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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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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 scaling or division by *max* should not be skipped even if not
otherwise needed to prevent overflow or loss of precision. 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 gets scaled to a magnitude below 1.0. The Veltkamp-Dekker splitting
algorithm gives a *hi* value that is correctly rounded to half algorithm gives a *hi* value that is correctly rounded to half
precision. When a value at or below 1.0 is correctly rounded, it 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). expansion of sqrt(h**2 + x) == h + x/(2*h) + O(x**2).
Essentially, this differential correction is equivalent to one 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. algorithm, effectively doubling the number of accurate bits.
This technique is used in Dekker's SQRT2 algorithm and again in This technique is used in Dekker's SQRT2 algorithm and again in
Borges' ALGORITHM 4 and 5. Borges' ALGORITHM 4 and 5.