DECFLOAT. Implement high-accuracy algorithm for SUM of values with exponenta
greater than 34.
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Key: CORE-6242
URL: http://tracker.firebirdsql.org/browse/CORE-6242
Project: Firebird Core
Issue Type: Improvement
Reporter: Pavel Zotov
Priority: Minor
Attachments: neumaier-klein-builin_sum_-_results_comparison.sql
As described here: https://en.wikipedia.org/wiki/Kahan_summation_algorithm -
there is several ways to reduce accumulation of round errors during make SUM
operation.
Consider script from attach and its results.
There is only one test case (column "test_no" = 1) which contains proper values
in all thee columns: SUM() as it is implemented now, Neumaier and Klein-Kahan
totalling. But these values has exponenta less than 34.
All other test cases contain at least one wrong result.
The best accuracy is demonstrated by Klein-Kahan algorithm, but is also has one
flaw: example where test_no = 5 (proper results there must be exactly 0).
It will be useful to have alternate implementation for SUM() ( say, "SUM2()"
?) which will use some of algorithm with compensation of running totals.
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