# Pi Calculation Benchmark: Performance Comparison of 34 Programming Languages

## Overview

This study compares the performance of 34 programming languages when calculating π (pi) with high precision. The benchmark uses Machin's formula and measures execution time across multiple decimal precision levels.

## Test Environment

**Hardware:**
- **Model:** MacBook Neo (Mac17,5)
- **Processor:** Apple A18 Pro
  - 6 cores: 2 performance cores + 4 efficiency cores
  - Architecture: ARM64
- **Memory:** 8 GB RAM
- **Operating System:** macOS (Darwin)

**Methodology:**
- Each language runs 4 times per test
- First run is considered "warmup" and excluded
- Results are the average of the 3 subsequent runs
- Time measured in milliseconds (ms)
- Memory measured in bytes via RSS (Resident Set Size)

## Method: Machin's Formula

All implementations use Machin's formula for π calculation:

```
π/4 = 4·arctan(1/5) - arctan(1/239)
```

Where arctan(x) is calculated using the Taylor series:

```
arctan(x) = x - x³/3 + x⁵/5 - x⁷/7 + ...
```

**Advantages of this method:**
1. Fast convergence (few terms required)
2. Simple implementation
3. High precision possible
4. Only integer arithmetic required

## Performance Reports

Detailed performance reports are available for each decimal precision level:

- **[1 Decimal](reports/1_decimals.md)** - Minimal precision
- **[2 Decimals](reports/2_decimals.md)** - Low precision
- **[5 Decimals](reports/5_decimals.md)** - Medium precision
- **[10 Decimals](reports/10_decimals.md)** - Standard precision
- **[100 Decimals](reports/100_decimals.md)** - High precision
- **[1000 Decimals](reports/1000_decimals.md)** - Very high precision
- **[2000 Decimals](reports/2000_decimals.md)** - Extreme precision

## Summary Results (100 Decimals)

### All Languages Performance

| Rank | Language | Time (ms) | Memory (bytes) | Type |
|------|-----------|-----------|----------------|------|
| 1 | Assembly | 9 | 966,656 | Compiled |
| 1 | C | 9 | 180,224 | Compiled |
| 1 | C++ | 9 | 196,608 | Compiled |
| 1 | Rust | 9 | 0 | Compiled |
| 1 | Go | 9 | 180,224 | Compiled |
| 1 | Nim | 9 | 0 | Compiled |
| 1 | Odin | 9 | 0 | Compiled |
| 1 | Haskell | 9 | 0 | Compiled |
| 9 | Fortran | 27 | 196,608 | Compiled |
| 10 | Crystal | 28 | 180,224 | Compiled |
| 11 | Lua | 29 | 0 | Interpreted |
| 12 | Swift | 29 | 262,144 | Compiled |
| 13 | Bash | 32 | 2,000,000 | Interpreted |
| 14 | Zig | 33 | 2,730,000 | Compiled |
| 15 | Objective-C | 31 | 752,000 | Compiled |
| 16 | Dart | 31 | 11,749,000 | JIT |
| 17 | D | 35 | 10,154,000 | Compiled |
| 18 | Perl | 55 | 2,000,000 | Interpreted |
| 19 | Python | 57 | 2,000,000 | Interpreted |
| 19 | Java | 57 | 2,000,000 | JIT |
| 19 | C# | 57 | 2,016,000 | JIT |
| 22 | Scala | 58 | 2,000,000 | JIT |
| 23 | Brainfuck | 54 | 2,005,000 | Interpreted |
| 24 | PHP | 77 | 2,032,000 | Interpreted |
| 25 | Ruby | 79 | 2,000,000 | Interpreted |
| 26 | Kotlin | 83 | 2,032,000 | JIT |
| 27 | JavaScript | 84 | 2,032,000 | Interpreted |
| 28 | Erlang | 130 | 2,037,000 | Interpreted |
| 29 | TypeScript | 154 | 2,032,000 | Interpreted |
| 30 | R | 349 | 2,032,000 | Interpreted |
| 31 | Julia | 290 | 2,032,000 | JIT |
| 32 | Elixir | 898 | 2,037,000 | Interpreted |

### Language Categories

**Compiled Languages (Native Code):**
- Fastest execution (9-35 ms)
- Minimal memory usage (0-966,656 bytes)
- Consistent performance across decimal levels

**JIT-Compiled Languages:**
- Moderate execution time (31-290 ms)
- Higher memory usage (~2 MB)
- Good performance after warmup

**Interpreted Languages:**
- Variable execution time (29-898 ms)
- Moderate memory usage (~2 MB)
- Performance varies widely

## Key Findings

1. **Compiled languages dominate**: C, Assembly, Rust, Go, and Nim all execute in ~9ms
2. **Memory efficiency varies**: Compiled languages use minimal memory, JIT/interpreted use ~2 MB
3. **Performance scaling**: Compiled languages maintain consistent performance across all decimal levels
4. **JIT overhead**: Java, C#, Kotlin show startup overhead but good performance
5. **Interpreted languages**: Python, Perl, PHP, Ruby, JavaScript show moderate performance

## Languages Tested

**Compiled (10):** Assembly, C, C++, Rust, Go, Nim, Odin, Fortran, Swift, Crystal

**JIT-Compiled (4):** Java, C#, Kotlin, Julia

**Interpreted (5):** Python, Perl, PHP, Ruby, JavaScript

**Other (15):** Bash, Brainfuck, D, Dart, Elixir, Erlang, Haskell, Lua, Objective-C, R, Scala, TypeScript, Vimscript, Wolfram, Zig

## Repository Structure

```
.
├── README.md                    # This file
├── reports/                     # Detailed performance reports
│   ├── summary.md              # Overall summary
│   ├── 1_decimals.md           # 1 decimal precision
│   ├── 2_decimals.md           # 2 decimals precision
│   ├── 5_decimals.md           # 5 decimals precision
│   ├── 10_decimals.md          # 10 decimals precision
│   ├── 100_decimals.md         # 100 decimals precision
│   ├── 1000_decimals.md       # 1000 decimals precision
│   └── 2000_decimals.md        # 2000 decimals precision
├── timelines/                   # Resource usage timeline data
├── assembly/                    # Assembly implementation
├── c/                          # C implementation
├── cpp/                        # C++ implementation
├── rust/                       # Rust implementation
└── ...                         # Other language implementations
```

## Running the Benchmark

```bash
# Build all languages
./build.sh

# Run all tests
./run_all.sh

# Run specific language
cd c && ./build.sh && ./print_hej

# Run detailed profiling (breaks down execution time)
./profile_detailed.sh 100
```

## Detailed Profiling

The benchmark includes a detailed profiling system that breaks down execution time into components:

- **Startup Time**: Runtime initialization, library loading, JIT compilation
- **Calculation Time**: Algorithm execution, numerical operations
- **I/O Time**: Output formatting, result printing

See [PROFILING.md](PROFILING.md) for detailed documentation.

## License

MIT License - See LICENSE file for details.

---

*Generated from Pi Calculation Benchmark - Apple A18 Pro Performance Study*