> For the complete documentation index, see [llms.txt](https://docs.ionprotocol.io/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.ionprotocol.io/devs/smart-contract-architecture/libraries/math/wadraymath.md).

# WadRayMath

[Git Source](https://github.com/Ion-Protocol/ion-protocol/blob/88cc595825f1dc2eb738fb93e172a3e8ab7a5c43/src/libraries/math/WadRayMath.sol)

This library provides mul/div\[up/down] functionality for WAD, RAY and RAD with phantom overflow protection as well as scale\[up/down] functionality for WAD, RAY and RAD.

### [Functions](broken://pages/jm31EM4gWXTfb5CMs4fr) <a href="#functions" id="functions"></a>

#### [wadMulDown](broken://pages/jm31EM4gWXTfb5CMs4fr) <a href="#wadmuldown" id="wadmuldown"></a>

Multiplies two WAD numbers and returns the result as a WAD rounding the result down.

```
function wadMulDown(uint256 a, uint256 b) internal pure returns (uint256);
```

**Parameters**

| Name | Type      | Description   |
| ---- | --------- | ------------- |
| `a`  | `uint256` | Multiplicand. |
| `b`  | `uint256` | Multiplier.   |

#### [wadMulUp](broken://pages/jm31EM4gWXTfb5CMs4fr) <a href="#wadmulup" id="wadmulup"></a>

Multiplies two WAD numbers and returns the result as a WAD rounding the result up.

```
function wadMulUp(uint256 a, uint256 b) internal pure returns (uint256);
```

**Parameters**

| Name | Type      | Description   |
| ---- | --------- | ------------- |
| `a`  | `uint256` | Multiplicand. |
| `b`  | `uint256` | Multiplier.   |

#### [wadDivDown](broken://pages/jm31EM4gWXTfb5CMs4fr) <a href="#waddivdown" id="waddivdown"></a>

Divides two WAD numbers and returns the result as a WAD rounding the result down.

```
function wadDivDown(uint256 a, uint256 b) internal pure returns (uint256);
```

**Parameters**

| Name | Type      | Description |
| ---- | --------- | ----------- |
| `a`  | `uint256` | Dividend.   |
| `b`  | `uint256` | Divisor.    |

#### [wadDivUp](broken://pages/jm31EM4gWXTfb5CMs4fr) <a href="#waddivup" id="waddivup"></a>

Divides two WAD numbers and returns the result as a WAD rounding the result up.

```
function wadDivUp(uint256 a, uint256 b) internal pure returns (uint256);
```

**Parameters**

| Name | Type      | Description |
| ---- | --------- | ----------- |
| `a`  | `uint256` | Dividend.   |
| `b`  | `uint256` | Divisor.    |

#### [rayMulDown](broken://pages/jm31EM4gWXTfb5CMs4fr) <a href="#raymuldown" id="raymuldown"></a>

Multiplies two RAY numbers and returns the result as a RAY rounding the result down.

```
function rayMulDown(uint256 a, uint256 b) internal pure returns (uint256);
```

**Parameters**

| Name | Type      | Description  |
| ---- | --------- | ------------ |
| `a`  | `uint256` | Multiplicand |
| `b`  | `uint256` | Multiplier   |

#### [rayMulUp](broken://pages/jm31EM4gWXTfb5CMs4fr) <a href="#raymulup" id="raymulup"></a>

Multiplies two RAY numbers and returns the result as a RAY rounding the result up.

```
function rayMulUp(uint256 a, uint256 b) internal pure returns (uint256);
```

**Parameters**

| Name | Type      | Description  |
| ---- | --------- | ------------ |
| `a`  | `uint256` | Multiplicand |
| `b`  | `uint256` | Multiplier   |

#### [rayDivDown](broken://pages/jm31EM4gWXTfb5CMs4fr) <a href="#raydivdown" id="raydivdown"></a>

Divides two RAY numbers and returns the result as a RAY rounding the result down.

```
function rayDivDown(uint256 a, uint256 b) internal pure returns (uint256);
```

**Parameters**

| Name | Type      | Description |
| ---- | --------- | ----------- |
| `a`  | `uint256` | Dividend    |
| `b`  | `uint256` | Divisor     |

#### [rayDivUp](broken://pages/jm31EM4gWXTfb5CMs4fr) <a href="#raydivup" id="raydivup"></a>

Divides two RAY numbers and returns the result as a RAY rounding the result up.

```
function rayDivUp(uint256 a, uint256 b) internal pure returns (uint256);
```

**Parameters**

| Name | Type      | Description |
| ---- | --------- | ----------- |
| `a`  | `uint256` | Dividend    |
| `b`  | `uint256` | Divisor     |

#### [radMulDown](broken://pages/jm31EM4gWXTfb5CMs4fr) <a href="#radmuldown" id="radmuldown"></a>

Multiplies two RAD numbers and returns the result as a RAD rounding the result down.

```
function radMulDown(uint256 a, uint256 b) internal pure returns (uint256);
```

**Parameters**

| Name | Type      | Description  |
| ---- | --------- | ------------ |
| `a`  | `uint256` | Multiplicand |
| `b`  | `uint256` | Multiplier   |

#### [radMulUp](broken://pages/jm31EM4gWXTfb5CMs4fr) <a href="#radmulup" id="radmulup"></a>

Multiplies two RAD numbers and returns the result as a RAD rounding the result up.

```
function radMulUp(uint256 a, uint256 b) internal pure returns (uint256);
```

**Parameters**

| Name | Type      | Description  |
| ---- | --------- | ------------ |
| `a`  | `uint256` | Multiplicand |
| `b`  | `uint256` | Multiplier   |

#### [radDivDown](broken://pages/jm31EM4gWXTfb5CMs4fr) <a href="#raddivdown" id="raddivdown"></a>

Divides two RAD numbers and returns the result as a RAD rounding the result down.

```
function radDivDown(uint256 a, uint256 b) internal pure returns (uint256);
```

**Parameters**

| Name | Type      | Description |
| ---- | --------- | ----------- |
| `a`  | `uint256` | Dividend    |
| `b`  | `uint256` | Divisor     |

#### [radDivUp](broken://pages/jm31EM4gWXTfb5CMs4fr) <a href="#raddivup" id="raddivup"></a>

Divides two RAD numbers and returns the result as a RAD rounding the result up.

```
function radDivUp(uint256 a, uint256 b) internal pure returns (uint256);
```

**Parameters**

| Name | Type      | Description |
| ---- | --------- | ----------- |
| `a`  | `uint256` | Dividend    |
| `b`  | `uint256` | Divisor     |

#### [scaleUpToWad](broken://pages/jm31EM4gWXTfb5CMs4fr) <a href="#scaleuptowad" id="scaleuptowad"></a>

Scales a value up from WAD. NOTE: The `scale` value must be less than 18.

```
function scaleUpToWad(uint256 value, uint256 scale) internal pure returns (uint256);
```

**Parameters**

| Name    | Type      | Description            |
| ------- | --------- | ---------------------- |
| `value` | `uint256` | to scale up.           |
| `scale` | `uint256` | of the returned value. |

#### [scaleUpToRay](broken://pages/jm31EM4gWXTfb5CMs4fr) <a href="#scaleuptoray" id="scaleuptoray"></a>

Scales a value up from RAY. NOTE: The `scale` value must be less than 27.

```
function scaleUpToRay(uint256 value, uint256 scale) internal pure returns (uint256);
```

**Parameters**

| Name    | Type      | Description            |
| ------- | --------- | ---------------------- |
| `value` | `uint256` | to scale up.           |
| `scale` | `uint256` | of the returned value. |

#### [scaleUpToRad](broken://pages/jm31EM4gWXTfb5CMs4fr) <a href="#scaleuptorad" id="scaleuptorad"></a>

Scales a value up from RAD. NOTE: The `scale` value must be less than 45.

```
function scaleUpToRad(uint256 value, uint256 scale) internal pure returns (uint256);
```

**Parameters**

| Name    | Type      | Description            |
| ------- | --------- | ---------------------- |
| `value` | `uint256` | to scale up.           |
| `scale` | `uint256` | of the returned value. |

#### [scaleDownToWad](broken://pages/jm31EM4gWXTfb5CMs4fr) <a href="#scaledowntowad" id="scaledowntowad"></a>

Scales a value down to WAD. NOTE: The `scale` value must be greater than 18.

```
function scaleDownToWad(uint256 value, uint256 scale) internal pure returns (uint256);
```

**Parameters**

| Name    | Type      | Description            |
| ------- | --------- | ---------------------- |
| `value` | `uint256` | to scale down.         |
| `scale` | `uint256` | of the returned value. |

#### [scaleDownToRay](broken://pages/jm31EM4gWXTfb5CMs4fr) <a href="#scaledowntoray" id="scaledowntoray"></a>

Scales a value down to RAY. NOTE: The `scale` value must be greater than 27.

```
function scaleDownToRay(uint256 value, uint256 scale) internal pure returns (uint256);
```

**Parameters**

| Name    | Type      | Description            |
| ------- | --------- | ---------------------- |
| `value` | `uint256` | to scale down.         |
| `scale` | `uint256` | of the returned value. |

#### [scaleDownToRad](broken://pages/jm31EM4gWXTfb5CMs4fr) <a href="#scaledowntorad" id="scaledowntorad"></a>

Scales a value down to RAD. NOTE: The `scale` value must be greater than 45.

```
function scaleDownToRad(uint256 value, uint256 scale) internal pure returns (uint256);
```

**Parameters**

| Name    | Type      | Description            |
| ------- | --------- | ---------------------- |
| `value` | `uint256` | to scale down.         |
| `scale` | `uint256` | of the returned value. |

#### [scaleUp](broken://pages/jm31EM4gWXTfb5CMs4fr) <a href="#scaleup" id="scaleup"></a>

Scales a value up from one fixed-point precision to another.

```
function scaleUp(uint256 value, uint256 from, uint256 to) internal pure returns (uint256);
```

**Parameters**

| Name    | Type      | Description              |
| ------- | --------- | ------------------------ |
| `value` | `uint256` | to scale up.             |
| `from`  | `uint256` | Precision to scale from. |
| `to`    | `uint256` | Precision to scale to.   |

#### [scaleDown](broken://pages/jm31EM4gWXTfb5CMs4fr) <a href="#scaledown" id="scaledown"></a>

Scales a value down from one fixed-point precision to another.

```
function scaleDown(uint256 value, uint256 from, uint256 to) internal pure returns (uint256);
```

**Parameters**

| Name    | Type      | Description              |
| ------- | --------- | ------------------------ |
| `value` | `uint256` | to scale down.           |
| `from`  | `uint256` | Precision to scale from. |
| `to`    | `uint256` | Precision to scale to.   |

### [Errors](broken://pages/jm31EM4gWXTfb5CMs4fr) <a href="#errors" id="errors"></a>

#### [NotScalingUp](broken://pages/jm31EM4gWXTfb5CMs4fr) <a href="#notscalingup" id="notscalingup"></a>

```
error NotScalingUp(uint256 from, uint256 to);
```

#### [NotScalingDown](broken://pages/jm31EM4gWXTfb5CMs4fr) <a href="#notscalingdown" id="notscalingdown"></a>

```
error NotScalingDown(uint256 from, uint256 to);
```