Ticks

Ticks are the fundamental unit of accounting within the dex. Each tick is an integer between 559,680 and -559,680. All tradeable liquidity, in the form of either PoolReserves or LimitOrderTranches is stored at a specific tick. Price for liquidity held at a tick is stored in the form of MakerPrice — the price at which the MakerDenom is being sold denominated in terms of the TakerDenom. The MakerPrice of liquidity being stored at tick i is determined by the function:

p(i) = 1.0001^{i}

Some examples:

Price of tick 0: $p(0) = 1.0001^0 = 1$
Price of tick 1: $p(1) = 1.0001^{1} = 1.0001$
Price of tick -1: $p(-1) = 1.0001^{-1} = \approx 0.9999$
Price of tick 4000: $p(4000) = 1.0001^{4000} \approx 1.4918$
Price of tick -4000: $p(-4000) = 1.0001^{-4000} \approx 0.6703$

MakerPrice can also be seen as the rate for converting MakerDenom to TakerDenom:

MakerDenom \cdot MakerPrice == TakerDenom

. Conversely, we can convert TakerDenom to MakerDenom as follows:

\frac{TakerDenom}{MakerPrice} == MakerDenom

. Given an intent to deposit ATOM and USDC into a pool (assuming no fee) with the Price of ATOM set at 10 USDCperATOM and implying a reciprocal USDC price of 0.1 ATOMperUSDC, the best tick index to deposit to will be +/-23027 given that the target price is 10. (we are selling 1 ATOM for 10 USDC) USDC liquidity will be placed at tick -23027, which implies a price of

1.0001^{-23027}

= 0.1ATOM ATOM liquidity will be placed at tick +23027, which implies a price of

1.0001^{23027}

= 10USDC A good way to think about price in this context is how much of TakerDenom Alice would receive if she sold a single MakerDenom and vice versa. In this case, she would receive 10 USDC given an input of 1 ATOM, and 0.1 ATOM given an input of 1 USDC. From this, the simple price heuristic is How much output given unit input. swapping 100 USDC for Atom:

100\cdot MakerPrice(USDC) = 100*0.1 = 10 ATOM

swapping 100 Atom for USDC:

100\cdot MakerPrice(ATOM) = 100*10 = 1000 USDC

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