I was looking into Core Foundation and CFDictionary, and in the Apple Documentation I found this,
The access time for a value in a CFDictionary object is guaranteed to
be at worst O(log N) for any implementation, but is often O(1)
(constant time). Insertion or deletion operations are typically in
constant time as well, but are O(N*log N) in the worst cases. It is
faster to access values through a key than accessing them directly.
Dictionaries tend to use significantly more memory than an array with
the same number of values
To my surprise, In CFDictionary source , I found this,
The access time for a value in the dictionary is guaranteed to be at
worst O(N) for any implementation, current and future, but will
often be O(1) (constant time). Insertion or deletion operations will
typically be constant time as well, but are O(N*N) in the worst case
in some implementations. Access of values through a key is faster
than accessing values directly (if there are any such operations).
Dictionaries will tend to use significantly more memory than a array
with the same number of values.
Why such difference..? or Am I looking in the wrong place?
Edit: In the apple OpenSource Browser, why are there so many folders which seems like different versions of Core Foundation, is it..? Which out of those is latest/relevant?
"In some implementations". Since you have the source, you can check easily what the worst case is for your implementation. For the worst case, assume that every object in the dictionary returns a hash value of 0 :-)
BTW. Worst case will happen when the hash table gets full and is rebuilt completely. That's why you use at amortised time, not at worst time, unless that worst time for a single insertion is important for you.
Related
What is the time complexity of Map.containsKey and Map.containsValue in Dart? I'd like to know for the following implementations:
LinkedHashMap
HashMap
SplayTreeMap
I assume for the hash map implementations containsKey is amortized constant time and containsValue is probably linear time. For SplayTreeMap, containsKey is probably logarithmic time while containsValue is probably still linear time. However, the documentation seems to be silent on the issue. The best I could find was for LinkedHashMap, which says:
An insertion-ordered [Map] with expected constant-time lookup.
This doesn't specify if you are looking up the key or the value, but presumably this is referring to the key.
The docs for Set (if you navigate to the implementations), on the other hand, are not silent. They give the time complexity.
I assume this is an oversight in the documentation, but perhaps they are silent because there is no guaranteed time complexity. (That's would be strange, though, because it goes against developer expectations.)
For containsKey, it's the same time as doing a lookup.
HashMap and LinkedHashMap: Expected constant time, worst-case linear time for degenerate hashCodes.
SplayTreeMap, ammortized logarithmic time.
For containsValue, it's linear in the number of elements (at least). It simply does the equivalent of map.values.contains(...). There is no efficient way to find a single value in a map, so there is no better way than looking through all of them in some order.
Some potential HashMap implementations can be extra expensive because they traverse the entire backing store, and if the map had been grown big first, then had a lot of elements removed, then it might have a backing store which is significantly larger than its number of elements. Other implementations auto-shrink, or keep elements in a contiguous area, and won't have that problem.
Very implementation dependent. No promises which implementation Dart uses.
I've noticed that booleans occupy a whole byte, despite only needing 1 bit. I was wondering whether we could have something like
struct smartbool{char data;}
, which would store 8 booleans at once.
I am aware that it would take more time to retrieve data, although would the tradeoff be a practical application in some scenarios?
Am I missing something about the memory usage of booleans?
Normally variables are aligned on word boundaries, memory use is balanced against efficiency of access. For one-off boolean variables it may not make sense to store them in a denser form.
If you do need a bunch of booleans you can use things like this BitSet data structure: https://docs.oracle.com/en/java/javase/12/docs/api/java.base/java/util/BitSet.html.
There is a type of database index that stores booleans efficiently:
https://en.wikipedia.org/wiki/Bitmap_index. The less space an index takes up the easier it is to keep in memory.
There are already widely used data types that support multiple booleans, they are called integers. you can store and retrieve multiple booleans in an integral type, using bitwise operations, screening out the bits you don't care about with a pattern of bits called a bitmask.
This sort of "packing" is certainly possible and sometimes useful, as a memory-saving optimization. Many languages and libraries provide a way to make it convenient, e.g. std::vector<bool> in C++ is meant to be implemented this way.
However, it should be done only when the programmer knows it will happen and specifically wants it. There is a tradeoff in speed: if bits are used, then setting / clearing / testing a specific bool requires first computing a mask with an appropriate shift, and setting or clearing it now requires a read-modify-write instead of just a write.
And there is a more serious issue in multithreaded programs. Languages like C++ promise that different threads can freely modify different objects, including different elements of the same array, without needing synchronization or causing a data race. For instance, if we have
bool a, b; // not atomic
void thread1() { /* reads and writes a */ }
void thread2() { /* reads and writes b */ }
then this is supposed to work fine. But if the compiler made a and b two different bits in the same byte, concurrent accesses to them would be a data race on that byte, and could cause incorrect behavior (e.g. if the read-modify-writes being done by the two threads were interleaved). The only way to make it safe would be to require that both threads use atomic operations for all their accesses, which are typically many times slower. And if the compiler could freely pack bools in this way, then every operation on a potentially shared bool would have to be made atomic, throughout the entire program. That would be prohibitively expensive.
So this is fine if the programmer wants to pack bools to save memory, is willing to take the hit to speed, and can guarantee that they won't be accessed concurrently. But they should be aware that it's happening, and have control over whether it does.
(Indeed, some people feel that having C++ provide this with vector<bool> was a mistake, since programmers have to know that it is a special exception to the otherwise general rule that vector<T> behaves like an array of T, and different elements of the vector can safely be accessed concurrently. Perhaps they should have left vector<bool> to work in the naive way, and given a different name to the packed version, similar to std::bitset.)
I am trying to squeeze every bit of efficiency out of my application I am working on.
I have a couple arrays that follow the following conditions:
They are NEVER appended to, I always calculate the index myself
The are allocated once and never change size
It would be nice if they were thread safe as long as it doesn't cost performance
Some hold primitives like floats, or unsigned ints. One of them does hold a class.
Most of these arrays at some point are passed into a glBuffer
Never cleared just overwritten
Some of the arrays individual elements are changed entirely by = others are changed by +=
I currently am using swift native arrays and am allocating them like var arr = [GLfloat](count: 999, repeatedValue: 0) however I have been reading a lot of documentation and it sounds like Swift arrays are much more abstract then a traditional C-style array. I am not even sure if they are allocated in a block or more like a linked list with bits and pieces thrown all over the place. I believe by doing the code above you cause it to allocate in a continuous block but i'm not sure.
I worry that the abstract nature of Swift arrays is something that is wasting a lot of precious processing time. As you can see by my above conditions I dont need any of the fancy appending, or safety features of Swift arrays. I just need it simple and fast.
My question is: In this scenario should I be using some other form of array? NSArray, somehow get a C-style array going, create my own data type?
Im looking into thread safety, would a different array type that was more thread safe such as NSArray be any slower?
Note that your requirements are contradictory, particularly #2 and #7. You can't operate on them with += and also say they will never change size. "I always calculate the index myself" also doesn't make sense. What else would calculate it? The requirements for things you will hand to glBuffer are radically different than the requirements for things that will hold objects.
If you construct the Array the way you say, you'll get contiguous memory. If you want to be absolutely certain that you have contiguous memory, use a ContiguousArray (but in the vast majority of cases this will give you little to no benefit while costing you complexity; there appear to be some corner cases in the current compiler that give a small advantage to ContinguousArray, but you must benchmark before assuming that's true). It's not clear what kind of "abstractness" you have in mind, but there's no secrets about how Array works. All of stdlib is open source. Go look and see if it does things you want to avoid.
For certain kinds of operations, it is possible for other types of data structures to be faster. For instance, there are cases where a dispatch_data is better and cases where a regular Data would be better and cases where you should use a ManagedBuffer to gain more control. But in general, unless you deeply know what you're doing, you can easily make things dramatically worse. There is no "is always faster" data structure that works correctly for all the kinds of uses you describe. If there were, that would just be the implementation of Array.
None of this makes sense to pursue until you've built some code and started profiling it in optimized builds to understand what's going on. It is very likely that different uses would be optimized by different kinds of data structures.
It's very strange that you ask whether you should use NSArray, since that would be wildly (orders of magnitude) slower than Array for dealing with very large collections of numbers. You definitely need to experiment with these types a bit to get a sense of their characteristics. NSArray is brilliant and extremely fast for certain problems, but not for that one.
But again, write a little code. Profile it. Look at the generated assembler. See what's happening. Watch particularly for any undesired copying or retain counting. If you see that in a specific case, then you have something to think about changing data structures over. But there's no "use this to go fast." All the trade-offs to achieve that in the general case are already in Array.
I have 1000 float datas in an array. I want to separate into different classes, lets say 4 classes. Their sizes are unpredictable. I could easily hold them in a linked list in a CPU implementation, but in OpenCL kernel, is there an opportunity like that? In my mind there are 3 solution to this problem.
First, arrays with length 1000 constructed in number of classes, which is memory costly.
Second, I allocate an array with length 1000 and separate them into parts. However, I may transport the values from and index into different index, becuase I don't know the size of each classes and they may exceed the size which I provided for each.
Third, and better in my opinion, I get two different array with same length. One of them stores data, the other one stores pointers. For example, in i-th index of data array, the value is stored which belongs to 2nd class. Additionally in i-th index of pointer to the next data which belongs to 2nd class. But this is good for just atomic type (like int, float, char etc) linked lists.
I am new in OpenCL. I haven't known lots of features of it yet. If there is a better way, please don't share with me and others.
Using pointers on GPU is usually very bad idea. Major amount of data resides in global memory, and to fetch it quickly the access should be coalesced. Using pointers breaks the access pattern totally, making it essentially random. It's not very good on CPUs too since it cause a lot of cache misses, but CPUs have larger caches and "smarter" internal logic, so it's usually not so important, but sometimes cache-aware memory access pattern can increase CPU application's speed by nearly order of magnitude. On GPUs coalesced global memory access is one of most important optimizations, and pointers can't provide it.
If you are not extremely short on memory, I'd suggest to use first way and preallocate arrays large enough to hold all data. If you are really short on memory, you could use textures to store your data and pointer arrays, but it depends on the algorithm whether it would provide any benefits or not.
I'm pretty sure this is a silly newbie question but I didn't know it so I had to ask...
Why do we use data structures, like Linked List, Binary Search Tree, etc? (when no dynamic allocation is needed)
I mean: wouldn't it be faster if we kept a single variable for a single object? Wouldn't that speed up access time? Eg: BST possibly has to run through some pointers first before it gets to the actual data.
Except for when dynamic allocation is needed, is there a reason to use them?
Eg: using linked list/ BST / std::vector in a situation where a simple (non-dynamic) array could be used.
Each thing you are storing is being kept in it's own variable (or storage location). Data structures apply organization to your data. Imagine if you had 10,000 things you were trying to track. You could store them in 10,000 separate variables. If you did that, then you'd always be limited to 10,000 different things. If you wanted more, you'd have to modify your program and recompile it each time you wanted to increase the number. You might also have to modify the code to change the way in which the calculations are done if the order of the items changes because the new one is introduced in the middle.
Using data structures, from simple arrays to more complex trees, hash tables, or custom data structures, allows your code to both be more organized and extensible. Using an array, which can either be created to hold the required number of elements or extended to hold more after it's first created keeps you from having to rewrite your code each time the number of data items changes. Using an appropriate data structure allows you to design algorithms based on the relationships between the data elements rather than some fixed ordering, giving you more flexibility.
A simple analogy might help to understand. You could, for example, organize all of your important papers by putting each of them into separate filing cabinet. If you did that you'd have to memorize (i.e., hard-code) the cabinet in which each item can be found in order to use them effectively. Alternatively, you could store each in the same filing cabinet (like a generic array). This is better in that they're all in one place, but still not optimum, since you have to search through them all each time you want to find one. Better yet would be to organize them by subject, putting like subjects in the same file folder (separate arrays, different structures). That way you can look for the file folder for the correct subject, then find the item you're looking for in it. Depending on your needs you can use different filing methods (data structures/algorithms) to better organize your information for it's intended use.
I'll also note that there are times when it does make sense to use individual variables for each data item you are using. Frequently there is a mixture of individual variables and more complex structures, using the appropriate method depending on the use of the particular item. For example, you might store the sum of a collection of integers in a variable while the integers themselves are stored in an array. A program would need to be pretty simple though before the introduction of data structures wouldn't be appropriate.
Sorry, but you didn't just find a great new way of doing things ;) There are several huge problems with this approach.
How could this be done without requring programmers to massively (and nontrivially) rewrite tons of code as soon as the number of allowed items changes? Even when you have to fix your data structure sizes at compile time (e.g. arrays in C), you can use a constant. Then, changing a single constant and recompiling is sufficent for changes to that size (if the code was written with this in mind). With your approach, we'd have to type hundreds or even thousands of lines every time some size changes. Not to mention that all this code would be incredibly hard to read, write, maintain and verify. The old truism "more lines of code = more space for bugs" is taken up to eleven in such a setting.
Then there's the fact that the number is almost never set in stone. Even when it is a compile time constant, changes are still likely. Writing hundreds of lines of code for a minor (if it exists at all) performance gain is hardly ever worth it. This goes thrice if you'd have to do the same amount of work again every time you want to change something. Not to mention that it isn't possible at all once there is any remotely dynamic component in the size of the data structures. That is to say, it's very rarely possible.
Also consider the concept of implicit and succinct data structures. If you use a set of hard-coded variables instead of abstracting over the size, you still got a data structure. You merely made it implicit, unrolled the algorithms operating on it, and set its size in stone. Philosophically, you changed nothing.
But surely it has a performance benefit? Well, possible, although it will be tiny. But it isn't guaranteed to be there. You'd save some space on data, but code size would explode. And as everyone informed about inlining should know, small code sizes are very useful for performance to allow the code to be in the cache. Also, argument passing would result in excessive copying unless you'd figure out a trick to derive the location of most variables from a few pointers. Needless to say, this would be nonportable, very tricky to get right even on a single platform, and liable to being broken by any change to the code or the compiler invocation.
Finally, note that a weaker form is sometimes done. The Wikipedia page on implicit and succinct data structures has some examples. On a smaller scale, some data structures store much data in one place, such that it can be accessed with less pointer chasing and is more likely to be in the cache (e.g. cache-aware and cache-oblivious data structures). It's just not viable for 99% of all code and taking it to the extreme adds only a tiny, if any, benefit.
The main benefit to datastructures, in my opinion, is that you are relationally grouping them. For instance, instead of having 10 separate variables of class MyClass, you can have a datastructure that groups them all. This grouping allows for certain operations to be performed because they are structured together.
Not to mention, having datastructures can potentially enforce type security, which is powerful and necessary in many cases.
And last but not least, what would you rather do?
string string1 = "string1";
string string2 = "string2";
string string3 = "string3";
string string4 = "string4";
string string5 = "string5";
Console.WriteLine(string1);
Console.WriteLine(string2);
Console.WriteLine(string3);
Console.WriteLine(string4);
Console.WriteLine(string5);
Or...
List<string> myStringList = new List<string>() { "string1", "string2", "string3", "string4", "string5" };
foreach (string s in myStringList)
Console.WriteLine(s);