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Merged
rhettinger merged 5 commits into from
Sep 6, 2020
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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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Improve wording for the accuracy paragraph
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@rhettinger
rhettinger committed Sep 6, 2020
commit b6ecce695e06d536ae333f8013b6bf511f95e9b2
13 changes: 7 additions & 6 deletions Modules/mathmodule.c
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Expand Up @@ -2479,12 +2479,13 @@ This technique is used in Dekker's SQRT2 algorithm and again in
Borges' ALGORITHM 4 and 5.

Without proof for all cases, hypot() cannot claim to be always
correctly rounded. However, the accuracy of "h + x / (2.0 * h)" for
n <= 1000 is at least 100 bits prior to the final rounding step. [6]
Also, hypot() was tested against a Decimal implementation with prec=300.
After 100 million trials no incorrectly rounded examples were found.
In addition, perfect commutativity (all permutations are equal) was
verified for 1 billion random inputs with n=5. [7]
correctly rounded. However for n <= 1000, prior to the final addition
that rounds the overall result, the internal accuracy of "h" together
with its correction of "x / (2.0 * h)" is at least 100 bits. [6]
Also, hypot() was tested against a Decimal implementation with
prec=300. After 100 million trials, no incorrectly rounded examples
were found. In addition, perfect commutativity (all permutations are
exactly equal) was verified for 1 billion random inputs with n=5. [7]

References:

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