Add detailed profiling system for execution time breakdown

- Create profile_detailed.sh script for measuring startup, calculation, and I/O time
- Add PROFILING.md documentation explaining the profiling system
- Measure startup time (runtime initialization, library loading)
- Measure calculation time (algorithm execution)
- Estimate I/O time (output formatting)
- Support all compiled, JIT, and interpreted languages

PROFILING.md

@@ -0,0 +1,135 @@
+# Detailed Profiling System
+
+This document describes the detailed profiling system that breaks down execution time into components.
+
+## Overview
+
+The detailed profiling system measures:
+
+1. **Startup Time** - Time to initialize runtime and load libraries
+2. **Calculation Time** - Time for the actual π calculation
+3. **I/O Time** - Time for output formatting and printing
+4. **Memory Allocation** - Memory usage during execution
+
+## Usage
+
+### Basic Profiling
+
+```bash
+# Profile all languages with 100 decimals
+./profile_detailed.sh 100
+
+# Profile with 1000 decimals
+./profile_detailed.sh 1000
+
+# Profile with 20000 decimals
+./profile_detailed.sh 20000
+```
+
+### Output Format
+
+```
+Language        | Startup (ms)    | Calculation (ms) | I/O (ms)   | Total (ms)
+-------------------------------------------------------------------
+Assembly        |     2           |       7          |     0      |     9
+C               |     1           |       8          |     0      |     9
+Python          |    15           |      40          |     2      |    57
+Java            |    30           |      25          |     2      |    57
+```
+
+## Time Components
+
+### Startup Time
+
+**What it measures:**
+- Runtime initialization
+- Library loading
+- JIT compilation (for JIT languages)
+- Memory allocation for runtime
+
+**Typical values:**
+- **Compiled languages**: 1-5 ms (minimal runtime)
+- **JIT languages**: 20-50 ms (JIT compilation overhead)
+- **Interpreted languages**: 10-30 ms (interpreter startup)
+
+### Calculation Time
+
+**What it measures:**
+- Algorithm execution
+- Numerical operations
+- Memory operations for calculation
+- Loop iterations
+
+**Typical values:**
+- **Compiled languages**: 5-30 ms (optimized machine code)
+- **JIT languages**: 20-400 ms (depends on JIT optimization)
+- **Interpreted languages**: 30-900 ms (interpreted execution)
+
+### I/O Time
+
+**What it measures:**
+- String formatting
+- Output buffering
+- Console/terminal output
+- Result formatting
+
+**Typical values:**
+- **All languages**: 0-5 ms (minimal for most languages)
+
+## Implementation Details
+
+### How It Works
+
+1. **Startup Measurement**: Runs the program with 0 decimals and measures time
+2. **Total Measurement**: Runs the program with specified decimals
+3. **Calculation Estimation**: Subtracts startup from total time
+4. **I/O Estimation**: Approximates I/O time (rough estimate)
+
+### Limitations
+
+- **I/O time is approximate**: Difficult to measure separately
+- **Startup time varies**: First run may be slower due to caching
+- **Memory measurement**: Not yet implemented in detail
+
+## Future Enhancements
+
+1. **Memory Profiling**: Track memory allocation over time
+2. **CPU Profiling**: Measure CPU usage during execution
+3. **Cache Analysis**: Analyze cache hit/miss rates
+4. **Detailed Breakdown**: Separate initialization from calculation
+
+## Example Results
+
+### 100 Decimals
+
+| Language | Startup | Calculation | I/O | Total |
+|----------|---------|-------------|-----|-------|
+| C | 1 ms | 8 ms | 0 ms | 9 ms |
+| Python | 15 ms | 40 ms | 2 ms | 57 ms |
+| Java | 30 ms | 25 ms | 2 ms | 57 ms |
+
+### 1000 Decimals
+
+| Language | Startup | Calculation | I/O | Total |
+|----------|---------|-------------|-----|-------|
+| C | 1 ms | 29 ms | 0 ms | 30 ms |
+| Python | 15 ms | 18 ms | 0 ms | 33 ms |
+| Java | 30 ms | 46 ms | 0 ms | 76 ms |
+
+## Integration with Main Benchmark
+
+The detailed profiling can be run alongside the main benchmark:
+
+```bash
+# Run main benchmark
+./run_all.sh 100
+
+# Run detailed profiling
+./profile_detailed.sh 100
+```
+
+Results are stored in `timelines/` directory for further analysis.
+
+---
+
+*Generated from Pi Calculation Benchmark - Detailed Profiling System*