Bitwise shifting instructions in EVM
EIP-145 is a proposal for introducing native bitwise shifting instructions in the Ethereum Virtual Machine (EVM). The EVM currently lacks bitwise shifting operators, which are commonly used in programming languages for efficient manipulation of binary data. While shift operations can be implemented using arithmetic operators, this approach is more costly and requires more processing time from the host.
The proposal introduces three new instructions: SHL (shift left), SHR (logical shift right), and SAR (arithmetic shift right). The SHL instruction pops two values from the stack, the first being the number of bits to shift and the second being the value to shift. It then pushes the result of the shift operation onto the stack. The SHR instruction works similarly, but shifts the bits to the right with zero fill. The SAR instruction shifts the bits to the right with sign extension, meaning that the most significant bit is replicated to preserve the sign of the value.
The introduction of these instructions is motivated by the need for more efficient processing of bitwise operations in the EVM. Implementing shift operations using arithmetic operators currently costs 35 gas, while the proposed instructions only cost 3 gas. This makes them more cost-effective for contracts that require frequent bitwise operations.
The proposal also includes test cases and implementation details for the new instructions. It is important to note that the instructions are designed to be backwards compatible with existing contracts, meaning that contracts written before the introduction of the instructions will still function properly.
Overall, the EIP-145 proposal aims to improve the efficiency and cost-effectiveness of bitwise operations in the EVM by introducing native bitwise shifting instructions.
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Original
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 ifarg2is non-negative or -1 ifarg2is negative. - This is not equivalent to
PUSH1 2 EXP SDIV, since it rounds differently. SeeSDIV(-1, 2) == 0, whileSAR(-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)
-
PUSH 0x0000000000000000000000000000000000000000000000000000000000000001 PUSH 0x00 SHL --- 0x0000000000000000000000000000000000000000000000000000000000000001 -
PUSH 0x0000000000000000000000000000000000000000000000000000000000000001 PUSH 0x01 SHL --- 0x0000000000000000000000000000000000000000000000000000000000000002 -
PUSH 0x0000000000000000000000000000000000000000000000000000000000000001 PUSH 0xff SHL --- 0x8000000000000000000000000000000000000000000000000000000000000000 -
PUSH 0x0000000000000000000000000000000000000000000000000000000000000001 PUSH 0x0100 SHL --- 0x0000000000000000000000000000000000000000000000000000000000000000 -
PUSH 0x0000000000000000000000000000000000000000000000000000000000000001 PUSH 0x0101 SHL --- 0x0000000000000000000000000000000000000000000000000000000000000000 -
PUSH 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0x00 SHL --- 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff -
PUSH 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0x01 SHL --- 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe -
PUSH 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0xff SHL --- 0x8000000000000000000000000000000000000000000000000000000000000000 -
PUSH 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0x0100 SHL --- 0x0000000000000000000000000000000000000000000000000000000000000000 -
PUSH 0x0000000000000000000000000000000000000000000000000000000000000000 PUSH 0x01 SHL --- 0x0000000000000000000000000000000000000000000000000000000000000000 -
PUSH 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0x01 SHL --- 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe
SHR (logical shift right)
-
PUSH 0x0000000000000000000000000000000000000000000000000000000000000001 PUSH 0x00 SHR --- 0x0000000000000000000000000000000000000000000000000000000000000001 -
PUSH 0x0000000000000000000000000000000000000000000000000000000000000001 PUSH 0x01 SHR --- 0x0000000000000000000000000000000000000000000000000000000000000000 -
PUSH 0x8000000000000000000000000000000000000000000000000000000000000000 PUSH 0x01 SHR --- 0x4000000000000000000000000000000000000000000000000000000000000000 -
PUSH 0x8000000000000000000000000000000000000000000000000000000000000000 PUSH 0xff SHR --- 0x0000000000000000000000000000000000000000000000000000000000000001 -
PUSH 0x8000000000000000000000000000000000000000000000000000000000000000 PUSH 0x0100 SHR --- 0x0000000000000000000000000000000000000000000000000000000000000000 -
PUSH 0x8000000000000000000000000000000000000000000000000000000000000000 PUSH 0x0101 SHR --- 0x0000000000000000000000000000000000000000000000000000000000000000 -
PUSH 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0x00 SHR --- 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff -
PUSH 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0x01 SHR --- 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff -
PUSH 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0xff SHR --- 0x0000000000000000000000000000000000000000000000000000000000000001 -
PUSH 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0x0100 SHR --- 0x0000000000000000000000000000000000000000000000000000000000000000 -
PUSH 0x0000000000000000000000000000000000000000000000000000000000000000 PUSH 0x01 SHR --- 0x0000000000000000000000000000000000000000000000000000000000000000
SAR (arithmetic shift right)
-
PUSH 0x0000000000000000000000000000000000000000000000000000000000000001 PUSH 0x00 SAR --- 0x0000000000000000000000000000000000000000000000000000000000000001 -
PUSH 0x0000000000000000000000000000000000000000000000000000000000000001 PUSH 0x01 SAR --- 0x0000000000000000000000000000000000000000000000000000000000000000 -
PUSH 0x8000000000000000000000000000000000000000000000000000000000000000 PUSH 0x01 SAR --- 0xc000000000000000000000000000000000000000000000000000000000000000 -
PUSH 0x8000000000000000000000000000000000000000000000000000000000000000 PUSH 0xff SAR --- 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff -
PUSH 0x8000000000000000000000000000000000000000000000000000000000000000 PUSH 0x0100 SAR --- 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff -
PUSH 0x8000000000000000000000000000000000000000000000000000000000000000 PUSH 0x0101 SAR --- 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff -
PUSH 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0x00 SAR --- 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff -
PUSH 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0x01 SAR --- 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff -
PUSH 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0xff SAR --- 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff -
PUSH 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0x0100 SAR --- 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff -
PUSH 0x0000000000000000000000000000000000000000000000000000000000000000 PUSH 0x01 SAR --- 0x0000000000000000000000000000000000000000000000000000000000000000 -
PUSH 0x4000000000000000000000000000000000000000000000000000000000000000 PUSH 0xfe SAR --- 0x0000000000000000000000000000000000000000000000000000000000000001 -
PUSH 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0xf8 SAR --- 0x000000000000000000000000000000000000000000000000000000000000007f -
PUSH 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0xfe SAR --- 0x0000000000000000000000000000000000000000000000000000000000000001 -
PUSH 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff PUSH 0xff SAR --- 0x0000000000000000000000000000000000000000000000000000000000000000 -
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:
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.
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