LockupMath

Git Source

Title: LockupMath

Provides functions for calculating the streamed amounts in Lockup streams. Note that 'streamed' is synonymous with 'vested'.

Functions

calculateStreamedAmountLD

Calculates the streamed amount of LD streams.

The LD streaming model uses the following distribution function:

$$f(x) = x^{exp} * csa + \Sigma(esa)$$

Where:

• $x$ is the elapsed time divided by the total duration of the current segment.
• $exp$ is the current segment exponent.
• $csa$ is the current segment amount.
• $\Sigma(esa)$ is the sum of all streamed segments' amounts. Notes:

1. Normalization to 18 decimals is not needed because there is no mix of amounts with different decimals.
2. The stream's start time must be in the past so that the calculations below do not overflow.
3. The stream's end time must be in the future so that the loop below does not panic with an "index out of bounds" error. Assumptions:
4. The sum of all segment amounts does not overflow uint128 and equals the deposited amount.
5. The first segment's timestamp is greater than the start time.
6. The last segment's timestamp equals the end time.
7. The segment timestamps are arranged in ascending order.

function calculateStreamedAmountLD(
    uint128 depositedAmount,
    uint40 endTime,
    LockupDynamic.Segment[] calldata segments,
    uint40 startTime,
    uint128 withdrawnAmount
)
    external
    view
    returns (uint128);

calculateStreamedAmountLL

Calculates the streamed amount of LL streams.

The LL streaming model uses the following distribution function:

$$f(x) = \begin{cases} s, & \text{block timestamp} < \text{cliff time} \\ x \cdot sa + s + c, & \text{block timestamp} \geq \text{cliff time} \end{cases}$$

Where:

• $sa$ is the streamable amount, i.e. deposited amount minus unlock amounts' sum.
• $s$ is the start unlock amount.
• $c$ is the cliff unlock amount.
• $x$ is the elapsed time percentage with discrete unlocks: $$x = \frac{\lfloor \text{time elapsed} / \text{granularity} \rfloor \times \text{granularity}}{\text{streamable time}}$$ The floor division in the numerator creates discrete unlock steps at every granularity seconds. Assumptions:

1. The sum of the unlock amounts (start and cliff) does not overflow uint128 and is less than or equal to the deposit amount.
2. The start time is before the end time.
3. If the cliff time is not zero, it is after the start time and before the end time.
4. Granularity is less than or equal to the streamable range.
5. Granularity is not zero.

function calculateStreamedAmountLL(
    uint40 cliffTime,
    uint128 depositedAmount,
    uint40 endTime,
    uint40 granularity,
    uint40 startTime,
    LockupLinear.UnlockAmounts calldata unlockAmounts,
    uint128 withdrawnAmount
)
    external
    view
    returns (uint128);

calculateStreamedAmountLPG

Calculates the streamed amount of LPG streams.

The LPG streaming model uses all-or-nothing unlock based on price threshold:

$$f(x) = \begin{cases} \text{deposited}, & \text{block timestamp} \geq \text{end time OR latest price} \geq \text{target price} \\ 0, & \text{otherwise} \end{cases}$$

Assumptions:

1. The stream is not canceled.
2. The oracle is assumed to be returning the correct price.

function calculateStreamedAmountLPG(
    uint128 deposited,
    uint40 endTime,
    LockupPriceGated.UnlockParams memory unlockParams
)
    external
    view
    returns (uint128);

calculateStreamedAmountLT

Calculates the streamed amount of LT streams.

The LT streaming model uses the following distribution function:

$$f(x) = \Sigma(eta)$$

Where:

• $\Sigma(eta)$ is the sum of all streamed tranches' amounts. Assumptions:

1. The sum of all tranche amounts does not overflow uint128, and equals the deposited amount.
2. The first tranche's timestamp is greater than the start time.
3. The last tranche's timestamp equals the end time.
4. The tranche timestamps are arranged in ascending order.

function calculateStreamedAmountLT(
    uint128 depositedAmount,
    uint40 endTime,
    uint40 startTime,
    LockupTranched.Tranche[] calldata tranches
)
    external
    view
    returns (uint128);