Update

optimization.md

@@ -20,9 +20,10 @@ These are mainly for [C](c.md), but may be usable in other languages as well.
 - **You can use good-enough [approximations](approximation.md) instead of completely accurate calculations**, e.g. taxicab distance instead of Euclidean distance, and gain speed or memory without trading.
 - **Use quick opt-out conditions**: many times before performing some expensive calculation you can quickly check whether it's even worth performing it and potentially skip it. For example in physics [collision detections](collision_detection.md) you may first quickly check whether the bounding spheres of the bodies collide before running an expensive precise collision detection -- if bounding spheres of objects don't collide, it is not possible for the bodies to collide and so we can skip further collision detection. 
 - **Operations on static data can be accelerated with accelerating structures** ([look-up tables](lut.md) for functions, [indices](indexing.md) for database lookups, spatial grids for collision checking, ...).
-- **Use powers of 2** whenever possible, this is efficient thanks to computers working in binary. Not only may this help nice utilization and alignment of memory, but mainly multiplication and division can be optimized by the compiler to mere bit shifts which is a tremendous speedup.
+- **Use powers of 2** (1, 2, 4, 8, 16, 32, ...) whenever possible, this is efficient thanks to computers working in binary. Not only may this help nice utilization and alignment of memory, but mainly multiplication and division can be optimized by the compiler to mere bit shifts which is a tremendous speedup.
 - **Write [cache-friendly](cache-friendly.md) code** (minimize long jumps in memory).
 - **Compare to [0](zero.md) rather than other values**. There's usually an instruction that just checks the zero flag which is faster than loading and comparing two arbitrary numbers.
+- **Use [bit tricks](bit_hack.md)**, hacks for manipulating binary numbers in clever ways only using very basic operations without which one might naively write complex inefficient code with loops and branches. Example of a simple bit trick is checking if a number is power of two as `!(x & (x - 1)) && x`.
 - **Consider moving computation from run time to compile time**. E.g. if you make a resolution of your game constant (as opposed to a variable), the compiler will be able to partially precompute expressions with the display dimensions and so speed up your program (but you won't be able to dynamically change resolution).
 - On some platforms such as [ARM](arm.md) the first **arguments to a function may be passed via registers**, so it may be better to have fewer parameters in functions.
 - **Optimize when you already have a working code**. As [Donald Knuth](knuth.md) put it: "premature optimization is the root of all evil". Nevertheless you should get used to simple nobrainer efficient patterns by default and just write them automatically.
@@ -45,4 +46,8 @@ Nubs often ask this and this can also be a very nontrivial question. Generally f
 
 The highest-level optimization is done as part of the initial design of the program, before any line of code gets written. This includes the choice of data structures and mathematical models you're going to be using, the very foundation around which you'll be building your castle. This happens in your head at the time you're forming an idea for a program, e.g. you're choosing between [server-client](server_client.md) or [P2P](p2p.md), [monolithic or micro kernel](kernel.md), [raytraced](ray_tracing.md) or [rasterized](rasterization.md) graphics etc. These choices affect greatly the performance of your program but can hardly be changed once the program is completed, so they need to be made beforehand. **This requires wide knowledge and experience** as you work by intuition.
 
-Another kind of optimization done during development is just automatically writing good code, i.e. being familiar with specific patterns and using them without much thought. For example if you're computing some value inside a loop and this value doesn't change between iterations, you just automatically put computation of that value **before** the loop. Without this you'd simply end up with a shitty code that would have to be rewritten line by line at the end. Yes, compilers can often do this simple kind of optimization for you, but you don't want to rely on it.
+Another kind of optimization done during development is just automatically writing good code, i.e. being familiar with specific patterns and using them without much thought. For example if you're computing some value inside a loop and this value doesn't change between iterations, you just automatically put computation of that value **before** the loop. Without this you'd simply end up with a shitty code that would have to be rewritten line by line at the end. Yes, compilers can often do this simple kind of optimization for you, but you don't want to rely on it.
+
+## See Also
+
+- [bit hacks](bit_hack.md)