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Merged
rhettinger merged 5 commits into from
Sep 6, 2020
Merged

bpo-41513: Expand comments #22123

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0f7a2ff
Note performance aspects of using multiple accumulators
rhettinger Sep 6, 2020
7a29756
Add accuracy notes
rhettinger Sep 6, 2020
971ae45
Show where each footnote applies
rhettinger Sep 6, 2020
080c68a
Better wording for the incremental loop costs
rhettinger Sep 6, 2020
b6ecce6
Improve wording for the accuracy paragraph
rhettinger Sep 6, 2020
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Better wording for the incremental loop costs
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@rhettinger
rhettinger committed Sep 6, 2020
commit 080c68a3748e701f65244f984a61e6eecbe0b2f7
5 changes: 3 additions & 2 deletions Modules/mathmodule.c
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Expand Up @@ -2458,8 +2458,9 @@ Since lo**2 is less than 1/2 ulp(csum), we have csum+lo*lo == csum.
To minimize loss of information during the accumulation of fractional
values, each term has a separate accumulator. This also breaks up
sequential dependencies in the inner loop so the CPU can maximize
floating point throughput. [5] On a 2.6 GHz Haswell, moving from
hypot(x,y) to hypot(x,y,z) costs only 5ns.
floating point throughput. [5] On a 2.6 GHz Haswell, adding one
dimension has an incremental cost of only 5ns -- for example when
moving from hypot(x,y) to hypot(x,y,z).

The square root differential correction is needed because a
correctly rounded square root of a correctly rounded sum of
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