[algorithms.tex] improve the range for the error bound of mpc_sqrt

git-svn-id: svn://scm.gforge.inria.fr/svn/mpc/trunk@1283 211d60ee-9f03-0410-a15a-8952a2c7a4e4

1 files changed, 4 insertions, 0 deletions

diff --git a/doc/algorithms.tex b/doc/algorithms.tex
index 810d06d..3ab0849 100644
--- a/doc/algorithms.tex
+++ b/doc/algorithms.tex
@@ -1033,6 +1033,10 @@ there is $0 < \xi < \epsilon_1$ with
 \end {equation}
 For instance $\epsilon \leq \epsilon_1$ for $\epsilon_1 \leq \frac {3}{4}$.
 
+We even have $\epsilon \leq \epsilon_1$ for $\epsilon_1 \leq 1$,
+since $1 - \sqrt{1-x}$ is bounded by $x$
+for $0 < x \leq 1$, which comes from $1 - x \leq \sqrt{1-x}$.
+
 
 \subsubsection {Logarithm}