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Optimization

Optimization means making a program more efficient in terms of consumption of some computing resource or by any similar metric, commonly aiming for greater execution speed or lower memory usage (but also e.g. lower power consumption, lower network usage etc.) while preserving how the program functions externally; this can be done manually (by rewriting parts of your program) or automatically (typically by compiler when it's translating your program). Unlike refactoring, which aims primarily for a better readability of source code, optimization changes the inner behavior of the executed program to a more optimal one. Apart from optimizing programs/algorithms we may also more widely talk about optimizing e.g. data structures, file formats, hardware, protocol and so on.

Manual Optimization

These are optimizations you do yourself by writing better code.

General Tips'N'Tricks

These are mainly for C, but may be usable in other languages as well.

Tell your compiler to actually optimize (-O3, -Os flags etc.). Also check out further compiler flags that may help you turn off unnecessary things you don't need, AND try out different compilers, some may just produce better code. If you are brave also check even more aggressive flags like -Ofast and -Oz, which may be even faster than -03, but may break your program too.
gprof is a utility you can use to profile your code.
<stdint.h> has fast type nicknames, types such as uint_fast32_t which picks the fastest type of at least given width on given platform.
Actually measure the performance to see if your optimizations work or not. Sometimes things behave counterintuitively and you end up making your program perform worse by trying to optimize it! Also make sure that you MEASURE THE PERFORMANCE CORRECTLY, many beginners for example just try to measure run time of a single simple function call which doesn't really work, you want to try to measure something like a million of such function calls in a loop and then average the time.
Keywords such as inline, static, const and register can help compiler optimize well.
Optimize the bottlenecks! 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. 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 (more demanding on CPU).
Static things are faster and smaller than dynamic 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 -- 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 (faster/smaller) vs variables, static vs dynamic typing, normal vs dynamic arrays etc.
Be smart, use math, for example simplify expressions using known formulas, minimize logic circuits etc. Example: let's say you want to compute the radius of a zero-centered bounding sphere of an N-point point cloud. 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.
Avoid branches (ifs) if you can (remember ternary operators, 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 if possible (calling a function costs something).
Use good enough approximations instead of completely accurate calculations, e.g. taxicab distance instead of Euclidean distance, capsule shape to represent the player's collision shape rather than the 3D model's mesh etc. With a physics engine instead of running the simulation at the same FPS as rendering, you may just run it at half and interpolate between two physics states at every other frame. Nice examples can also be found in computer graphics, e.g. some software renderers use perspective-correct texturing only for large near triangles and cheaper affine texturing for other triangles, which mostly looks OK.
Use quick bailout 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 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 for functions, indices for database lookups, spatial grids for collision checking, various trees ...).
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.
Memory alignment usually helps speed, i.e. variables at "nice addresses" (usually multiples of the platform's native integer size) are faster to access, but this may cost some memory (the gaps between aligned data).
Write cache-friendly code (minimize long jumps in memory).
Compare to 0 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, 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, see preprocessor, macros and metaprogramming. 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 the first arguments to a function may be passed via registers, so it may be better to have fewer parameters in functions.
Passing arguments costs something: passing a value to a function requires a push onto the stack and later its pop, so minimizing the number of parameters a function has, using global variables to pass arguments and doing things like passing structs by pointers rather than by value can help speed. { from Game Programming Gurus -drummyfish }
Optimize when you already have a working code. As Donald Knuth 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. Also do one optimization at a time, don't try to put in more optimizations at once.
Use your own caches where they help, for example if you're frequently working with some database item you better pull it to memory and work with it there, then write it back once you're done (as opposed to communicating with the DB there and back).
Single compilation unit (one big program without linking) can help compiler optimize better because it can see the whole code at once, not just its parts. It will also make your program compile faster.
Search literature for algorithms with better complexity class (sorts are a nice example).
For the sake of simple computers such as embedded platforms avoid floating point as that is often painfully slowly emulated in software. Use fixed point, or at least offer it as a fallback. This also applies to other hardware requirements such as GPU 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.
Factoring out invariants from loops and early branching can create a speed up: it's sometimes possible to factor things out of loops (or even long non-looping code that just repeats some things), i.e. 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. Consider e.g. while (a) if (b) func1(); else func2(); -- if b doesn't change inside the loop, you can rewrite this as if (b) while (a) func1(); else while (a) func2();. Or in while (a) b += c * d; if c and d don't change (are invariant), we can rewrite to cd = c * d; while (a) b += cd;. And so on.
Division can be replaced by multiplication by reciprocal, i.e. x / y = x * 1/y. The point is that multiplication is usually faster than division. This may not help us when performing a single division by variable value (as we still have to divide 1 by y) but it does help when we need to divide many numbers by the same variable number OR when we know the divisor at compile time; we save time by precomputing the reciprocal before a loop or at compile time. Of course this can also easily be done with fixed point and integers!
Consider the difference between logical and bitwise operators! For example AND and OR boolean functions in C have two variants, one bitwise (& and |) and one logical (&& and ||) -- they behave a bit differently but sometimes you may have a choice which one to use, then consider this: bitwise operators usually translate to only a single fast (and small) instruction while the logical ones usually translate to a branch (i.e. multiple instructions with potentially slow jumps), however logical operators may be faster because they are evaluated as short circuit (e.g. if first operand of OR is true, second operand is not evaluated at all) while bitwise operators will evaluate all operands.
Consider the pros and cons of using indices vs pointers: When working with arrays you usually have the choice of using either pointers or indices, each option has advantages and disadvantages; working with pointers may be faster and produce smaller code (fewer instructions), but array indices are portable, may be smaller and safer. E.g. imagine you store your game sprites as a continuous array of images in RAM and your program internally precomputes a table that says where each image starts -- here you can either use pointers (which say directly the memory address of each image) or indices (which say the offset from the start of the big image array): using indices may be better here as the table may potentially be smaller (an index into relatively small array doesn't have to be able to keep any possible memory address) and the table may even be stored to a file and just loaded next time (whereas pointers can't because on next run the memory addresses may be different), however you'll need a few extra instructions to access any image (adding the index to the array pointer), which will however most definitely be negligible.
Reuse variables 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; of course a prerequisite for "merging" variables is that the variables aren't used at the same time.
To save memory use compression techniques. Compression doesn't always have to mean you use a typical compression algorithm such as jpeg or LZ77, you may simply just throw in a few compression techniques such as run length or word dictionaries into your data structures. E.g. in Anarch maps are kept small by consisting of a small dictionary of tile definitions and map cells referring to this dictionary (which makes the cells much smaller than if each one held a complete tile definition).
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 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. A good approach is to optimize for the weakest platform you want to support -- if it runs fasts on a weak platform, a "better" platform will most likely still run it fast.
Prefer preincrement over postincrement (typically e.g. in a for loop), i.e. rather do ++i than i++ as the latter is a bit more complex and normally generates more instructions.
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.
With more than two branches use switch instead of ifs (if possible) -- it should be common knowledge but some newcomers may not know that switch is fundamentally different from if branches: switch statement generates a jump table that can branch into one of many case labels in constant time, as opposed to a series of if statements which keeps checking conditions one by one, however switch only supports conditions of exact comparison. So prefer using switch when you have many conditions to check (but know that switch can't always be used, e.g. for string comparisons). Switch also allows hacks such as label fall through which may help some optimizations.
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.
Similarly order if-sequences and switch cases from most probable: If you have a sequences of ifs such as if (x) ... else if (y) ... else if (z) ..., make it so that the most likely condition to hold gets checked first, then second most likely etc. Compiler most likely can't know the probabilities of the conditions so it can't automatically help with this. Do the same with the switch statement -- even though switch typically gets compiled to a table of jump addresses, in which case order of the cases doesn't matter, it may also get compiled in a way similar to the if sequence (e.g. as part of size optimization if the cases are sparse) and then it may matter again.
Variable aliasing: If in a function you are often accessing a variable through some complex dereference of multiple pointers, it may help to rather load it to a local variable at the start of the function and then work with that variable, as dereferencing pointers costs something. { from Game Programming Gurus -drummyfish }
You can save space by "squeezing" variables -- this is a space-time tradeoff, it's a no brainer but nubs may be unaware of it -- for example you may store 2 4bit values in a single char variable (8bit data type), one in the lower 4bits, one in the higher 4bits (use bit shifts etc.). So instead of 16 memory-aligned booleans you may create one int and use its individual bits for each boolean value. This is useful in environments with extremely limited RAM such as 8bit Arduinos.
Consider lazy evaluation (only evaluate what's actually needed).
You can optimize critical parts of code in assembly, 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! So ALWAYS have a C (or whatever language you are using) fallback code for other platforms, use ifdefs to switch to the fallback version on platforms running on different assembly languages.
Loop unrolling/splitting/fusion, function inlining etc.: there are optimizations that are usually done by high level languages at assembly level (e.g. loop unrolling physically replaces a loop by repeated commands which gains speed but also makes the program bigger). However if you're writing in assembly or have a dumb compiler (or are even writing your own) you may do these manually, e.g. with macros/templates etc. Sometimes you can hint a compiler to perform these optimizations, so look this up.
Parallelism (multithreading, compute shaders, ...) can astronomically accelerate many programs, it is one of the most effective techniques of speeding up programs -- we can simply perform several computations at once and save a lot of time -- but there are a few notes. Firstly not all problems can be parallelized, some problem are sequential in nature, even though most problems can probably be parallelized to some degree. Secondly it is hard to do, opens the door for many new types of bugs, requires hardware support (software simulated parallelism can't work here of course) and introduces dependencies; in other words it is huge bloat, we don't recommend parallelization unless a very, very good reason is given. Optional use of SIMD instructions can be a reasonable midway to going full parallel computation.
Optimizing data: it's important to remember we can optimize both algorithm AND data, for example in a 3D game we may simplify our 3D models, remove parts of a level that will never be seen etc.
Specialized hardware (e.g. a GPU) astronomically accelerates programs, but as with the previous point, portablity and simplicity greatly suffers, your program becomes bloated and gains dependencies, always consider using specialized hardware and offer software fallbacks.
Smaller code may also be faster as it allows to fit more instructions into cache.
Do not optimize everything and for any cost: optimization often makes the code more cryptic, it may bloat it, bring in more bugs etc. Only optimize if it is worth the prize. { from Game Programming Gurus -drummyfish }

When To Actually Optimize?

Nubs often ask this and this can also be a very nontrivial question. Generally fine, sophisticated optimization should come as one of the last steps in development, when you actually have a working thing. These are optimizations requiring significant energy/time to implement -- you don't want to spend resources on this at the stage when they may well be dropped in the end, or they won't matter because they'll be outside the bottleneck. However there are two "exceptions".

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 or P2P, monolithic or micro kernel, raytraced or rasterized 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.

Automatic Optimization

Automatic optimization is typically performed by the compiler; usually the programmer has the option to tell the compiler how much and in what way to optimize (no optimization, mild optimization, aggressive optimization, optimization for speed, size; check e.g. the man pages of gcc where you can see how to turn on even specific types of optimizations). Some compilers perform extremely complex reasoning to make the code more efficient, the whole area of optimization is a huge science -- here we'll only take a look at the very basic techniques. We see optimizations as transformations of the code that keep the semantics the same but minimize or maximize some measure (e.g. execution time, memory usage, power usage, network usage etc.). Automatic optimizations are usually performed on the intermediate representation (e.g. bytecode) as that's the ideal way (we only write the optimizer once), however some may be specific to some concrete instruction set -- these are sometimes called peephole optimizations and have to be delayed until code generation.

The following are some common methods of automatic optimization (also note that virtually any method from the above mentioned manual optimizations can be applied if only the compiler can detect the possibility of applying it):

{ Tip: man pages of gcc or possibly other compilers detail specific optimizations they perform under the flags that turn them on, so see these man pages for a similar overview. ~drummyfish }

Replacing instructions with faster equivalents: we replace an instruction (or a series of instructions) with another one that does the same thing but faster (or with fewer instructions etc.). Typical example is replacing multiplication by power of two with a bit shift (e.g. x * 8 is the same as x << 3).
Inlining: a function call may usually (not always though, consider e.g. recursion) be replaced by the function code itself inserted in the place of the call (so called inlining). This is faster but usually makes the code bigger so the compiler has to somehow judge and decide when it's worth to inline a function -- this may be affected e.g. by the function size (inlining a short function won't make the code that much bigger), programmer's hints (inline keyword, optimize for speed rather than size etc.) or guesstimating how often the function will be called. Function that is only called in one place can be safely inlined.
Loop unrolling: duplicates the body of a loop, making the code bigger but increasing its speed (a condition check is saved). E.g. for (int i = 0; i < 3; ++i) func(); may be replaced with func(); func(); func();. Unrolling may be full or just partial.
Lazy evaluation/short circuit/test reordering: the principles of lazy evaluation (evaluate function only when we actually need it) and short circuit evaluation (don't further evaluate functions when it's clear we won't need them) may be auto inserted into the code to make it more efficient. Test reordering may lead to first testing simpler things (e.g. equality comparison) and leaving complex tests (function calls etc.) for later.
Algebraic laws, expression evaluation: expressions may be partially preevaluated and manipulated to stay mathematically equivalent while becoming easier to evaluate, for example 1 + 3 + 5 * 3 * x / 6 may be transformed to just 4 + 5 * x / 2.
Removing instructions that cancel out: for example in Brainfuck the series of instructions +++-- may be shortened to just +.
Removing instructions that do nothing: generated code may contain instructions that just do nothing, e.g. NOPs that were used as placeholders that never got replaced; these can be just removed.
Register allocation: most frequently used variables should be kept in CPU registers for fastest access.
Removing branches: branches are often expensive due to not being CPU pipeline friendly, they can sometimes be replaced by a branch-free code, e.g. if (a == b) c = 1; else c = 0; can be replaced with c = a == b;.
Memory alignment, reordering etc.: data stored in memory may be reorganized for better efficiency, e.g. an often accessed array of bytes may actually be made into array of ints so that each item resides exactly on one address (which takes fewer instructions to access and is therefore faster). Data may also be reordered to be more cache friendly.
Generating lookup tables: if the optimizer judges some function to be critical in terms of speed, it may auto generate a lookup table for it, i.e. precompute its values and so sacrifice some memory for making it run extremely fast.
Dead code removal: parts of code that aren't used can be just removed, making the generated program smaller -- this includes e.g. functions that are present in a library which however aren't used by the specific program or blocks of code that become unreachable e.g. due to some #define that makes an if condition always false etc.
Compression: compression methods may be applied to make data smaller and optimize for size (for the price of increased CPU usage).
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