Optimize muldiv

[0xVolosnikov]

This pull request contains two small changes to the mulDiv function to slightly optimize gas.

Reduce stack operations in mulDiv

The product of x and y to obtain the least significant bits of the result is moved above, to the place where the variable prod0 is declared.

https://github.com/vladyan18/openzeppelin-contracts/blob/e54956d8453f04f59491511df8d353dbaab98202/contracts/utils/math/Math.sol#L127

uint256 prod0 = x * y; // Least significant 256 bits of the product
uint256 prod1; // Most significant 256 bits of the product
assembly {
  let mm := mulmod(x, y, not(0))
  prod1 := sub(sub(mm, prod0), lt(mm, prod0))
}

Rationale: with compiler optimization enabled, the old implementation led to unnecessary initialization of the variable by zero. As a result, this initialization also added unnecessary stack operations below in the code. Since this code is in an unchecked block, calculating the product in assembly does not provide gas savings by itself.

Gas tests, small inputs. Optimizer 200 runs, 0.8.20
Gas before: 198
Gas after: 190 (-4%)

Simplify twos calculation in mulDiv

An easier method was used to factor powers of two out of denominator due to which the number of necessary operations is reduced by one.

https://github.com/vladyan18/openzeppelin-contracts/blob/e54956d8453f04f59491511df8d353dbaab98202/contracts/utils/math/Math.sol#L165

uint256 twos = denominator & (0 - denominator);

Rationale: the previous implementation uses a unary negation operation and ends up needing more operations to get the same result. The proposed line gives the same result inside an unchecked block with fewer operations.

Gas tests, big inputs. Optimizer 200 runs, 0.8.20
Gas before: 497
Gas after: 494 (-0.6%)

PR Checklist

• Tests
• Documentation
• Changeset entry (run npx changeset add)

Probably new tests and documentation are not required for this pull request.

[changeset-bot]

🦋 Changeset detected

Latest commit: 9a86e03

The changes in this PR will be included in the next version bump.

This PR includes changesets to release 1 package

Name	Type
openzeppelin-solidity	Patch

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[Amxx]

That is indeed a good solution !

[Amxx]

For the record, before solidity v8, the code used to be uint256 twos = -denominator & denominator; but solidity 0.8 forbid the -x syntax for unsigned integers. Doing (0-x) indeed fixes it.

[Amxx]

These are great findings !

[ernestognw]

Thanks!

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