One of my favourite programming tasks is to create a program in under 4k. This is something the Demoscene excel at (see scene.org awards).
Some of my favourites are:
Void 3 by Kolor, an oldschool DOS intro, with a voice synthesizer. Awesome DIY.
Of course, achieving this seems impossible, however a few tools make this easier. I used many of these tools and tricks to create my 3kb entry to the global game jam. First of all a drop/compression tool. Crinkler has eliminated the need for com/cob droppers and gives excellent compression. This little tool has made most of my 4k productions possible.
IN4K has plenty of tools and code examples to help you learn the trade, but Iñigo Quilez has an excellent set of beginner projects. (Not the most optimized ones out there, but still a fantastic starting point). FIT have an excellent set of demoscene resources, including source code to some fantastic 4k intros (plus synthesizers!). Ryg/Farbrausch has some interesting reads as well.
The other thing that you will find when making 4K intros is the lack of maths functions (which you can get around by using intrinsics /QIfist in MSVC, or something like that), and by writing them yourself in assembly.
The next problem is often getting rid of the C standard library, in particular rand(). This is where Linear congruential generator (LCG) come in handy. This is where IQ comes handy again with a 'better, smaller and faster random number generator'. And again, this isn't the fastest or most optimal, but it will do. Finally you will probably want to allocate memory dynamically, and on Windows you can simply use:
GlobalAlloc instead. (Feel free to overide operator new and use your standard C++ coding style).
If your really looking to crunch size, then stick to values that will compress well (ie: powers of 2), but the latest crinkler can drop floating precision for you anyway, so I'm not sure how much you save with this trick these days...
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