From 6027cc1317ca68ec3b6383ae6b64ca813690ffa9 Mon Sep 17 00:00:00 2001
From: zimmerma <zimmerma@211d60ee-9f03-0410-a15a-8952a2c7a4e4>
Date: Wed, 5 Sep 2012 14:45:35 +0000
Subject: [TODO] added pointers for AGM

git-svn-id: svn://scm.gforge.inria.fr/svn/mpc/trunk@1258 211d60ee-9f03-0410-a15a-8952a2c7a4e4
---
 TODO | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

(limited to 'TODO')

diff --git a/TODO b/TODO
index f6e5622..1b10204 100644
--- a/TODO
+++ b/TODO
@@ -29,7 +29,10 @@ New functions to implement:
   mpc_erfc, mpc_exp2, mpc_expm1, mpc_log1p, mpc_log2, mpc_lgamma, mpc_tgamma
   http://lists.gforge.inria.fr/pipermail/mpc-discuss/2012-March/001090.html
 - from Andreas Enge and Philippe Théveny 17 July 2008
-  agm (and complex logarithm with agm ?)
+  agm (and complex logarithm with agm ?). For the error analysis, one can
+  start from Theorem 1 of http://www.lix.polytechnique.fr/Labo/Regis.Dupont/preprints/Dupont_FastEvalMod.ps.gz, and probably the best is to compute AGM(a,b)
+  as a*AGM(1,b/a) with |b/a| <= 1. In such a way, after one step all values
+  are in the same quadrant, and no cancellation occurs any more.
 - from Andreas Enge 25 June 2009:
   correctly rounded roots of unity zeta_n^i
 - implement a root-finding algorithm using the Durand-Kerner method
-- 
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