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0.2.3

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accurpy

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

Published1 Dec 2025

Direct dependencies1

Transitive dependenciesNot calculated

README

Version 0.2.3 documentation

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

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Package / target	Requirement	Relationship
numpy Environment { "extras": "", "marker": null, "requires_python": ">=3.8", "evaluation": "NOT_EVALUATED" }	`numpy>=1.20`	runtime

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accurpy-0.2.3-cp313-cp313-win_amd64.whl

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accurpy-0.2.3.tar.gz

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accurpy/accurpy

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