TickMath
Converts between prices and ticks, where each tick represents an increase in price of 0.01%. Ticks are used instead of liquidation prices to limit the number of possible buckets where a position can land, and allows for batched liquidations.
The formula for calculating the price from a tick is: price = 1.0001^(tick).
The formula for calculating the tick from a price is: tick = log_1.0001(price).
State Variables
MIN_TICK
The minimum price we want to resolve is 10_000 wei (1e-14 USD), which equates to 1.0001^-322378.
int24 public constant MIN_TICK = -322_378;
MAX_TICK
The maximum tick is determined by the limits of the libraries used for math and testing.
int24 public constant MAX_TICK = 980_000;
MIN_PRICE
The minimum representable values for the price.
uint256 public constant MIN_PRICE = 10_000;
MAX_PRICE
The maximum representable values for the price.
uint256 public constant MAX_PRICE = 3_620_189_675_065_328_806_679_850_654_316_367_931_456_599_175_372_999_068_724_197;
LN_BASE
Pre-computed value for ln(1.0001).
int256 public constant LN_BASE = 99_995_000_333_308;
Functions
maxUsableTick
Gets the largest usable tick, given a tick spacing.
function maxUsableTick(int24 tickSpacing) external pure returns (int24 tick_);
Parameters
| Name | Type | Description |
|---|---|---|
tickSpacing | int24 | Only uses ticks that are a multiple of this value. |
Returns
| Name | Type | Description |
|---|---|---|
tick_ | int24 | The largest tick that can be used. |
minUsableTick
Gets the smallest usable tick, given a tick spacing.
function minUsableTick(int24 tickSpacing) external pure returns (int24 tick_);
Parameters
| Name | Type | Description |
|---|---|---|
tickSpacing | int24 | Only uses ticks that are a multiple of this value. |
Returns
| Name | Type | Description |
|---|---|---|
tick_ | int24 | The smallest tick that can be used. |
getPriceAtTick
Gets the price at a given tick.
Calculates the price as 1.0001^tick = e^(tick * ln(1.0001)).
function getPriceAtTick(int24 tick) public pure returns (uint256 price_);
Parameters
| Name | Type | Description |
|---|---|---|
tick | int24 | The tick. |
Returns
| Name | Type | Description |
|---|---|---|
price_ | uint256 | The corresponding price. |
getTickAtPrice
Gets the tick corresponding to a price, rounded down towards negative infinity.
log_1.0001(price) = ln(price)/ln(1.0001) gives the tick.
function getTickAtPrice(uint256 price) external pure returns (int24 tick_);
Parameters
| Name | Type | Description |
|---|---|---|
price | uint256 | The price. |
Returns
| Name | Type | Description |
|---|---|---|
tick_ | int24 | The largest tick whose price is less than or equal to the given price. |
Errors
TickMathInvalidTickSpacing
The provided tick spacing is invalid (zero).
error TickMathInvalidTickSpacing();
TickMathInvalidTick
The provided tick is out of bounds.
error TickMathInvalidTick();
TickMathInvalidPrice
The provided price is out of bounds.
error TickMathInvalidPrice();