I have an application in which I have to store a couple of millions of integers, I have to store them in a Look up table, obviously I cannot store such amount of data in memory and in my requirements I am very limited I have to store the data in an embebedded system so I am very limited in the space, so I would like to ask you about recommended methods that I can use for the reduction of the look up table. I cannot use function approximation such as neural networks, the values needs to be in a table. The range of the integers is not known at the moment. When I say integers I mean a 32 bit value.
Basically the idea is use some copmpression method to reduce the amount of memory but without losing many precision. This thing needs to run in hardware so the computation overhead cannot be very high.
In my algorithm I have to access to one value of the table do some operations with it and after update the value. In the end what I should have is a function which I pass an index to it and then I get a value, and after I have to use another function to write a value in the table.
I found one called tile coding , this one is based on several look up tables, does anyone know any other method?.
Thanks.
I'd look at the types of numbers you need to store and pull out the information that's common for many of them. For example, if they're tightly clustered, you can take the mean, store it, and store the offsets. The offsets will have fewer bits than the original numbers. Or, if they're more or less uniformly distributed, you can store the first number and then store the offset to the next number.
It would help to know what your key is to look up the numbers.
I need more detail on the problem. If you cannot store the real value of the integers but instead an approximation, that means you are going to reduce (throw away) some of the data (detail), correct? I think you are looking for a hash, which can be an artform in itself. For example say you have 32 bit values, one hash would be to take the 4 bytes and xor them together, this would result in a single 8 bit value, reducing your storage by a factor of 4 but also reducing the real value of original data. Typically you could/would go further and perhaps and only use a few of those 8 bits , say the lower 4 and reduce the value further.
I think my real problem is either you need the data or you dont, if you need the data you need to compress it or find more memory to store it. If you dont, then use a hash of some sort to reduce the number of bits until you reach the amount of memory you have for storage.
Read http://www.cs.ualberta.ca/~sutton/RL-FAQ.html
"Function approximation" refers to the
use of a parameterized functional form
to represent the value function
(and/or the policy), as opposed to a
simple table."
Perhaps that applies. Also, update your question with additional facts -- don't merely answer in the comments.
Edit.
A bit array can easily store a bit for each of your millions of numbers. Let's say you have numbers in the range of 1 to 8 million. In a single megabyte of storage you can have a 1 bit for each number in your set and a 0 for each number not in your set.
If you have numbers in the range of 1 to 32 million, you'll require 4Mb of memory for a big table of all 32M distinct numbers.
See my answer to Modern, high performance bloom filter in Python? for a Python implementation of a bit array of unlimited size.
If you are merely looking for the presence of the number in question a bloom filter, might be what you are looking for. Honestly though your question is fairly vague and confusing. It would help to explain what Q values are, and what you do with them once you find them in the table.
If your set of integers is homongenous, then you could try a hash table, because there is a trick you can use to cut the size of the stored integers, in your case, in half.
Assume the integer, n, because its set is homogenous can be the hash. Assume you have 0x10000 (16k) buckets. Each bucket index, iBucket = n&FFFF. Each item in a bucket need only store 16 bits, since the first 16 bits are the bucket index. The other thing you have to do to keep the data small is to put the count of items in the bucket, and use an array to hold the items in the bucket. Using a linked list will be too large and slow. When you iterate the array looking for a match, remember you only need to compare the 16 bits that are stored.
So assuming a bucket is a pointer to the array and a count. On a 32 bit system, this is 64 bits max. If the number of ints was small enough we might be able to do some fancy things and use 32 bits for a bucket. 16k * 8 bytes = 524k, 2 million shorts = 4mb. So this gets you a method to lookup the ints and about 40% compression.
Related
I am trying to build a Sieve of Eratosthenes in Lua and i tried several things but i see myself confronted with the following problem:
The tables of Lua are to small for this scenario. If I just want to create a table with all numbers (see example below), the table is too "small" even with only 1/8 (...) of the number (the number is pretty big I admit)...
max = 600851475143
numbers = {}
for i=1, max do
table.insert(numbers, i)
end
If I execute this script on my Windows machine there is an error message saying: C:\Program Files (x86)\Lua\5.1\lua.exe: not enough memory. With Lua 5.3 running on my Linux machine I tried that too, error was just killed. So it is pretty obvious that lua can´t handle the amount of entries.
I don´t really know whether it is just impossible to store that amount of entries in a lua table or there is a simple solution for this (tried it by using a long string aswell...)? And what exactly is the largest amount of entries in a Lua table?
Update: And would it be possible to manually allocate somehow more memory for the table?
Update 2 (Solution for second question): The second question is an easy one, I just tested it by running every number until the program breaks: 33.554.432 (2^25) entries fit in one one-dimensional table on my 12 GB RAM system. Why 2^25? Because 64 Bit per number * 2^25 = 2147483648 Bits which are exactly 2 GB. This seems to be the standard memory allocation size for the Lua for Windows 32 Bit compiler.
P.S. You may have noticed that this number is from the Euler Project Problem 3. Yes I am trying to accomplish that. Please don´t give specific hints (..). Thank you :)
The Sieve of Eratosthenes only requires one bit per number, representing whether the number has been marked non-prime or not.
One way to reduce memory usage would be to use bitwise math to represent multiple bits in each table entry. Current Lua implementations have intrinsic support for bitwise-or, -and etc. Depending on the underlying implementation, you should be able to represent 32 or 64 bits (number flags) per table entry.
Another option would be to use one or more very long strings instead of a table. You only need a linear array, which is really what a string is. Just have a long string with "t" or "f", or "0" or "1", at every position.
Caveat: String manipulation in Lua always involves duplication, which rapidly turns into n² or worse complexity in terms of performance. You wouldn't want one continuous string for the whole massive sequence, but you could probably break it up into blocks of a thousand, or of some power of 2. That would reduce your memory usage to 1 byte per number while minimizing the overhead.
Edit: After noticing a point made elsewhere, I realized your maximum number is so large that, even with a bit per number, your memory requirements would optimally be about 73 gigabytes, which is extremely impractical. I would recommend following the advice Piglet gave in their answer, to look at Jon Sorenson's version of the sieve, which works on segments of the space instead of the whole thing.
I'll leave my suggestion, as it still might be useful for Sorenson's sieve, but yeah, you have a bigger problem than you realize.
Lua uses double precision floats to represent numbers. That's 64bits per number.
600851475143 numbers result in almost 4.5 Terabytes of memory.
So it's not Lua's or its tables' fault. The error message even says
not enough memory
You just don't have enough RAM to allocate that much.
If you would have read the linked Wikipedia article carefully you would have found the following section:
As Sorenson notes, the problem with the sieve of Eratosthenes is not
the number of operations it performs but rather its memory
requirements.[8] For large n, the range of primes may not fit in
memory; worse, even for moderate n, its cache use is highly
suboptimal. The algorithm walks through the entire array A, exhibiting
almost no locality of reference.
A solution to these problems is offered by segmented sieves, where
only portions of the range are sieved at a time.[9] These have been
known since the 1970s, and work as follows
...
I have some questions regarding the optimal entry size setting for Redis hash sets.
In this example memory-optimization they use 100 hash entries
per key but use hash-max-zipmap-entries 256 ? Why not
hash-max-zipmap-entries 100 or 128?
On the redis website (above link) they used max hash entry size of
100, but in this post instagram, they mention 1000 entries. So
does this mean the optimal setting is a function of the product of
hash-max-zipmap-entries & hash-max-zipmap-value ?(ie in this case
Instagram has smaller hash-values than memory optimization example?)
Your comments/clarifications are much appreciated.
The key is, from here:
manipulating the compact versions of these [ziplist] structures can become slow as they grow longer
and
[as ziplists grow longer] fetching/updating individual fields of a HASH, Redis will have to decode many individual entries, and CPU caches won’t be as effective
So to your questions
This page just shows an example and I doubt the author gave much thought to the exact values. In real life, IF you wanted to take advantage of ziplists, and you knew your number of entries per hash was <100, then setting it at 100, 128 or 256 would make no difference. hash-max-zipmap-entries is only the LIMIT over which you're telling Redis to change the encoding from ziplist to hash.
There may be some truth in your "product of hash-max-zipmap-entries & hash-max-zipmap-value" idea, but I'm speculating. More importantly, first you have to define "optimal" based on what you want to do. If you want to do lots of HSET/HGETs in a large ziplist, it will be slower than if you used a hash. But if you never get/update single fields only ever do HMSET/HGETALL on a key, large ziplists wouldn't slow you down. The Instagram 1000 was THEIR optimal number based on THEIR specific data, use cases, and Redis function call frequencies.
You encouraged me to read both links and it seems that you are asking for "default value for hash table size".
I don't think that it's possible to say that one number is universal for all possibilities. The described mechanism is similar to standard hash mapping. Look at http://en.wikipedia.org/wiki/Hash_table
If you have small size of hash-table, it means that many various hash values point into the same array, where the equals method is used to find out the item.
On the other hand, large hash table means that it allocates large memory along with many empty fields. But this scales well as the algorithm uses O(1) big O notation and there is no equals searching for the item.
In general the size of the table IMHO depends on the overall count of all elements you expect to put into the table and it also depends on the diversity of the key. I mean if every hash start with "0001" not even size=100000 would help you.
Quick question on memory locations in IA-32 assembly language that i cannot seem to find the answer for anywhere else.
On IA-32 each memory address is 4 bytes long (e.g. 0x0040120e). Each of these addresses points to a 1 byte value (or in the case of a larger value, the first byte of it). Now look at these two simple IA-32 assembly language statements:
var1 db 2
var2 db 3
This will place var1 and var2 in adjacent memory cells (let's say 0x0040120e and 0f). Now I realize that the define directive db allocates 1 byte to the value. But, in the case above I have two values (2 and 3) that in fact only requires two bits each, to be stored.
Questions:
When using the db directive, do these two values still consume a full byte, even though they are smaller than 1 byte?
Is using a full byte for values that could get away with less, still the common way to go (as we have so much memory that we don't care)?
Does integers 0 to 255 then generally take up 1 byte and integers 256 to (2^16 - 1) take up 2 bytes (a word), etc.?
Thank you,
Magnus
EDIT 1: Made questions more clear (apologies for the back and forth)
EDIT 2: Added a structured reply below, based on other posters' input
yes. the B in DB is for Byte.
You could use a nibble for each, like so:
combined db 0x23
but you'd have to
a) shift the result for 4 bits right if you need the "2".
b) mask the leftmost 4 bits if you need the "3".
Hardly worth the effort these days ;-)
Yes, since the architecture is byte-addressable and cannot address anything smaller than a byte.
This means that data requiring less than one byte will need to share its address with other data.
In practice this means that you're going to have to know which bits in the pointed-out byte are used for this particular value.
For hardware registers this sort of mapping is very common.
EDIT: Ah, you seem to mean "values of the same variable" when you said "2 and 3". I thought you meant 2-bit and 3-bit values. You need to decide how many bits are needed at most for a particular variable, for all the values you need that variable to be able to store. There are variable-length encodings for integers of course, but that's generally rarely used in assembly and not what you'd typically use for some general-purpose variable.
You generally should expect to reserve all bits required for all values that a variable need to hold, up front. Otherwise, if you're worried about "wasting memory", you would need to move all other variables as soon as you get some "vacant bits" somewhere. That would end up costing fantastically much. Also, knowing the size of a variable is constant makes it possible to generate (or write) the proper code to handle it, otherwise you would of course also need to explicitly store somewhere "the size of the value held in variable x is now y bits". That becomes extremely painful very very quickly.
My initial question was a bit unstructured, so for the benefit of other searchers stopping by here I will use the answers received from #unwind and #geert3 to create a structured response. Again, this was my fault due to the initial poor structuring and creds for the answers goes to #unwind and #geert3.
When using the db directive you allocate 1 byte to the variable, and even if the variable takes up less space than 1 byte, it will still consume that full 1-byte address spot. As one might guess, that wastes a few bits of memory, but that is okay as you have enough memory and not too bothered about wasting a couple of bits. The reason you want to use the full 1-byte memory location is that it is easier to reference the variable when it is alone in the address slot (see #geert3's note on how to access it if you use less than a byte), and additionally, in case you want to reuse the variable later, it is great to know you have space for any number up to 255.
Yes, see answer to 1
Yes, you would normally allocate multiples of a byte to a variable, in a byte-addressable system
I would like to store millions of data lines that looks like this:
key, value
key is an integer in the range of (0 to 5,000,000); all values are unique;
value is an unsigned int16 value (0 to 65535)
the key is to store the data while taking the LEAST AMOUNT OF DISK SPACE, and yet, be able to query the data. can you think of any algorithms / smart schemes for data storage that would be helpful?
just in case it matters, I use Linux.
One option would be, if the key values are not important data but rather just index data to utilize a flat file of bits ( with a descriptive header ). Every 16 bits is a value and the nth value would then be (n - 1) * 16 bits from the end of the header.
Additionally, if the key value does matter, a set flat file of about 10MB would allow for the entire key space to be stored without storing actual keys. The 16 bits that are at the (n - 1) * 16 offset would be that key's value.
That would probably be the least space intensive method for storage, as it would be only the data that is literally required. ( Though, if you are only interested in say 100k values and one has a key of 5 million you do end up with a lot of wasted space, which wouldn't be there with an actual key,value addressing system. So this methodology only achieves a minimum disk storage for sets of tightly grouped values or many many numbers (over about the 2 million mark ).
how do you plan to use stored data? with random or sequential access? for sequential access you can use any archiving algorithm, e.g. LZMA. Random access doesn't leave you a lot of space for improvements.
can you see any patterns of this data? e.g. if the difference between adjacent keys/values are often small you can store only packed differences. and million of other possible approaches.
[EDIT] also you can check techniques used for data compression in network communication
[EDIT1] and you can check this Google Code Integer Array Compression project
This depend upon the operation and data. I would first recommend "just using a database" (a simple key-value store such as BDB/EhCache [read: Key Value store], for instance :-)
Mimisbrunnr also has a good answer if all the keys are used.
If the keys are near constant/read-only and only a relatively small percent of the keys are used, consider the use of a (disk-based) Heap data-structure (very similar to an Array-based Heap; Heaps need not be Array-based). Robert Sedgewick had a good book from the late 80's that had a very lean implementation, but I forget the name. A Heap will be more beneficial when compared to a flat index with a smaller proportion of used keys and at full-load will have worse storage requirements.
(If abstracted, the used method could be switched and/or a hybrid heap with indexed/sequenced leaf-node values could be used [along with Huffman encoding or whatnot], but that is just adding far more complications. Keep it simple ... hence first suggestion of an existing key/value store ;-)
Happy coding.
Have you considered using a database designed for mobile devices such as SQL Server Compact, or another similar database? These will have a small footprint on the disk, while still providing the full search power you need.
Another example of a compact database engine is KeyDB for linux:
http://3d2f.com/programs/11-989-keydb-download.shtml
I've been using the TBucketList and TObjectBucketList for all my hashing needs, but never experiemented with switching the number of buckets. I vaguely remember what this means from Data Structures class, but could someone elaborated on the nuances of this particular class in Delphi
The following table lists the possible values:
Value Number of buckets
bl2 2
bl4 4
bl8 8
bl16 16
bl32 32
bl64 64
bl128 128
bl256 256
TBucketList and TObjectBucketList store pointers. The hash function they use simply masks out the upper bits of the address. How many bits get masked out depends on how many buckets the object has. If you use bl2, for example, 31 bits get masked out and only one bit of the address determines the bucket. With bl256, an entire byte of the pointer gets used. It's one of the middle two bytes. The trade-off is simply the number of buckets you'll have. A bucket only takes eight bytes, so having 256 of them isn't a huge cost.
Aside from that, TBucketList is just an ordinary hash table like you learned about in your data-structure class.
TIntegerBucketList uses the same hash function as the others. If you want a more sophisticated hash function, write a descendant of TCustomBucketList and override the BucketFor method. In your descendant class, you can also assign the protected BucketCount property to use something other than the counts provided by TBucketList. Note that the class makes no effort to redistribute items due to a change in the bucket count, so don't re-assign BucketCount after items have already been added to the list unless you plan to do the redistribution yourself.