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Diffstat (limited to 'doc')
| -rw-r--r-- | doc/algorithms.bib | 8 | ||||
| -rw-r--r-- | doc/algorithms.tex | 6 |
2 files changed, 14 insertions, 0 deletions
diff --git a/doc/algorithms.bib b/doc/algorithms.bib index 2232a0e..eb4855e 100644 --- a/doc/algorithms.bib +++ b/doc/algorithms.bib @@ -36,3 +36,11 @@ number = 4, pages = {359--367} } + +@Misc{CrTh10, + author = {John E. Cremona and Thotsaphon Thongjunthug}, + title = {The complex {AGM}, periods of elliptic curves over {\C} and complex elliptic logarithms}, + howpublished = {\url{http://arxiv.org/abs/1011.0914}}, + year = 2010, + note = {31 pages}} + 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 |