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In the Exchange contract of Uniswap v1, the addLiquidity function involves calculating token_amount using the formula

token_amount: uint256 = msg.value * token_reserve / eth_reserve + 1

Why is there a + 1 in the code? Should it not be written as below?

token_amount: uint256 = msg.value * token_reserve / eth_reserve
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The expression msg.value * token_reserve / eth_reserve is the floor of the real amount.

So msg.value * token_reserve / eth_reserve + 1 is most likely intended to be the ceiling of it.

BTW, it's not an ideal way for computing ceiling.

When msg.value * token_reserve is divisible by eth_reserve, it actually gives 'ceiling plus 1'.

IMO, they should have used (msg.value * token_reserve - 1) / eth_reserve + 1.

But the 1 stands for '1 wei', so it's probably not that critical either way...

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