uxarray.utils.computing._fast_two_sum

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uxarray.utils.computing._fast_two_sum#

uxarray.utils.computing._fast_two_sum(a, b)#

Compute a fast error-free transformation of the sum of two floating- point numbers.

This function is a faster alternative to _two_sum for computing the sum of two floating-point numbers a and b, such that a + b = x + y exactly. Note: |a| must be no less than |b|.

Parameters:

  • a (float) – The floating-point numbers to be added. It is required that |a| >= |b|.

  • b (float) – The floating-point numbers to be added. It is required that |a| >= |b|.

Returns:

The rounded sum of a and b, and the error term. The error term represents the difference between the exact sum and the rounded sum.

Return type:

tuple of float

Raises:

ValueError – If |a| < |b|.

Examples

>>> _fast_two_sum(2.0, 1.0)
(3.0, 0.0)

>>> _fast_two_sum(1.0, 2.0)
Traceback (most recent call last):
    ...
ValueError: |a| must be greater than or equal to |b|.

T. J. Dekker. A Floating-Point Technique for Extending the Available Precision. Numerische Mathematik, 18(3), 224–242,1971. 10.1007/BF01397083. Available at: https://doi.org/10.1007/BF01397083.

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