Update

optimization.md

@@ -12,6 +12,7 @@ These are mainly for [C](c.md), but may be usable in other languages as well.
 - **Keywords such as `inline`, `static` and `const` can help compiler optimize well**.
 - **Optimize the [bottlenecks](bottleneck.md)!** Optimizing in the wrong place is a complete waste of time. If you're optimizing a part of code that's taking 1% of your program's run time, you will never speed up your program by more than that 1% even if you speed up the specific part by 10000%. Bottlenecks are usually inner-most loops of the main program loop, you can identify them with [profiling](profiling.md).
 - **You can almost always trade space (memory usage) for time (CPU demand) and vice versa** and you can also fine-tune this. You typically gain speed by precomputation (look up tables, more demanding on memory) and memory with compression (more demanding on CPU).
+- **Be smart, use [math](math.md)**. Example: let's say you want to compute the radius of a zero-centered [bounding sphere](bounding_sphere.md) of an *N*-point [point cloud](point_cloud.md). Naively you might be computing the Euclidean distance (*sqrt(x^2 + y^2 + z^2)*) to each point and taking a maximum of them, however you can just find the maximum of squared distances (*x^2 + y^2 + z^2*) and return a square root of that maximum. This saves you a computation of *N - 1* square roots.
 - **Learn about [dynamic programming](dynamic_programming.md)**.
 - **Avoid branches (ifs)** if you can (remember [ternary operators](ternary_operator.md), loop conditions etc. are branches as well). They break prediction in CPU pipelines and instruction preloading and are often source of great performance losses. Don't forget that you can many times compare and use the result of operations without using any branching (e.g. `x = (y == 5) + 1;` instead of `x = (y == 5) ? 2 : 1;`).
 - **Use iteration instead of [recursion](recursion.md)** if possible (calling a function costs something).