Update

optimization.md

@@ -14,7 +14,7 @@ These are mainly for [C](c.md), but may be usable in other languages as 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). Generally initialization code that runs only once in a long time doesn't need much optimization -- no one is going to care if a program starts up 1 millisecond faster (but of course in special cases such as launching many processes this may start to matter).
 - **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](compression.md) (more demanding on CPU).
 - **[Static](static.md) things are faster and smaller than [dynamic](dynamic.md) things.** This means that things that are somehow fixed/unchangeable are better in terms of performance (and usually also safer and better testable) than things that are allowed to change during [run time](runtime.md) -- for example calling a function directly (e.g. `myVar = myFunc();`) is both faster and requires fewer instructions than calling a function by pointer (e.g. `myVar = myFuncPointer();`): the latter is more flexible but for the price of performance, so if you don't need flexibility (dynamic behavior), use static behavior. This also applies to using [constants](constant.md) (faster/smaller) vs [variables](variable.md), static vs dynamic [typing](typing.md), normal vs dynamic [arrays](array.md) etc.
-- **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.
+- **Be smart, use [math](math.md)**, for example simplify [expressions](expression.md) using known formulas, minimize [logic circuits](logic_circuit.md) etc. 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).