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Compensated Summation with Kahan

Reduce floating-point drift with Kahan and Neumaier compensated summation, and see where plain left-to-right addition loses a value.

PythonData Integrity

Code

snippet
def kahan_sum(values: list[float]) -> float:
    total = 0.0
    compensation = 0.0
    for value in values:
        adjusted = value - compensation
        updated = total + adjusted
        compensation = (updated - total) - adjusted
        total = updated
    return total


def neumaier_sum(values: list[float]) -> float:
    total = 0.0
    compensation = 0.0
    for value in values:
        updated = total + value
        if abs(total) >= abs(value):
            compensation += (total - updated) + value
        else:
            compensation += (value - updated) + total
        total = updated
    return total + compensation


if __name__ == "__main__":
    values = [1e16, 1.0, -1e16, 1.0]
    print("naive:", sum(values))
    print("kahan:", kahan_sum(values))
    print("neumaier:", neumaier_sum(values))

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