From 51914c72b61bb0f61e8ea940af047c0956618e82 Mon Sep 17 00:00:00 2001 From: Fredrik Johansson Date: Tue, 30 Jul 2013 15:44:40 +0200 Subject: [PATCH] some todo entries --- todo.txt | 14 ++++++++++++++ 1 file changed, 14 insertions(+) diff --git a/todo.txt b/todo.txt index 1d278d93..a8ba4d9b 100644 --- a/todo.txt +++ b/todo.txt @@ -75,6 +75,8 @@ * Rewrite fmprb_div (similar to fmprb_mul) * Faster elementary functions at low precision (especially log/arctan). + Use Brent's algorithm (http://maths-people.anu.edu.au/~brent/pd/RNC7t4.pdf): + atan(x) = atan(p/q) + atan((q*x-p)/(q+p*x)) * Document fmpz_extras @@ -95,3 +97,15 @@ * Look at using the exponential to compute the complex sine/cosine series +* Extend sieving to power series evaluation of the zeta function (when + computing a small number of derivatives). Also save a factor two in + the sieving by skipping even terms. Then also use binary splitting + to speed up the tail evaluation when computing a large number of derivatives. + +* Extend Stirling series code to compute polygamma functions (i.e. starting + the series from some derivative), and optimize for a small number of + derivatives by using a direct recurrence instead of binary splitting. + +* Fall back to the real code when evaluating gamma functions (or their + power series) at points that happen to be real +