From 637925339bcd70e5e77d3db825a6591bb894f970 Mon Sep 17 00:00:00 2001 From: enge Date: Thu, 18 Jun 2009 15:28:17 +0000 Subject: algorithms.tex: corrected small error in mpc_sqrt git-svn-id: svn://scm.gforge.inria.fr/svn/mpc/trunk@611 211d60ee-9f03-0410-a15a-8952a2c7a4e4 --- doc/algorithms.tex | 4 ++-- 1 file 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}. -- cgit v1.2.1