improve speed of asin for 1+i*y with tiny y

git-svn-id: svn://scm.gforge.inria.fr/svn/mpc/trunk@1402 211d60ee-9f03-0410-a15a-8952a2c7a4e4

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