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@@ -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