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, fm_scaled
# Compute FM(x) * exp(x) - the numerically stable form
result = syncF(1.0)
# Compute FM(x) = exp(-x) * integral of t^(-1/2) * exp(-t) / (1 + t/x) dt
result_scaled = fm_scaled(1.0)
# Works with numpy arrays
import numpy as np
x = np.linspace(0.001, 100, 1000)
y = syncF(x)
Performance
The C extension uses METH_O calling convention with PyFloat_AS_DOUBLE for minimal overhead:
| x range | syncF(x) time | Notes |
|---|---|---|
| Small (1e-8) | ~38 ns | Cube-root expansion |
| Wide (1.0) | ~45 ns | Rational approximation |
| Large (1e10) | ~32 ns | Asymptotic expansion |
Comparable to math.sin (~38 ns) - only ~20 ns above the minimum possible CPython C-extension overhead (~16 ns for extract+create).
Array throughput: ~10 ns/element.
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
1 maintainer
Metadata
1 maintainer
Release files for accurpy 0.2.3
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