> 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/exponential.md).

# Exponential.sol

View Source: [contracts/Exponential.sol](https://app.gitbook.com/s/-MQ0mmOovvt0G2zyJIgA/contracts/Exponential.sol)

**↗ Extends:** [**ErrorReporter**](https://app.gitbook.com/s/-MQ0mmOovvt0G2zyJIgA/docs/ErrorReporter.md)**,** [**CarefulMath**](https://app.gitbook.com/s/-MQ0mmOovvt0G2zyJIgA/docs/CarefulMath.md) **↘ Derived Contracts:** [**AlkemiEarnPublic**](https://app.gitbook.com/s/-MQ0mmOovvt0G2zyJIgA/docs/AlkemiEarnPublic.md)**,** [**AlkemiEarnVerified**](https://app.gitbook.com/s/-MQ0mmOovvt0G2zyJIgA/docs/AlkemiEarnVerified.md)**,** [**AlkemiRateModel**](https://app.gitbook.com/s/-MQ0mmOovvt0G2zyJIgA/docs/AlkemiRateModel.md)**,** [**ExchangeRateModel**](https://app.gitbook.com/s/-MQ0mmOovvt0G2zyJIgA/docs/ExchangeRateModel.md)**,** [**PriceOracle**](https://app.gitbook.com/s/-MQ0mmOovvt0G2zyJIgA/docs/PriceOracle.md)

### Structs

#### Exp

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

### Contract Members

**Constants & Variables**

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

### Functions

* getExp(uint256 num, uint256 denom)
* addExp(struct Exponential.Exp a, struct Exponential.Exp b)
* subExp(struct Exponential.Exp a, struct Exponential.Exp b)
* mulScalar(struct Exponential.Exp a, uint256 scalar)
* divScalar(struct Exponential.Exp a, uint256 scalar)
* divScalarByExp(uint256 scalar, struct Exponential.Exp divisor)
* mulExp(struct Exponential.Exp a, struct Exponential.Exp b)
* divExp(struct Exponential.Exp a, struct Exponential.Exp b)
* truncate(struct Exponential.Exp exp)
* lessThanExp(struct Exponential.Exp left, struct Exponential.Exp right)
* lessThanOrEqualExp(struct Exponential.Exp left, struct Exponential.Exp right)
* greaterThanExp(struct Exponential.Exp left, struct Exponential.Exp right)
* isZeroExp(struct Exponential.Exp value)

#### getExp

Creates an exponential from numerator and denominator values. Note: Returns an error if (`num` \* 10e18) > MAX\_INT, or if `denom` is zero.

```javascript
function getExp(uint256 num, uint256 denom) internal pure
returns(enum ErrorReporter.Error, struct Exponential.Exp)
```

**Arguments**

| Name  | Type    | Description |
| ----- | ------- | ----------- |
| num   | uint256 |             |
| denom | uint256 |             |

#### addExp

Adds two exponentials, returning a new exponential.

```javascript
function addExp(struct Exponential.Exp a, struct Exponential.Exp b) internal pure
returns(enum ErrorReporter.Error, struct Exponential.Exp)
```

**Arguments**

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

#### subExp

Subtracts two exponentials, returning a new exponential.

```javascript
function subExp(struct Exponential.Exp a, struct Exponential.Exp b) internal pure
returns(enum ErrorReporter.Error, struct Exponential.Exp)
```

**Arguments**

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

#### mulScalar

Multiply an Exp by a scalar, returning a new Exp.

```javascript
function mulScalar(struct Exponential.Exp a, uint256 scalar) internal pure
returns(enum ErrorReporter.Error, struct Exponential.Exp)
```

**Arguments**

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

#### divScalar

Divide an Exp by a scalar, returning a new Exp.

```javascript
function divScalar(struct Exponential.Exp a, uint256 scalar) internal pure
returns(enum ErrorReporter.Error, struct Exponential.Exp)
```

**Arguments**

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

#### divScalarByExp

Divide a scalar by an Exp, returning a new Exp.

```javascript
function divScalarByExp(uint256 scalar, struct Exponential.Exp divisor) internal pure
returns(enum ErrorReporter.Error, struct Exponential.Exp)
```

**Arguments**

| Name    | Type                   | Description |
| ------- | ---------------------- | ----------- |
| scalar  | uint256                |             |
| divisor | struct Exponential.Exp |             |

#### mulExp

Multiplies two exponentials, returning a new exponential.

```javascript
function mulExp(struct Exponential.Exp a, struct Exponential.Exp b) internal pure
returns(enum ErrorReporter.Error, struct Exponential.Exp)
```

**Arguments**

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

#### divExp

Divides two exponentials, returning a new exponential. (a/scale) / (b/scale) = (a/scale) \* (scale/b) = a/b, which we can scale as an Exp by calling getExp(a.mantissa, b.mantissa)

```javascript
function divExp(struct Exponential.Exp a, struct Exponential.Exp b) internal pure
returns(enum ErrorReporter.Error, struct Exponential.Exp)
```

**Arguments**

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

#### truncate

Truncates the given exp to a whole number value. For example, truncate(Exp{mantissa: 15 *(10\**18)}) = 15

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

**Arguments**

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

#### lessThanExp

Checks if first Exp is less than second Exp.

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

**Arguments**

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

#### lessThanOrEqualExp

Checks if left Exp <= right Exp.

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

**Arguments**

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

#### greaterThanExp

Checks if first Exp is greater than second Exp.

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

**Arguments**

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

#### isZeroExp

returns true if Exp is exactly zero

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

**Arguments**

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