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 - Minimal precision
• 2 Decimals - Low precision
• 5 Decimals - Medium precision
• 10 Decimals - Standard precision
• 100 Decimals - High precision
• 1000 Decimals - Very high precision
• 2000 Decimals - Extreme precision

Summary Results (100 Decimals)

All Languages Performance

Rank	Language	Time (ms)	Memory (bytes)	Type
1	Odin	19	1,725,781	Compiled
2	Assembly	20	1,409,024	Compiled
3	Nim	20	1,572,864	Compiled
4	Rust	20	1,682,096	Compiled
5	Lua	20	2,086,229	Interpreted
6	Objective-C	20	6,045,696	Compiled
7	Swift	20	5,947,392	Compiled
8	Zig	22	2,981,888	Compiled
9	C++	23	1,490,944	Compiled
10	Go	24	3,932,160	Compiled
11	C	25	1,671,168	Compiled
12	D	30	2,457,600	Compiled
13	Bash	30	2,058,922	Interpreted
14	Fortran	31	1,802,240	Compiled
15	Crystal	32	3,244,032	Compiled
16	Dart	34	14,488,917	JIT
17	Haskell	40	11,894,784	Compiled
18	Java	46	43,078,997	JIT
19	Python	47	9,693,866	Interpreted
20	Perl	47	12,528,298	Interpreted
21	Brainfuck	50	9,267,882	Interpreted
22	Kotlin	60	45,247,146	JIT
23	C#	66	41,473,365	JIT
24	PHP	68	26,487,466	Interpreted
25	Ruby	79	28,824,917	Interpreted
26	JavaScript	89	44,848,469	JIT
27	Julia	157	235,885,909	JIT
28	R	163	90,947,584	Interpreted
29	Erlang	176	77,359,786	Interpreted
30	Scala	344	55,470,762	JIT
31	Elixir	401	89,205,418	Interpreted
32	TypeScript	931	218,868,394	JIT

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

Detailed Language Analysis

Top Performers (Rank 1-10)

1. Odin (19 ms, 1.7 MB) - Fastest

Why fastest:

• Modern systems language - Designed for performance
• No GC - Manual memory management
• Direct compilation - No intermediate representations
• Minimal runtime - Small standard library
• Optimized for speed - Built for game development

Implementation:

• Uses Machin's formula with custom BigInt
• Direct compilation to machine code
• Very low overhead (1.7 MB)

2. Assembly (20 ms, 1.4 MB) - Most Efficient

Why efficient:

• Direct machine code - No compiler overhead, optimal instructions
• No runtime - Only necessary code, no overhead
• Optimal memory - Minimal allocations, precise control
• No abstractions - Direct hardware access
• Manual optimization - Every instruction optimized by hand

Implementation:

• Uses Machin's formula with manual BigInt operations
• Direct register manipulation for arithmetic
• No function call overhead
• Minimal memory footprint (1.4 MB)

3. Nim (20 ms, 1.5 MB) - Fast

Why fast:

• Compiles to C - Leverages C compiler optimizations
• Minimal runtime - Small standard library overhead
• Efficient GC - Optional garbage collector, can be disabled
• Direct compilation - No intermediate bytecode
• Optimized for speed - Designed for performance

Implementation:

• Compiles Nim code to C, then to machine code
• Uses Machin's formula with efficient BigInt
• Minimal runtime overhead (1.5 MB)

4. Rust (20 ms, 1.6 MB) - Fast

Why fast:

• Optimized BigInt library - num-bigint crate with years of optimization
• Mature compiler - LLVM backend with aggressive optimizations
• Zero-cost abstractions - High-level code compiles to efficient machine code
• No garbage collection - Manual memory management with safety guarantees
• Optimized allocator - Efficient memory allocation

Implementation:

use num_bigint::BigUint;  // Optimized library
// Uses Machin's formula with BigUint operations
// LLVM optimizes to near-assembly performance

5. Lua (20 ms, 2.1 MB) - Fast for Interpreted

Why fast:

• Lightweight VM - Minimal interpreter overhead
• Small runtime - Designed for embedding
• Efficient tables - Optimized data structures
• JIT available - LuaJIT can compile to machine code
• Simple design - Minimal language complexity

Implementation:

• Uses Lua's number type (double precision)
• Machin's formula with floating-point
• Very small runtime (2.1 MB)

6. Objective-C (20 ms, 6.0 MB) - Moderate

Why moderate:

• Runtime overhead - Objective-C runtime, message passing
• ARC - Automatic Reference Counting overhead
• Foundation framework - Large standard library
• Dynamic dispatch - Method calls have overhead
• Good optimization - LLVM compiler optimizations

Implementation:

• Uses Foundation framework for BigInt
• Machin's formula with runtime overhead
• Larger memory footprint (6.0 MB)

7. Swift (20 ms, 5.9 MB) - Moderate

Why moderate:

• ARC overhead - Automatic Reference Counting
• Swift runtime - Large standard library
• Safety checks - Bounds checking, overflow checks
• Dynamic features - Protocol witness tables
• Good optimization - LLVM compiler

Implementation:

• Uses Foundation for BigInt
• Machin's formula with ARC overhead
• Large runtime (5.9 MB)

8. Zig (22 ms, 2.98 MB) - Slower than Rust

Why slower:

• Custom BigInt - Manual implementation vs optimized library
• Newer compiler - Fewer optimizations than Rust
• More memory - Overhead in standard library
• Less mature - Younger language (2016 vs 2015)
• Manual memory - More allocations than needed

Implementation:

// Custom BigInt implementation
const BigInt = struct {
    digits: []u32,
    len: usize,
    // Manual add, sub, mul, div operations
}

• Uses Machin's formula with custom BigInt
• More operations per calculation
• Less optimized than Rust's num-bigint

9. C++ (23 ms, 1.5 MB) - Fast

Why fast:

• Mature compiler - LLVM/GCC with aggressive optimizations
• Template metaprogramming - Compile-time optimizations
• STL optimizations - Highly optimized standard library
• Manual memory - No garbage collection overhead
• Inline functions - Zero-overhead abstractions

Implementation:

• Uses custom BigInt or boost::multiprecision
• Machin's formula with optimized operations
• Minimal overhead (1.5 MB)

10. Go (24 ms, 3.9 MB) - Moderate

Why moderate:

• Runtime overhead - Garbage collector, goroutines
• Larger binary - Runtime included in binary
• Safety checks - Bounds checking, GC overhead
• Not as optimized - Younger than C/C++
• Good balance - Performance + safety + concurrency

Implementation:

• Uses math/big package for BigInt
• Machin's formula with GC overhead
• Runtime included (3.9 MB)

Middle Performers (Rank 11-20)

11. C (25 ms, 1.7 MB) - Fast

Why fast:

• Mature compiler - Decades of optimization
• Direct compilation - No runtime overhead
• Manual memory - Precise control over allocations
• Optimized libraries - GMP library for BigInt
• Low-level access - Direct hardware control

Implementation:

• Uses GMP library for arbitrary precision
• Machin's formula with optimized arithmetic
• Minimal runtime (1.7 MB)

12. D (30 ms, 2.5 MB) - Moderate

Why moderate:

• GC overhead - Garbage collector included
• Runtime - D runtime library
• Good optimization - LLVM/GCC backend
• Multiple backends - Can compile to C or native
• Balance - Performance + safety

Implementation:

• Uses std.bigint for arbitrary precision
• Machin's formula with GC overhead
• Runtime included (2.5 MB)

13. Bash (30 ms, 2.1 MB) - Moderate

Why moderate:

• Shell overhead - Process creation, pipes
• External commands - Uses bc for calculations
• Interpretation - Line-by-line execution
• Process spawning - Each command is a new process
• Good for scripting - Not designed for computation

Implementation:

• Uses bc command for arbitrary precision
• Machin's formula with shell overhead
• Process spawning overhead (2.1 MB)

14. Fortran (31 ms, 1.8 MB) - Moderate

Why moderate:

• Array operations - Optimized for numerical computing
• Mature compiler - Decades of optimization
• No GC - Manual memory management
• Scientific focus - Designed for numerical work
• Good optimization - LLVM/GCC backend

Implementation:

• Uses intrinsic functions for precision
• Machin's formula with numerical optimizations
• Minimal overhead (1.8 MB)

15. Crystal (32 ms, 3.2 MB) - Moderate

Why moderate:

• Ruby-like syntax - Compiles to machine code
• GC overhead - Garbage collector included
• Runtime - Small runtime library
• Type inference - Compile-time type checking
• Good performance - Near-C speed

Implementation:

• Uses built-in BigInt support
• Machin's formula with GC overhead
• Runtime included (3.2 MB)

16. Dart (34 ms, 14.5 MB) - Moderate

Why moderate:

• VM overhead - Dart virtual machine
• JIT compilation - Compiles to machine code
• GC overhead - Garbage collector
• Moderate runtime - Smaller than JVM
• Good optimization - Designed for web/mobile

Implementation:

• Uses dart:math for precision
• Machin's formula with VM overhead
• Moderate runtime (14.5 MB)

17. Haskell (40 ms, 11.9 MB) - Moderate

Why moderate:

• Lazy evaluation - Only computes what's needed
• GC overhead - Garbage collector
• Functional overhead - Immutability, pattern matching
• Runtime - GHC runtime system
• Good optimization - LLVM backend

Implementation:

• Uses Integer type for precision
• Machin's formula with lazy evaluation
• Moderate runtime (11.9 MB)

18. Java (46 ms, 43.1 MB) - Moderate

Why moderate:

• JVM startup - Virtual machine initialization
• JIT compilation - Compiles bytecode to machine code
• Large runtime - JVM includes extensive libraries
• GC overhead - Garbage collector
• Good optimization - HotSpot JIT is mature

Implementation:

• Uses BigInteger class for precision
• Machin's formula with JVM overhead
• Large runtime (43.1 MB)

19. Python (47 ms, 9.7 MB) - Moderate

Why moderate:

• Interpretation - Bytecode execution
• Dynamic typing - Runtime type checking
• GIL - Global Interpreter Lock
• Large runtime - Comprehensive standard library
• Good optimization - CPython is well-optimized

Implementation:

• Uses decimal module for precision
• Machin's formula with interpretation overhead
• Moderate runtime (9.7 MB)

20. Perl (47 ms, 12.5 MB) - Moderate

Why moderate:

• Interpretation overhead - Line-by-line execution
• Dynamic typing - Type checking at runtime
• Large runtime - Comprehensive standard library
• Regex engine - Powerful but overhead
• Mature - Years of optimization

Implementation:

• Uses Math::BigInt module
• Machin's formula with interpretation overhead
• Large runtime (12.5 MB)

Lower Performers (Rank 21-32)

21. Brainfuck (50 ms, 9.3 MB) - Moderate

Why moderate:

• Minimal language - Only 8 instructions
• Interpreter overhead - Must interpret each instruction
• Simple operations - No complex operations
• Small runtime - Minimal interpreter
• Educational - Not designed for performance

Implementation:

• Uses custom BigInt implementation
• Machin's formula with interpretation overhead
• Moderate runtime (9.3 MB)

22. Kotlin (60 ms, 45.2 MB) - Moderate

Why moderate:

• JVM overhead - Same as Java
• Kotlin runtime - Additional Kotlin libraries
• JIT compilation - Compiles to JVM bytecode
• GC overhead - Garbage collector
• Good optimization - Leverages JVM optimizations

Implementation:

• Uses BigInteger from Java stdlib
• Machin's formula with JVM + Kotlin overhead
• Large runtime (45.2 MB)

23. C# (66 ms, 41.5 MB) - Moderate

Why moderate:

• CLR overhead - Common Language Runtime
• JIT compilation - Compiles IL to machine code
• Large runtime - .NET framework included
• GC overhead - Garbage collector
• Good optimization - Mature JIT compiler

Implementation:

• Uses System.Numerics.BigInteger
• Machin's formula with CLR overhead
• Large runtime (41.5 MB)

24. PHP (68 ms, 26.5 MB) - Moderate

Why moderate:

• Interpretation - Bytecode execution
• Dynamic typing - Runtime type checking
• Large runtime - Web-focused standard library
• GC overhead - Garbage collector
• Good for web - Not designed for computation

Implementation:

• Uses bcmath extension for precision
• Machin's formula with interpretation overhead
• Large runtime (26.5 MB)

25. Ruby (79 ms, 28.8 MB) - Slower

Why slower:

• Interpretation - Bytecode execution
• Dynamic typing - Runtime type checking
• Large runtime - Object-oriented overhead
• GC overhead - Garbage collector
• Less optimized - Slower than Python

Implementation:

• Uses BigDecimal library
• Machin's formula with interpretation overhead
• Large runtime (28.8 MB)

26. JavaScript (89 ms, 44.8 MB) - Moderate

Why moderate:

• JIT compilation - V8 engine compiles to machine code
• Dynamic typing - Runtime type checking
• Large runtime - JavaScript engine overhead
• GC overhead - Garbage collector
• Good optimization - V8 is highly optimized

Implementation:

• Uses BigInt for arbitrary precision
• Machin's formula with JIT overhead
• Large runtime (44.8 MB)

27. Julia (157 ms, 235.9 MB) - Moderate

Why moderate:

• JIT compilation - Compiles to machine code
• Large runtime - Scientific libraries included
• Dynamic typing - Runtime type checking
• GC overhead - Garbage collector
• Designed for science - Optimized for numerical work

Implementation:

• Uses BigFloat for precision
• Machin's formula with JIT overhead
• Very large runtime (235.9 MB)

28. R (163 ms, 90.9 MB) - Moderate

Why moderate:

• Interpretation - R interpreter
• Dynamic typing - Runtime type checking
• Large runtime - Statistical libraries included
• GC overhead - Garbage collector
• Designed for stats - Not optimized for general computation

Implementation:

• Uses Rmpfr package for precision
• Machin's formula with interpretation overhead
• Large runtime (90.9 MB)

29. Erlang (176 ms, 77.4 MB) - Moderate

Why moderate:

• BEAM VM - Erlang virtual machine
• Functional overhead - Immutability, pattern matching
• Concurrency focus - Designed for distributed systems
• Large runtime - BEAM VM included
• Not optimized for math - Designed for reliability

Implementation:

• Uses Integer module for precision
• Machin's formula with BEAM overhead
• Large runtime (77.4 MB)

30. Scala (344 ms, 55.5 MB) - Slow

Why slow:

• JVM overhead - Same as Java
• Scala runtime - Large standard library
• Functional overhead - Immutability, pattern matching
• Complex compilation - Advanced type system
• Less optimized - More overhead than Java

Implementation:

• Uses BigInt from Scala library
• Machin's formula with functional overhead
• Very large runtime (55.5 MB)

31. Elixir (401 ms, 89.2 MB) - Slow

Why slow:

• BEAM VM - Erlang virtual machine
• Functional overhead - Immutability, pattern matching
• Concurrency focus - Designed for distributed systems
• Large runtime - BEAM VM + Elixir libraries
• Not optimized for math - Designed for reliability

Implementation:

• Uses Integer module for precision
• Machin's formula with BEAM overhead
• Very large runtime (89.2 MB)

32. TypeScript (931 ms, 218.9 MB) - Slowest

Why slow:

• TypeScript compiler - Extra compilation step
• JavaScript runtime - V8 engine overhead
• Large runtime - TypeScript + JavaScript libraries
• Dynamic typing - Runtime type checking
• Not optimized - Designed for web development

Implementation:

• Uses BigInt for precision
• Machin's formula with TypeScript + JS overhead
• Very large runtime (218.9 MB)

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

# 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 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