Bitwise operations

The bitwise operations AND, XOR and OR are available using the bitwise() module from the Cairo common library.

• bitwise_and(x, y), the result of bitwise AND operation on x and y.
• bitwise_xor(x, y), the result of bitwise XOR operation on x and y.
• bitwise_or(x, y), the result of bitwise OR operation on x and y.

All three operations may also be obtained with the bitwise_operations(x, y) function.

%builtins bitwise

from starkware.cairo.common.cairo_builtins import BitwiseBuiltin
from starkware.cairo.common.bitwise import (bitwise_operations,
bitwise_and, bitwise_xor, bitwise_or)


func main{bitwise_ptr: BitwiseBuiltin*}() -> ():
    # Define two binary numbers, a and b,
    # using powers of 2 representation.

    # Binary: a = 1100.
    let a = 1 * 2**3 + 1 * 2**2 + 0 * 2**1 + 0 * 2**0
    assert a = 1 * 8 + 1 * 4 + 0 * 2 + 0 * 1
    assert a = 12  # Decimal representation.

    # Binary: b = 1010.
    let b = 1 * 2**3 + 0 * 2**2 + 1 * 2**1 + 0 * 2**0
    assert b = 1 * 8 + 0 * 4 + 1 * 2 + 0 * 1
    assert b = 10  # Decimal representation.

    # 1100 AND 1010 = 1000.
    let (a_and_b) = bitwise_and(a, b)
    assert a_and_b = 1 * 2**3 + 0 * 2**2 + 0 * 2**1 + 0 * 2**0

    # 1100 XOR 1010 = 0110.
    let (a_xor_b) = bitwise_xor(a, b)
    assert a_xor_b = 0 * 2**3 + 1 * 2**2 + 1 * 2**1 + 0 * 2**0

    # 1100 OR 1010 = 1110.
    let (a_or_b) = bitwise_or(a, b)
    assert a_or_b = 1 * 2**3 + 1 * 2**2 + 1 * 2**1 + 0 * 2**0

    # User defined values x and y. Returns all three operations.
    let (and, xor, or) = bitwise_operations(a, b)
    # Check that they match the result above.
    assert and = a_and_b
    assert xor = a_xor_b
    assert or = a_or_b

    # Bitwise operations must be less than 251-bit.
    # let (c) = bitwise_or(2**251, 2**3)  # Fails.
    let (c) = bitwise_or(2**250, 2**3)
    assert c = 2**250 + 2**3

    return ()
end

Save as program.cairo

Compile and run

Note that the bitwise builtin requires the all layout.

cairo-compile program.cairo --output=compiled_program.json

cairo-run --program=compiled_program.json \
    --program_input=input.json --print_output --layout=all

---

StarkNet

Cairo programs may use bitwise operations and below is a preview of how an equivalent StarkNet contract would look once they are enabled.

%lang starknet
%builtins bitwise

from starkware.cairo.common.cairo_builtins import BitwiseBuiltin
from starkware.cairo.common.bitwise import (bitwise_operations,
bitwise_and, bitwise_xor, bitwise_or)

@view
func check_bitwise{bitwise_ptr: BitwiseBuiltin*}() -> ():
    # Define two binary numbers, a and b,
    # using powers of 2 representation.

    # Binary: a = 1100.
    let a = 1 * 2**3 + 1 * 2**2 + 0 * 2**1 + 0 * 2**0
    assert a = 1 * 8 + 1 * 4 + 0 * 2 + 0 * 1
    assert a = 12  # Decimal representation.

    # Binary: b = 1010.
    let b = 1 * 2**3 + 0 * 2**2 + 1 * 2**1 + 0 * 2**0
    assert b = 1 * 8 + 0 * 4 + 1 * 2 + 0 * 1
    assert b = 10  # Decimal representation.

    # 1100 AND 1010 = 1000.
    let (a_and_b) = bitwise_and(a, b)
    assert a_and_b = 1 * 2**3 + 0 * 2**2 + 0 * 2**1 + 0 * 2**0

    # 1100 XOR 1010 = 0110.
    let (a_xor_b) = bitwise_xor(a, b)
    assert a_xor_b = 0 * 2**3 + 1 * 2**2 + 1 * 2**1 + 0 * 2**0

    # 1100 OR 1010 = 1110.
    let (a_or_b) = bitwise_or(a, b)
    assert a_or_b = 1 * 2**3 + 1 * 2**2 + 1 * 2**1 + 0 * 2**0

    # User defined values x and y. Returns all three operations.
    let (and, xor, or) = bitwise_operations(a, b)
    # Check that they match the result above.
    assert and = a_and_b
    assert xor = a_xor_b
    assert or = a_or_b

    # Bitwise operations must be less than 251-bit.
    # let (c) = bitwise_or(2**251, 2**3)  # Fails.
    let (c) = bitwise_or(2**250, 2**3)
    assert c = 2**250 + 2**3

    return ()
end

Save as bitwise.cairo. Compilation will be enabled in the future.