Risk of multiplication overflow

[QGarchery]

https://github.com/morpho-labs/morpho-blue-oracles/blob/0007653923d96e2d817f79b4a0e0fec87857e486/src/ChainlinkOracle.sol#L55
Can't this multiplication overflow and revert? We could use uniswap's 512-bit multiplication do circumvent this

Originally posted by @Rubilmax in #1 (comment)

[QGarchery]

Confirming the issue

Write numerator = pB1*1e(fpB1) * pB2*1e(fpB2) * SCALE_FACTOR as the multiplication that can overflow. We have SCALE_FACTOR = 1e(36 + dQ1 + fpQ1 + fpQ2 - dB1 - fpB1 - fpB2), so:

numerator = pB1 * pB2 * 1e(36 + dQ1 + fpQ1 + fpQ2 - dB1)

If fpQ1 = 18, fpQ2 = 18 and Q1 has 12 more decimals than B1, we get:
numerator = pB1 * pB2 * 1e(84)
So even if the prices pB1 and pB2 are 1 we get an overflow. This is not even taking into account the vault parameter.

Possible solutions

I think that there are 3 possible ways to go further on this issue:

1. analyze the current oracles. It may be ok to leave it like that if in practice it cannot overflow for all the first markets that will be deployed on Blue. Moreover, doing this analysis can help understand which quantities are contributing the most to the overflow.
2. use 512 bit multiplication and division. This is the idea shown in fix(oracle): use 512 bit multiplication #36, using a mulDiv(a, b, c) operation with full precision. This is not trivial because it requires to decide on how to split the whole multiplication in the numerator into the 2 factors a and b.
3. use a sample amount. The oracle would pass a sample amount of asset C, and we would use the feeds to determine how much it is worth in terms of asset B1 (call it qB1) and how much it is worth in terms of asset Q1 (call it qQ1) step by step. Each step would represent an amount of tokens, so it should not overflow. The final result can given by comparing qB1 to qQ1. This solution would essentially require a rewrite of the oracle

[Rubilmax]

I don't get why in solution 3 we have to rewrite the oracle: can't we just assume sample = 1 and re-order multiplications and divisions?

But in this case the 512-bit multiplication would be closer to the real-number solution

[QGarchery]

I don't get why in solution 3 we have to rewrite the oracle: can't we just assume sample = 1 and re-order multiplications and divisions?

If we assume we only compute amounts, sample = 1 usually does not give enough precision. This is similar to this comment, where the amount you get after one step would be 1 whereas the price is 1.03

But in this case the 512-bit multiplication would be closer to the real-number solution

True, but at the same time I'm not sure about the guarantees it gives. I guess it depends on how you split the factors a and b. The solution with the sample amounts should never overflow with a reasonable sample, because each step represents an amount

[MerlinEgalite]

I'd be in favor of option 2