# Utility functions for handling price, sqrt price, and tick index

This document provides an overview of commonly used utility methods and helper functions in the Cetus SDK.

### Core Concepts

#### Price, Tick Index, and Sqrt Price

| Concept    | Definition                                 | Features                                           | Application                                           |
| ---------- | ------------------------------------------ | -------------------------------------------------- | ----------------------------------------------------- |
| Price      | Token exchange ratio (e.g., token1/token0) | Continuous value, updates in real-time             | Directly determines trading rates                     |
| Tick Index | Discretized price interval index           | Spacing determined by fee tiers                    | Manages liquidity distribution ranges                 |
| Sqrt Price | Square root of price                       | Stored as fixed-point numbers (e.g., sqrtPriceX64) | Simplifies on-chain calculations, improves efficiency |

**Notes:**

1. **Price**
   * Represents the real-time ratio between two tokens (e.g., ETH/USDC)
2. **Tick Index**
   * Derived from P = 1.0001^i, where i is the Tick Index
   * Liquidity can only be provided at discrete Ticks (e.g., multiples of 10)
3. **Sqrt Price**
   * Used for computational efficiency (avoids floating-point operations)
   * In Uniswap V3, stored as sqrtPriceX64 (Q64 fixed-point format)

### 1. Tick index to price

when you want to open position, you don't know how to set your tick\_lower and tick\_upper.

```typescript
import { TickMath } from '@cetusprotocol/common-sdk'
// decimalsA and decimalsB means the decimal of coinA and coinB
const price = TickMath.tickIndexToPrice(tick_index, decimals_a, decimals_b)
```

### 2. Price to tick index

```typescript
import { TickMath } from '@cetusprotocol/common-sdk'
// decimalsA and decimalsB means the decimal of coinA and coinB
const price = TickMath.priceToTickIndex(tick_index, decimals_a, decimals_b)
```

### 3. Tick index to sqrt price x64

```typescript
import { TickMath } from '@cetusprotocol/common-sdk'
const sqrt_price_x64 = TickMath.tickIndexToSqrtPriceX64(tick_index)
```

### 4. Sqrt price x64 to tick index

```typescript
import { TickMath } from '@cetusprotocol/common-sdk'
const tick_index = TickMath.sqrtPriceX64ToTickIndex(sqrt_price_x64)
```

### 5. Price to sqrt price

```typescript
import { TickMath } from '@cetusprotocol/common-sdk'
const sqrt_price_x64 = TickMath.priceToSqrtPriceX64(price, decimals_a, decimals_b)
```

### 6. Sqrt price to price

```typescript
import { TickMath } from '@cetusprotocol/common-sdk'
const price = TickMath.sqrtPriceX64ToPrice(sqrt_price_x64, decimals_a, decimals_b)
```

### 7. Convert the tick index from i32 to u32

```typescript
import { asUintN } from '@cetusprotocol/common-sdk'
const tick_lower_i32 = -100
const tick_lower_u32 = asUintN(BigInt(tick_lower_i32)).toString()

const tick_upper_i32 = 100
const tick_upper_u32 = asUintN(BigInt(tick_upper_i32)).toString()
```


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