# Multiplication after division in StableEarnerRateModel leads to loss of precision Low/Info · Three Sigma · Stablecoin framework · 8th January, 2024 Finding 3S-M^0-L01 of the M^0 Minter Gateway security review. - Protocol: https://www.m0.org/ - Report: /reports/m-0 - Codebase: https://github.com/0xsimao/ttg/tree/a8127901fa1f24a2e821cf4d9854a1aa6ac8088c - Source: https://cdn.sanity.io/files/qoqld077/production/1cdafafad874aba76e062ad8c216c98338c096db.pdf --- ### Description In the [StableEarnerRateModel.getSafeEarnerRate](https://github.com/MZero-Labs/protocol/blob/3499f50ff3382729f3e59565b19386ba61ef8e36/src/rateModels/StableEarnerRateModel.sol#L69-L117) function, there's a log calculation detailed in a comment: ```solidity // 6. ln(1 + (totalActive * (delta_minterIndex - 1) / totalEarning)) * SECONDS_PER_YEAR / dt = earnerRate ``` The code implementation of the log argument calculation follows the comment, but using fixed point arithmetic with 12 decimals. The problem is that a division by 1e12 is immediately followed by a 1e12 multiplication: 1e12 + ((((uint256(totalActiveOwedM_) * (deltaMinterIndex_ - 1e12)) / 1e12) * 1e12) / totalEarningSupply_) That division combined with the multiplication should cancel out in real world math. But because of integer division, this sets the first 12 decimals to zero. ### Recommendation Remove the division and multiplication by 1e12. ### Status Addressed in [#cac3c24](https://github.com/MZero-Labs/protocol/commit/cac3c24b038d9d6c71bad1132b9f4617e91ef2f1). --- Related findings: - [Precision Loss in `notifyRewardAmount` Function Causes Unclaimable RewardToken](https://0xsimao.com/findings/exactly-protocol-update-staking-contract-ii-precision-notify-reward-unclaimable): Exactly Protocol Update - Staking Contract