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Use Kahan summation for fsum and fsumf #742

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Use Kahan summation for fsum and fsumf #742

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Commits on Feb 14, 2023

  1. Use Kahan summation for fsum and fsumf 

    This compensated summation gives a more precise result than the original
algorithm, as demonstrated through extra precision in the tests. It also
drops recursion and the extra branching.

I used double precision internally for fsumf since I assume its purpose
is to interface with single precision, not necessary constrain itself to
only using single precision. If needed, it can be trivially changed to
use single precision internally while still passing the tests.

In fsumf, naive summation using double precision is likely sufficient,
and more precise than single precision Kaham summation. In other words,
Kahan summation with double precision in fsumf may be overkill.

In the fsumf test, neither 10000.1 nor 1.1 can be represented exactly.
The former is rounded down and the latter is rounded up (by less) to the
nearest representable value. As a result, the most precise sum is just
shy of the "obvious" result.
    @skeeto
    skeeto committed Feb 14, 2023
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