diff options
Diffstat (limited to 'TODO')
| -rw-r--r-- | TODO | 30 |
1 files changed, 23 insertions, 7 deletions
@@ -1,13 +1,23 @@ +From Andreas Enge 27 August 2012: +Implement im(atan(x+i*y)) as +1/4 * [log1p (4y / (x^2 +(1-y)^2))] +(see http://lists.gforge.inria.fr/pipermail/mpc-discuss/2012-August/001196.html) + +From Andreas Enge 23 July 2012: +go through tests and move them to the data files if possible +(see, for instance, tcos.c) + From Andreas Enge 31 August 2011: implement mul_karatsuba with three multiplications at precision around p, instead of two at precision 2*p and one at precision p requires analysis of error propagation -From Andreas Enge 30 August 2011: -As soon as dependent on mpfr>=3, remove auxiliary functions from -get_version.c and update mpc.h. -Use MPFR_RND? instead of GMP_RND?, and remove workarounds for MPFR_RNDA from -mpc-impl.h. +From Andreas Enge 05 July 2012: +Add support for rounding mode MPFR_RNDA. + +From Andreas Enge and Paul Zimmermann 6 July 2012: +Improve speed of Im (atan) for x+i*y with small y, for instance by using +the Taylor series directly. Bench: - from Andreas Enge 9 June 2009: @@ -19,13 +29,19 @@ 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 - (cf http://en.wikipedia.org/wiki/Durand%E2%80%93Kerner_method) + (cf http://en.wikipedia.org/wiki/Durand%E2%80%93Kerner_method). See also the CEVAL algorithm from Yap and Sagraloff: http://www.mpi-inf.mpg.de/~msagralo/ceval.pdf + A good starting point for the Durand-Kerner and Aberth methods is the + paper by Dario Bini "Numerical computation of polynomial zeros by means of + Aberth's method", Numerical Algorithms 13 (1996), 179-200. New tests to add: - from Andreas Enge and Philippe Théveny 9 April 2008 |