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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 0e5c66d..4dc9095 100644 --- a/doc/algorithms.tex +++ b/doc/algorithms.tex @@ -892,11 +892,11 @@ by a call to \texttt {mpc\_abs}; $|x|$ is added with an error of \ulp{1}, since both terms are positive; division by~$2$ is free of error. So $w^2$ is computed with a cumulated error of \ulp{2}. This error of \ulp{2} propagates as is through the real square root: -since we rounded down the argument, we have $\epsilon_1^- = 0$ in +Since we rounded down the argument, we have $\epsilon_1^- = 0$ in \eqref {eq:proprealsqrt}; an error of \ulp{1} needs to be added for the rounding of $w$, so that the total error is \ulp{3}. -$t$ is rounded up. Plugging the error of \ulp{3} for $w$ and \ulp{0} for $y$ into +$t$ is rounded away. Plugging the error of \ulp{3} for $w$ and \ulp{0} for $y$ into \eqref {eq:proprealdiv} shows that the propagated error of real division is \ulp{6}, to which an additional rounding error of \ulp{1} has to be added for a total error of \ulp{7}. |