Words and Buttons Online

This is the source code for Words and Buttons Online — a collection of interactive tutorials, guides, and quizzes about maths, algorithms, and programming.

All the code is licensed under The Unlicense.

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Rational interpolation Rational interpolation is a step forward from polynomial interpolation towards rational splines. With rational interpolation, you can build functions that run through a set of points and also have vertical asymptotes whenever you want. With this capability, you can now model functions like logarithms better. ^#demos ^#mathematics
Either your estimates suck or your job does This page uses polynomial modeling to show why software engineering tasks are often impossible to estimate. ^#mathematics ^#programming
Static typing isn’t free. Where do you think the C++ angry mob comes from? Type inference works like logic deduction so any program in a statically typed language is two programs. The first one is the thing you sell, and the second – is a model that undergoes some sort of verification every time you run a compiler. This second program, although, often being written unknowingly, is not a free bonus, it’s something you have to pay for in several ways. ^#programming ^#tutorials
Check if your performance intuition still works with CUDA An interactive quiz about microoptimizations in CUDA. 10 rounds, two pieces of code per each, you get to guess which is the faster. ^#programming ^#quizzes
A picture is worth a thousand tags This shows how a picture can be turned into an HTML table. With this, you can not only have nicer tables or uglier pictures, but you can have something that is both at the same time. ^#demos
Redundant stories about redundancy Component redundancy is used heavily in safety-critical and mission-critical systems for reliability improvement. But outside this niche, it's surprisingly little known in the world of software. Which is a shame since it's a simple but economical idea. It costs nothing to keep in mind, and it saves you a lot on hotfixes and emergency repairs. ^#programming
Challenge your performance intuition with C++ sine One more interactive quiz. This time, it's all about the sine function. Which one is faster and when? ^#programming ^#quizzes
Complex numbers and conformal mapping This explains the geometry of complex numbers. Explains conformal transformations, introduces analytic functions, and shows that analytic complex functions are conformal. And using the connection between the geometry and the analysis explains it all in just some five minutes. ^#mathematics ^#tutorials
Lagrange polynomial as a gateway drug to basis splines This explains Lagrange interpolation: what is the Lagrange polynomial, why does it run through all the points, what is the basis polynomial, and how come it's a polynomial in the first place. ^#mathematics ^#tutorials
Trippy polynomials in arctangent scale This shows the global properties of polynomials, their derivatives, and explains how the Maclaurine and Taylor series work all with animated plots in arctangent scale. ^#mathematics ^#tutorials
Partial order and non-Boolean logic Non-Boolean logics are rare but not extinct. Interval logic is one example. Sometimes, you can implement a logic you want within total order or partial order but sometimes even that isn't enough and you need an even more general relation. With operator overloading, you have the freedom to go there but you also have less assurance when working within the total order. ^#mathematics ^#tutorials
Yet another alternative to floating-point numbers This shows how computable intervals written in rational bounds may not only account for the input error but keep computational error under control as well. ^#mathematics ^#programming ^#quizzes
Why is it ok to divide by 0.0? This explains why dividing by zero in floating-point numbers is ok. ^#mathematics ^#programming
Can we use lemniscates for ultra-cheap vector graphics? This depicts an old idea of using multifocal lemniscates to draw arbitrary shapes. In some applications, this may be indeed an economical alternative to splines. ^#demos ^#mathematics
Bi-whatever transformations An interactive explanation of how polynomial transformations such as trilinear or biquadratic or even linear-cubic work, and how to craft your own. ^#demos ^#mathematics
Arctangent scale. It's like the logarithmic scale but infinite An interactive demo of how, with arctangent used as a scale, we can show any function on a screen. And not just a fragment of it but the whole function. ^#demos ^#mathematics
Image darning A simple image processing algorithm that cleans up dirt stains from old newspapers. I called it “darning” because of how it works. ^#algorithms ^#demos ^#mathematics
Error codes are not numbers. But they are. Can we exploit that? An interactive explanation of how we can use floating-point NaNs as error code holders in C++. ^#demos ^#mathematics ^#programming
Binary search An interactive demo of the binary search algorithm along with its one slightly more obscure but promising variant. ^#algorithms ^#tutorials
Honeycomb texture generator This generates honeycomb textures of a special quasi-irrational form. Explanation included. ^#demos ^#mathematics
Sine and cosine A pair of interactive mnemonics for sine and cosine. There are also examples of practical usage. Basically, the second half of a tutorial is about how the first half was made. ^#mathematics ^#tutorials
Challenge your performance intuition with nanosecond sorting And yet another interactive quiz where you get to estimate the performance difference between several variants of the same code. ^#programming ^#quizzes
SWInE: Simplicial Weight Interpolation and Extrapolation An alternative to splines nobody knows about. The localization of Shepard's method for a simplicial complex. ^#demos ^#mathematics
Quadratic splines are useful too This explains simple quadratic splines, how to craft one yourself, and why. ^#demos ^#mathematics
Circles and lines vs. polynomial splines An alternative to polynomial splines. Smooth parametric curves made from arcs and line segments. ^#demos ^#mathematics
SymPy makes math fun again An introduction into symbolic computations in Python. Don't worry, it's much simpler than it sounds. It's about making Python do your math for you with very little investment in the technology. ^#mathematics ^#programming ^#tutorials
Yet another floating-point tutorial Most of what you should know about floating-point numbers put together in an interactive tutorial with quests and puzzles. ^#mathematics ^#programming ^#tutorials
Lexical differential highlighting instead of syntax highlighting This type of highlighting is ideal for assembly. With it, the things that shouldn't seem similar usually don't. ^#demos ^#programming
Interactive mnemonics for dot and cross vector products Just a pair of mnemonics for dot and cross vector products. They present the functions, show how they work, and why one is dot and the other is cross. ^#mathematics ^#tutorials
Simple image vectorization This is an example of an image vectorization algorithm. It shows the bilinear interpolation, polynomial approximation, differential analysis, and iterative algorithms working together to solve a practical problem ^#algorithms ^#demos ^#mathematics
The simplest possible smooth contouring algorithm A 3-part smooth contouring algorithm that shows partial derivatives, gradients, and parametric polynomials working together. ^#algorithms ^#demos ^#mathematics
Using logical operators for logical operations is good This is the follow-up for the “Challenge your intuition with C++ operators”. It shows that despite the occasional gains from a better compilation, using the proper operators is still beneficial in the long run. ^#programming ^#quizzes
Challenge your performance intuition with C++ operators Another interactive quiz where you get to estimate the performance difference between several variants of the same code. ^#programming ^#quizzes
Fortran is still a thing A short essay about Fortran in the modern world. ^#programming
Why Erlang is among the few true computer languages Usually, a language is something that is used for bilateral communication. For programming languages, this is often untrue. Erlang shows how this can be achieved still. ^#programming
If I were to invent a programming language for the 21st century A short essay about the evolution of programming languages. ^#programming
A cheap trick to speed up recursion in C++ More often than not, recursion is not your performance problem, to begin with. But even if it is, you can often avoid recursion altogether. When for some reason you can't, this trick helps. ^#demos ^#programming
Polynomial approximation and interpolation This explains approximation and interpolation, how to use polynomials for that, and how to make both concepts work together. ^#mathematics ^#tutorials
Interactive explanation of marching cubes and dual contouring Marching cubes and dual contouring are often used for mesh generation. This explanation shows how they work, what are their differences, similarities, and limitations. ^#algorithms ^#mathematics ^#tutorials
Logic programming in C++ This shows that there is an invisible Prolog in every C++ compiler. It's up to you what to do with it but it's there. ^#programming ^#tutorials
Tries as the evolution of nothing Trie is a data structure. Like “tree” but different. This tutorial explains the concept behind the trie, what makes it efficient, and when. ^#algorithms ^#programming ^#tutorials
Programmer's guide to linear equations This is an introduction to linear equation systems. It explains linear dependency, under- and over-specification, direct and iterative solvers. The guide should give you enough knowledge to find a proper solution for your task but not enough to implement one efficiently yourself. ^#mathematics ^#tutorials
Estimating floating-point error the easy way An explanation of how to measure computational error while working with floating-point numbers, and why. ^#demos ^#mathematics ^#programming
APL deserves its renaissance too APL tutorial explaining the meaning of life←{↑1 ⍵∨.∧3 4=+/,¯1 0 1∘.⊖¯1 0 1∘.⌽⊂⍵} ^#programming ^#tutorials
NURBS is just an acronym NURBS stands for the non-uniform rational basis spline. There are three separate concepts. This guide walks you through these concepts one by one. ^#mathematics ^#tutorials
Playing a game of chance with C++ inline keyword It's about one particular aspect of C++ compilation that makes programming with the “inline” into a game of chance. ^#programming
How much math can you do in 10 lines of Python An interactive introduction into concise Python / basic linear algebra. ^#mathematics ^#programming
Outperforming everything with anything A 100 lines of Python code that substitute the compiler front-end for a specific computation. This shows that you don't need a “fast” compiling language to write efficient code. In fact, a compilation is only one of the multiple ways to achieve speed. ^#demos ^#programming
Programmer's guide to polynomials and splines This is a brief introduction into polynomials. From how to make a polynomial run through your set of points to how to make it into a spline. ^#mathematics ^#tutorials
Vastly outperforming LAPACK with C++ metaprogramming Still not really about LAPACK. It's a second part of the “outperforming” series explaining how the C++ metaprogramming can appear useful for efficient code generation. ^#demos ^#programming
Outperforming LAPACK with C metaprogramming Ok, it's not really about LAPACK. You can consider it clickbait if you wish. It's about how to tell a compiler to write the code you want with a limited arsenal of tools the C language provides. ^#demos ^#programming
Can you tell an assembly language when you see one? An interactive quiz featuring several obscure high-level languages and assembly variants. ^#programming ^#quizzes
Mathematical analysis explained with Python, blood, and TNT A brief introduction to mathematical analysis with a little SymPy on the side. The page explains how to disassemble a function, and how to assemble it back from the derivatives. ^#mathematics ^#tutorials
Even if you can't write assembly like a poet, you can read disassembly like a hunter This is a very concise introduction to x86 disassembly. It shows that you probably have all the skills to start reading disassembly right now even if you thought it was too complicated for you. It really isn't, see it for yourself. ^#programming ^#tutorials
An interactive introduction to iterative algorithms An interactive explanation of how iterative algorithms work. This explains convergence and the exit condition problem on an oversimplified linear system solver. ^#algorithms ^#demos ^#mathematics
Challenge your performance intuition with C++ magic squares An interactive quiz where you get to estimate the performance difference between several variants of the same code. ^#programming ^#quizzes
Interactive guide to homogeneous coordinates This interactive guide shows how homogeneous coordinates actually make programming geometry simpler and not more complicated. The page explains the extra coordinate, matrices, and generalized transformations. Most of what you need to know about projective geometry as a practicing programmer is here. ^#mathematics ^#tutorials
So you think you know C? It's a C test. If you think you know C, take this test. It only has 5 questions. ^#programming ^#quizzes
Learn you a Lisp in 0 minutes A short quiz to reveal your hidden knowledge of Lisp. ^#programming ^#quizzes

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