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Fix typos in comment (GH-21966)

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Raymond Hettinger 2020-08-26 13:09:40 -07:00 committed by GitHub
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commit 82e79480d6
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1 changed files with 2 additions and 2 deletions
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Modules/mathmodule.c
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@ -2440,7 +2440,7 @@ addend should be in the range: 0.5 <= |x| <= 1.0. Accordingly,
scaling or division by *max* should not be skipped even if not
otherwise needed to prevent overflow or loss of precision.
The assertion that hi*hi >= 1.0 is a bit subtle. Each vector element
The assertion that hi*hi <= 1.0 is a bit subtle. Each vector element
gets scaled to a magnitude below 1.0. The Veltkamp-Dekker splitting
algorithm gives a *hi* value that is correctly rounded to half
precision. When a value at or below 1.0 is correctly rounded, it
@ -2458,7 +2458,7 @@ The correction is the first order term of the Maclaurin series
expansion of sqrt(h**2 + x) == h + x/(2*h) + O(x**2).
Essentially, this differential correction is equivalent to one
refinement step in the Newton divide-and-average square root
refinement step in Newton's divide-and-average square root
algorithm, effectively doubling the number of accurate bits.
This technique is used in Dekker's SQRT2 algorithm and again in
Borges' ALGORITHM 4 and 5.