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 PriceMakerToTaker -- the rate at which the MakerDenom (the liquidity stored at the tick) can be coverted to the TakerDenom. The PriceMakerToTaker 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: $p(1) = 1.0001^{-1} \approx 0.9999$
• Price of tick -1: $p(-1) = 1.0001^{1} = ​1.0001$
• Price of tick 4000: ​$p(4000) = 1.0001^{-4000} \approx ​0.6703$
• Price of tick -4000: ​$p(-4000) = 1.0001^{4000} \approx 1.4918$

In this way, liquidity held at a tick can also be thought of as an offer to buy the opposing a token in the pair at a rate of PriceMakeToTaker MakerDenoms per TakerDenom.

Conversely, price can also be thought of as the price of the MakerDenom as denominated in the TakerDenom, or the sell price for the MakerDenom. This would be expressed as follows:

$$price(i) = 1/1.0001^{i}$$

Both versions yeild the same result.

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. (1 ATOM yields 10 USDC)

USDC liquidity will be placed at tick -23027, which implies a price of $1.0001^{+23027}$ = 10

ATOM liquidity will be placed at tick +23027, which implies a price of $1.0001^{-23027}$ = 0.1

A good way to think about price in this context is how much of MakerDenom Alice would receive if she swapped a single TakerDenom 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: $100\cdot PriceMakerToTaker(ATOM) = 100*0.1 = 10 ATOM$

swapping 100 Atom for USDC: $100\cdot PriceMakerToTaker(USDC) = 100*10 = 1000 USDC$