [MAX - 1n, MAX] });
lt(frame);

console.log(frame.stack); // [1n]

Unsigned Treatment

// 2^255 is treated as large positive (not negative)
const SIGN_BIT = 1n << 255n;

// 1 < 2^255 = 1 (true, unsigned comparison)
const frame = createFrame({ stack: [1n, SIGN_BIT] });
lt(frame);

console.log(frame.stack); // [1n]
// In signed comparison (SLT), this would be 0 because 2^255 = -2^255 (negative)

Gas Cost

Cost: 3 gas (GasFastestStep) LT shares the lowest gas tier with other comparison and basic operations:

LT, GT, SLT, SGT, EQ (comparisons)
ISZERO, NOT
ADD, SUB

Comparison:

LT/GT/EQ: 3 gas
MUL/DIV: 5 gas
ADDMOD: 8 gas

Edge Cases

Boundary Values

const MAX = (1n << 256n) - 1n;

// 0 < MAX = 1
lt(createFrame({ stack: [0n, MAX] }));  // [1n]

// MAX < 0 = 0
lt(createFrame({ stack: [MAX, 0n] }));  // [0n]

// MAX < MAX = 0
lt(createFrame({ stack: [MAX, MAX] }));  // [0n]

Sign Bit Set

// Values with bit 255 set are large positive (unsigned)
const SIGN_BIT = 1n << 255n;  // 2^255

// SIGN_BIT is treated as 2^255, not -2^255
// 2^255 < 1 = 0 (false, unsigned)
lt(createFrame({ stack: [SIGN_BIT, 1n] }));  // [0n]

// Compare with SLT (signed):
// SLT would return 1 because 2^255 = -2^255 < 1 (signed)

Stack Underflow

// Not enough stack items
const frame = createFrame({ stack: [5n] });
const err = lt(frame);

console.log(err); // { type: "StackUnderflow" }
console.log(frame.stack); // [5n] (unchanged)

Out of Gas

// Insufficient gas
const frame = createFrame({ stack: [5n, 10n], gasRemaining: 2n });
const err = lt(frame);

console.log(err); // { type: "OutOfGas" }
console.log(frame.gasRemaining); // 0n

Large Values

// Arbitrary precision supported
const a = 123456789012345678901234567890n;
const b = 987654321098765432109876543210n;

const frame = createFrame({ stack: [a, b] });
lt(frame);

console.log(frame.stack); // [1n] (a < b)

Common Usage

Bounds Checking

// require(index < length)
assembly {
    if iszero(lt(index, length)) {
        revert(0, 0)
    }
}

Range Validation

// Check if value < max
assembly {
    let valid := lt(value, max)
    if iszero(valid) {
        revert(0, 0)
    }
}

Loop Conditions

// for (uint i = 0; i < n; i++)
assembly {
    let i := 0
    for {} lt(i, n) { i := add(i, 1) } {
        // Loop body
    }
}

Minimum Value

// min(a, b)
assembly {
    let minimum := a
    if lt(b, a) {
        minimum := b
    }
}

Array Access Safety

// Safe array access
assembly {
    if lt(index, arrLength) {
        let value := sload(add(arrSlot, index))
        // Use value
    }
}

Implementation

TypeScript

/**
 * LT opcode (0x10) - Less than comparison (unsigned)
 */
export function handle(frame: FrameType): EvmError | null {
  // Consume gas (GasFastestStep = 3)
  const gasErr = consumeGas(frame, FastestStep);
  if (gasErr) return gasErr;

  // Pop operands (b is top, a is second)
  const bResult = popStack(frame);
  if (bResult.error) return bResult.error;
  const b = bResult.value;

  const aResult = popStack(frame);
  if (aResult.error) return aResult.error;
  const a = aResult.value;

  // Compare: a < b (unsigned)
  const result = a < b ? 1n : 0n;

  // Push result
  const pushErr = pushStack(frame, result);
  if (pushErr) return pushErr;

  // Increment PC
  frame.pc += 1;
  return null;
}

Testing

Test Coverage

import { describe, it, expect } from 'vitest';
import { handle as LT } from './0x10_LT.js';

describe('LT (0x10)', () => {
  it('returns 1 when a < b', () => {
    const frame = createFrame([10n, 20n]);
    expect(LT(frame)).toBeNull();
    expect(frame.stack).toEqual([1n]);
    expect(frame.pc).toBe(1);
    expect(frame.gasRemaining).toBe(997n);
  });

  it('returns 0 when a >= b (equal)', () => {
    const frame = createFrame([20n, 20n]);
    expect(LT(frame)).toBeNull();
    expect(frame.stack).toEqual([0n]);
  });

  it('returns 0 when a > b', () => {
    const frame = createFrame([30n, 20n]);
    expect(LT(frame)).toBeNull();
    expect(frame.stack).toEqual([0n]);
  });

  it('handles 0 < 1', () => {
    const frame = createFrame([0n, 1n]);
    expect(LT(frame)).toBeNull();
    expect(frame.stack).toEqual([1n]);
  });

  it('handles max uint256 values', () => {
    const MAX = (1n << 256n) - 1n;
    const frame = createFrame([MAX - 1n, MAX]);
    expect(LT(frame)).toBeNull();
    expect(frame.stack).toEqual([1n]);
  });

  it('treats all values as unsigned', () => {
    // 2^255 is large positive as unsigned
    const SIGN_BIT = 1n << 255n;
    const frame = createFrame([1n, SIGN_BIT]);
    expect(LT(frame)).toBeNull();
    expect(frame.stack).toEqual([1n]); // 1 < 2^255
  });

  it('returns StackUnderflow with insufficient stack', () => {
    const frame = createFrame([10n]);
    expect(LT(frame)).toEqual({ type: 'StackUnderflow' });
  });

  it('returns OutOfGas when insufficient gas', () => {
    const frame = createFrame([10n, 20n], 2n);
    expect(LT(frame)).toEqual({ type: 'OutOfGas' });
  });

  it('preserves stack below compared values', () => {
    const frame = createFrame([100n, 200n, 10n, 20n]);
    expect(LT(frame)).toBeNull();
    expect(frame.stack).toEqual([100n, 200n, 1n]);
  });
});

Edge Cases Tested

Basic comparisons (a < b, a = b, a > b)
Zero comparisons (0 < 1, 1 < 0)
Maximum values (MAX-1 < MAX)
Unsigned treatment (sign bit set)
Stack underflow (< 2 items)
Out of gas (< 3 gas)
Large arbitrary values
Stack preservation

Security

Unsigned vs Signed Confusion

CRITICAL: LT treats all values as unsigned. Do not use for signed integer comparisons:

// VULNERABLE: Using LT for signed values
function withdraw(int256 amount) {
    // LT treats -1 as 2^256-1 (huge positive!)
    assembly {
        if lt(balance, amount) {  // WRONG!
            revert(0, 0)
        }
    }
    // Negative amounts bypass the check
}

// CORRECT: Use SLT for signed comparisons
function withdraw(int256 amount) {
    assembly {
        if slt(balance, amount) {  // Correct
            revert(0, 0)
        }
    }
}

Off-by-One Errors

// VULNERABLE: Wrong boundary
require(index <= array.length);  // Allows out-of-bounds!

// CORRECT: Strict less than
require(index < array.length);  // Max valid: length - 1

Integer Overflow Before Comparison

// VULNERABLE: Overflow corrupts comparison
uint256 sum = a + b;  // May wrap to small value
require(sum > a);     // Check may incorrectly pass

// CORRECT: Check before operation
require(a <= type(uint256).max - b);
uint256 sum = a + b;

Type Width Issues

// VULNERABLE: Comparing different widths
uint256 large = type(uint256).max;
uint128 small = type(uint128).max;

// Implicit cast may truncate
require(large < small);  // Type confusion

// CORRECT: Explicit same-width comparison
require(uint256(large) < uint256(small));

Optimizations

Inversion Patterns

// These are equivalent:
// a < b  ===  !(a >= b)

assembly {
    // Direct
    let less := lt(a, b)

    // Inverted (sometimes useful in complex conditions)
    let less := iszero(or(gt(a, b), eq(a, b)))
}

Short-Circuit Evaluation

// Evaluate cheapest condition first
assembly {
    if lt(index, length) {
        // Only check expensive condition if first passes
        if expensiveCheck() {
            // Execute
        }
    }
}

Constant Comparison

// Compiler may optimize constant comparisons
assembly {
    if lt(value, 100) {  // Constant 100
        // Optimized by EVM implementations
    }
}

Benchmarks

LT is one of the fastest EVM operations: Execution time (relative):

LT: 1.0x (baseline)
GT/EQ: 1.0x
ISZERO: 0.95x
ADD: 1.0x
MUL: 1.5x

Gas efficiency:

3 gas per comparison
~333,333 comparisons per million gas
Highly optimized in all EVM implementations

References

Yellow Paper - Section 9.1 (Comparison Operations)
EVM Codes - LT
Solidity Docs - Comparison Operators

GT - Greater than (unsigned)
SLT - Signed less than
SGT - Signed greater than
EQ - Equality check
ISZERO - Zero check

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Developer Documentation

Generated API (TypeDoc)

​Overview

​Specification

​Behavior

​Examples

​Basic Comparison

​Equal Values

​Greater Value

​Zero Comparison

​Maximum Values

​Unsigned Treatment

​Gas Cost

​Edge Cases

​Boundary Values

​Sign Bit Set

​Stack Underflow

​Out of Gas

​Large Values

​Common Usage

​Bounds Checking

​Range Validation

​Loop Conditions

​Minimum Value

​Array Access Safety

​Implementation

​Testing

​Test Coverage

​Edge Cases Tested

​Security

​Unsigned vs Signed Confusion

​Off-by-One Errors

​Integer Overflow Before Comparison

​Type Width Issues

​Optimizations

​Inversion Patterns

​Short-Circuit Evaluation

​Constant Comparison

​Benchmarks

​References

​Related Documentation

Overview

Specification

Behavior

Examples

Basic Comparison

Equal Values

Greater Value

Zero Comparison

Maximum Values

Unsigned Treatment

Gas Cost

Edge Cases

Boundary Values

Sign Bit Set

Stack Underflow

Out of Gas

Large Values

Common Usage

Bounds Checking

Range Validation

Loop Conditions

Minimum Value

Array Access Safety

Implementation

Testing

Test Coverage

Edge Cases Tested

Security

Unsigned vs Signed Confusion

Off-by-One Errors

Integer Overflow Before Comparison

Type Width Issues

Optimizations

Inversion Patterns

Short-Circuit Evaluation

Constant Comparison

Benchmarks

References

Related Documentation