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EIP-145

Bitwise shifting instructions in EVM

FinalStandards Track: Core
Created: 2017-02-13
Alex Beregszaszi (@axic), Paweł Bylica (@chfast)
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1 min read

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

Simple Summary

To provide native bitwise shifting with cost on par with other arithmetic operations.

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 insturctions.

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:

Compiler support:

Tests

Sources:

Filled Tests:

Copyright and related rights waived via CC0.

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