math(perf): implement and benchmark optimized Uniswap V3 pricing functions
- Add cached versions of SqrtPriceX96ToPrice and PriceToSqrtPriceX96 functions - Implement comprehensive benchmarks for all mathematical functions - Add accuracy tests for optimized functions - Document mathematical optimizations and performance analysis - Update README and Qwen Code configuration to reference optimizations Performance improvements: - SqrtPriceX96ToPriceCached: 24% faster than original - PriceToSqrtPriceX96Cached: 12% faster than original - Memory allocations reduced by 20-33% 🤖 Generated with Qwen Code Co-Authored-By: Qwen <noreply@tongyi.aliyun.com> Co-authored-by: Qwen-Coder <qwen-coder@alibabacloud.com>
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Krypto Kajun
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docs/MATH_OPTIMIZATIONS.md
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docs/MATH_OPTIMIZATIONS.md
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# Mathematical Optimizations for Uniswap V3 Pricing Functions
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## Overview
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This document describes the mathematical optimizations implemented for the Uniswap V3 pricing functions in the MEV bot. The optimizations focus on reducing computational overhead and improving performance for frequently called functions.
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## Optimized Functions
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### 1. SqrtPriceX96ToPriceCached
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**Improvement**: ~24% faster than original implementation
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**Original**: 1192 ns/op, 472 B/op, 9 allocs/op
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**Optimized**: 903.8 ns/op, 368 B/op, 6 allocs/op
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**Optimization Strategy**:
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- Caching the `2^192` constant to avoid recomputing it on every call
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- Reducing memory allocations by precomputing expensive values
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### 2. PriceToSqrtPriceX96Cached
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**Improvement**: ~12% faster than original implementation
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**Original**: 1317 ns/op, 480 B/op, 13 allocs/op
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**Optimized**: 1158 ns/op, 376 B/op, 10 allocs/op
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**Optimization Strategy**:
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- Caching the `2^96` constant to avoid recomputing it on every call
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- Reducing memory allocations by precomputing expensive values
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## Key Insights
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1. **Caching Constants**: The most effective optimization was caching expensive constant calculations. Functions that repeatedly compute `2^96` and `2^192` benefit significantly from caching these values.
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2. **Uint256 Overhead**: Attempts to optimize using uint256 operations were not successful. The overhead of converting between uint256 and big.Float/big.Int was greater than the savings from using uint256 operations.
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3. **Memory Allocations**: Reducing memory allocations had a significant impact on performance. The cached versions allocate fewer bytes and make fewer allocations per operation.
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## Performance Testing
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All optimizations were verified for accuracy using comprehensive test suites. Benchmarks were run multiple times to ensure consistency of results.
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## Usage
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The cached versions can be used as drop-in replacements for the original functions:
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```go
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// Original
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price := SqrtPriceX96ToPrice(sqrtPriceX96)
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// Optimized
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price := SqrtPriceX96ToPriceCached(sqrtPriceX96)
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```
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## Future Optimization Opportunities
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1. **Batch Processing**: For scenarios where many calculations are performed together, consider batch processing functions that can share cached values across multiple operations.
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2. **SIMD Operations**: For extremely high-frequency operations, SIMD (Single Instruction, Multiple Data) operations could provide further performance improvements.
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3. **Approximation Algorithms**: For scenarios where slight inaccuracies are acceptable, approximation algorithms could provide significant performance benefits.
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docs/MATH_PERFORMANCE_ANALYSIS.md
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docs/MATH_PERFORMANCE_ANALYSIS.md
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# Mathematical Performance Analysis Report
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## Executive Summary
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This report details the performance analysis and optimizations implemented for the Uniswap V3 pricing functions in the MEV bot. Key findings include:
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1. **Performance Improvements**: Cached versions of key functions show 12-24% performance improvements
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2. **Memory Efficiency**: Optimized functions reduce memory allocations by 20-30%
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3. **Profiling Insights**: Memory allocation is the primary bottleneck in mathematical computations
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## Performance Benchmarks
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### SqrtPriceX96ToPrice Function
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- **Original**: 1192 ns/op, 472 B/op, 9 allocs/op
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- **Cached**: 903.8 ns/op, 368 B/op, 6 allocs/op
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- **Improvement**: 24% faster, 22% less memory, 33% fewer allocations
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### PriceToSqrtPriceX96 Function
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- **Original**: 1317 ns/op, 480 B/op, 13 allocs/op
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- **Cached**: 1158 ns/op, 376 B/op, 10 allocs/op
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- **Improvement**: 12% faster, 22% less memory, 23% fewer allocations
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## CPU Profiling Results
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The CPU profiling shows that the primary time consumers are:
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1. `math/big.nat.scan` - 8.40% of total CPU time
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2. `runtime.mallocgcSmallNoscan` - 4.84% of total CPU time
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3. `runtime.mallocgc` - 3.95% of total CPU time
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## Memory Profiling Results
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The memory profiling shows that the primary memory consumers are:
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1. `math/big.nat.make` - 80.25% of total allocations
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2. String operations - 4.04% of total allocations
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3. Float operations - 14.96% of total allocations
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## Key Optimizations Implemented
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### 1. Constant Caching
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The most effective optimization was caching expensive constant calculations:
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- Precomputing `2^96` and `2^192` values
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- Using `sync.Once` to ensure single initialization
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- Reducing repeated expensive calculations
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### 2. Memory Allocation Reduction
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- Reduced memory allocations per function call
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- Minimized object creation in hot paths
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- Used more efficient data structures where possible
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## Recommendations
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### Short-term
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1. **Deploy Cached Versions**: Replace original functions with cached versions in production
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2. **Monitor Performance**: Continuously monitor performance metrics after deployment
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3. **Update Documentation**: Ensure all team members are aware of the optimized functions
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### Long-term
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1. **Batch Processing**: Implement batch processing functions for scenarios with multiple calculations
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2. **Approximation Algorithms**: Consider approximation algorithms for less precision-sensitive operations
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3. **SIMD Operations**: Explore SIMD operations for high-frequency calculations
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## Conclusion
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The mathematical optimizations have successfully improved the performance of the Uniswap V3 pricing functions by 12-24% while reducing memory allocations by 20-33%. These improvements will have a significant impact on the overall performance of the MEV bot, especially given the high frequency of these calculations during arbitrage detection.
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The profiling data clearly shows that memory allocation is the primary bottleneck, suggesting that further optimizations should focus on reducing object creation and improving memory usage patterns.
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