Explorations in better, faster, stronger code.
Approximating is always fun. Some approximations are well known, like Zu Chongzhi s, , that is fairly precise (it gives 6 digits). We can derive a good approximation using continue fractions, series, or some spigot algorithm. We can also use Monte Carlo methods, such as drawing uniformly distributed values inside a square, count those who falls [ ]
The best case depth for a search tree is , if is the arity (or branching) of the tree. Intuitively, we know that if we increase , the depth goes down, but is that all there is to it? And if not, how do we chose the optimal branching ? While it s true that an [ ]
Preparing lecture notes (or videos) sometimes brings you to revisit things you ve known for a while, but haven t really taken time to formalize properly. One of those things is fixed-point arithmetic. Fixed-point arithmetic joins the advantage of representing fractional values while maintaining a great simplicity in the operations. Contrary to floating point, arithmetic on fixed-points [ ]
This week, I ll show my mirror assembly to reverse the image in hardware for the lightboard. If you can mirror the image in post-production, some cameras can t do it either (and in Zoom, it seems that mirror image is only for your display only, not the image you send, and therefore is perfectly useless), so [ ]
Last time, I gave the instruction on how to build a lightboard, but not much in terms of how you actually use it. Now I ve been giving lectures from it (with graduate students as test subjects), I ve started recording for the undergrad courses, and so I ve tweaked my setup and learnt a few tricks. This [ ]
The C99 stdint.h header provides a plethora of type definition for platform-independent safe code: int_fast16_t, for example, provides an integer that plays well with the machine but has at least 16 bits. The int_fastxx_t and int_leastxx_t defines doesn t guarantee a tight fit, they provide an machine-efficient fit. They find the fastest type of integer for [ ]
As you may have noticed, a global pandemics got many of us working from home. While one can argue that you can do accounting from home, it s a lot more complicated to teach from home. Pretty much everyone is trying to figure that one out. For my part, I decided that zoom and the virtual [ ]
Evaluating polynomials is not a thing I do very often. When I do, it s for interpolation and splines; and traditionally those are done with relatively low degree polynomials cubic at most. There are a few rather simple tricks you can use to evaluate them efficiently, and we ll have a look at them. A polynomial is an [ ]
(and its logarithm) keep showing up in the analysis of algorithm. Unfortunately, it s very often unwieldy, and we use approximations of (or ) to simplify things. Let s examine a few! First, we have the most known of these approximations, the famous Stirling formula : , Where the terms at the right are known as Stirling Series [ ]
In this quarantine week, let s answer a (not that) simple question: how many bits do you need to encode sound and images with a satisfying dynamic range? Let s see what hypotheses are useful, and how we can use them to get a good idea on the number of bits needed. For Sound I have shown [ ]