Bitwise shifting instructions in EVM

Abstract

Native bitwise shifting instructions are introduced, which are more efficient processing wise on the host and are cheaper to use by a contract.

Motivation

EVM is lacking bitwise shifting operators, but supports other logical and arithmetic operators. Shift operations can be implemented via arithmetic operators, but that has a higher cost and requires more processing time from the host. Implementing SHL and SHR using arithmetic cost each 35 gas, while the proposed instructions take 3 gas.

Specification

The following instructions are introduced:

0x1b: SHL (shift left)

The SHL instruction (shift left) pops 2 values from the stack, first arg1 and then arg2, and pushes on the stack arg2 shifted to the left by arg1 number of bits. The result is equal to

(arg2 * 2^arg1) mod 2^256

Notes:

• The value (arg2) is interpreted as an unsigned number.
• The shift amount (arg1) is interpreted as an unsigned number.
• If the shift amount (arg1) is greater or equal 256 the result is 0.
• This is equivalent to PUSH1 2 EXP MUL.

0x1c: SHR (logical shift right)

The SHR instruction (logical shift right) pops 2 values from the stack, first arg1 and then arg2, and pushes on the stack arg2 shifted to the right by arg1 number of bits with zero fill. The result is equal to

floor(arg2 / 2^arg1)

Notes:

• The value (arg2) is interpreted as an unsigned number.
• The shift amount (arg1) is interpreted as an unsigned number.
• If the shift amount (arg1) is greater or equal 256 the result is 0.
• This is equivalent to PUSH1 2 EXP DIV.

0x1d: SAR (arithmetic shift right)

The SAR instruction (arithmetic shift right) pops 2 values from the stack, first arg1 and then arg2, and pushes on the stack arg2 shifted to the right by arg1 number of bits with sign extension. The result is equal to

floor(arg2 / 2^arg1)

Notes:

• The value (arg2) is interpreted as a signed number.
• The shift amount (arg1) is interpreted as an unsigned number.
• If the shift amount (arg1) is greater or equal 256 the result is 0 if arg2 is non-negative or -1 if arg2 is negative.
• This is not equivalent to PUSH1 2 EXP SDIV, since it rounds differently. See SDIV(-1, 2) == 0, while SAR(-1, 1) == -1.

The cost of the shift instructions is set at verylow tier (3 gas).

Rationale

Instruction operands were chosen to fit the more natural use case of shifting a value already on the stack. This means the operand order is swapped compared to most arithmetic instructions.

Backwards Compatibility

The newly introduced instructions have no effect on bytecode created in the past.

Test Cases

SHL (shift left)

1. PUSH 0x0000000000000000000000000000000000000000000000000000000000000001 PUSH 0x00 SHL --- 0x0000000000000000000000000000000000000000000000000000000000000001
2. PUSH 0x0000000000000000000000000000000000000000000000000000000000000001 PUSH 0x01 SHL --- 0x0000000000000000000000000000000000000000000000000000000000000002
3. PUSH 0x0000000000000000000000000000000000000000000000000000000000000001 PUSH 0xff SHL --- 0x8000000000000000000000000000000000000000000000000000000000000000
4. PUSH 0x0000000000000000000000000000000000000000000000000000000000000001 PUSH 0x0100 SHL --- 0x0000000000000000000000000000000000000000000000000000000000000000
5. PUSH 0x0000000000000000000000000000000000000000000000000000000000000001 PUSH 0x0101 SHL --- 0x0000000000000000000000000000000000000000000000000000000000000000
6. PUSH 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0x00 SHL --- 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
7. PUSH 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0x01 SHL --- 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe
8. PUSH 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0xff SHL --- 0x8000000000000000000000000000000000000000000000000000000000000000
9. PUSH 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0x0100 SHL --- 0x0000000000000000000000000000000000000000000000000000000000000000
10. PUSH 0x0000000000000000000000000000000000000000000000000000000000000000 PUSH 0x01 SHL --- 0x0000000000000000000000000000000000000000000000000000000000000000
11. PUSH 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0x01 SHL --- 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe

SHR (logical shift right)

1. PUSH 0x0000000000000000000000000000000000000000000000000000000000000001 PUSH 0x00 SHR --- 0x0000000000000000000000000000000000000000000000000000000000000001
2. PUSH 0x0000000000000000000000000000000000000000000000000000000000000001 PUSH 0x01 SHR --- 0x0000000000000000000000000000000000000000000000000000000000000000
3. PUSH 0x8000000000000000000000000000000000000000000000000000000000000000 PUSH 0x01 SHR --- 0x4000000000000000000000000000000000000000000000000000000000000000
4. PUSH 0x8000000000000000000000000000000000000000000000000000000000000000 PUSH 0xff SHR --- 0x0000000000000000000000000000000000000000000000000000000000000001
5. PUSH 0x8000000000000000000000000000000000000000000000000000000000000000 PUSH 0x0100 SHR --- 0x0000000000000000000000000000000000000000000000000000000000000000
6. PUSH 0x8000000000000000000000000000000000000000000000000000000000000000 PUSH 0x0101 SHR --- 0x0000000000000000000000000000000000000000000000000000000000000000
7. PUSH 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0x00 SHR --- 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
8. PUSH 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0x01 SHR --- 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
9. PUSH 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0xff SHR --- 0x0000000000000000000000000000000000000000000000000000000000000001
10. PUSH 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0x0100 SHR --- 0x0000000000000000000000000000000000000000000000000000000000000000
11. PUSH 0x0000000000000000000000000000000000000000000000000000000000000000 PUSH 0x01 SHR --- 0x0000000000000000000000000000000000000000000000000000000000000000

SAR (arithmetic shift right)

1. PUSH 0x0000000000000000000000000000000000000000000000000000000000000001 PUSH 0x00 SAR --- 0x0000000000000000000000000000000000000000000000000000000000000001
2. PUSH 0x0000000000000000000000000000000000000000000000000000000000000001 PUSH 0x01 SAR --- 0x0000000000000000000000000000000000000000000000000000000000000000
3. PUSH 0x8000000000000000000000000000000000000000000000000000000000000000 PUSH 0x01 SAR --- 0xc000000000000000000000000000000000000000000000000000000000000000
4. PUSH 0x8000000000000000000000000000000000000000000000000000000000000000 PUSH 0xff SAR --- 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
5. PUSH 0x8000000000000000000000000000000000000000000000000000000000000000 PUSH 0x0100 SAR --- 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
6. PUSH 0x8000000000000000000000000000000000000000000000000000000000000000 PUSH 0x0101 SAR --- 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
7. PUSH 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0x00 SAR --- 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
8. PUSH 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0x01 SAR --- 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
9. PUSH 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0xff SAR --- 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
10. PUSH 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0x0100 SAR --- 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
11. PUSH 0x0000000000000000000000000000000000000000000000000000000000000000 PUSH 0x01 SAR --- 0x0000000000000000000000000000000000000000000000000000000000000000
12. PUSH 0x4000000000000000000000000000000000000000000000000000000000000000 PUSH 0xfe SAR --- 0x0000000000000000000000000000000000000000000000000000000000000001
13. PUSH 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0xf8 SAR --- 0x000000000000000000000000000000000000000000000000000000000000007f
14. PUSH 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0xfe SAR --- 0x0000000000000000000000000000000000000000000000000000000000000001
15. PUSH 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0xff SAR --- 0x0000000000000000000000000000000000000000000000000000000000000000
16. PUSH 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0x0100 SAR --- 0x0000000000000000000000000000000000000000000000000000000000000000

Implementation

Client support:

• cpp-ethereum: https://github.com/ethereum/cpp-ethereum/pull/4054

Compiler support:

• Solidity/LLL: https://github.com/ethereum/solidity/pull/2541

Tests

Sources:

• https://github.com/ethereum/tests/tree/develop/src/GeneralStateTestsFiller/stShift

Filled Tests:

• https://github.com/ethereum/tests/tree/develop/GeneralStateTests/stShift
• https://github.com/ethereum/tests/tree/develop/BlockchainTests/GeneralStateTests/stShift

Copyright

Copyright and related rights waived via CC0.