# PriceHelper

[Git Source](https://github.com/traderjoe-xyz/joe-v2/blob/16f011d25e6bf6d0a0c479974345b623d491104f/src/libraries/PriceHelper.sol)

**Author:**\
Trader Joe

This library contains functions to calculate prices

## State Variables

### REAL\_ID\_SHIFT

```solidity
int256 private constant REAL_ID_SHIFT = 1 << 23;
```

## Functions

### getPriceFromId

*Calculates the price from the id and the bin step*

```solidity
function getPriceFromId(uint24 id, uint16 binStep) internal pure returns (uint256 price);
```

**Parameters**

| Name      | Type     | Description  |
| --------- | -------- | ------------ |
| `id`      | `uint24` | The id       |
| `binStep` | `uint16` | The bin step |

**Returns**

| Name    | Type      | Description                                      |
| ------- | --------- | ------------------------------------------------ |
| `price` | `uint256` | The price as a 128.128-binary fixed-point number |

### getIdFromPrice

*Calculates the id from the price and the bin step*

```solidity
function getIdFromPrice(uint256 price, uint16 binStep) internal pure returns (uint24 id);
```

**Parameters**

| Name      | Type      | Description                                      |
| --------- | --------- | ------------------------------------------------ |
| `price`   | `uint256` | The price as a 128.128-binary fixed-point number |
| `binStep` | `uint16`  | The bin step                                     |

**Returns**

| Name | Type     | Description |
| ---- | -------- | ----------- |
| `id` | `uint24` | The id      |

### getBase

*Calculates the base from the bin step, which is `1 + binStep / BASIS_POINT_MAX`*

```solidity
function getBase(uint16 binStep) internal pure returns (uint256);
```

**Parameters**

| Name      | Type     | Description  |
| --------- | -------- | ------------ |
| `binStep` | `uint16` | The bin step |

**Returns**

| Name     | Type      | Description   |
| -------- | --------- | ------------- |
| `<none>` | `uint256` | base The base |

### getExponent

*Calculates the exponent from the id, which is `id - REAL_ID_SHIFT`*

```solidity
function getExponent(uint24 id) internal pure returns (int256);
```

**Parameters**

| Name | Type     | Description |
| ---- | -------- | ----------- |
| `id` | `uint24` | The id      |

**Returns**

| Name     | Type     | Description           |
| -------- | -------- | --------------------- |
| `<none>` | `int256` | exponent The exponent |

### convertDecimalPriceTo128x128

*Converts a price with 18 decimals to a 128.128-binary fixed-point number*

```solidity
function convertDecimalPriceTo128x128(uint256 price) internal pure returns (uint256);
```

**Parameters**

| Name    | Type      | Description                |
| ------- | --------- | -------------------------- |
| `price` | `uint256` | The price with 18 decimals |

**Returns**

| Name     | Type      | Description                                        |
| -------- | --------- | -------------------------------------------------- |
| `<none>` | `uint256` | price128x128 The 128.128-binary fixed-point number |

### convert128x128PriceToDecimal

*Converts a 128.128-binary fixed-point number to a price with 18 decimals*

```solidity
function convert128x128PriceToDecimal(uint256 price128x128) internal pure returns (uint256);
```

**Parameters**

| Name           | Type      | Description                           |
| -------------- | --------- | ------------------------------------- |
| `price128x128` | `uint256` | The 128.128-binary fixed-point number |

**Returns**

| Name     | Type      | Description                      |
| -------- | --------- | -------------------------------- |
| `<none>` | `uint256` | price The price with 18 decimals |


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