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| author | Philippe Theveny <philippe.theveny@laposte.net> | 2014-01-20 17:05:47 +0000 |
|---|---|---|
| committer | Philippe Theveny <philippe.theveny@laposte.net> | 2014-01-20 17:05:47 +0000 |
| commit | 6bf41d383facbfc69ced85ad17a28f118b764f3a (patch) | |
| tree | df89dc30217afed9fb19db5063ae22983934b89c /doc/algorithms.tex | |
| parent | 4167cb23a2b6f74bb4acff38f80e9c777db5571e (diff) | |
| download | mpc-git-benchs_tests.tar.gz | |
Synchronize with r1413 from trunk.benchs_tests
git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/mpc/branches/benchs_tests@1414 211d60ee-9f03-0410-a15a-8952a2c7a4e4
Diffstat (limited to 'doc/algorithms.tex')
| -rw-r--r-- | doc/algorithms.tex | 6 |
1 files changed, 6 insertions, 0 deletions
diff --git a/doc/algorithms.tex b/doc/algorithms.tex index 669d651..d9acd15 100644 --- a/doc/algorithms.tex +++ b/doc/algorithms.tex @@ -17,6 +17,7 @@ \newcommand {\Ulp}{{\operatorname {ulp}}} \DeclareMathOperator{\Exp}{\operatorname {Exp}} \newcommand {\atantwo}{\operatorname {atan2}} +\newcommand {\asin}{\operatorname {asin}} \newcommand{\error}{\operatorname {error}} \newcommand{\relerror}{\operatorname {relerror}} \newcommand{\Norm}{\operatorname {N}} @@ -1142,6 +1143,11 @@ k_R=\left\{ \right. \end{equation*} +\subsection {\texttt {mpc\_asin}} + +For $0 \leq y \leq 1$, we have $|\Re \asin (1 \pm iy) - \pi/2| +\leq y^{1/2}$, and $|\Im \asin (1 \pm iy) \mp y^{1/2}| \leq (1/12) y^{3/2}$. + \subsection {\texttt {mpc\_pow}} The main issue for the power function is to be able to recognize when the |