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Constants

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B_IN_Q72​

*This basis was a modification to Uniswap V3's basis, to fit ticks into int16 instead of int24. We use the form 2929−1\frac{2^{9}}{2^{9}-1} which is just under 1.002. This basis format gives smaller errors since the fraction is more compatible with binary Q128 fractions since the base is inverted in the tick math library before multiplications are applied.

2929−1−1⋅21281000110000−1⋅212829−129⋅225610000⋅2256100013396177529230460055269227039016280391683402823669209384634633746074317682114560000100010xff8000000000000000000000000000000xfffcb933bd6fad37aa2d162d1a594001\begin{align*} & \frac{2^{9}}{2^{9}-1}^{-1} \cdot 2^{128} & & \frac{10001}{10000}^{-1} \cdot 2^{128} \\ & \frac{2^{9}-1}{2^{9}} \cdot 2^{256} & & \frac{10000\cdot2^{256}}{10001} \\ & 339617752923046005526922703901628039168 & & \frac{3402823669209384634633746074317682114560000}{10001} \\ & 0xff800000000000000000000000000000 & & 0xfffcb933bd6fad37aa2d162d1a594001 \\ \end{align*}

We use this constant outside of the tick math library, and use a Q72 as that format is easier to work with multiplication without overflows.

>>> hex(int(mpm.nint(mpm.fdiv(2**9, 2**9-1) * 2**72)))
```*


```solidity
uint256 constant B_IN_Q72 = 0x1008040201008040201;

TRANCHE_B_IN_Q72​

*In Saturation we combine 25 ticks to make one tranche.

>>> hex(int(mpm.nint(mpm.fdiv(2**9, 2**9-1)**25 * 2**72)))
```*


```solidity
uint256 constant TRANCHE_B_IN_Q72 = 0x10cd2b2ae53a69d3552;

LENDING_TICK_NOT_AVAILABLE​

Represents the absence of a valid lending tick, initialized to int16 minimum value since a type(int16).min < MIN_TICK.

int16 constant LENDING_TICK_NOT_AVAILABLE = type(int16).min;

ZERO_ADDRESS​

the default zero address

address constant ZERO_ADDRESS = address(0);

Q16​

2**16

uint256 constant Q16 = 0x10000;

Q32​

2**32

uint256 constant Q32 = 0x100000000;

Q56​

2**56.

uint256 constant Q56 = 0x100000000000000;

Q64​

2**64.

uint256 constant Q64 = 0x10000000000000000;

Q72​

2**72.

uint256 constant Q72 = 0x1000000000000000000;

Q88​

2**88.

uint256 constant Q88 = 0x10000000000000000000000;

Q112​

2**112.

uint256 constant Q112 = 0x10000000000000000000000000000;

Q128​

2**128.

uint256 constant Q128 = 0x100000000000000000000000000000000;

Q144​

2**144.

uint256 constant Q144 = 0x1000000000000000000000000000000000000;

Q200​

2**200.

uint256 constant Q200 = 0x100000000000000000000000000000000000000000000000000;

BIPS​

number of bips in 1, 1 bips = 0.01%.

uint256 constant BIPS = 10_000;

INITIAL_LENDING_FEE_BIPS​

Initial fee applied to all newly opened debts and flash loans. This upfront fee prevents griefing attacks via "dust" positions—small debts that would be unprofitable for liquidators to close. The fee accumulates in the protocol, creating an economic incentive to liquidate these positions if they become eligible for liquidation. 5 bips = 0.05%.

uint256 constant INITIAL_LENDING_FEE_BIPS = 5;

DEFAULT_MID_TERM_INTERVAL​

Default mid-term interval config used at the time of GeometricTWAP initialization.

uint16 constant DEFAULT_MID_TERM_INTERVAL = 8;

MINIMUM_LIQUIDITY​

minimum liquidity to initialize a pool, amount is burned to eliminate the threat of donation attacks.

uint256 constant MINIMUM_LIQUIDITY = 1000;

MINIMUM_LONG_TERM_TIME_UPDATE_CONFIG​

Represents the minimum time period required between recorded long-term intervals. Calculated as the product of DEFAULT_MID_TERM_INTERVAL and GeometricTWAP. MINIMUM_LONG_TERM_INTERVAL_FACTOR.

uint24 constant MINIMUM_LONG_TERM_TIME_UPDATE_CONFIG = 112;

MAX_TICK_DELTA​

MAX_TICK_DELTA limits the newTick to be within the outlier range of the current mid-term price.

int256 constant MAX_TICK_DELTA = 10;

DEFAULT_TICK_DELTA_FACTOR​

DEFAULT_TICK_DELTA_FACTOR is used when the long-term buffer is initialized.

int256 constant DEFAULT_TICK_DELTA_FACTOR = 1;

LTVMAX_IN_MAG2​

the system loan to value minimum, 75% * 100.

uint256 constant LTVMAX_IN_MAG2 = 75;

ALLOWED_LIQUIDITY_LEVERAGE​

the system allowed leverage exposures with similar underlying assets, ie L is half X and half Y, so we allow 100X leverage of borrowed X and Y against L.

uint256 constant ALLOWED_LIQUIDITY_LEVERAGE = 100;

ALLOWED_LIQUIDITY_LEVERAGE_MINUS_ONE​

Allowed leverage minus one.

uint256 constant ALLOWED_LIQUIDITY_LEVERAGE_MINUS_ONE = 99;

N_TIMES_FEE​

constant used in Quadratic swap fees that controls the speed at which fees increase with respect to the price change.

uint256 constant N_TIMES_FEE = 20;

MAG1​

Magnitude 1

uint256 constant MAG1 = 10;

MAG2​

Magnitude 2

uint256 constant MAG2 = 100;

MAG4​

Magnitude 4

uint256 constant MAG4 = 10_000;

MAG6​

Magnitude 6

uint256 constant MAG6 = 1_000_000;

SAT_PERCENTAGE_DELTA_4_WAD​

Saturation percentages in WADs

uint256 constant SAT_PERCENTAGE_DELTA_4_WAD = 94.1795538580338563e16;

SAT_PERCENTAGE_DELTA_5_WAD​

uint256 constant SAT_PERCENTAGE_DELTA_5_WAD = 92.3156868017020937e16;

SAT_PERCENTAGE_DELTA_6_WAD​

uint256 constant SAT_PERCENTAGE_DELTA_6_WAD = 90.4887067368814135e16;

SAT_PERCENTAGE_DELTA_7_WAD​

uint256 constant SAT_PERCENTAGE_DELTA_7_WAD = 88.6978836489829983e16;

SAT_PERCENTAGE_DELTA_DEFAULT_WAD​

uint256 constant SAT_PERCENTAGE_DELTA_DEFAULT_WAD = 95e16;

LIQUIDITY_INTEREST_RATE_MAGNIFICATION​

uint256 constant LIQUIDITY_INTEREST_RATE_MAGNIFICATION = 5;

MAX_SATURATION_PERCENT_IN_WAD​

Maximum percentage for the saturation allowed, used to limit the maximum saturation per tranche.

uint256 constant MAX_SATURATION_PERCENT_IN_WAD = 0.95e18;

MAX_UTILIZATION_PERCENT_IN_WAD​

Maximum percentage for the utilization allowed.

uint256 constant MAX_UTILIZATION_PERCENT_IN_WAD = 0.9e18;

SECONDS_IN_YEAR​

uint256 constant SECONDS_IN_YEAR = 365 days;

INTEREST_PERIOD_FOR_SWAP​

The interval for swap to check borrowed interest to update reserves. Updating once a day would limit rate change in price to 0.003% if one reserve had max interest and the other had none. It also would require 40 days to go from 94% depletion to 95% depletion. ref: https://www.desmos.com/calculator/sxfc3tcz8c

uint32 constant INTEREST_PERIOD_FOR_SWAP = 1 days - 1;

DEFAULT_INTEREST_PERIOD​

The interval for non-swap to check borrowed interest to update reserves.

uint32 constant DEFAULT_INTEREST_PERIOD = 0;

BUFFER​

Buffer ratio at which lending of the scarce asset stops. Derived from 95 / 5.

uint256 constant BUFFER = 19;

BUFFER_NUMERATOR​

Numerator buffer used for depleted-asset threshold calculations. Derived from 100 / 5.

uint256 constant BUFFER_NUMERATOR = 20;

BUFFER_OBS​

Observation buffer used when computing the new tick from reserves. Derived from 45 / 5.

uint256 constant BUFFER_OBS = 9;

BUFFER_OBS_NUMERATOR​

Observation buffer numerator used for depleted-asset threshold calculations. Derived from 50 / 5.

uint256 constant BUFFER_OBS_NUMERATOR = 10;