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UniswapV2 Swap Fee Math
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| getAmountOut | |
| uint amountInWithFee = amountIn.mul(997); | |
| uint numerator = amountInWithFee.mul(reserveOut); | |
| uint denominator = reserveIn.mul(1000).add(amountInWithFee); | |
| amountOut = numerator / denominator; | |
| (_tokenOutReserves * _tokenInReserves) | |
| amountOut = _tokenOutReserves - ------------------------------------- | |
| (_tokenOutReserves + _amountTokenIn) | |
| _tokenOutReserves(_tokenInReserves + _amountTokenIn) - ((_tokenOutReserves * _tokenInReserves) | |
| amountOut = --------------------------------------------------------------------------------------- | |
| (_tokenInReserves + _amountTokenIn)) | |
| Add fees | |
| _tokenOutReserves * _amountTokenIn * 99.7% | |
| amountOut = ----------------------------------------------------- | |
| (_tokenInReserves) + (_amountTokenIn * 99.7%) | |
| _tokenOutReserves * _amountTokenIn * 997/1000 | |
| amountOut = ----------------------------------------------------- | |
| (_tokenInReserves) + (_amountTokenIn * 997/1000) | |
| _tokenOutReserves * _amountTokenIn * 997 | |
| amountOut = ----------------------------------------------------- | |
| (_tokenInReserves * 1000) + (_amountTokenIn * 997/1000)1000 | |
| _tokenOutReserves * _amountTokenIn * 997 | |
| amountOut = ----------------------------------------------------- | |
| (_tokenInReserves * 1000) + (_amountTokenIn * 997) | |
| getAmountIn | |
| uint numerator = reserveIn.mul(amountOut).mul(1000); | |
| uint denominator = reserveOut.sub(amountOut).mul(997); | |
| amountIn = (numerator / denominator).add(1); | |
| (_tokenOutReserves * _tokenInReserves) | |
| amountIn = ---------------------------------------- - _tokenInReserves | |
| (_tokenOutReserves - $amountTokenOut) | |
| (_tokenOutReserves * _tokenInReserves) - _tokenInReserves(_tokenOutReserves - $amountTokenOut) | |
| amountIn = ---------------------------------------------------------------------------------------------- | |
| (_tokenOutReserves - $amountTokenOut) | |
| _tokenInReserves * $amountTokenOut | |
| amountIn = -------------------------------------- | |
| _tokenOutReserves - $amountTokenOut | |
| Add fees | |
| _tokenInReserves * $amountTokenOut | |
| amountIn * 99.7% = ----------------------------------------------------- | |
| _tokenOutReserves - $amountTokenOut | |
| _tokenInReserves * $amountTokenOut | |
| amountIn * 997/1000 = ----------------------------------------------------- | |
| _tokenOutReserves - $amountTokenOut | |
| _tokenInReserves * $amountTokenOut * 1000 | |
| amountIn = ----------------------------------------------------- | |
| 997(_tokenOutReserves - $amountTokenOut) | |
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