Why DS-Math add WAD/2 or RAY/2 in WAD,RAY multiply function

Question

//rounds to zero if x*y < WAD / 2
function wmul(uint x, uint y) internal pure returns (uint z) {
    z = add(mul(x, y), WAD / 2) / WAD;
}
//rounds to zero if x*y < WAD / 2
function rmul(uint x, uint y) internal pure returns (uint z) {
    z = add(mul(x, y), RAY / 2) / RAY;
}

I think it'll add artifact small number ex. 2WAD x 1WAD = 2WAD + 0.5 Is it for safety reasons?

and what is

//rounds to zero if x*y < WAD / 2

I can’t figure it out.

DS-Math

Exactly for the reason stated in the comment at the top of each function - rounds to zero if x*y < WAD / 2. — goodvibration, Nov 28 '20 at 09:04
BTW, there seem to be a copy/paste mistake in the comment on the second function, where it should be RAY instead of WAD. — goodvibration, Nov 28 '20 at 09:05

score 4 · Accepted Answer · answered Nov 28 '20 at 09:08

4

x * y < WAD / 2 ==>

x * y + WAD / 2 < WAD ==>

(x * y + WAD / 2) / WAD == 0

answered Nov 28 '20 at 09:08

goodvibration

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score 1 · Answer 2 · answered Dec 30 '21 at 14:00

So the rounds to zero comment is true regardless of addition of WAD / 2 since solidity always rounds down to zero. The case that + WAD / 2 does is rounds the value up when the tenths place of the fixed point decimal is greater than 5.

Looking at some examples expressed in decimals (in Solidity this is in WAD precision):

if x * y = 1.2 then x * y + 0.5 = 1.7. Both of these round down to 1 in Solidity

if x * y = 1.7 then x * y + 0.5 = 2.2. The first equation will round down to 1 and the second equation will round down to 2.

This is the effect of adding WAD / 2.

Why DS-Math add WAD/2 or RAY/2 in WAD,RAY multiply function

2 Answers2