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DOC: Mention and try to explain pairwise summation in sum #13737

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Jun 11, 2019
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DOC: Mention and try to explain pairwise summation in sum #13737

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DOC: Mention and try to explain pairwise summation in sum
seberg Jun 7, 2019
c1fdef8
DOC: Fixup review comment, also its math.fsum not sum itself
seberg Jun 8, 2019
86235ec
DOC: add Marten's comment about f8, and smuggle in "partial" to pairwise
seberg Jun 10, 2019
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19 changes: 19 additions & 0 deletions numpy/core/fromnumeric.py
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Original file line number Diff line number Diff line change
Expand Up @@ -2104,6 +2104,8 @@ def sum(a, axis=None, dtype=None, out=None, keepdims=np._NoValue,
--------
ndarray.sum : Equivalent method.

add.reduce : Equivalent functionality of `add`.

cumsum : Cumulative sum of array elements.

trapz : Integration of array values using the composite trapezoidal rule.
Expand All @@ -2120,6 +2122,23 @@ def sum(a, axis=None, dtype=None, out=None, keepdims=np._NoValue,
>>> np.sum([])
0.0

For floating point numbers the numerical precision of sum (and
``np.add.reduce``) is in general limited by directly adding each number
individually to the result causing rounding errors in every step.
However, often numpy will use a numerically better approach (partial
pairwise summation) leading to improved precision in many use-cases.
This improved precision is always provided when no ``axis`` is given.
When ``axis`` is given, it will depend on which axis is summed.
Technically, to provide the best speed possible, the improved precision
is only used when the summation is along the fast axis in memory.
Note that the exact precision may vary depending on other parameters.
In contrast to NumPy, Python's ``math.fsum`` function uses a slower but
more precise approach to summation.
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Is it worth adding that for lower-precision floats such as f4, one can pass in dtype='f8' to increase precision?

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I guess so, although it is growing so long... Maybe the real solution would be to have a longer paragraph about floating point rounding in the user guide and link that...

Especially when summing a large number of lower precision floating point
numbers, such as ``float32``, numerical errors can become significant.
In such cases it can be advisable to use `dtype="float64"` to use a higher
precision for the output.

Examples
--------
>>> np.sum([0.5, 1.5])
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