ISZERO (0x15) - Voltaire

Overview

Opcode: 0x15 Introduced: Frontier (EVM genesis) ISZERO checks if a 256-bit value is zero. Returns 1 if the value is zero, 0 otherwise. This is the most efficient way to check for zero values and implements boolean NOT when used with boolean (0/1) values. ISZERO is a specialized form of EQ optimized for the common case of checking equality to zero.

Specification

Stack Input:

a (top)

Stack Output:

a == 0 ? 1 : 0

Gas Cost: 3 (GasFastestStep) Operation:

result = (a == 0) ? 1 : 0

Behavior

ISZERO pops one value from the stack and pushes 1 if it is zero, otherwise 0:

If a == 0: Result is 1 (true)
If a != 0: Result is 0 (false)

This operation is functionally equivalent to EQ(a, 0) but uses only one stack item.

Examples

Zero Check

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

// 0 is zero = 1 (true)
const frame = createFrame({ stack: [0n] });
const err = iszero(frame);

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

Non-Zero Check

// 42 is not zero = 0 (false)
const frame = createFrame({ stack: [42n] });
const err = iszero(frame);

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

Boolean NOT

// ISZERO implements boolean NOT for 0/1 values
// NOT 1 = 0
const frame1 = createFrame({ stack: [1n] });
iszero(frame1);
console.log(frame1.stack); // [0n]

// NOT 0 = 1
const frame2 = createFrame({ stack: [0n] });
iszero(frame2);
console.log(frame2.stack); // [1n]

Large Value Check

// Any non-zero value returns 0
const MAX = (1n << 256n) - 1n;
const frame = createFrame({ stack: [MAX] });
iszero(frame);

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

Small Non-Zero

// 1 is not zero
const frame = createFrame({ stack: [1n] });
iszero(frame);

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

Gas Cost

Cost: 3 gas (GasFastestStep) ISZERO shares the lowest gas tier with other comparison operations:

ISZERO, EQ, LT, GT, SLT, SGT
NOT
ADD, SUB

Comparison:

ISZERO: 3 gas
EQ: 3 gas (ISZERO is equivalent to EQ(x, 0))
LT/GT: 3 gas

Edge Cases

Zero Value

// Only returns 1 for exactly zero
iszero(createFrame({ stack: [0n] }));  // [1n]

Non-Zero Values

// All non-zero values return 0
iszero(createFrame({ stack: [1n] }));  // [0n]
iszero(createFrame({ stack: [42n] }));  // [0n]

const MAX = (1n << 256n) - 1n;
iszero(createFrame({ stack: [MAX] }));  // [0n]

Boolean Values

// ISZERO(1) = 0 (NOT true = false)
iszero(createFrame({ stack: [1n] }));  // [0n]

// ISZERO(0) = 1 (NOT false = true)
iszero(createFrame({ stack: [0n] }));  // [1n]

Stack Underflow

// Empty stack
const frame = createFrame({ stack: [] });
const err = iszero(frame);

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

Out of Gas

// Insufficient gas
const frame = createFrame({ stack: [0n], gasRemaining: 2n });
const err = iszero(frame);

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

Common Usage

Boolean NOT

// Invert boolean condition
assembly {
    let condition := lt(a, b)
    let notCondition := iszero(condition)

    if notCondition {
        // Execute if a >= b
    }
}

Zero Address Check

// require(addr != address(0))
assembly {
    if iszero(addr) {
        revert(0, 0)
    }
}

Non-Zero Validation

// require(value != 0)
assembly {
    if iszero(value) {
        revert(0, 0)
    }
}

Bounds Checking with Inversion

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

// Equivalent to: if (index >= length) revert

Conditional Logic

// if (balance == 0)
assembly {
    if iszero(balance) {
        // Handle zero balance
    }
}

Boolean Coercion

// Convert any non-zero value to boolean true (1)
assembly {
    let bool := iszero(iszero(value))
    // Double ISZERO: 0 -> 1 -> 0, non-zero -> 0 -> 1
}

Implementation

TypeScript

/**
 * ISZERO opcode (0x15) - Check if value is zero
 */
export function handle(frame: FrameType): EvmError | null {
  // Consume gas (GasFastestStep = 3)
  const gasErr = consumeGas(frame, FastestStep);
  if (gasErr) return gasErr;

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

  // Check if zero
  const result = a === 0n ? 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 ISZERO } from './0x15_ISZERO.js';

describe('ISZERO (0x15)', () => {
  it('returns 1 when value is zero', () => {
    const frame = createFrame([0n]);
    expect(ISZERO(frame)).toBeNull();
    expect(frame.stack).toEqual([1n]);
    expect(frame.pc).toBe(1);
    expect(frame.gasRemaining).toBe(997n);
  });

  it('returns 0 when value is non-zero', () => {
    const frame = createFrame([42n]);
    expect(ISZERO(frame)).toBeNull();
    expect(frame.stack).toEqual([0n]);
  });

  it('returns 0 for 1', () => {
    const frame = createFrame([1n]);
    expect(ISZERO(frame)).toBeNull();
    expect(frame.stack).toEqual([0n]);
  });

  it('returns 0 for max uint256', () => {
    const MAX = (1n << 256n) - 1n;
    const frame = createFrame([MAX]);
    expect(ISZERO(frame)).toBeNull();
    expect(frame.stack).toEqual([0n]);
  });

  it('implements boolean NOT', () => {
    // NOT true (1) = false (0)
    const frame1 = createFrame([1n]);
    expect(ISZERO(frame1)).toBeNull();
    expect(frame1.stack).toEqual([0n]);

    // NOT false (0) = true (1)
    const frame2 = createFrame([0n]);
    expect(ISZERO(frame2)).toBeNull();
    expect(frame2.stack).toEqual([1n]);
  });

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

  it('returns OutOfGas when insufficient gas', () => {
    const frame = createFrame([0n], 2n);
    expect(ISZERO(frame)).toEqual({ type: 'OutOfGas' });
  });

  it('preserves stack below checked value', () => {
    const frame = createFrame([100n, 200n, 0n]);
    expect(ISZERO(frame)).toBeNull();
    expect(frame.stack).toEqual([100n, 200n, 1n]);
  });
});

Edge Cases Tested

Zero value (0 -> 1)
Non-zero values (42 -> 0, 1 -> 0)
Maximum value (MAX -> 0)
Boolean NOT behavior
Stack underflow (empty stack)
Out of gas (< 3 gas)
Stack preservation

Security

Zero Address Validation

CRITICAL: Always check for zero address in transfers and approvals:

// VULNERABLE: Missing zero address check
function transfer(address to, uint256 amount) {
    balances[to] += amount;  // Can burn tokens to 0x0
}

// CORRECT: Explicit zero check
function transfer(address to, uint256 amount) {
    require(to != address(0), "zero address");
    balances[to] += amount;
}

// Assembly version
assembly {
    if iszero(to) {
        revert(0, 0)
    }
}

Division by Zero Prevention

// VULNERABLE: Division by zero returns 0 in EVM (no error)
function calculateShare(uint256 total, uint256 shares) returns (uint256) {
    return total / shares;  // Returns 0 if shares == 0
}

// CORRECT: Explicit validation
function calculateShare(uint256 total, uint256 shares) returns (uint256) {
    require(shares != 0, "zero shares");
    return total / shares;
}

// Assembly version
assembly {
    if iszero(shares) {
        revert(0, 0)
    }
}

Non-Zero Requirement

// VULNERABLE: Accepting zero amounts
function deposit(uint256 amount) {
    balances[msg.sender] += amount;  // Allows 0, wasting gas
}

// CORRECT: Require non-zero
function deposit(uint256 amount) {
    require(amount != 0, "zero amount");
    balances[msg.sender] += amount;
}

// Assembly version
assembly {
    if iszero(amount) {
        revert(0, 0)
    }
}

Boolean Logic Errors

// VULNERABLE: Incorrect negation
function isInvalid(bool valid) returns (bool) {
    // Wrong: assumes valid is 0/1, but bool could be any non-zero
    return !valid;
}

// CORRECT: Explicit boolean handling
function isInvalid(bool valid) returns (bool) {
    return !valid;  // Solidity handles bool correctly
}

// Assembly: coerce to proper boolean first
assembly {
    let validBool := iszero(iszero(valid))  // Coerce to 0/1
    let invalid := iszero(validBool)
}

Optimizations

Boolean NOT

// ISZERO is the cheapest boolean NOT
assembly {
    let notValue := iszero(value)  // 3 gas
}

// More expensive alternatives:
assembly {
    // Using EQ (same gas, but less clear)
    let notValue := eq(value, 0)  // 3 gas

    // Using XOR (more expensive)
    let notValue := xor(value, 1)  // 3 gas (only works for 0/1)
}

Double Negation (Boolean Coercion)

// Convert any value to strict boolean (0 or 1)
assembly {
    let bool := iszero(iszero(value))  // 6 gas
    // 0 -> 1 -> 0
    // non-zero -> 0 -> 1
}

// Useful for ensuring boolean semantics

Zero Check vs EQ

// Checking if value is zero
assembly {
    let isZero := iszero(value)  // 3 gas, clearer intent
}

// Equivalent but less idiomatic:
assembly {
    let isZero := eq(value, 0)  // 3 gas, same cost
}

// Prefer ISZERO for zero checks (better readability)

Inverted Conditions

// Instead of: if (a < b) revert
// More efficient: if (!(a < b)) continue
assembly {
    if iszero(lt(a, b)) {
        // a >= b, continue
    }
}

// Saves a jump in some cases

Benchmarks

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

ISZERO: 0.95x (slightly faster than EQ)
EQ: 1.0x
LT/GT: 1.0x
ADD: 1.0x
MUL: 1.5x

Gas efficiency:

3 gas per zero check
~333,333 checks per million gas
Highly optimized (single comparison to zero)

Usage patterns:

Zero checks: 3 gas
Boolean NOT: 3 gas
Boolean coercion (double ISZERO): 6 gas

References

Yellow Paper - Section 9.1 (Comparison Operations)
EVM Codes - ISZERO
Solidity Docs - Boolean Operations

EQ - Equality check (ISZERO is specialized EQ)
NOT - Bitwise NOT (different from boolean NOT)
LT - Less than (often used with ISZERO for >=)
GT - Greater than (often used with ISZERO for ≤)

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Generated API (TypeDoc)

​Overview

​Specification

​Behavior

​Examples

​Zero Check

​Non-Zero Check

​Boolean NOT

​Large Value Check

​Small Non-Zero

​Gas Cost

​Edge Cases

​Zero Value

​Non-Zero Values

​Boolean Values

​Stack Underflow

​Out of Gas

​Common Usage

​Boolean NOT

​Zero Address Check

​Non-Zero Validation

​Bounds Checking with Inversion

​Conditional Logic

​Boolean Coercion

​Implementation

​Testing

​Test Coverage

​Edge Cases Tested

​Security

​Zero Address Validation

​Division by Zero Prevention

​Non-Zero Requirement

​Boolean Logic Errors

​Optimizations

​Boolean NOT

​Double Negation (Boolean Coercion)

​Zero Check vs EQ

​Inverted Conditions

​Benchmarks

​References

​Related Documentation

Overview

Specification

Behavior

Examples

Zero Check

Non-Zero Check

Boolean NOT

Large Value Check

Small Non-Zero

Gas Cost

Edge Cases

Zero Value

Non-Zero Values

Boolean Values

Stack Underflow

Out of Gas

Common Usage

Boolean NOT

Zero Address Check

Non-Zero Validation

Bounds Checking with Inversion

Conditional Logic

Boolean Coercion

Implementation

Testing

Test Coverage

Edge Cases Tested

Security

Zero Address Validation

Division by Zero Prevention

Non-Zero Requirement

Boolean Logic Errors

Optimizations

Boolean NOT

Double Negation (Boolean Coercion)

Zero Check vs EQ

Inverted Conditions

Benchmarks

References

Related Documentation