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Expand file tree Collapse file tree Original file line number Diff line number Diff line change @@ -2440,7 +2440,7 @@ addend should be in the range: 0.5 <= |x| <= 1.0. Accordingly,
24402440scaling or division by *max* should not be skipped even if not
24412441otherwise needed to prevent overflow or loss of precision.
24422442
2443- The assertion that hi*hi > = 1.0 is a bit subtle. Each vector element
2443+ The assertion that hi*hi < = 1.0 is a bit subtle. Each vector element
24442444gets scaled to a magnitude below 1.0. The Veltkamp-Dekker splitting
24452445algorithm gives a *hi* value that is correctly rounded to half
24462446precision. 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
24582458expansion of sqrt(h**2 + x) == h + x/(2*h) + O(x**2).
24592459
24602460Essentially, this differential correction is equivalent to one
2461- refinement step in the Newton divide-and-average square root
2461+ refinement step in Newton's divide-and-average square root
24622462algorithm, effectively doubling the number of accurate bits.
24632463This technique is used in Dekker's SQRT2 algorithm and again in
24642464Borges' ALGORITHM 4 and 5.
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