SGT (0x13) - Voltaire

Overview

Opcode: 0x13 Introduced: Frontier (EVM genesis) SGT performs signed greater than comparison on two 256-bit integers interpreted as two’s complement signed values. Returns 1 if the first value is strictly greater than the second, 0 otherwise. Values are in the range -2^255 to 2^255 - 1. This operation complements SLT for implementing signed conditional logic and range checks.

Specification

Stack Input:

a (top)
b

Stack Output:

signed(a) > signed(b) ? 1 : 0

Gas Cost: 3 (GasFastestStep) Operation:

// Interpret as signed two's complement
signed_a = a >= 2^255 ? a - 2^256 : a
signed_b = b >= 2^255 ? b - 2^256 : b
result = (signed_a > signed_b) ? 1 : 0

Behavior

SGT pops two values from the stack, interprets them as signed 256-bit two’s complement integers, compares them, and pushes 1 if signed(a) > signed(b), otherwise 0:

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

Two’s complement interpretation:

Bit 255 = 0: Positive (0 to 2^255 - 1)
Bit 255 = 1: Negative (-2^255 to -1)

Examples

Positive Values

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

// 20 > 10 = 1 (both positive)
const frame = createFrame({ stack: [20n, 10n] });
const err = sgt(frame);

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

Positive Greater Than Negative

// 10 > -1 = 1 (true)
const NEG_1 = (1n << 256n) - 1n;  // Two's complement -1
const frame = createFrame({ stack: [10n, NEG_1] });
sgt(frame);

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

Negative Less Than Positive

// -1 > 10 = 0 (false, -1 < 10)
const NEG_1 = (1n << 256n) - 1n;
const frame = createFrame({ stack: [NEG_1, 10n] });
sgt(frame);

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

Negative Value Comparison

// -5 > -10 = 1 (true)
const NEG_5 = (1n << 256n) - 5n;
const NEG_10 = (1n << 256n) - 10n;
const frame = createFrame({ stack: [NEG_5, NEG_10] });
sgt(frame);

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

Zero Boundary

// 0 > -1 = 1 (true)
const NEG_1 = (1n << 256n) - 1n;
const frame = createFrame({ stack: [0n, NEG_1] });
sgt(frame);

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

// 1 > 0 = 1 (true)
const frame2 = createFrame({ stack: [1n, 0n] });
sgt(frame2);
console.log(frame2.stack); // [1n]

Minimum and Maximum

// MAX_INT256 > MIN_INT256 = 1
const MIN_INT256 = 1n << 255n;  // -2^255
const MAX_INT256 = (1n << 255n) - 1n;  // 2^255 - 1
const frame = createFrame({ stack: [MAX_INT256, MIN_INT256] });
sgt(frame);

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

Contrast with Unsigned GT

// 2^255 has bit 255 set
const SIGN_BIT = 1n << 255n;

// SGT: -2^255 > 1 = 0 (false, signed)
const frame1 = createFrame({ stack: [SIGN_BIT, 1n] });
sgt(frame1);
console.log(frame1.stack); // [0n]

// GT: 2^255 > 1 = 1 (true, unsigned - 2^255 is huge positive)
const frame2 = createFrame({ stack: [SIGN_BIT, 1n] });
gt(frame2);
console.log(frame2.stack); // [1n]

Gas Cost

Cost: 3 gas (GasFastestStep) SGT shares the lowest gas tier with all comparison operations:

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

Comparison:

SGT/SLT/GT/LT: 3 gas
MUL/DIV: 5 gas
SDIV/SMOD: 5 gas

Edge Cases

Signed Boundary Values

const MIN_INT256 = 1n << 255n;  // -2^255
const MAX_INT256 = (1n << 255n) - 1n;  // 2^255 - 1
const NEG_1 = (1n << 256n) - 1n;  // -1

// MAX > MIN
sgt(createFrame({ stack: [MAX_INT256, MIN_INT256] }));  // [1n]

// MIN < MAX
sgt(createFrame({ stack: [MIN_INT256, MAX_INT256] }));  // [0n]

// 0 > -1
sgt(createFrame({ stack: [0n, NEG_1] }));  // [1n]

// -1 < 0
sgt(createFrame({ stack: [NEG_1, 0n] }));  // [0n]

Equal Values

// Any value compared to itself
const NEG_10 = (1n << 256n) - 10n;

sgt(createFrame({ stack: [20n, 20n] }));  // [0n]
sgt(createFrame({ stack: [NEG_10, NEG_10] }));  // [0n]
sgt(createFrame({ stack: [0n, 0n] }));  // [0n]

Sign Bit Boundary

// Just below sign bit (largest positive)
const MAX_POS = (1n << 255n) - 1n;

// Just at sign bit (smallest negative)
const MIN_NEG = 1n << 255n;

// Unsigned: MIN_NEG > MAX_POS
gt(createFrame({ stack: [MIN_NEG, MAX_POS] }));  // [1n]

// Signed: MIN_NEG < MAX_POS
sgt(createFrame({ stack: [MIN_NEG, MAX_POS] }));  // [0n]

Stack Underflow

// Not enough stack items
const frame = createFrame({ stack: [10n] });
const err = sgt(frame);

console.log(err); // { type: "StackUnderflow" }
console.log(frame.stack); // [10n] (unchanged)

Out of Gas

// Insufficient gas
const frame = createFrame({ stack: [20n, 10n], gasRemaining: 2n });
const err = sgt(frame);

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

Common Usage

Positive Value Check

// Check if value is positive (> 0)
assembly {
    let isPositive := sgt(value, 0)
    if iszero(isPositive) {
        revert(0, 0)
    }
}

Signed Upper Bounds

// require(signedValue <= max)  ===  require(!(signedValue > max))
assembly {
    if sgt(signedValue, max) {
        revert(0, 0)
    }
}

Maximum of Signed Values

// max(a, b) for signed integers
assembly {
    let maximum := a
    if sgt(b, a) {
        maximum := b
    }
}

Signed Range Validation

// Check if value in signed range (min, max)
assembly {
    let inRange := and(
        sgt(value, min),      // value > min
        iszero(sgt(value, max))  // value <= max
    )
}

Non-Negative Check

// require(value >= 0)  ===  require(!(value < 0))
assembly {
    if slt(value, 0) {
        revert(0, 0)
    }
}
// Equivalent:
assembly {
    if iszero(or(sgt(value, 0), iszero(value))) {
        revert(0, 0)
    }
}

Implementation

TypeScript

/**
 * SGT opcode (0x13) - Signed greater than comparison
 */
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;

  // Convert to signed and compare
  const aSigned = toSigned256(a);
  const bSigned = toSigned256(b);
  const result = aSigned > bSigned ? 1n : 0n;

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

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

/**
 * Convert unsigned 256-bit to signed two's complement
 */
function toSigned256(value: bigint): bigint {
  const MAX_INT256 = 1n << 255n;
  if (value >= MAX_INT256) {
    return value - (1n << 256n);
  }
  return value;
}

Testing

Test Coverage

import { describe, it, expect } from 'vitest';
import { handle as SGT } from './0x13_SGT.js';

describe('SGT (0x13)', () => {
  it('returns 1 when a > b (both positive)', () => {
    const frame = createFrame([30n, 20n]);
    expect(SGT(frame)).toBeNull();
    expect(frame.stack).toEqual([1n]);
    expect(frame.gasRemaining).toBe(997n);
  });

  it('returns 1 when positive > negative', () => {
    const NEG_1 = (1n << 256n) - 1n;
    const frame = createFrame([10n, NEG_1]);
    expect(SGT(frame)).toBeNull();
    expect(frame.stack).toEqual([1n]); // 10 > -1
  });

  it('returns 0 when negative < positive', () => {
    const NEG_1 = (1n << 256n) - 1n;
    const frame = createFrame([NEG_1, 10n]);
    expect(SGT(frame)).toBeNull();
    expect(frame.stack).toEqual([0n]); // -1 < 10
  });

  it('compares negative numbers correctly', () => {
    const NEG_5 = (1n << 256n) - 5n;
    const NEG_10 = (1n << 256n) - 10n;
    const frame = createFrame([NEG_5, NEG_10]);
    expect(SGT(frame)).toBeNull();
    expect(frame.stack).toEqual([1n]); // -5 > -10
  });

  it('handles 0 > -1', () => {
    const NEG_1 = (1n << 256n) - 1n;
    const frame = createFrame([0n, NEG_1]);
    expect(SGT(frame)).toBeNull();
    expect(frame.stack).toEqual([1n]);
  });

  it('handles MAX_INT256 > MIN_INT256', () => {
    const MIN = 1n << 255n;
    const MAX = (1n << 255n) - 1n;
    const frame = createFrame([MAX, MIN]);
    expect(SGT(frame)).toBeNull();
    expect(frame.stack).toEqual([1n]);
  });

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

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

  it('preserves stack below compared values', () => {
    const frame = createFrame([100n, 200n, 30n, 20n]);
    expect(SGT(frame)).toBeNull();
    expect(frame.stack).toEqual([100n, 200n, 1n]);
  });
});

Edge Cases Tested

Positive value comparisons
Positive greater than negative
Negative less than positive
Negative value comparisons (-5 > -10)
Zero boundary (0 > -1, 1 > 0)
MAX_INT256 and MIN_INT256
Equal values
Stack underflow
Out of gas
Stack preservation

Security

Critical: Signed vs Unsigned Confusion

COMMON VULNERABILITY: Using GT instead of SGT for signed values:

// VULNERABLE: Using GT for signed comparison
function isPositive(int256 value) returns (bool) {
    // GT treats -1 as 2^256-1 (huge positive!)
    assembly {
        return(0, gt(value, 0))  // WRONG!
    }
    // Returns true for negative values!
}

// CORRECT: Use SGT for signed values
function isPositive(int256 value) returns (bool) {
    assembly {
        return(0, sgt(value, 0))  // Correct
    }
}

Type Safety Issues

// VULNERABLE: Mixed signed/unsigned
function checkLimit(uint256 unsigned, int256 signed) {
    // Direct comparison uses unsigned semantics
    require(unsigned > signed);  // Type confusion!
}

// CORRECT: Explicit type handling
function checkLimit(uint256 unsigned, int256 signed) {
    require(signed >= 0, "negative value");
    require(unsigned > uint256(signed));
}

Overflow in Signed Operations

// VULNERABLE: Overflow before comparison
int256 result = a - b;  // May overflow
require(result > 0);    // Check may be wrong

// CORRECT: Check before operation
if (a > 0 && b < 0) {
    require(a <= type(int256).max + b, "overflow");
}
int256 result = a - b;

Sign Extension Errors

// VULNERABLE: Wrong sign extension
function extend(int8 small) returns (int256) {
    // Casting through uint loses sign
    return int256(uint256(uint8(small)));  // Wrong!
}

// CORRECT: Direct sign extension
function extend(int8 small) returns (int256) {
    return int256(small);  // Preserves sign
}

Optimizations

Relationship to SLT

// These are equivalent:
// a > b  ===  b < a

assembly {
    let greater := sgt(a, b)
    // Same as:
    let greater := slt(b, a)
}

// Choose based on stack layout to minimize swaps

Positive Check Optimization

// Check if value > 0
assembly {
    let isPos := sgt(value, 0)  // 3 gas
}

// Equivalent but more expensive:
assembly {
    let notNeg := iszero(slt(value, 0))  // 6 gas
    let notZero := iszero(iszero(value)) // 6 gas
    let isPos := and(notNeg, notZero)    // 9 gas total
}

Inversion Pattern

// Direct comparison (preferred)
assembly {
    let greater := sgt(a, b)  // 3 gas
}

// Inverted (avoid - more expensive)
assembly {
    let greater := iszero(or(slt(a, b), eq(a, b)))  // 12 gas
}

Benchmarks

SGT performance matches other comparison operations: Execution time (relative):

SGT: 1.05x (slightly slower due to sign conversion)
SLT: 1.05x
GT/LT/EQ: 1.0x
ISZERO: 0.95x

Gas efficiency:

3 gas per signed comparison
~333,333 comparisons per million gas
Sign conversion adds negligible overhead

References

Yellow Paper - Section 9.1 (Comparison Operations)
EVM Codes - SGT
Two’s Complement - Wikipedia
Solidity Docs - Integer Types

SLT - Signed less than
GT - Unsigned greater than
LT - Unsigned less than
SDIV - Signed division
SMOD - Signed modulo

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Developer Documentation

Generated API (TypeDoc)

​Overview

​Specification

​Behavior

​Examples

​Positive Values

​Positive Greater Than Negative

​Negative Less Than Positive

​Negative Value Comparison

​Zero Boundary

​Minimum and Maximum

​Contrast with Unsigned GT

​Gas Cost

​Edge Cases

​Signed Boundary Values

​Equal Values

​Sign Bit Boundary

​Stack Underflow

​Out of Gas

​Common Usage

​Positive Value Check

​Signed Upper Bounds

​Maximum of Signed Values

​Signed Range Validation

​Non-Negative Check

​Implementation

​Testing

​Test Coverage

​Edge Cases Tested

​Security

​Critical: Signed vs Unsigned Confusion

​Type Safety Issues

​Overflow in Signed Operations

​Sign Extension Errors

​Optimizations

​Relationship to SLT

​Positive Check Optimization

​Inversion Pattern

​Benchmarks

​References

​Related Documentation

Overview

Specification

Behavior

Examples

Positive Values

Positive Greater Than Negative

Negative Less Than Positive

Negative Value Comparison

Zero Boundary

Minimum and Maximum

Contrast with Unsigned GT

Gas Cost

Edge Cases

Signed Boundary Values

Equal Values

Sign Bit Boundary

Stack Underflow

Out of Gas

Common Usage

Positive Value Check

Signed Upper Bounds

Maximum of Signed Values

Signed Range Validation

Non-Negative Check

Implementation

Testing

Test Coverage

Edge Cases Tested

Security

Critical: Signed vs Unsigned Confusion

Type Safety Issues

Overflow in Signed Operations

Sign Extension Errors

Optimizations

Relationship to SLT

Positive Check Optimization

Inversion Pattern

Benchmarks

References

Related Documentation