Bitwise shifting instructions in EVM

EIPS/eip-145.md

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+## Preamble
+
+    EIP: 145
+    Title: Bitwise shifting instructions in EVM
+    Author: Alex Beregszaszi, Paweł Bylica
+    Type: Standard Track
+    Category: Core
+    Status: Draft
+    Created: 2017-02-13
+
+
+## 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 arithmetics 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, `arg1` and `arg2`, and pushes on the stack the second popped value `arg2` shifted to the left by the number of bits in the first popped value `arg1`. 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, `arg1` and `arg2`, and pushes on the stack the second popped value `arg2` shifted to the right by the number of bits in the first popped value `arg1` 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, `arg1` and `arg2`, and pushes on the stack the second popped value `arg2` shifted to the right by the number of bits in the first popped value `arg1` 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
+
+TBA
+
+## Implementation
+
+Client support:
+- cpp-ethereum: https://github.com/ethereum/cpp-ethereum/pull/4054
+
+Compiler support:
+- Solidity/LLL: https://github.com/ethereum/solidity/pull/2541
+
+## Copyright
+
+Copyright and related rights waived via [CC0](https://creativecommons.org/publicdomain/zero/1.0/).