# ISlippageCurve

### psi

```solidity
function psi(uint256 _b, uint256 _l, uint8 _decimals) external view returns (uint256 _psi)
```

Calculates the output of the function Psi for input values b and l

#### **Parameters**

| Name       | Type    | Description                                                               |
| ---------- | ------- | ------------------------------------------------------------------------- |
| \_b        | uint256 | the input value `b`                                                       |
| \_l        | uint256 | the input value `l`                                                       |
| \_decimals | uint8   | the number of decimals used for \_b and \_l and also for the return value |

#### **Return Values**

| Name  | Type    | Description        |
| ----- | ------- | ------------------ |
| \_psi | uint256 | the value Psi(b,l) |

***

### inverseDiagonal

```solidity
function inverseDiagonal(uint256 _b, uint256 _l, uint256 _capitalB, uint8 _decimals) external view returns (uint256 _t)
```

Given b,l and B >= Psi(b, l), this function determines the unique t>=0 such that Psi(b+t, l+t) = B

#### **Parameters**

| Name       | Type    | Description                                                                        |
| ---------- | ------- | ---------------------------------------------------------------------------------- |
| \_b        | uint256 | the input value `b`                                                                |
| \_l        | uint256 | the input value `l`                                                                |
| \_capitalB | uint256 | the input value `B`                                                                |
| \_decimals | uint8   | the number of decimals used for \_b, \_l, \_capitalB and also for the return value |

#### **Return Values**

| Name | Type    | Description  |
| ---- | ------- | ------------ |
| \_t  | uint256 | the number t |

***

### inverseHorizontal

```solidity
function inverseHorizontal(uint256 _b, uint256 _l, uint256 _capitalB, uint8 _decimals) external view returns (uint256 _t)
```

Given b,l and B >= Psi(b, l), this function determines the unique t>=0 such that Psi(b+t, l) = B

#### **Parameters**

| Name       | Type    | Description                                                                        |
| ---------- | ------- | ---------------------------------------------------------------------------------- |
| \_b        | uint256 | the input value `b`                                                                |
| \_l        | uint256 | the input value `l`                                                                |
| \_capitalB | uint256 | the input value `B`                                                                |
| \_decimals | uint8   | the number of decimals used for \_b, \_l, \_capitalB and also for the return value |

#### **Return Values**

| Name | Type    | Description  |
| ---- | ------- | ------------ |
| \_t  | uint256 | the number t |


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