UniswapV3FullRangeMath

Title: UniswapV3FullRangeMath

Author: Modified from Uniswap V3 — TickMath

(https://github.com/Uniswap/v3-core/blob/main/contracts/libraries/TickMath.sol) and LiquidityAmounts (https://github.com/Uniswap/v3-periphery/blob/main/contracts/libraries/LiquidityAmounts.sol).

Pure-math helpers the Lattice UniswapV3Adapter needs to value a full-range position from a TWAP tick: getSqrtRatioAtTick (tick → sqrtPriceX96) and getAmountsForLiquidity (liquidity + price range → (amount0, amount1)). Stateless utility library — no own storage, no facet, no interface file (Lattice utility-library pattern).

The original Uniswap libraries target Solidity 0.7/0.8 with explicit unchecked blocks; the ports here preserve the exact arithmetic (wrapping is intentional and required for the magic constants) inside unchecked so the bit-twiddling matches the canonical results. MIN_TICK / MAX_TICK are the v3 tick bounds; a full-range position uses the min/max usable ticks (these bounds floored/ceiled to the pool's tickSpacing), computed by the caller. The ports' FullMath.mulDiv calls go through Math.mulDiv: the same 512-bit floor division with identical results, except that a zero denominator or an overflowing quotient reverts with Panic(0x12) / Panic(0x11), where this library's own port (through 0.4.0) raised Error("mulDiv:0") / Error("mulDiv:OF").

Constants

MIN_TICK

The minimum tick that may be used on any pool (TickMath.MIN_TICK).

int24 internal constant MIN_TICK = -887272;

MAX_TICK

The maximum tick that may be used on any pool (TickMath.MAX_TICK).

int24 internal constant MAX_TICK = 887272;

MIN_SQRT_RATIO

The minimum value getSqrtRatioAtTick can return (== getSqrtRatioAtTick(MIN_TICK)).

uint160 internal constant MIN_SQRT_RATIO = 4295128739;

MAX_SQRT_RATIO

The maximum value getSqrtRatioAtTick can return (== getSqrtRatioAtTick(MAX_TICK)).

uint160 internal constant MAX_SQRT_RATIO = 1461446703485210103287273052203988822378723970342;

Functions

getSqrtRatioAtTick

Calculates sqrt(1.0001^tick) * 2^96 (a Q64.96 sqrt price) for the given tick.

Verbatim port of Uniswap V3 TickMath.getSqrtRatioAtTick. The chained conditional multiplications reconstruct the fixed-point sqrt-ratio from the tick's set bits; the magic constants and wrapping multiplies are exactly the v3 originals and MUST run unchecked.

function getSqrtRatioAtTick(int24 tick) internal pure returns (uint160 sqrtPriceX96);

Parameters

Name	Type	Description
tick	`int24`	The tick to convert; must satisfy `MIN_TICK <= tick <= MAX_TICK`.

Returns

Name	Type	Description
sqrtPriceX96	`uint160`	The sqrt(token1/token0) ratio as a Q64.96 value.

getAmount0ForLiquidity

Computes the token0 amount for liquidity between two sqrt prices.

Port of Uniswap V3 LiquidityAmounts.getAmount0ForLiquidity. Assumes sqrtA <= sqrtB.

function getAmount0ForLiquidity(uint160 sqrtA, uint160 sqrtB, uint128 liquidity)
        internal
        pure
        returns (uint256 amount0);

Parameters

Name	Type	Description
sqrtA	`uint160`
sqrtB	`uint160`
liquidity	`uint128`

Returns

Name	Type	Description
amount0	`uint256`

getAmount1ForLiquidity

Computes the token1 amount for liquidity between two sqrt prices.

Port of Uniswap V3 LiquidityAmounts.getAmount1ForLiquidity. Assumes sqrtA <= sqrtB.

function getAmount1ForLiquidity(uint160 sqrtA, uint160 sqrtB, uint128 liquidity)
        internal
        pure
        returns (uint256 amount1);

Parameters

Name	Type	Description
sqrtA	`uint160`
sqrtB	`uint160`
liquidity	`uint128`

Returns

Name	Type	Description
amount1	`uint256`

getAmountsForLiquidity

Computes (amount0, amount1) currently composing liquidity at the current sqrt price, for a position spanning [sqrtLower, sqrtUpper].

Port of Uniswap V3 LiquidityAmounts.getAmountsForLiquidity. Three regimes:

price below the range → all token0;

price inside the range → a split of both (the full-range, in-price case);

price above the range → all token1.

function getAmountsForLiquidity(uint160 sqrtCurrent, uint160 sqrtLower, uint160 sqrtUpper, uint128 liquidity)
        internal
        pure
        returns (uint256 amount0, uint256 amount1);

Parameters

Name	Type	Description
sqrtCurrent	`uint160`	The current sqrt price (Q64.96), e.g. derived from the TWAP tick.
sqrtLower	`uint160`	The sqrt price at the position's lower tick.
sqrtUpper	`uint160`	The sqrt price at the position's upper tick.
liquidity	`uint128`	The position's liquidity.

Returns

Name	Type	Description
amount0	`uint256`
amount1	`uint256`

getLiquidityForAmount0

Computes the liquidity for a given token0 amount between two sqrt prices.

Port of Uniswap V3 LiquidityAmounts.getLiquidityForAmount0. Assumes sqrtA <= sqrtB.

function getLiquidityForAmount0(uint160 sqrtA, uint160 sqrtB, uint256 amount0)
        internal
        pure
        returns (uint128 liquidity);

Parameters

Name	Type	Description
sqrtA	`uint160`
sqrtB	`uint160`
amount0	`uint256`

Returns

Name	Type	Description
liquidity	`uint128`

getLiquidityForAmount1

Computes the liquidity for a given token1 amount between two sqrt prices.

Port of Uniswap V3 LiquidityAmounts.getLiquidityForAmount1. Assumes sqrtA <= sqrtB.

function getLiquidityForAmount1(uint160 sqrtA, uint160 sqrtB, uint256 amount1)
        internal
        pure
        returns (uint128 liquidity);

Parameters

Name	Type	Description
sqrtA	`uint160`
sqrtB	`uint160`
amount1	`uint256`

Returns

Name	Type	Description
liquidity	`uint128`

getLiquidityForAmounts

Computes the maximum liquidity for (amount0, amount1) at the current sqrt price over the range [sqrtLower, sqrtUpper] (the liquidity actually mintable from both amounts).

Port of Uniswap V3 LiquidityAmounts.getLiquidityForAmounts. In-range (the full-range, in-price case) takes the binding minimum of the two single-token liquidities.

function getLiquidityForAmounts(
        uint160 sqrtCurrent,
        uint160 sqrtLower,
        uint160 sqrtUpper,
        uint256 amount0,
        uint256 amount1
    ) internal pure returns (uint128 liquidity);

Parameters

Name	Type	Description
sqrtCurrent	`uint160`
sqrtLower	`uint160`
sqrtUpper	`uint160`
amount0	`uint256`
amount1	`uint256`

Returns

Name	Type	Description
liquidity	`uint128`

fullRangeTicks

Returns the min/max usable ticks for a full-range position on a pool with the given tickSpacing (the v3 tick bounds floored/ceiled to a multiple of tickSpacing).

function fullRangeTicks(int24 tickSpacing) internal pure returns (int24 tickLower, int24 tickUpper);

Parameters

Name	Type	Description
tickSpacing	`int24`	The pool's tick spacing (must be > 0).

Returns

Name	Type	Description
tickLower	`int24`	The lowest initializable tick (full-range lower bound).
tickUpper	`int24`	The highest initializable tick (full-range upper bound).

valueInToken0

Values a sqrt-priced (amount0, amount1) pair in token0 units at price sqrtPriceX96.

token1→token0 conversion: the pool price is token1/token0 = sqrtPriceX96^2 / 2^192, so amount1 (token1 units) is worth amount1 * 2^192 / sqrtPriceX96^2 in token0 units. Done in two mulDiv steps so the * 2^96 factors never overflow.

function valueInToken0(uint256 amount0, uint256 amount1, uint160 sqrtPriceX96)
        internal
        pure
        returns (uint256 value0);

Parameters

Name	Type	Description
amount0	`uint256`	The token0 amount (already in token0 units).
amount1	`uint256`	The token1 amount to convert to token0 units.
sqrtPriceX96	`uint160`	The sqrt price (Q64.96) to value at.

Returns

Name	Type	Description
value0	`uint256`	`amount0 + (amount1 valued in token0)`.

Errors

TickOutOfBounds

Thrown when a tick passed to getSqrtRatioAtTick is out of the v3 bounds.

error TickOutOfBounds(int24 tick);

Parameters

Name	Type	Description
tick	`int24`