How computationally expensive are various fundamental floating point mathematical operations?  Here's a quick and dirty benchmark, which, although surely quite naive, seems to capture the rough relative cost of a few operations. Motivation This quarter I am taking a course on numerical linear algebra.  Naturally, we are covering topics like the fundamentals of floating point arithmetic, numerical … Continue reading A simple benchmark of various math operations →

How computationally expensive are various fundamental floating point mathematical operations?  Here’s a quick and dirty benchmark, which, although surely quite naive, seems to capture the rough relative cost of a few operations. Motivation This quarter I am taking a course on numerical linear algebra.  Naturally, we are covering topics like the fundamentals of floating point arithmetic, numerical stability, matrix decompositions, and algorithm analysis. In a few of our assignments, we are tasked with [...]

I recently saw a tweet from Ryan Riley linking to an article exploring F# performance and floating point processing: This blog post highlighted some perf issues (minor) in #fsharp that surprised me. http://t.co/D2Q6ZtorhW Anyone able to explain? — Ryan Riley (@panesofglass) September 18, 2014 I poked around the code and tested it a bit myself, and … Continue reading Response to "Little Performance Explorations: F#" →

I recently saw a tweet from Ryan Riley linking to an article exploring F# performance and floating point processing: This blog post highlighted some perf issues (minor) in #fsharp that surprised me. http://t.co/D2Q6ZtorhW Anyone able to explain?— Ryan Riley (@panesofglass) September 18, 2014 I poked around the code and tested it a bit myself, and figured I would take up the author’s  call for feedback. Comments on the original blog are locked down, so I’ve written up my results here, instead. Initial[...]

@StevenStrogatz posed a fun question this evening: If an elliptical swimming pool has a one-foot wide border around it, is the outer edge of the border also an ellipse?— Steven Strogatz (@stevenstrogatz) June 28, 2014 People quickly realized the answer is “no,” but how to show it? I’ll let someone else do the formal proof, but a quick visualization makes it pretty obvious. Play around with the sliders below to see when the border is close to being an ellipse, and when it’s not. document.write(''); var [...]