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August 31st, 2013, 11:29 PM  #1 
Newbie Joined: Aug 2013 Posts: 3 Thanks: 0  Compacting data into a 16bit integer
I'm a working on a video game where we need to optimize the information we send as network packets. Right now we are using multiple 16 bit packets to send very small values of data which is very inefficient as we want to run as lean as we can over internet. We are not as strong with math as far as making algorithms as we would like. The idea is to take ... Data type 1: 1 to 640 Data type 2: 1 to 480 Data type 3: 1 to 64 ... and combine them into one 16 bit integer using an algorithm (with 65536 combinations). We want to have it where it can be decoded where we can pull three unique values of the different data types out of the one 16 bit integer. Does anyone have any ideas or solutions on how to do this? We would need a way to encode and decode it obviously and how to do this from a programmers standpoint without highend equation notation. We're sure it's probably quite simple but we can't seem to wrap our heads around it enough and would greatly appreciate your help. Thank you very much for reading. 
September 1st, 2013, 07:13 AM  #2  
Senior Member Joined: Mar 2012 From: Belgium Posts: 653 Thanks: 11  Re: Compacting data into a 16bit integer Quote:
Your data types should get smaller or your integer must get bigger then 16 bit integer  
September 1st, 2013, 12:51 PM  #3 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 933 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Compacting data into a 16bit integer
You need more than 24 bits to store that much information, 16 bits won't do it. Possible ways out include:

September 1st, 2013, 04:51 PM  #4 
Newbie Joined: Aug 2013 Posts: 3 Thanks: 0  Re: Compacting data into a 16bit integer
Unfortunately, the worst case we are looking for is just using the two data types and we cannot condense their fidelity as they are coordinates. If they were under 256 it would be as simple as converting both data types to binary, shifting their bits into the 16 bit places and converting back to decimal (which unfortunately we have to do with the software we are using). Example: [color=#BF0000]Data type 1 (0 255 range): 125 Decimal, (01111101 Binary)[/color] [color=#0000FF]Data type 2 (0  255 range): 54 Decimal, (00110110 Binary)[/color] Shuffling the data type 1 bits into the 1st, 3rd, 5th, 7th, 9th, 11th, 13th and 15th digits of the 16bit integer. Shuffling the data type 2 bits into the 2nd, 4th, 6th, 8th, 10th, 12th, 14th and 16th digit of the 16 bit integer. [color=#BF0000]0[/color] [color=#0000FF]0[/color] [color=#BF0000]1[/color] [color=#0000FF]0[/color] [color=#BF0000]1[/color] [color=#0000FF]1[/color] [color=#BF0000]1[/color] [color=#0000FF]1[/color] [color=#BF0000]1[/color] [color=#0000FF]0[/color] [color=#BF0000]1[/color] [color=#0000FF]1[/color] [color=#BF0000]0[/color] [color=#0000FF]1[/color] [color=#BF0000]1[/color] [color=#0000FF]0[/color] = 763 decimal I'm still confident though that with 65536 combinations of a 16 bit integer there is an algorithm to insert the two data types at 1 to 640 and 1 to 480 ... just might need a cytologist to figure it out. Thank you guys for the input thus far . 
September 1st, 2013, 08:35 PM  #5  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 933 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Compacting data into a 16bit integer Quote:
But in any case 16 bits is too small to fit the desired data, since 2^26 < 640 * 480.  
September 1st, 2013, 10:13 PM  #6  
Senior Member Joined: Mar 2012 From: Belgium Posts: 653 Thanks: 11  Re: Compacting data into a 16bit integer Quote:
He is completely right. This job can't be done. I will try to illustrate this with an example. Assume we have only 3 bits (8 combinations). And we want to store 2 data types. Data type 1: 14 Data type 2: 13 Similarly this should not be possible since 2^3<3*4 We 'encode' the numbers with a function f(x,y) lets say. Then we get 12 different 'encryptions' f(1,1) f(1,2) f(1,3) f(2,1) f(2,2) f(2,3) f(3,1) f(3,2) f(3,3) f(4,1) f(4,2) f(4,3) In order to decrypt this we need all of those encryptions should be distinct. Lets say f(1,3)=5 and that f(3,1)=5 This would mean that a computer gets in hes decryption function g(x) He gets two times g(5). He might be able to figure out that x=1 or 3 and y = 3 or 1 But he won't be able to find which one of those he has to use. That's why all the encryptions should be distinct. Now let's take a look at the 3 bit binary system. 000 001 010 011 100 101 110 111 Let's say they are the solutions of our encryptions then we can do something like this. 000=f(1,1) 001=f(2,1) 010=f(3,1) 011=f(4,1) 100=f(1,2) 101=f(2,2) 110=f(3,2) 111=f(4,2) Now where would you place f(1,3) f(2,3) f(3,3) and f(4,3) ? nowhere because there is no place left for all values to be distinct. I hope you understood now why this is not possible. My example was with much lower numbers because I can't start writing 65536 combinations here right ? But it still works the same how big or how small your amount of digits get.  
September 1st, 2013, 11:25 PM  #7 
Newbie Joined: Aug 2013 Posts: 3 Thanks: 0  Re: Compacting data into a 16bit integer
Ahhh, point taken. Thank you for taking the time to explain , that was a lot of work. We've decided to use the bitshuffling idea I explained previously but use a 32 bit integer instead of 16 and convert the data types into 10 and 9 binary digits. And to be honest, that works on so many other levels that it was really easier to decide that than my convoluted idea. You're a scholar and a saint sir and your time is appreciated! 

Tags 
16bit, compacting, data, integer 
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