Let’s take a look at the following libraryfrom Solmate:
This might look scary for a new juniorauditor. The good news is - it isn’t scary for much longer!
Lets dive into it:
First you can see the library name:“FixedPointMathLib”, which is nothing else than arithmetic operations forfloating numbers, remember, solidity cannot handle this natively since itrounds down.
Example: There is no 100e18 * 0.5, yousimply cannot do this in solidity.
So this library aims to solve this problem,let’s specifically focus on the first 4 operations and dissect them. Generallyit can be explained to operate with fixed float numbers using 1e18 as base.This means if i want to do 100 * 0.5, i can simply do 100 * 0.5e18 / 1e18 -thats all the magic behind it.
Examples with 0.5 as multiplier / divisor:
1. mulWadDown: 99e18 * 0.5
To multiply 99 (in WAD, which is99×101899×1018) by 0.5 (which must also be represented in WAD as0.5×10180.5×1018 or 0.5e180.5e18) and round down:
uint256 result =FixedPointMathLib.mulWadDown(99e18, 0.5e18); = 45.5e18
2. mulWadUp: 99e18 * 0.5
Using the same numbers for mulWadUp:
uint256 result =FixedPointMathLib.mulWadUp(99e18, 0.5e18); = 45.5e18
3. divWadDown: 99e / 0.5
For divWadDown, which divides twofixed-point numbers and rounds the result down:
uint256 result =FixedPointMathLib.divWadDown(99e18, 0.5e18);
Since divWadDown rounds down, the result is198e18, but in this case, there is no fractional part to round down from, sothe result remains 198e18.
4. divWadUp: 99e180 / 0.5
For divWadUp, which also divides twofixed-point numbers but rounds the result up:
uint256 result =FixedPointMathLib.divWadUp(99e18, 0.5e18);
However, divWadUp would round up if therewas any fractional part. In this scenario, since the division results in anexact number without a fractional remainder, rounding up does not change theresult, and it remains 198e18.
The good thing about this library is thatyou can determine explicitly if it rounds up or down, which is not possiblewith AAVE’s WadRayMath library.
