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----
-eip: 5000
-title: MULDIV instruction
-description: Introduce a new instruction to perform x * y / z in 512-bit precision
-author: Harikrishnan Mulackal (@hrkrshnn), Alex Beregszaszi (@axic), Paweł Bylica (@chfast)
-discussions-to: https://ethereum-magicians.org/t/muldiv-instruction/9930
-status: Draft
-type: Standards Track
-category: Core
-created: 2022-03-14
----
-
-## Abstract
-
-Introduce a new instruction, `MULDIV(x, y, z)`, to perform `((x * y) / z) % 2**256` in 512-bit precision. `z = 0` is a special case for `(x * y) % 2**256`.
-
-## Motivation
-
-Fixed point operations in high level languages are very commonly used on Ethereum, especially in the domain of financial applications.
-
-While fixed point addition and subtraction can be done with merely `add` and `sub` respectively, being able to efficiently do fixedpoint multiplication and division is a very sought after feature. A commonly used workaround relies on a `mulmod`-based, rather complex implementation (taking around 50 instructions, excluding stack manipulation). This instruction reduces that to a single opcode.
-
-A secondary use case is likely in cryptographic applications, where the `muldiv` instruction allows full precision 256x256->512 multiplication. `mul(x y)` (or `muldiv(x, y, 1)`) computes the lower order 256 bits and `muldiv(x, y, 0)` computes the higher order 256 bits.
-
-Finally we aimed to provide an instruction which can be efficiently used both in *checked* and *unchecked arithmetic* use cases. By *checked* we mean to abort on conditions including division-by-zero and wrapping behaviour.
-
-## Specification
-
-A new instruction is introduced: `MULDIV` (`0x1e`).
-
-- Pops 3 values from the stack, first `x`, then `y` and `z`.
-- If `z == 0`, `r = (uint512(x) * y) / 2**256`.
-- Otherwise `r = (uint512(x) * y / z) % 2**256`, where the intermediate calculation is performed with 512-bit precision.
-- Pushes `r` on the stack.
-
-```python
-# operations `*` and `//` are done in 512 bit precision
-def muldiv(x, y, z):
-    if z == 0:
-        return (x * y) // (2**256)
-    else:
-        return ((x * y) // z) % (2**256)
-```
-The cost of the instruction is 8 gas (aka `mid`), the same as for `addmod` and `mulmod`.
-
-## Rationale
-
-### The special 0 case
-
-All the arithmetic instructions in EVM handle division or modulo 0 specially: the instructions return 0. We have decided to break consistency in order to provide a flexible opcode, which can be used to detect wrapping behaviour.
-
-Alternate options include:
-- Returning a flag for wrapping
-- Returning two stack items, higher and lower order bits
-- Compute the higher order 256 bits in EVM:
-```solidity
-/// Returns `hi` such that `x × y = hi × 2**256 + mul(x, y)`
-function hob(uint x, uint y) returns (uint hi) {
-    uint uint_max = type(uint).max;
-    assembly {
-        let lo := mul(x, y)
-        let mm := mulmod(x, y, uint_max)
-        hi := sub(sub(mm, lo), lt(mm, lo))
-    }
-}
-```
-
-While this feature is clever and useful, callers must be aware that unlike other EVM instructions, passing 0 will have a vastly different behaviour.
-
-### Argument ordering
-
-The order of arguments matches `addmod` and `mulmod`.
-
-## Backwards Compatibility
-
-This is a new instruction not present pior.
-
-## Test Cases
-
-```
-PUSH 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
-PUSH 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
-PUSH 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
-MULDIV
----
-0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
-```
-
-
-```
-PUSH 0x0000000000000000000000000000000000000000000000000000000000000000
-PUSH 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
-PUSH 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
-MULDIV
----
-0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe
-```
-
-```
-PUSH 0x0000000000000000000000000000000000000000000000000de0b6b3a7640000
-PUSH 0x000000000000000000000000000000000000000000000000016345785d8a0000
-PUSH 0x00000000000000000000000000000000000000000000d3c21bcecceda1000000
-MULDIV
----
-0x00000000000000000000000000000000000000000000152d02c7e14af6800000
-```
-
-## Security Considerations
-
-TBA
-
-## Copyright
-
-Copyright and related rights waived via [CC0](https://creativecommons.org/publicdomain/zero/1.0/).