Cython vs Python Performance for Array Operations

MediumPerformance Optimization

Example:

Input:

n = 10000
operations = [{'name': 'add', 'python_per_elem_ns': 120.0, 'cython_per_elem_ns': 8.0, 'numpy_per_elem_ns': 1.5, 'python_overhead_ns': 500.0, 'cython_overhead_ns': 300.0, 'numpy_overhead_ns': 3000.0}]

Output:

{'operations': [{'name': 'add', 'python_us': 1200.5, 'cython_us': 80.3, 'numpy_us': 18.0, 'cython_speedup': 14.95, 'numpy_speedup': 66.69, 'best': 'numpy'}], 'pipeline_python_us': 1200.5, 'pipeline_cython_us': 80.3, 'pipeline_numpy_us': 18.0, 'recommended': 'numpy', 'crossover_sizes': {'add': 416}}

Reasoning:

Python time: (500 + 10000120)/1000 = 1200.5 us. Cython time: (300 + 100008)/1000 = 80.3 us. NumPy time: (3000 + 10000*1.5)/1000 = 18.0 us. At n=10000, NumPy is fastest despite its higher overhead (3000 ns vs 300 ns for Cython) because its per-element cost (1.5 ns) is much lower than Cython's (8.0 ns). The crossover point where NumPy overtakes Cython is ceil((3000-300)/(8-1.5)) = ceil(415.38) = 416 elements. Below this size, Cython's lower overhead makes it faster.

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Cython vs Python Performance for Array Operations

MediumPerformance Optimization

Model the running time of each array operation under three implementations (pure Python, Cython, NumPy) and summarise the pipeline.

Inputs: n (array size) and operations, a list of dicts with name, <method>_per_elem_ns and <method>_overhead_ns for method in python, cython, numpy.

Per operation:

Time in microseconds for each method: $(\text{overhead\_ns} + n \cdot \text{per\_elem\_ns}) / 1000$ .
cython_speedup, numpy_speedup: Python time divided by that method's time.
best: the method with the lowest time; on ties the alphabetically first (cython < numpy < python).
Crossover size: the smallest integer $n$ at which NumPy beats Cython, $\lceil (\text{numpy\_oh} - \text{cython\_oh}) / (\text{cython\_pe} - \text{numpy\_pe}) \rceil$ . Use -1 if cython_per_elem_ns <= numpy_per_elem_ns, and 0 if the ratio is $\le 0$ .

Pipeline: sum each method's unrounded times over all operations; recommended is the method with the lowest total (same tie rule).

Return a dict with:

operations: list of dicts with name, python_us, cython_us, numpy_us, cython_speedup, numpy_speedup, best
pipeline_python_us, pipeline_cython_us, pipeline_numpy_us
recommended
crossover_sizes: {name: crossover}

All floats rounded to 2 decimals.