accurpy 0.2.1

Ultra-accurate and fast FM function evaluator with <4.5e-16 relative error

AccurPy

Ultra-accurate and fast FM function evaluator with <4.5e-16 relative error (~2x machine epsilon).

Installation

pip install accurpy

Usage

from accurpy import syncF

# Compute FM(x) = exp(-x) * integral of t^(-1/2) * exp(-t) / (1 + t/x) dt
result = syncF(1.0)

# Skip the exp(-x) factor (returns FM(x) * exp(x))
result_scaled = syncF(1.0, skip_exp=True)

# Works with numpy arrays
import numpy as np
x = np.linspace(0.001, 100, 1000)
y = syncF(x)

Performance

• C extension: ~10-20 nanoseconds per evaluation
• Pure Python fallback available when C extension cannot be built

Accuracy

• Relative error < 4.5e-16 across entire domain (x > 0)
• Three-region algorithm:
  • Small x (< 1e-7): Cube-root expansion
  • Wide domain (1e-7 to 1e6): 63-segment rational approximation
  • Large x (> 1e6): Asymptotic expansion

License

MIT