mev-beta/docs/MATH_PERFORMANCE_ANALYSIS.md

Mathematical Performance Analysis

This document provides a detailed analysis of the performance characteristics of Uniswap V3 pricing functions in the MEV bot, including benchmark results and optimization impact.

Benchmark Methodology

All benchmarks were run on the same hardware configuration:

• OS: Linux
• CPU: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
• Go version: 1.24+

Benchmarks were executed using the command:

go test -bench=. -benchmem ./pkg/uniswap/

Detailed Benchmark Results

SqrtPriceX96 to Price Conversion

Function	Operations/sec	Time/op	Memory/op	Allocs/op
Original (SqrtPriceX96ToPrice)	908,228	1406 ns/op	472 B/op	9 allocs/op
Cached (SqrtPriceX96ToPriceCached)	1,240,842	1060 ns/op	368 B/op	6 allocs/op
Optimized (SqrtPriceX96ToPriceOptimized)	910,021	1379 ns/op	520 B/op	10 allocs/op

Improvement with Caching:

• Performance: 24.6% faster
• Memory: 22.0% reduction
• Allocations: 33.3% reduction

Price to SqrtPriceX96 Conversion

Function	Operations/sec	Time/op	Memory/op	Allocs/op
Original (PriceToSqrtPriceX96)	827,798	1324 ns/op	480 B/op	13 allocs/op
Cached (PriceToSqrtPriceX96Cached)	973,719	1072 ns/op	376 B/op	10 allocs/op
Optimized (PriceToSqrtPriceX96Optimized)	763,767	1695 ns/op	496 B/op	14 allocs/op

Improvement with Caching:

• Performance: 19.0% faster
• Memory: 21.7% reduction
• Allocations: 23.1% reduction

Tick to SqrtPriceX96 Conversion

Function	Operations/sec	Time/op	Memory/op	Allocs/op
Original (TickToSqrtPriceX96)	1,173,708	1018 ns/op	288 B/op	8 allocs/op
Optimized (TickToSqrtPriceX96Optimized)	1,000,000	1079 ns/op	320 B/op	9 allocs/op

SqrtPriceX96 to Tick Conversion

Function	Operations/sec	Time/op	Memory/op	Allocs/op
Original (SqrtPriceX96ToTick)	719,307	1628 ns/op	440 B/op	9 allocs/op
Optimized (GetTickAtSqrtPrice)	707,721	1654 ns/op	504 B/op	11 allocs/op

Tick Calculation Helpers

Function	Operations/sec	Time/op	Memory/op	Allocs/op
GetNextTick	1,000,000,000+	0.4047 ns/op	0 B/op	0 allocs/op
GetPreviousTick	1,000,000,000+	0.4728 ns/op	0 B/op	0 allocs/op

Performance Analysis

Key Performance Insights

1. Caching Constants is Highly Effective: The most significant performance improvements came from caching the expensive constants (2^96 and 2^192) rather than recomputing them on each function call.

2. Memory Allocations are a Bottleneck: Functions with fewer memory allocations consistently perform better. The cached versions reduced allocations by 20-33%, which directly correlates with improved performance.

3. uint256 Optimization Results are Mixed: While uint256 operations can be faster for certain calculations, our attempts to optimize with uint256 showed mixed results. The SqrtPriceX96ToPriceOptimized function showed modest improvements, but PriceToSqrtPriceX96Optimized actually performed worse than the original.

4. Simple Functions are Extremely Fast: Helper functions like GetNextTick and GetPreviousTick that perform simple arithmetic operations are extremely fast, with sub-nanosecond execution times.

Bottleneck Identification

Profiling revealed that the primary performance bottlenecks are:

1. Memory Allocation: Creating new big.Float and big.Int objects for calculations
2. Constant Computation: Repeatedly calculating 2^96 and 2^192
3. Type Conversions: Converting between different numeric types (big.Int, big.Float, uint256)

Optimization Impact on MEV Bot

These optimizations will have a significant impact on the MEV bot's performance:

1. Higher Throughput: With 12-24% faster pricing calculations, the bot can process more arbitrage opportunities per second.

2. Lower Latency: Reduced execution time for critical path calculations means faster decision-making.

3. Reduced Resource Usage: Fewer memory allocations mean less pressure on the garbage collector, resulting in more consistent performance.

4. Scalability: The optimizations make it more feasible to run the bot on less powerful hardware or to run multiple instances simultaneously.

Recommendations

1. Continue Using Cached Versions: The cached versions of SqrtPriceX96ToPrice and PriceToSqrtPriceX96 should be used in production as they provide consistent performance improvements.

2. Re-evaluate uint256 Approach: The mixed results with uint256 optimizations suggest that more careful analysis is needed. Consider profiling specific use cases to determine when uint256 provides benefits.

3. Monitor Performance in Production: Continue monitoring performance metrics in production to identify any new bottlenecks that may emerge under real-world conditions.

4. Consider Lookup Tables: For frequently used values, pre-computed lookup tables could provide additional performance improvements.

Future Work

1. Profile Real-World Usage: Conduct profiling of the bot under actual arbitrage detection workloads to identify additional optimization opportunities.

2. Explore Approximation Algorithms: For less precision-sensitive calculations, faster approximation algorithms could be considered.

3. Investigate Assembly Optimizations: For critical paths, hand-optimized assembly implementations could provide further gains.

4. Expand Benchmark Suite: Add more comprehensive benchmarks that cover edge cases and a wider range of input values.