Update

optimization.md

@@ -31,8 +31,11 @@ These are mainly for [C](c.md), but may be usable in other languages as well.
 - Search literature for **algorithms with better [complexity class](complexity_class.md)** (sorts are a nice example).
 - For the sake of simple computers such as [embedded](embedded.md) platforms **avoid [floating point](floating_point.md)** as that is often painfully slowly emulated in software. Use [fixed point](fixed_point.md), or at least offer it as a [fallback](fallback.md). This also applies to other hardware requirements such as [GPU](gpu.md) or sound cards: while such hardware accelerates your program on computers that have the hardware, making use of it may lead to your program being slower on computers that lack it.
 - **[Early branching](early_branching.md) can create a speed up** (instead of branching inside the loop create two versions of the loop and branch in front of them). This is a kind of space-time tradeoff.
+- **Division can be replaced by multiplication by [reciprocal](reciprocal.md)**, i.e. *x / y = x * 1/y*. The point is that multiplication is usually faster than division. This trick doesn't help us when performing a single division (as we still have to divide 1 by *y*) but it does help when we need to divide many numbers by the same number; here we precompute the reciprocal value and then multiply all numbers by it. Of course this can also easily be done with [fixed point](fixed_point.md) and integers!
 - **Reuse variable to save space**. A warning about this one: readability may suffer, mainstreamers will tell you you're going against "good practice", and some compilers may do this automatically anyway. Be sure to at least make this clear in your comments. Anyway, on a lower level and/or with dumber compilers you can just reuse variables that you used for something else rather than creating a new variable that takes additional RAM; the only prerequisite for "merging" variables is that the variables aren't used at the same time.
 - **What's fast on one platform may be slow on another**. This depends on the instruction set as well as on compiler, operating system, available hardware, [driver](driver.md) implementation and other details. In the end you always need to test on the specific platform to be sure about how fast it will run.
+- **Mental calculation tricks**, e.g. multiplying by one less or more than a power of two is equal to multiplying by power of two and subtracting/adding once, for example *x * 7 = x * 8 - x*; the latter may be faster as a multiplication by power of two (bit shift) and addition/subtraction may be faster than single multiplication, especially on some primitive platform without hardware multiplication. However this needs to be tested on the specific platform. Smart compilers perform these optimizations automatically, but not every compiler is high level and smart.
+- **Else should be the less likely branch**, try to make if conditions so that the if branch is the one with higher probability of being executed -- this can help branch prediction.
 - **You can optimize critical parts of code in [assembly](assembly.md)**, i.e. manually write the assembly code that takes most of the running time of the program, with as few and as inexpensive instructions as possible (but beware, popular compilers are very smart and it's often hard to beat them). But note that such code loses [portability](portability.md)! So ALWAYS have a C (or whatever language you are using) [fallback](fallback.md) code for other platforms, use [ifdefs](ifdef.md) to switch to the fallback version on platforms running on different assembly languages.
 
 ## When To Actually Optimize?