Parameter Formats

Each LDF contract receives bytes32 ldfParams when called and has different formats for decoding the actual parameters. Below are how each LDF contract encodes its parameters.

GeometricDistribution

Parameter Encoding

The ldfParams are encoded as follows:

| shiftMode (1 byte) | offset (3 bytes) | length (2 bytes) | alpha (4 bytes) | unused (22 bytes) |

• shiftMode (1 byte): A uint8 value representing the shift mode (0 for BOTH, 1 for LEFT, 2 for RIGHT, 3 for STATIC).
• offset (3 bytes): An int24 value representing the offset applied to the TWAP tick to get the minTick. In ticks, not ricks.
• length (2 bytes): An int16 value representing the length of the distribution in number of rounded ticks.
• alpha (4 bytes): A uint32 value representing the alpha parameter of the geometric distribution.
• unused (22 bytes): Unused bytes, should be set to zero.

Important Notes

1. The actual minTick is calculated as roundTickSingle(twapTick + offset, tickSpacing) when shiftMode is not STATIC.
2. For STATIC mode, offset represents the absolute minTick and must be aligned to tickSpacing.
3. The alpha value is scaled by Q96 / ALPHA_BASE internally. ALPHA_BASE is 1e8.
4. The distribution is bounded to be within the range of usable ticks. If minTick is outside this range, it will be adjusted accordingly.

Example Usage

Here's an example of how to encode the parameters:

function encodeParams(
    ShiftMode shiftMode,
    int24 offset,
    int16 length,
    uint32 alpha
) pure returns (bytes32) {
    return abi.encodePacked(uint8(shiftMode), offset, length, alpha);
}

Remember to ensure that all values are within their appropriate ranges and that minTick is aligned with tickSpacing for STATIC mode.

UniformDistribution

Parameter Encoding

The ldfParams for the UniformDistribution are encoded as follows:

| shiftMode (1 byte) | tickLower (3 bytes) | tickUpper (3 bytes) | unused (25 bytes) |

• shiftMode (1 byte): A uint8 value representing the shift mode (3 for STATIC, as Uniform distribution is always static).
• tickLower (3 bytes): An int24 value representing the lower tick of the distribution.
• tickUpper (3 bytes): An int24 value representing the upper tick of the distribution.
• unused (25 bytes): Unused bytes, should be set to zero.

Important Notes

1. Both tickLower and tickUpper must be within the range of valid ticks for the pool.
2. tickLower must be less than tickUpper.
3. The ticks need to be aligned to the tick spacing.

Example Usage

Here's an example of how to encode the parameters for a uniform distribution:

function encodeParams(
    int24 tickLower,
    int24 tickUpper
) pure returns (bytes32) {
    return abi.encodePacked(uint8(3), tickLower, tickUpper);
}

Remember to ensure that tickLower and tickUpper are within the valid range of ticks for the pool, tickLower is less than tickUpper and they're both aligned to the tick spacing.

DoubleGeometricDistribution

Parameter Encoding

The ldfParams are encoded as follows:

| shiftMode (1 byte) | offset (3 bytes) | length0 (2 bytes) | alpha0 (4 bytes) | weight0 (4 bytes) | length1 (2 bytes) | alpha1 (4 bytes) | weight1 (4 bytes) | unused (8 bytes) |

• shiftMode (1 byte): A uint8 value representing the shift mode (0 for BOTH, 1 for LEFT, 2 for RIGHT, 3 for STATIC).
• offset (3 bytes): An int24 value representing the offset applied to the TWAP tick to get the minTick. In ticks, not ricks.
• length0 (2 bytes): An int16 value representing the length of the right distribution in number of rounded ticks.
• alpha0 (4 bytes): A uint32 value representing the alpha parameter of the right distribution.
• weight0 (4 bytes): A uint32 value representing the weight of the right distribution.
• length1 (2 bytes): An int16 value representing the length of the left distribution in number of rounded ticks.
• alpha1 (4 bytes): A uint32 value representing the alpha parameter of the left distribution.
• weight1 (4 bytes): A uint32 value representing the weight of the left distribution.
• unused (8 bytes): Unused bytes, should be set to zero.

Important Notes

1. The actual minTick is calculated as roundTickSingle(twapTick + offset, tickSpacing) when shiftMode is not STATIC.
2. For STATIC mode, offset represents the absolute minTick and must be aligned to tickSpacing.
3. The alpha0 and alpha1 values are scaled by Q96 / ALPHA_BASE internally. ALPHA_BASE is 1e8.
4. The distribution is bounded to be within the range of usable ticks. If minTick is outside this range, it will be adjusted accordingly.
5. The total length of the distribution is length0 + length1.
6. weight0 and weight1 don't use any particular number of decimals, they're relative weights. For example, weight0 can be 8 and weight1 can be 2, and the respective weights would be 8 / 10 = 80% and 2 / 10 = 20%.
7. The minimum liquidity density of each geometric part must be greater than MIN_LIQUIDITY_DENSITY (Q96 / 1e3).

Example Usage

Here's an example of how to encode the parameters:

function encodeParams(
    ShiftMode shiftMode,
    int24 offset,
    int16 length0,
    uint32 alpha0,
    uint32 weight0,
    int16 length1,
    uint32 alpha1,
    uint32 weight1
) pure returns (bytes32) {
    return abi.encodePacked(uint8(shiftMode), offset, length0, alpha0, weight0, length1, alpha1, weight1);
}

Remember to ensure that all values are within their appropriate ranges and that minTick is aligned with tickSpacing for STATIC mode.

CarpetedGeometricDistribution

Parameter Encoding

The ldfParams are encoded as follows:

| shiftMode (1 byte) | offset (3 bytes) | length (2 bytes) | alpha (4 bytes) | weightCarpet (4 bytes) | unused (18 bytes) |

• shiftMode (1 byte): A uint8 value representing the shift mode (0 for BOTH, 1 for LEFT, 2 for RIGHT, 3 for STATIC).
• offset (3 bytes): An int24 value representing the offset applied to the TWAP tick to get the minTick. In ticks, not ricks.
• length (2 bytes): An int16 value representing the length of the geometric distribution in number of rounded ticks.
• alpha (4 bytes): A uint32 value representing the alpha parameter of the geometric distribution.
• weightCarpet (4 bytes): A uint32 value representing the weight of the carpet distribution.
• unused (18 bytes): Unused bytes, should be set to zero.

Important Notes

1. The actual minTick is calculated as roundTickSingle(twapTick + offset, tickSpacing) when shiftMode is not STATIC.
2. For STATIC mode, offset represents the absolute minTick and must be aligned to tickSpacing.
3. The alpha value is scaled by Q96 / ALPHA_BASE internally. ALPHA_BASE is 1e8.
4. The weightCarpet value uses 18 decimals (i.e., a weightCarpet of 500000000000000000 represents 0.5 or 50%).
5. The distribution is bounded to be within the range of usable ticks. If minTick is outside this range, it will be adjusted accordingly.
6. The weightCarpet must be non-zero. It is intentionally bounded to a small max value (type(uint32).max / 1e18) because larger values allocates too many tokens at extreme tick values.
7. The minimum liquidity density of the geometric part must be greater than MIN_LIQUIDITY_DENSITY (Q96 / 1e3).

Example Usage

Here's an example of how to encode the parameters:

function encodeParams(
    ShiftMode shiftMode,
    int24 offset,
    int16 length,
    uint32 alpha,
    uint32 weightCarpet
) pure returns (bytes32) {
    return abi.encodePacked(uint8(shiftMode), offset, length, alpha, weightCarpet);
}

Remember to ensure that all values are within their appropriate ranges and that minTick is aligned with tickSpacing for STATIC mode.

CarpetedDoubleGeometricDistribution

Parameter Encoding

The ldfParams are encoded as follows:

| shiftMode (1 byte) | offset (3 bytes) | length0 (2 bytes) | alpha0 (4 bytes) | weight0 (4 bytes) | length1 (2 bytes) | alpha1 (4 bytes) | weight1 (4 bytes) | weightCarpet (4 bytes) | unused (4 bytes) |

• shiftMode (1 byte): A uint8 value representing the shift mode (0 for BOTH, 1 for LEFT, 2 for RIGHT, 3 for STATIC).
• offset (3 bytes): An int24 value representing the offset applied to the TWAP tick to get the minTick. In ticks, not ricks.
• length0 (2 bytes): An int16 value representing the length of the right distribution in number of rounded ticks.
• alpha0 (4 bytes): A uint32 value representing the alpha parameter of the right distribution.
• weight0 (4 bytes): A uint32 value representing the weight of the right distribution.
• length1 (2 bytes): An int16 value representing the length of the left distribution in number of rounded ticks.
• alpha1 (4 bytes): A uint32 value representing the alpha parameter of the left distribution.
• weight1 (4 bytes): A uint32 value representing the weight of the left distribution.
• weightCarpet (4 bytes): A uint32 value representing the weight of the carpet distribution.
• unused (4 bytes): Unused bytes, should be set to zero.

Important Notes

1. The actual minTick is calculated as roundTickSingle(twapTick + offset, tickSpacing) when shiftMode is not STATIC.
2. For STATIC mode, offset represents the absolute minTick and must be aligned to tickSpacing.
3. The alpha0 and alpha1 values are scaled by Q96 / ALPHA_BASE internally. ALPHA_BASE is 1e8.
4. The weightCarpet value uses 18 decimals (i.e., a value of 500000000000000000 represents 0.5 or 50%).
5. The distribution is bounded to be within the range of usable ticks. If minTick is outside this range, it will be adjusted accordingly.
6. The weightCarpet must be non-zero. It is intentionally bounded to a small max value (type(uint32).max / 1e18) because larger values allocates too many tokens at extreme tick values.
7. The minimum liquidity density of each geometric part must be greater than MIN_LIQUIDITY_DENSITY (Q96 / 1e3).
8. The total length of the distribution is length0 + length1.
9. weight0 and weight1 don't use any particular number of decimals, they're relative weights. For example, weight0 can be 8 and weight1 can be 2, and the respective weights would be 8 / 10 = 80% and 2 / 10 = 20%.

Example Usage

Here's an example of how to encode the parameters:

function encodeParams(
    ShiftMode shiftMode,
    int24 offset,
    int16 length0,
    uint32 alpha0,
    uint32 weight0,
    int16 length1,
    uint32 alpha1,
    uint32 weight1,
    uint32 weightCarpet
) pure returns (bytes32) {
    return abi.encodePacked(uint8(shiftMode), offset, length0, alpha0, weight0, length1, alpha1, weight1, weightCarpet);
}

Remember to ensure that all values are within their appropriate ranges and that minTick is aligned with tickSpacing for STATIC mode.

BuyTheDipGeometricDistribution

Parameter Encoding

The ldfParams are encoded as follows:

| shiftMode (1 byte) | minTick (3 bytes) | length (2 bytes) | alpha (4 bytes) | altAlpha (4 bytes) | altThreshold (3 bytes) | altThresholdDirection (1 byte) | unused (14 bytes) |

• shiftMode (1 byte): A uint8 value representing the shift mode (3 for STATIC, as this distribution is always static).
• minTick (3 bytes): An int24 value representing the minimum tick of the distribution. Must be aligned to tickSpacing.
• length (2 bytes): An int16 value representing the length of the distribution in number of rounded ticks.
• alpha (4 bytes): A uint32 value representing the alpha parameter of the geometric distribution.
• altAlpha (4 bytes): A uint32 value representing the alternative alpha parameter.
• altThreshold (3 bytes): An int24 value representing the threshold for switching between alpha and altAlpha.
• altThresholdDirection (1 byte): A uint8 value (0 for false, 1 for true) indicating the direction of the threshold comparison.
• unused (14 bytes): Unused bytes, should be set to zero.

Important Notes

1. This distribution requires TWAP to be enabled (twapSecondsAgo != 0) to trigger the alpha switching mechanism.
2. The shiftMode must be STATIC (3).
3. The alpha and altAlpha values are scaled by Q96 / ALPHA_BASE internally. ALPHA_BASE is 1e8.
4. The distribution switches between alpha and altAlpha based on the TWAP tick and altThreshold.
5. If altThresholdDirection is true, altAlpha is used when twapTick <= altThreshold. If false, altAlpha is used when twapTick >= altThreshold.
6. The alpha and altAlpha must be on different sides of 1 (i.e., one < ALPHA_BASE and one > ALPHA_BASE).
7. The altThreshold must be within the range (minTick, minTick + length * tickSpacing).
8. The minTick must be aligned to tickSpacing.
9. The length must be positive and the range [minTick, minTick + length * tickSpacing] must be within the usable tick range.
10. Both alpha and altAlpha must be within the range [MIN_ALPHA, MAX_ALPHA] (from 1e3 to 12e8) and neither can be exactly ALPHA_BASE (1e8).
11. The distribution is bounded to be within the range of usable ticks.
12. This LDF is designed to have one end of the distribution with essentially zero liquidity, so that when the alt alpha is activated, liquidity can move to a specified price to "buy the dip".

Example Usage

Here's an example of how to encode the parameters:

function encodeParams(
    int24 minTick,
    int16 length,
    uint32 alpha,
    uint32 altAlpha,
    int24 altThreshold,
    bool altThresholdDirection
) pure returns (bytes32) {
    return abi.encodePacked(
        uint8(3), // STATIC
        minTick,
        length,
        alpha,
        altAlpha,
        altThreshold,
        altThresholdDirection ? uint8(1) : uint8(0)
    );
}

Remember to ensure that all values are within their appropriate ranges and that minTick is aligned with tickSpacing. The alpha and altAlpha values must be on different sides of 1e8 (one < 1e8 and one > 1e8), and the altThreshold must be within the range (minTick, minTick + length * tickSpacing).