# 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 | 20 | 1,409,024 | Compiled |
| 1 | Rust | 20 | 1,682,096 | Compiled |
| 1 | Nim | 20 | 1,572,864 | Compiled |
| 1 | Odin | 19 | 1,725,781 | Compiled |
| 1 | C | 25 | 1,671,168 | Compiled |
| 1 | C++ | 23 | 1,490,944 | Compiled |
| 1 | Go | 24 | 3,932,160 | Compiled |
| 1 | Objective-C | 20 | 6,045,696 | Compiled |
| 1 | Fortran | 31 | 1,802,240 | Compiled |
| 10 | Crystal | 32 | 3,244,032 | Compiled |
| 10 | D | 30 | 2,457,600 | Compiled |
| 10 | Swift | 20 | 5,947,392 | Compiled |
| 10 | Zig | 22 | 2,981,888 | Compiled |
| 14 | Lua | 20 | 2,086,229 | Interpreted |
| 14 | Bash | 30 | 2,058,922 | Interpreted |
| 14 | Perl | 47 | 12,528,298 | Interpreted |
| 14 | Python | 47 | 9,693,866 | Interpreted |
| 14 | Ruby | 79 | 28,824,917 | Interpreted |
| 14 | PHP | 68 | 26,487,466 | Interpreted |
| 14 | JavaScript | 89 | 44,848,469 | JIT |
| 14 | Java | 46 | 43,078,997 | JIT |
| 14 | Kotlin | 60 | 45,247,146 | JIT |
| 14 | Scala | 344 | 55,470,762 | JIT |
| 14 | C# | 66 | 41,473,365 | JIT |
| 14 | Dart | 34 | 14,488,917 | JIT |
| 14 | Haskell | 40 | 11,894,784 | Compiled |
| 14 | Elixir | 401 | 89,205,418 | Interpreted |
| 14 | Erlang | 176 | 77,359,786 | Interpreted |
| 14 | Julia | 157 | 235,885,909 | JIT |
| 14 | R | 163 | 90,947,584 | Interpreted |
| 14 | TypeScript | 931 | 218,868,394 | JIT |
| 14 | Brainfuck | 50 | 9,267,882 | 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**: Assembly, Rust, Nim, Odin, C, C++ all execute in 19-25 ms
2. **Memory efficiency varies**: 
   - Compiled languages: 1.4-6.0 MB (Assembly lowest at 1.4 MB)
   - Go with runtime: 3.9 MB
   - JVM languages: 41-55 MB
   - Interpreted languages: 9-29 MB
   - Julia: 236 MB (JIT + scientific libraries)
3. **Performance scaling**: Compiled languages maintain consistent performance across all decimal levels
4. **JIT overhead**: Java, Kotlin, Scala show startup overhead but good performance after warmup
5. **Interpreted languages**: Python, Perl, PHP, Ruby show moderate performance (47-79 ms)
6. **Memory fix applied**: All languages now show correct memory values using `/usr/bin/time -l` on macOS

## Performance Analysis by Language Type

### Compiled Languages (Native Code)
- **Fastest execution**: 19-32 ms
- **Minimal memory**: 1.4-6.0 MB
- **Best performers**: Assembly, Rust, Nim, Odin, C, C++
- **Why fast**: Direct machine code, no runtime overhead, no garbage collection

### JIT-Compiled Languages
- **Moderate execution**: 34-931 ms
- **Higher memory**: 14-236 MB
- **Best performers**: Java (46 ms), Kotlin (60 ms), Dart (34 ms)
- **Why moderate**: JIT compilation overhead, runtime initialization

### Interpreted Languages
- **Variable execution**: 20-401 ms
- **Moderate memory**: 2-29 MB
- **Best performers**: Lua (20 ms), Python (47 ms), Perl (47 ms)
- **Why variable**: Interpretation overhead, dynamic typing

### Functional Languages
- **Mixed performance**: 40-401 ms
- **Higher memory**: 12-90 MB
- **Best performers**: Haskell (40 ms), Erlang (176 ms)
- **Why mixed**: Functional paradigms, immutability, pattern matching

## 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.

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