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-rw-r--r-- | doc/algorithms.tex | 4 |
1 files changed, 2 insertions, 2 deletions
diff --git a/doc/algorithms.tex b/doc/algorithms.tex index 31b664f..f67054f 100644 --- a/doc/algorithms.tex +++ b/doc/algorithms.tex @@ -1904,7 +1904,7 @@ in the place of $n - 1$. \subsection {\texttt {mpc\_cmp\_abs}} Let $z_1 = x_1 + i y_1$ and $z_2 = x_2 + i y_2$. We want to check whether -the absolute values $|z_1|$ and $|z_2|$ are equal and, if not, which of them +$|z_1|$ and $|z_2|$ are equal and, if not, which of them is smaller; equivalently (and more efficiently), we may compare their squares $x_1^2 + y_1^2$ and $x_2^2 + y_2^2$. The following algorithm is obviously correct, but it is a priori not clear @@ -1942,7 +1942,7 @@ quasi-linear complexity. \begin {proof} We assume that the algorithm has not terminated after the third step with a working precision of $p' \geq 4p$, that is, $n_1 = n_2$ and neither -$n_1$ nor $n_2$ has been computed eaxctly, and derive a contradiction. +$n_1$ nor $n_2$ has been computed exactly, and derive a contradiction. If any of $x_1$, $y_1$, $x_2$ or $y_2$ equals~$0$, then the algorithm has either finished in the second step, or the corresponding norm is computed |