Comments for Fredrik Johansson's blog

Comment on Machin-like formulas for logarithms by commenter

commenter — Wed, 27 Mar 2013 02:49:23 +0000

Looks like the internet might have pulled through with a faster recipe for fmprb_const_log10_eval

http://mathoverflow.net/questions/125629/machin-like-formulas-for-logarithms/125687#125687

Comment on Machin-like formulas for logarithms by Fredrik

Fredrik — Mon, 25 Mar 2013 14:16:31 +0000

Nope. If you frequent some forum where people might be interested in looking at it, feel free to post it there!

Comment on Machin-like formulas for logarithms by commenter

commenter — Mon, 25 Mar 2013 14:06:35 +0000

> Here is a challenge: for a positive integer n,
> what is the most efficient set of hyperbolic arctangents…

Have you posted this challenge to internet maths forums?

Comment on Implementing log-gamma using the Stirling series by Fredrik

Fredrik — Sun, 23 Sep 2012 21:47:20 +0000

The main technical advantage compared to MPFI is that it’s just as fast as non-interval floating-point arithmetic at very high precision (with MPFI, you typically lose a factor two efficiency in both memory and time, because both endpoints are computed and stored to full precision). Integers are also represented more compactly, which helps implementing certain algorithms more efficiently (e.g. binary splitting evaluation of hypergeometric series).

On the feature level, MPFI mostly covers the range of the C math library, while Arb includes things like fast polynomial and power series arithmetic (I will soon be adding complex numbers, matrices, and more special functions).

I’m not sure what you mean by porting features from MPFI into Arb. Any particular MPFI function or code that uses MPFI should be straightforward to port, except perhaps for a handful that rely specifically on the semantics of the endpoint representation.

Comment on Implementing log-gamma using the Stirling series by commenter

commenter — Sun, 23 Sep 2012 21:06:38 +0000

I love the idea that people are creating low-level free software libraries to allow more advanced numerical applications, but is there a link that explains how this will be better than mpfi? To me it looks almost exactly the same, except that arb represents the midpoint and radius using arbitrary precision floating point whereas mpfi represents the lower and upper bounds using arbitrary precision floating point. Also, can mpfi features be directly ported into arb?

Comment on Blog moved by Aaron Meurer

Aaron Meurer — Wed, 01 Feb 2012 04:34:50 +0000

Cool. Your posts are always interesting, so I look forward to reading them whenever you do write them.

Comment on 3D visualization of complex functions with matplotlib by gv

gv — Wed, 29 Sep 2010 17:51:58 +0000

This is a great tool for calculus. I think that you can visualize better those figure with it.

Comment on Mpmath 0.14 released by Fredrik Johansson

Fredrik Johansson — Tue, 24 Aug 2010 21:01:11 +0000

Hi Morovia,

What do you mean by roots of 2-D array? You mean the locations where a 2-D array is zero?

You can't plot an array directly with cplot. You could use matplotlib for this. Look at the cplot source code in mpmath's visualization.py and look at how it calls matplotlib.

Comment on Mpmath 0.14 released by morovia

morovia — Tue, 24 Aug 2010 05:23:40 +0000

The graphics are nice. Kindly answer
the following queries.

How can I find roots of 2-D array with complex type ? Is it possible to plot the zeros of this complex array (equivalent to implicitplot). I dont know how to pass the 2D array to cplot ? Kindly respond.

Thanks Morovia.

Comment on Sage Days 23, and Bessel function zeros by Fredrik Johansson

Fredrik Johansson — Wed, 14 Jul 2010 22:48:27 +0000

Kris: it's the derivative.