# ExponentialNoError

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})`.

## expScale

```solidity
uint256 expScale
```

## doubleScale

```solidity
uint256 doubleScale
```

## halfExpScale

```solidity
uint256 halfExpScale
```

## mantissaOne

```solidity
uint256 mantissaOne
```

## Exp

```solidity
struct Exp {
  uint256 mantissa;
}
```

## Double

```solidity
struct Double {
  uint256 mantissa;
}
```

## truncate

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

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

## mul\_ScalarTruncate

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

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

## mul\_ScalarTruncateAddUInt

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

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

## lessThanExp

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

*Checks if first Exp is less than second Exp.*

## lessThanOrEqualExp

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

*Checks if left Exp <= right Exp.*

## greaterThanExp

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

*Checks if left Exp > right Exp.*

## isZeroExp

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

*returns true if Exp is exactly zero*

## safe224

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

## safe32

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

## add\_

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

## add\_

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

## add\_

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

## add\_

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

## sub\_

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

## sub\_

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

## sub\_

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

## sub\_

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

## mul\_

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

## mul\_

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

## mul\_

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

## mul\_

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

## mul\_

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

## mul\_

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

## mul\_

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

## mul\_

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

## div\_

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

## div\_

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

## div\_

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

## div\_

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

## div\_

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

## div\_

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

## div\_

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

## div\_

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

## fraction

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