Automated Market Maker (AMM)

Constant product formula implementation with TWAP oracles and multi-hop swapping

Automated Market Maker (AMM) Programs in HolyC

This guide provides comprehensive coverage of implementing Automated Market Maker protocols on Solana using HolyC. AMMs are fundamental DeFi primitives that enable decentralized token exchanges through algorithmic price discovery.

Overview

An Automated Market Maker is a decentralized exchange protocol that uses mathematical formulas to price assets and provide liquidity. Instead of traditional order books, AMMs use liquidity pools and pricing algorithms to facilitate trades.

Key Concepts

Liquidity Pools: Collections of tokens locked in smart contracts that provide liquidity for trading pairs.

Constant Product Formula: The most common AMM formula, where x * y = k, ensuring that the product of token reserves remains constant.

Liquidity Providers (LPs): Users who deposit tokens into liquidity pools and earn fees from trades.

Slippage: Price impact of trades, especially significant for large orders relative to pool size.

AMM Architecture

Core Components

  1. Pool Management: Creating and managing liquidity pools
  2. Swap Engine: Executing token swaps with price calculation
  3. Liquidity Operations: Adding and removing liquidity
  4. Fee Collection: Distributing trading fees to liquidity providers
  5. Oracle Integration: Price feeds and arbitrage protection

Account Structure

// Pool account stores the state of a trading pair
struct Pool {
    U8[32] token_a_mint;        // Token A mint address
    U8[32] token_b_mint;        // Token B mint address
    U64 token_a_reserve;        // Token A reserves in pool
    U64 token_b_reserve;        // Token B reserves in pool
    U64 total_lp_supply;        // Total LP token supply
    U64 fee_numerator;          // Fee rate numerator (e.g., 3 for 0.3%)
    U64 fee_denominator;        // Fee rate denominator (e.g., 1000)
    U8[32] lp_mint;            // LP token mint address
    U8[32] authority;          // Pool authority
    Bool is_initialized;        // Pool initialization status
};

// User position in liquidity pool
struct LiquidityPosition {
    U8[32] pool;               // Pool address
    U8[32] owner;              // Position owner
    U64 lp_tokens;             // LP tokens held
    U64 last_fee_collection;   // Last fee collection timestamp
};

Implementation Guide

Pool Initialization

Pool creation establishes a new trading pair with initial parameters:

U0 initialize_pool(U8* token_a_mint, U8* token_b_mint, U64 fee_rate) {
    // Validate token mints are different
    if (compare_pubkeys(token_a_mint, token_b_mint)) {
        PrintF("ERROR: Cannot create pool with identical tokens\n");
        return;
    }
    
    // Generate pool PDA
    U8[32] pool_address;
    U8 bump_seed;
    find_program_address(&pool_address, &bump_seed, token_a_mint, token_b_mint);
    
    // Initialize pool account
    Pool* pool = get_account_data(pool_address);
    copy_pubkey(pool->token_a_mint, token_a_mint);
    copy_pubkey(pool->token_b_mint, token_b_mint);
    pool->token_a_reserve = 0;
    pool->token_b_reserve = 0;
    pool->total_lp_supply = 0;
    pool->fee_numerator = fee_rate;
    pool->fee_denominator = 1000;
    pool->is_initialized = True;
    
    PrintF("Pool initialized for token pair\n");
}

Liquidity Provision

Adding liquidity to pools requires maintaining the current price ratio:

U0 add_liquidity(U8* pool_address, U64 token_a_amount, U64 token_b_amount) {
    Pool* pool = get_account_data(pool_address);
    
    if (!pool->is_initialized) {
        PrintF("ERROR: Pool not initialized\n");
        return;
    }
    
    U64 lp_tokens_to_mint;
    
    // Calculate LP tokens for first liquidity provision
    if (pool->total_lp_supply == 0) {
        lp_tokens_to_mint = sqrt(token_a_amount * token_b_amount);
        
        // Minimum liquidity lock to prevent division by zero
        if (lp_tokens_to_mint < 1000) {
            PrintF("ERROR: Insufficient initial liquidity\n");
            return;
        }
    } else {
        // Calculate proportional LP tokens for existing pool
        U64 lp_from_a = (token_a_amount * pool->total_lp_supply) / pool->token_a_reserve;
        U64 lp_from_b = (token_b_amount * pool->total_lp_supply) / pool->token_b_reserve;
        
        // Use minimum to maintain price ratio
        lp_tokens_to_mint = min(lp_from_a, lp_from_b);
        
        // Recalculate actual token amounts needed
        token_a_amount = (lp_tokens_to_mint * pool->token_a_reserve) / pool->total_lp_supply;
        token_b_amount = (lp_tokens_to_mint * pool->token_b_reserve) / pool->total_lp_supply;
    }
    
    // Transfer tokens to pool
    transfer_tokens_to_pool(pool->token_a_mint, token_a_amount);
    transfer_tokens_to_pool(pool->token_b_mint, token_b_amount);
    
    // Update pool reserves
    pool->token_a_reserve += token_a_amount;
    pool->token_b_reserve += token_b_amount;
    pool->total_lp_supply += lp_tokens_to_mint;
    
    // Mint LP tokens to provider
    mint_lp_tokens(pool->lp_mint, lp_tokens_to_mint);
    
    PrintF("Liquidity added: %d LP tokens minted\n", lp_tokens_to_mint);
}

Token Swapping

The core swap functionality implements the constant product formula:

U0 swap_tokens(U8* pool_address, U8* input_mint, U64 input_amount, U64 minimum_output) {
    Pool* pool = get_account_data(pool_address);
    
    if (!pool->is_initialized) {
        PrintF("ERROR: Pool not initialized\n");
        return;
    }
    
    Bool is_a_to_b = compare_pubkeys(input_mint, pool->token_a_mint);
    Bool is_b_to_a = compare_pubkeys(input_mint, pool->token_b_mint);
    
    if (!is_a_to_b && !is_b_to_a) {
        PrintF("ERROR: Invalid token for this pool\n");
        return;
    }
    
    U64 input_reserve;
    U64 output_reserve;
    
    if (is_a_to_b) {
        input_reserve = pool->token_a_reserve;
        output_reserve = pool->token_b_reserve;
    } else {
        input_reserve = pool->token_b_reserve;
        output_reserve = pool->token_a_reserve;
    }
    
    // Calculate output amount using constant product formula
    // account for fees: input_with_fee = input_amount * (1000 - fee_rate) / 1000
    U64 input_with_fee = input_amount * (pool->fee_denominator - pool->fee_numerator) / pool->fee_denominator;
    U64 output_amount = (input_with_fee * output_reserve) / (input_reserve + input_with_fee);
    
    // Slippage protection
    if (output_amount < minimum_output) {
        PrintF("ERROR: Slippage tolerance exceeded\n");
        return;
    }
    
    // Execute swap
    if (is_a_to_b) {
        pool->token_a_reserve += input_amount;
        pool->token_b_reserve -= output_amount;
        transfer_tokens_from_pool(pool->token_b_mint, output_amount);
    } else {
        pool->token_b_reserve += input_amount;
        pool->token_a_reserve -= output_amount;
        transfer_tokens_from_pool(pool->token_a_mint, output_amount);
    }
    
    transfer_tokens_to_pool(input_mint, input_amount);
    
    PrintF("Swap executed: %d input for %d output\n", input_amount, output_amount);
}

Liquidity Removal

Removing liquidity returns proportional amounts of both tokens:

U0 remove_liquidity(U8* pool_address, U64 lp_tokens_to_burn) {
    Pool* pool = get_account_data(pool_address);
    
    if (!pool->is_initialized) {
        PrintF("ERROR: Pool not initialized\n");
        return;
    }
    
    if (lp_tokens_to_burn > pool->total_lp_supply) {
        PrintF("ERROR: Insufficient LP tokens in pool\n");
        return;
    }
    
    // Calculate proportional token amounts
    U64 token_a_amount = (lp_tokens_to_burn * pool->token_a_reserve) / pool->total_lp_supply;
    U64 token_b_amount = (lp_tokens_to_burn * pool->token_b_reserve) / pool->total_lp_supply;
    
    // Update pool state
    pool->token_a_reserve -= token_a_amount;
    pool->token_b_reserve -= token_b_amount;
    pool->total_lp_supply -= lp_tokens_to_burn;
    
    // Transfer tokens to user
    transfer_tokens_from_pool(pool->token_a_mint, token_a_amount);
    transfer_tokens_from_pool(pool->token_b_mint, token_b_amount);
    
    // Burn LP tokens
    burn_lp_tokens(pool->lp_mint, lp_tokens_to_burn);
    
    PrintF("Liquidity removed: %d token A, %d token B\n", token_a_amount, token_b_amount);
}

Advanced Features

Price Oracle Integration

AMMs can serve as price oracles by tracking time-weighted average prices:

struct PriceOracle {
    U64 last_price_0;          // Last recorded price
    U64 last_price_1;          // Last recorded price (inverse)
    U64 last_update_timestamp; // Last price update time
    U64 price_cumulative_0;    // Cumulative price for TWAP
    U64 price_cumulative_1;    // Cumulative price for TWAP (inverse)
};

U0 update_price_oracle(Pool* pool, PriceOracle* oracle) {
    U64 current_timestamp = get_current_timestamp();
    U64 time_elapsed = current_timestamp - oracle->last_update_timestamp;
    
    if (time_elapsed > 0) {
        // Calculate current prices
        U64 price_0 = (pool->token_b_reserve * PRICE_PRECISION) / pool->token_a_reserve;
        U64 price_1 = (pool->token_a_reserve * PRICE_PRECISION) / pool->token_b_reserve;
        
        // Update cumulative prices for TWAP calculation
        oracle->price_cumulative_0 += oracle->last_price_0 * time_elapsed;
        oracle->price_cumulative_1 += oracle->last_price_1 * time_elapsed;
        
        // Store current state
        oracle->last_price_0 = price_0;
        oracle->last_price_1 = price_1;
        oracle->last_update_timestamp = current_timestamp;
    }
}

Multi-Hop Swapping

Enable swaps through multiple pools for better prices:

U0 multi_hop_swap(U8** pool_addresses, U8** token_path, U64 input_amount, U64 minimum_output) {
    U64 current_amount = input_amount;
    U64 hop_count = get_array_length(pool_addresses);
    
    for (U64 i = 0; i < hop_count; i++) {
        Pool* pool = get_account_data(pool_addresses[i]);
        U8* input_token = token_path[i];
        
        // Calculate output for this hop
        U64 hop_output = calculate_swap_output(pool, input_token, current_amount);
        
        // Execute swap
        swap_tokens(pool_addresses[i], input_token, current_amount, 0);
        
        current_amount = hop_output;
    }
    
    // Final slippage check
    if (current_amount < minimum_output) {
        PrintF("ERROR: Multi-hop slippage tolerance exceeded\n");
        revert_transaction();
        return;
    }
    
    PrintF("Multi-hop swap completed: %d final output\n", current_amount);
}

Security Considerations

Reentrancy Protection

Prevent reentrancy attacks during swaps and liquidity operations:

static Bool swap_lock = False;

U0 swap_tokens_with_lock(U8* pool_address, U8* input_mint, U64 input_amount, U64 minimum_output) {
    if (swap_lock) {
        PrintF("ERROR: Reentrant call detected\n");
        return;
    }
    
    swap_lock = True;
    swap_tokens(pool_address, input_mint, input_amount, minimum_output);
    swap_lock = False;
}

Integer Overflow Protection

Implement safe arithmetic operations:

U64 safe_multiply(U64 a, U64 b) {
    if (a == 0 || b == 0) return 0;
    
    U64 result = a * b;
    if (result / a != b) {
        PrintF("ERROR: Integer overflow detected\n");
        revert_transaction();
        return 0;
    }
    
    return result;
}

U64 safe_divide(U64 a, U64 b) {
    if (b == 0) {
        PrintF("ERROR: Division by zero\n");
        revert_transaction();
        return 0;
    }
    
    return a / b;
}

Flash Loan Protection

Prevent price manipulation through large single-transaction operations:

U0 validate_price_impact(Pool* pool, U64 input_amount, U64 input_reserve) {
    U64 price_impact = (input_amount * 100) / input_reserve;
    
    // Limit single transaction impact to 10%
    if (price_impact > 10) {
        PrintF("ERROR: Price impact too high: %d%%\n", price_impact);
        revert_transaction();
        return;
    }
}

Testing and Deployment

Unit Testing

Test individual AMM functions with various scenarios:

U0 test_swap_calculation() {
    // Test constant product formula implementation
    U64 reserve_a = 1000000;  // 1M tokens
    U64 reserve_b = 2000000;  // 2M tokens
    U64 input_amount = 1000;  // 1K token input
    
    U64 expected_output = calculate_expected_output(reserve_a, reserve_b, input_amount);
    U64 actual_output = calculate_swap_output_mock(reserve_a, reserve_b, input_amount);
    
    assert(actual_output == expected_output, "Swap calculation test failed");
    PrintF("Swap calculation test passed\n");
}

U0 test_liquidity_calculation() {
    // Test LP token calculation for various scenarios
    U64 reserve_a = 1000000;
    U64 reserve_b = 1000000;
    U64 total_supply = 1000000;
    
    U64 add_a = 10000;
    U64 add_b = 10000;
    
    U64 expected_lp = (add_a * total_supply) / reserve_a;
    U64 actual_lp = calculate_lp_tokens_mock(reserve_a, reserve_b, total_supply, add_a, add_b);
    
    assert(actual_lp == expected_lp, "LP calculation test failed");
    PrintF("LP calculation test passed\n");
}

Integration Testing

Test complete AMM workflows:

U0 test_full_amm_workflow() {
    // Initialize pool
    initialize_pool(TOKEN_A_MINT, TOKEN_B_MINT, 30); // 3% fee
    
    // Add initial liquidity
    add_liquidity(POOL_ADDRESS, 1000000, 1000000);
    
    // Perform swap
    swap_tokens(POOL_ADDRESS, TOKEN_A_MINT, 1000, 990);
    
    // Remove liquidity
    remove_liquidity(POOL_ADDRESS, 500000);
    
    PrintF("Full AMM workflow test completed\n");
}

Performance Optimization

Gas Efficiency

Optimize operations for minimal compute unit consumption:

// Use bitwise operations for power-of-2 calculations
U64 fast_divide_by_1000(U64 value) {
    // Approximate division by 1000 using bit shifts
    // 1000 ≈ 1024 = 2^10
    return value >> 10;
}

// Cache frequently accessed data
static Pool cached_pool;
static U8[32] cached_pool_address;

Pool* get_pool_cached(U8* pool_address) {
    if (!compare_pubkeys(pool_address, cached_pool_address)) {
        cached_pool = *get_account_data(pool_address);
        copy_pubkey(cached_pool_address, pool_address);
    }
    return &cached_pool;
}

Memory Management

Efficient account data handling:

// Minimize account data reads/writes
U0 batch_pool_updates(Pool* pool, U64 new_reserve_a, U64 new_reserve_b, U64 new_supply) {
    // Single write operation instead of multiple
    pool->token_a_reserve = new_reserve_a;
    pool->token_b_reserve = new_reserve_b;
    pool->total_lp_supply = new_supply;
}

Common Patterns and Best Practices

Error Handling

Implement comprehensive error handling:

enum AmmError {
    AMM_SUCCESS = 0,
    AMM_INVALID_POOL = 1,
    AMM_INSUFFICIENT_LIQUIDITY = 2,
    AMM_SLIPPAGE_EXCEEDED = 3,
    AMM_INVALID_TOKEN = 4,
    AMM_OVERFLOW = 5,
    AMM_REENTRANCY = 6
};

AmmError validate_swap_parameters(Pool* pool, U8* input_mint, U64 input_amount, U64 minimum_output) {
    if (!pool->is_initialized) {
        return AMM_INVALID_POOL;
    }
    
    if (input_amount == 0) {
        return AMM_INSUFFICIENT_LIQUIDITY;
    }
    
    if (!compare_pubkeys(input_mint, pool->token_a_mint) && 
        !compare_pubkeys(input_mint, pool->token_b_mint)) {
        return AMM_INVALID_TOKEN;
    }
    
    return AMM_SUCCESS;
}

Event Logging

Track important operations for monitoring:

U0 emit_swap_event(U8* pool, U8* user, U8* input_mint, U64 input_amount, U64 output_amount) {
    PrintF("SWAP_EVENT: pool=%s user=%s input_mint=%s input_amount=%d output_amount=%d\n",
           encode_base58(pool), encode_base58(user), encode_base58(input_mint), 
           input_amount, output_amount);
}

U0 emit_liquidity_event(U8* pool, U8* user, U64 token_a_amount, U64 token_b_amount, U64 lp_tokens) {
    PrintF("LIQUIDITY_EVENT: pool=%s user=%s token_a=%d token_b=%d lp_tokens=%d\n",
           encode_base58(pool), encode_base58(user), 
           token_a_amount, token_b_amount, lp_tokens);
}

This comprehensive guide provides the foundation for implementing sophisticated AMM protocols on Solana using HolyC. The examples demonstrate production-ready patterns that can be extended for specific use cases and requirements.