"Calculating Liquidity" formula question

[Zarfsec]

in the liquidity1() function, amount is multiplied by q96 to convert it into a Q64.96 number. Why are we not doing this in the liquidity0() function (and dividing by q96 instead)?

Also, amount_usdc is set to 5000 * 10**18. Since the USDC contract uses 6 decimals, shouldn't amount_usdc then be equal to 5000 * 10**6 instead?

[uniyj]

The sqrtps are stored as Q64.96. To get back to a "normal" number (not in Q64.96), you need to "compensate" for that q96 conversion.

For liquidity0(), you have two sqrtps multiplied together in the numerator, one of them is cancelled out by the lot of sqrtp in the denominator, so there is still one conversion of q96 left to be "compensated" for, and thus you just divide by q96 to cancel it out.

For liquidity1(), you only have the lot of sqrtp in the denominator, and to compensate for that you multiply by q96 to cancel it out.

For the decimals, I think it's just for simplicity that 18 decimals are assumed for both tokens, and thus it's not the real USDC ERC20 definition. If you want to use 6 decimals (to be "true" to USDC), the differences in decimals will be reflected in the prices (which will account for any difference in decimals between the two tokens), and they'll all come out in the wash from the formula eventually.