> For the complete documentation index, see [llms.txt](https://docs.alkemi.network/earn-contracts/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.alkemi.network/earn-contracts/docs/exponentialnoerror.md).

# Exponential module for storing fixed-precision decimals (ExponentialNoError.sol)

View Source: [contracts/ExponentialNoError.sol](https://github.com/AlkemiNetwork/alkemi-earn-contracts/tree/ae6d5c01ff8b3810c4005457ac7ce441ab1c7ec5/contracts/ExponentialNoError.sol)

**↘ Derived Contracts:** [**RewardControl**](/earn-contracts/docs/rewardcontrol.md)

Exp is a struct which stores decimals with a fixed precision of 18 decimal places. Thus, if we wanted to store the 5.1, mantissa would store 5.1e18. That is: `Exp({mantissa: 5100000000000000000})`.

### Structs

#### Exp

```javascript
struct Exp {
 uint256 mantissa
}
```

#### Double

```javascript
struct Double {
 uint256 mantissa
}
```

### Contract Members

**Constants & Variables**

```javascript
uint256 internal constant expScale;
uint256 internal constant doubleScale;
uint256 internal constant halfExpScale;
uint256 internal constant mantissaOne;
```

### Functions

* truncate(struct ExponentialNoError.Exp exp)
* mul\_ScalarTruncate(struct ExponentialNoError.Exp a, uint256 scalar)
* mul\_ScalarTruncateAddUInt(struct ExponentialNoError.Exp a, uint256 scalar, uint256 addend)
* lessThanExp(struct ExponentialNoError.Exp left, struct ExponentialNoError.Exp right)
* lessThanOrEqualExp(struct ExponentialNoError.Exp left, struct ExponentialNoError.Exp right)
* greaterThanExp(struct ExponentialNoError.Exp left, struct ExponentialNoError.Exp right)
* isZeroExp(struct ExponentialNoError.Exp value)
* safe224(uint256 n, string errorMessage)
* safe32(uint256 n, string errorMessage)
* add\_(struct ExponentialNoError.Exp a, struct ExponentialNoError.Exp b)
* add\_(struct ExponentialNoError.Double a, struct ExponentialNoError.Double b)
* add\_(uint256 a, uint256 b)
* add\_(uint256 a, uint256 b, string errorMessage)
* sub\_(struct ExponentialNoError.Exp a, struct ExponentialNoError.Exp b)
* sub\_(struct ExponentialNoError.Double a, struct ExponentialNoError.Double b)
* sub\_(uint256 a, uint256 b)
* sub\_(uint256 a, uint256 b, string errorMessage)
* mul\_(struct ExponentialNoError.Exp a, struct ExponentialNoError.Exp b)
* mul\_(struct ExponentialNoError.Exp a, uint256 b)
* mul\_(uint256 a, struct ExponentialNoError.Exp b)
* mul\_(struct ExponentialNoError.Double a, struct ExponentialNoError.Double b)
* mul\_(struct ExponentialNoError.Double a, uint256 b)
* mul\_(uint256 a, struct ExponentialNoError.Double b)
* mul\_(uint256 a, uint256 b)
* mul\_(uint256 a, uint256 b, string errorMessage)
* div\_(struct ExponentialNoError.Exp a, struct ExponentialNoError.Exp b)
* div\_(struct ExponentialNoError.Exp a, uint256 b)
* div\_(uint256 a, struct ExponentialNoError.Exp b)
* div\_(struct ExponentialNoError.Double a, struct ExponentialNoError.Double b)
* div\_(struct ExponentialNoError.Double a, uint256 b)
* div\_(uint256 a, struct ExponentialNoError.Double b)
* div\_(uint256 a, uint256 b)
* div\_(uint256 a, uint256 b, string errorMessage)
* fraction(uint256 a, uint256 b)

#### truncate

Truncates the given exp to a whole number value. For example, truncate(Exp{mantissa: 15 \* expScale}) = 15

```javascript
function truncate(struct ExponentialNoError.Exp exp) internal pure
returns(uint256)
```

**Arguments**

| Name | Type                          | Description |
| ---- | ----------------------------- | ----------- |
| exp  | struct ExponentialNoError.Exp |             |

#### mul\_ScalarTruncate

Multiply an Exp by a scalar, then truncate to return an unsigned integer.

```javascript
function mul_ScalarTruncate(struct ExponentialNoError.Exp a, uint256 scalar) internal pure
returns(uint256)
```

**Arguments**

| Name   | Type                          | Description |
| ------ | ----------------------------- | ----------- |
| a      | struct ExponentialNoError.Exp |             |
| scalar | uint256                       |             |

#### mul\_ScalarTruncateAddUInt

Multiply an Exp by a scalar, truncate, then add an to an unsigned integer, returning an unsigned integer.

```javascript
function mul_ScalarTruncateAddUInt(struct ExponentialNoError.Exp a, uint256 scalar, uint256 addend) internal pure
returns(uint256)
```

**Arguments**

| Name   | Type                          | Description |
| ------ | ----------------------------- | ----------- |
| a      | struct ExponentialNoError.Exp |             |
| scalar | uint256                       |             |
| addend | uint256                       |             |

#### lessThanExp

Checks if first Exp is less than second Exp.

```javascript
function lessThanExp(struct ExponentialNoError.Exp left, struct ExponentialNoError.Exp right) internal pure
returns(bool)
```

**Arguments**

| Name  | Type                          | Description |
| ----- | ----------------------------- | ----------- |
| left  | struct ExponentialNoError.Exp |             |
| right | struct ExponentialNoError.Exp |             |

#### lessThanOrEqualExp

Checks if left Exp <= right Exp.

```javascript
function lessThanOrEqualExp(struct ExponentialNoError.Exp left, struct ExponentialNoError.Exp right) internal pure
returns(bool)
```

**Arguments**

| Name  | Type                          | Description |
| ----- | ----------------------------- | ----------- |
| left  | struct ExponentialNoError.Exp |             |
| right | struct ExponentialNoError.Exp |             |

#### greaterThanExp

Checks if left Exp > right Exp.

```javascript
function greaterThanExp(struct ExponentialNoError.Exp left, struct ExponentialNoError.Exp right) internal pure
returns(bool)
```

**Arguments**

| Name  | Type                          | Description |
| ----- | ----------------------------- | ----------- |
| left  | struct ExponentialNoError.Exp |             |
| right | struct ExponentialNoError.Exp |             |

#### isZeroExp

returns true if Exp is exactly zero

```javascript
function isZeroExp(struct ExponentialNoError.Exp value) internal pure
returns(bool)
```

**Arguments**

| Name  | Type                          | Description |
| ----- | ----------------------------- | ----------- |
| value | struct ExponentialNoError.Exp |             |

#### safe224

```javascript
function safe224(uint256 n, string errorMessage) internal pure
returns(uint224)
```

**Arguments**

| Name         | Type    | Description |
| ------------ | ------- | ----------- |
| n            | uint256 |             |
| errorMessage | string  |             |

#### safe32

```javascript
function safe32(uint256 n, string errorMessage) internal pure
returns(uint32)
```

**Arguments**

| Name         | Type    | Description |
| ------------ | ------- | ----------- |
| n            | uint256 |             |
| errorMessage | string  |             |

#### add\_

```javascript
function add_(struct ExponentialNoError.Exp a, struct ExponentialNoError.Exp b) internal pure
returns(struct ExponentialNoError.Exp)
```

**Arguments**

| Name | Type                          | Description |
| ---- | ----------------------------- | ----------- |
| a    | struct ExponentialNoError.Exp |             |
| b    | struct ExponentialNoError.Exp |             |

#### add\_

```javascript
function add_(struct ExponentialNoError.Double a, struct ExponentialNoError.Double b) internal pure
returns(struct ExponentialNoError.Double)
```

**Arguments**

| Name | Type                             | Description |
| ---- | -------------------------------- | ----------- |
| a    | struct ExponentialNoError.Double |             |
| b    | struct ExponentialNoError.Double |             |

#### add\_

```javascript
function add_(uint256 a, uint256 b) internal pure
returns(uint256)
```

**Arguments**

| Name | Type    | Description |
| ---- | ------- | ----------- |
| a    | uint256 |             |
| b    | uint256 |             |

#### add\_

```javascript
function add_(uint256 a, uint256 b, string errorMessage) internal pure
returns(uint256)
```

**Arguments**

| Name         | Type    | Description |
| ------------ | ------- | ----------- |
| a            | uint256 |             |
| b            | uint256 |             |
| errorMessage | string  |             |

#### sub\_

```javascript
function sub_(struct ExponentialNoError.Exp a, struct ExponentialNoError.Exp b) internal pure
returns(struct ExponentialNoError.Exp)
```

**Arguments**

| Name | Type                          | Description |
| ---- | ----------------------------- | ----------- |
| a    | struct ExponentialNoError.Exp |             |
| b    | struct ExponentialNoError.Exp |             |

#### sub\_

```javascript
function sub_(struct ExponentialNoError.Double a, struct ExponentialNoError.Double b) internal pure
returns(struct ExponentialNoError.Double)
```

**Arguments**

| Name | Type                             | Description |
| ---- | -------------------------------- | ----------- |
| a    | struct ExponentialNoError.Double |             |
| b    | struct ExponentialNoError.Double |             |

#### sub\_

```javascript
function sub_(uint256 a, uint256 b) internal pure
returns(uint256)
```

**Arguments**

| Name | Type    | Description |
| ---- | ------- | ----------- |
| a    | uint256 |             |
| b    | uint256 |             |

#### sub\_

```javascript
function sub_(uint256 a, uint256 b, string errorMessage) internal pure
returns(uint256)
```

**Arguments**

| Name         | Type    | Description |
| ------------ | ------- | ----------- |
| a            | uint256 |             |
| b            | uint256 |             |
| errorMessage | string  |             |

#### mul\_

```javascript
function mul_(struct ExponentialNoError.Exp a, struct ExponentialNoError.Exp b) internal pure
returns(struct ExponentialNoError.Exp)
```

**Arguments**

| Name | Type                          | Description |
| ---- | ----------------------------- | ----------- |
| a    | struct ExponentialNoError.Exp |             |
| b    | struct ExponentialNoError.Exp |             |

#### mul\_

```javascript
function mul_(struct ExponentialNoError.Exp a, uint256 b) internal pure
returns(struct ExponentialNoError.Exp)
```

**Arguments**

| Name | Type                          | Description |
| ---- | ----------------------------- | ----------- |
| a    | struct ExponentialNoError.Exp |             |
| b    | uint256                       |             |

#### mul\_

```javascript
function mul_(uint256 a, struct ExponentialNoError.Exp b) internal pure
returns(uint256)
```

**Arguments**

| Name | Type                          | Description |
| ---- | ----------------------------- | ----------- |
| a    | uint256                       |             |
| b    | struct ExponentialNoError.Exp |             |

#### mul\_

```javascript
function mul_(struct ExponentialNoError.Double a, struct ExponentialNoError.Double b) internal pure
returns(struct ExponentialNoError.Double)
```

**Arguments**

| Name | Type                             | Description |
| ---- | -------------------------------- | ----------- |
| a    | struct ExponentialNoError.Double |             |
| b    | struct ExponentialNoError.Double |             |

#### mul\_

```javascript
function mul_(struct ExponentialNoError.Double a, uint256 b) internal pure
returns(struct ExponentialNoError.Double)
```

**Arguments**

| Name | Type                             | Description |
| ---- | -------------------------------- | ----------- |
| a    | struct ExponentialNoError.Double |             |
| b    | uint256                          |             |

#### mul\_

```javascript
function mul_(uint256 a, struct ExponentialNoError.Double b) internal pure
returns(uint256)
```

**Arguments**

| Name | Type                             | Description |
| ---- | -------------------------------- | ----------- |
| a    | uint256                          |             |
| b    | struct ExponentialNoError.Double |             |

#### mul\_

```javascript
function mul_(uint256 a, uint256 b) internal pure
returns(uint256)
```

**Arguments**

| Name | Type    | Description |
| ---- | ------- | ----------- |
| a    | uint256 |             |
| b    | uint256 |             |

#### mul\_

```javascript
function mul_(uint256 a, uint256 b, string errorMessage) internal pure
returns(uint256)
```

**Arguments**

| Name         | Type    | Description |
| ------------ | ------- | ----------- |
| a            | uint256 |             |
| b            | uint256 |             |
| errorMessage | string  |             |

#### div\_

```javascript
function div_(struct ExponentialNoError.Exp a, struct ExponentialNoError.Exp b) internal pure
returns(struct ExponentialNoError.Exp)
```

**Arguments**

| Name | Type                          | Description |
| ---- | ----------------------------- | ----------- |
| a    | struct ExponentialNoError.Exp |             |
| b    | struct ExponentialNoError.Exp |             |

#### div\_

```javascript
function div_(struct ExponentialNoError.Exp a, uint256 b) internal pure
returns(struct ExponentialNoError.Exp)
```

**Arguments**

| Name | Type                          | Description |
| ---- | ----------------------------- | ----------- |
| a    | struct ExponentialNoError.Exp |             |
| b    | uint256                       |             |

#### div\_

```javascript
function div_(uint256 a, struct ExponentialNoError.Exp b) internal pure
returns(uint256)
```

**Arguments**

| Name | Type                          | Description |
| ---- | ----------------------------- | ----------- |
| a    | uint256                       |             |
| b    | struct ExponentialNoError.Exp |             |

#### div\_

```javascript
function div_(struct ExponentialNoError.Double a, struct ExponentialNoError.Double b) internal pure
returns(struct ExponentialNoError.Double)
```

**Arguments**

| Name | Type                             | Description |
| ---- | -------------------------------- | ----------- |
| a    | struct ExponentialNoError.Double |             |
| b    | struct ExponentialNoError.Double |             |

#### div\_

```javascript
function div_(struct ExponentialNoError.Double a, uint256 b) internal pure
returns(struct ExponentialNoError.Double)
```

**Arguments**

| Name | Type                             | Description |
| ---- | -------------------------------- | ----------- |
| a    | struct ExponentialNoError.Double |             |
| b    | uint256                          |             |

#### div\_

```javascript
function div_(uint256 a, struct ExponentialNoError.Double b) internal pure
returns(uint256)
```

**Arguments**

| Name | Type                             | Description |
| ---- | -------------------------------- | ----------- |
| a    | uint256                          |             |
| b    | struct ExponentialNoError.Double |             |

#### div\_

```javascript
function div_(uint256 a, uint256 b) internal pure
returns(uint256)
```

**Arguments**

| Name | Type    | Description |
| ---- | ------- | ----------- |
| a    | uint256 |             |
| b    | uint256 |             |

#### div\_

```javascript
function div_(uint256 a, uint256 b, string errorMessage) internal pure
returns(uint256)
```

**Arguments**

| Name         | Type    | Description |
| ------------ | ------- | ----------- |
| a            | uint256 |             |
| b            | uint256 |             |
| errorMessage | string  |             |

#### fraction

```javascript
function fraction(uint256 a, uint256 b) internal pure
returns(struct ExponentialNoError.Double)
```

**Arguments**

| Name | Type    | Description |
| ---- | ------- | ----------- |
| a    | uint256 |             |
| b    | uint256 |             |