# LiquityMath.sol

View Source: [contracts/Dependencies/LiquityMath.sol](../contracts/Dependencies/LiquityMath.sol)

**LiquityMath**

## Contract Members
**Constants & Variables**

```js
uint256 internal constant DECIMAL_PRECISION;
uint256 internal constant NICR_PRECISION;

```

## Functions

- [_min(uint256 _a, uint256 _b)](#_min)
- [_max(uint256 _a, uint256 _b)](#_max)
- [decMul(uint256 x, uint256 y)](#decmul)
- [_decPow(uint256 _base, uint256 _minutes)](#_decpow)
- [_getAbsoluteDifference(uint256 _a, uint256 _b)](#_getabsolutedifference)
- [_computeNominalCR(uint256 _coll, uint256 _debt)](#_computenominalcr)
- [_computeCR(uint256 _coll, uint256 _debt, uint256 _price)](#_computecr)

---    

> ### _min

```solidity
function _min(uint256 _a, uint256 _b) internal pure
returns(uint256)
```

**Arguments**

| Name        | Type           | Description  |
| ------------- |------------- | -----|
| _a | uint256 |  | 
| _b | uint256 |  | 

<details>
	<summary><strong>Source Code</strong></summary>

```javascript
 _min(uint _a, uint _b) internal pure returns (uint) {
        return (_a < _b) ? _a : _b;
    }

    fu
```
</details>

---    

> ### _max

```solidity
function _max(uint256 _a, uint256 _b) internal pure
returns(uint256)
```

**Arguments**

| Name        | Type           | Description  |
| ------------- |------------- | -----|
| _a | uint256 |  | 
| _b | uint256 |  | 

<details>
	<summary><strong>Source Code</strong></summary>

```javascript
 _max(uint _a, uint _b) internal pure returns (uint) {
        return (_a >= _b) ? _a : _b;
    }

    /*
```
</details>

---    

> ### decMul

```solidity
function decMul(uint256 x, uint256 y) internal pure
returns(decProd uint256)
```

**Arguments**

| Name        | Type           | Description  |
| ------------- |------------- | -----|
| x | uint256 |  | 
| y | uint256 |  | 

<details>
	<summary><strong>Source Code</strong></summary>

```javascript
 decMul(uint x, uint y) internal pure returns (uint decProd) {
        uint prod_xy = x.mul(y);

        decProd = prod_xy.add(DECIMAL_PRECISION / 2).div(DECIMAL_PRECISION);
    }

    /*
```
</details>

---    

> ### _decPow

```solidity
function _decPow(uint256 _base, uint256 _minutes) internal pure
returns(uint256)
```

**Arguments**

| Name        | Type           | Description  |
| ------------- |------------- | -----|
| _base | uint256 |  | 
| _minutes | uint256 |  | 

<details>
	<summary><strong>Source Code</strong></summary>

```javascript
 _decPow(uint _base, uint _minutes) internal pure returns (uint) {

        if (_minutes > 525600000) {_minutes = 525600000;}  // cap to avoid overflow

        if (_minutes == 0) {return DECIMAL_PRECISION;}

        uint y = DECIMAL_PRECISION;
        uint x = _base;
        uint n = _minutes;

        // Exponentiation-by-squaring
        while (n > 1) {
            if (n % 2 == 0) {
                x = decMul(x, x);
                n = n.div(2);
            } else { // if (n % 2 != 0)
                y = decMul(x, y);
                x = decMul(x, x);
                n = (n.sub(1)).div(2);
            }
        }

        return decMul(x, y);
  }

    fu
```
</details>

---    

> ### _getAbsoluteDifference

```solidity
function _getAbsoluteDifference(uint256 _a, uint256 _b) internal pure
returns(uint256)
```

**Arguments**

| Name        | Type           | Description  |
| ------------- |------------- | -----|
| _a | uint256 |  | 
| _b | uint256 |  | 

<details>
	<summary><strong>Source Code</strong></summary>

```javascript
 _getAbsoluteDifference(uint _a, uint _b) internal pure returns (uint) {
        return (_a >= _b) ? _a.sub(_b) : _b.sub(_a);
    }

    fu
```
</details>

---    

> ### _computeNominalCR

```solidity
function _computeNominalCR(uint256 _coll, uint256 _debt) internal pure
returns(uint256)
```

**Arguments**

| Name        | Type           | Description  |
| ------------- |------------- | -----|
| _coll | uint256 |  | 
| _debt | uint256 |  | 

<details>
	<summary><strong>Source Code</strong></summary>

```javascript
 _computeNominalCR(uint _coll, uint _debt) internal pure returns (uint) {
        if (_debt > 0) {
            return _coll.mul(NICR_PRECISION).div(_debt);
        }
        // Return the maximal value for uint256 if the Trove has a debt of 0. Represents "infinite" CR.
        else { // if (_debt == 0)
            return 2**256 - 1;
        }
    }

    fu
```
</details>

---    

> ### _computeCR

```solidity
function _computeCR(uint256 _coll, uint256 _debt, uint256 _price) internal pure
returns(uint256)
```

**Arguments**

| Name        | Type           | Description  |
| ------------- |------------- | -----|
| _coll | uint256 |  | 
| _debt | uint256 |  | 
| _price | uint256 |  | 

<details>
	<summary><strong>Source Code</strong></summary>

```javascript
 _computeCR(uint _coll, uint _debt, uint _price) internal pure returns (uint) {
        if (_debt > 0) {
            uint newCollRatio = _coll.mul(_price).div(_debt);

            return newCollRatio;
        }
        // Return the maximal value for uint256 if the Trove has a debt of 0. Represents "infinite" CR.
        else { // if (_debt == 0)
            return 2**256 - 1; 
        }
    }
}

```
</details>

## Contracts

* [ActivePool](ActivePool.md)
* [ActivePoolStorage](ActivePoolStorage.md)
* [BaseMath](BaseMath.md)
* [BorrowerOperations](BorrowerOperations.md)
* [BorrowerOperationsScript](BorrowerOperationsScript.md)
* [BorrowerOperationsStorage](BorrowerOperationsStorage.md)
* [BorrowerWrappersScript](BorrowerWrappersScript.md)
* [CheckContract](CheckContract.md)
* [CollSurplusPool](CollSurplusPool.md)
* [CollSurplusPoolStorage](CollSurplusPoolStorage.md)
* [console](console.md)
* [Context](Context.md)
* [DefaultPool](DefaultPool.md)
* [DefaultPoolStorage](DefaultPoolStorage.md)
* [DocsCover](DocsCover.md)
* [DSAuth](DSAuth.md)
* [DSAuthEvents](DSAuthEvents.md)
* [DSAuthority](DSAuthority.md)
* [DSNote](DSNote.md)
* [DSProxy](DSProxy.md)
* [DSProxyCache](DSProxyCache.md)
* [DSProxyFactory](DSProxyFactory.md)
* [ERC20](ERC20.md)
* [ETHTransferScript](ETHTransferScript.md)
* [FeeDistributor](FeeDistributor.md)
* [FeeDistributorStorage](FeeDistributorStorage.md)
* [GasPool](GasPool.md)
* [HintHelpers](HintHelpers.md)
* [HintHelpersStorage](HintHelpersStorage.md)
* [IActivePool](IActivePool.md)
* [IBalanceRedirectPresale](IBalanceRedirectPresale.md)
* [IBorrowerOperations](IBorrowerOperations.md)
* [ICollSurplusPool](ICollSurplusPool.md)
* [IDefaultPool](IDefaultPool.md)
* [IERC20](IERC20.md)
* [IERC2612](IERC2612.md)
* [IExternalPriceFeed](IExternalPriceFeed.md)
* [IFeeDistributor](IFeeDistributor.md)
* [IFeeSharingProxy](IFeeSharingProxy.md)
* [ILiquityBase](ILiquityBase.md)
* [ILiquityBaseParams](ILiquityBaseParams.md)
* [IMasset](IMasset.md)
* [IMoCBaseOracle](IMoCBaseOracle.md)
* [Initializable](Initializable.md)
* [IPool](IPool.md)
* [IPriceFeed](IPriceFeed.md)
* [IRSKOracle](IRSKOracle.md)
* [ISortedTroves](ISortedTroves.md)
* [IStabilityPool](IStabilityPool.md)
* [ITroveManager](ITroveManager.md)
* [IWrbtc](IWrbtc.md)
* [IZUSDToken](IZUSDToken.md)
* [LiquityBase](LiquityBase.md)
* [LiquityBaseParams](LiquityBaseParams.md)
* [LiquityMath](LiquityMath.md)
* [LiquitySafeMath128](LiquitySafeMath128.md)
* [MoCMedianizer](MoCMedianizer.md)
* [MultiTroveGetter](MultiTroveGetter.md)
* [MultiTroveGetterStorage](MultiTroveGetterStorage.md)
* [NueToken](NueToken.md)
* [Ownable](Ownable.md)
* [PriceFeed](PriceFeed.md)
* [PriceFeedStorage](PriceFeedStorage.md)
* [ProxiableContract](ProxiableContract.md)
* [ProxiableContract2](ProxiableContract2.md)
* [Proxy](Proxy.md)
* [RskOracle](RskOracle.md)
* [SafeMath](SafeMath.md)
* [SortedTroves](SortedTroves.md)
* [SortedTrovesStorage](SortedTrovesStorage.md)
* [StabilityPool](StabilityPool.md)
* [StabilityPoolScript](StabilityPoolScript.md)
* [StabilityPoolStorage](StabilityPoolStorage.md)
* [Storage](Storage.md)
* [Storage2](Storage2.md)
* [TokenScript](TokenScript.md)
* [TroveManager](TroveManager.md)
* [TroveManagerBase](TroveManagerBase.md)
* [TroveManagerBase1MinuteBootstrap](TroveManagerBase1MinuteBootstrap.md)
* [TroveManagerRedeemOps](TroveManagerRedeemOps.md)
* [TroveManagerScript](TroveManagerScript.md)
* [TroveManagerStorage](TroveManagerStorage.md)
* [UpgradableProxy](UpgradableProxy.md)
* [ZUSDToken](ZUSDToken.md)
* [ZUSDTokenStorage](ZUSDTokenStorage.md)