flexfloat 0.3.0

A library for arbitrary precision floating point arithmetic

FlexFloat

A high-precision Python library for arbitrary precision floating-point arithmetic with growable exponents and fixed-size fractions. FlexFloat extends IEEE 754 double-precision format to handle numbers beyond the standard range while maintaining computational efficiency and precision consistency.

✨ Key Features

• 🔢 Growable Exponents: Dynamically expand exponent size to handle extremely large (>10^308) or small (<10^-308) numbers
• 🎯 Fixed-Size Fractions: Maintain IEEE 754-compatible 52-bit fraction precision for consistent accuracy
• ⚡ Full Arithmetic Support: Addition, subtraction, multiplication, division, and power operations
• 🔧 Multiple BitArray Backends: Choose between bool-list, int64-list, and big-integer implementations for optimal performance
• 🌟 Special Value Handling: Complete support for NaN, ±infinity, and zero values
• 🛡️ Overflow Protection: Automatic exponent growth prevents overflow/underflow errors
• 📊 IEEE 754 Baseline: Fully compatible with standard double-precision format as the starting point

🚀 Quick Start

Installation

pip install flexfloat

Basic Usage

from flexfloat import FlexFloat

# Create FlexFloat instances
a = FlexFloat.from_float(1.5)
b = FlexFloat.from_float(2.5)

# Perform arithmetic operations
result = a + b
print(result.to_float())  # 4.0

# Handle very large numbers that would overflow standard floats
large_a = FlexFloat.from_float(1e308)
large_b = FlexFloat.from_float(1e308)
large_result = large_a + large_b

# Result automatically grows exponent to handle the overflow
print(f"Exponent bits: {len(large_result.exponent)}")  # > 11 (grown beyond IEEE 754)
print(f"Can represent: {large_result}")  # No overflow!

Advanced Features

from flexfloat import FlexFloat, BigIntBitArray

# Use different BitArray implementations for specific needs
FlexFloat.set_bitarray_implementation(BigIntBitArray)

# Mathematical operations with unlimited precision
x = FlexFloat.from_float(2.0)
y = FlexFloat.from_float(3.0)

# Power operations
power_result = x ** y  # 2^3 = 8
print(power_result.to_float())  # 8.0

# Exponential using Euler's number
e_result = FlexFloat.e ** x  # e^2
print(f"e^2 ≈ {e_result.to_float()}")

# Absolute value operations
abs_result = abs(FlexFloat.from_float(-42.0))
print(f"|-42| = {abs_result.to_float()}")  # 42.0

# Working with extreme values
huge = FlexFloat.from_float(1e300)
extreme_product = huge * huge
print(f"Product: {extreme_product.to_float()}")  # Still computable!

# Precision demonstration
precise_calc = FlexFloat.from_float(1.0) / FlexFloat.from_float(3.0)
print(f"1/3 with 52-bit precision: {precise_calc}")

🔧 BitArray Backends

FlexFloat supports multiple BitArray implementations for different performance characteristics. You can use them directly or configure FlexFloat to use a specific implementation:

from flexfloat import (
    FlexFloat, 
    ListBoolBitArray,
    ListInt64BitArray,
    BigIntBitArray
)

# Configure FlexFloat to use a specific BitArray implementation
FlexFloat.set_bitarray_implementation(ListBoolBitArray)  # Default
flex_bool = FlexFloat.from_float(42.0)

FlexFloat.set_bitarray_implementation(ListInt64BitArray)  # For performance
flex_int64 = FlexFloat.from_float(42.0)

FlexFloat.set_bitarray_implementation(BigIntBitArray)  # For very large arrays
flex_bigint = FlexFloat.from_float(42.0)

# Use BitArray implementations directly
bits = [True, False, True, False]
bool_array = ListBoolBitArray.from_bits(bits)
int64_array = ListInt64BitArray.from_bits(bits)
bigint_array = BigIntBitArray.from_bits(bits)

Implementation Comparison

Implementation	Best For	Pros	Cons
ListBoolBitArray	Testing and development	Simple, flexible, easy to debug	Slower for large operations
ListInt64BitArray	Standard operations	Fast for medium-sized arrays, memory efficient	Some overhead for very small arrays
BigIntBitArray	Any usescases	Python already optimizes it	Overhead for small arrays

📚 API Reference

Core Operations

# Construction
FlexFloat.from_float(value: float) -> FlexFloat
FlexFloat(sign: bool, exponent: BitArray, fraction: BitArray)

# Conversion
flexfloat.to_float() -> float

# Arithmetic
a + b, a - b, a * b, a / b, a ** b
abs(a), -a

# Mathematical functions
FlexFloat.e ** x  # Exponential function
flexfloat.exp()   # Natural exponential
flexfloat.abs()   # Absolute value

# BitArray configuration
FlexFloat.set_bitarray_implementation(implementation: Type[BitArray])

Special Values

from flexfloat import FlexFloat

# Create special values
nan_val = FlexFloat.nan()
inf_val = FlexFloat.infinity()
neg_inf = FlexFloat.negative_infinity()
zero_val = FlexFloat.zero()

# Check for special values
if result.is_nan():
    print("Result is Not a Number")
if result.is_infinite():
    print("Result is infinite")

🧪 Development & Testing

Development Installation

git clone https://github.com/ferranSanchezLlado/flexfloat-py.git
cd flexfloat-py
pip install -e ".[dev]"

Running Tests

# Run all tests
python -m pytest tests/

# Run with coverage
python -m pytest tests/ --cov=flexfloat --cov-report=html

# Run specific test categories
python -m pytest tests/test_arithmetic.py  # Arithmetic operations
python -m pytest tests/test_conversions.py  # Number conversions
python -m pytest tests/test_bitarray.py  # BitArray implementations

Code Quality

# Format code
black flexfloat/ tests/

# Sort imports
isort flexfloat/ tests/

# Type checking
mypy flexfloat/

# Linting
pylint flexfloat/
flake8 flexfloat/

🎯 Use Cases

Scientific Computing

# Handle calculations that would overflow standard floats
from flexfloat import FlexFloat

# Factorial of large numbers
def flex_factorial(n):
    result = FlexFloat.from_float(1.0)
    for i in range(1, n + 1):
        result = result * FlexFloat.from_float(i)
    return result

large_factorial = flex_factorial(1000)  # No overflow!

Financial Calculations

# High-precision compound interest calculations
principal = FlexFloat.from_float(1000000.0)
rate = FlexFloat.from_float(1.05)  # 5% annual return
years = FlexFloat.from_float(100)

# Calculate compound interest over very long periods
final_amount = principal * (rate ** years)

Physics Simulations

# Handle extreme values in physics calculations
c = FlexFloat.from_float(299792458)  # Speed of light
mass = FlexFloat.from_float(1e-30)   # Atomic mass

# E = mc² with extreme precision
energy = mass * c * c

🏗️ Architecture

FlexFloat is built with a modular architecture:

flexfloat/
├── core.py              # Main FlexFloat class
├── types.py             # Type definitions
├── bitarray/            # BitArray implementations
│   ├── bitarray.py          # Abstract base class
│   ├── bitarray_bool.py     # List[bool] implementation
│   ├── bitarray_int64.py    # List[int64] implementation  
│   ├── bitarray_bigint.py   # Python int implementation
│   └── bitarray_mixins.py   # Common functionality
└── __init__.py          # Public API exports

Design Principles

1. IEEE 754 Compatibility: Start with standard double-precision format
2. Graceful Scaling: Automatically expand exponent when needed
3. Precision Preservation: Keep fraction size fixed for consistent accuracy
4. Performance Options: Multiple backends for different use cases
5. Pythonic Interface: Natural syntax for mathematical operations

📊 Performance Considerations

When to Use FlexFloat

✅ Good for:

• Calculations requiring numbers > 10^308 or < 10^-308
• Scientific computing with extreme values
• Financial calculations requiring high precision
• Preventing overflow/underflow in long calculations

❌ Consider alternatives for:

• Simple arithmetic with standard-range numbers
• Performance-critical tight loops
• Applications where standard float precision is sufficient

Optimization Tips

from flexfloat import FlexFloat, ListInt64BitArray, BigIntBitArray

# Choose the right BitArray implementation for your use case
# For standard operations with moderate precision
FlexFloat.set_bitarray_implementation(ListInt64BitArray)

# For most use cases, Python's int is already optimized
FlexFloat.set_bitarray_implementation(BigIntBitArray)

# Batch operations when possible
values = [FlexFloat.from_float(x) for x in range(1000)]
sum_result = sum(values, FlexFloat.zero())

# Use appropriate precision for your use case
if value_in_standard_range:
    result = float(flexfloat_result.to_float())  # Convert back if needed

📋 Roadmap

• Additional mathematical functions (sin, cos, tan, log, sqrt)
• Serialization support (JSON, pickle)
• Performance optimizations for large arrays
• Complex number support
• Decimal mode for exact decimal representation

📄 License

This project is licensed under the MIT License - see the LICENSE file for details.

🙏 Acknowledgments

• IEEE 754 standard for floating-point arithmetic foundation
• Python community for inspiration and best practices
• Contributors and users who help improve the library

📞 Support

• 📚 Documentation: Full API documentation available in docstrings
• 🐛 Issues: Report bugs on GitHub Issues
• 💬 Discussions: Join conversations on GitHub Discussions
• 📧 Contact: Reach out to the maintainer for questions