Convert binary string greater than 52 bits to single in Matlab? - matlab

Question

I'm trying to convert very long binary strings, often greater than 52 bits into numbers. I cannot have a fixed lookahead window because I am doing this to calculate a version of Lempel-Ziv complexity for neural data.
When I try to convert any long string, bin2dec throws and error that the binary string must be 52 bits or less.
Is there a way to get around this size limitation?

Answer 1

dec2bin throws that error because a single is not capable of storing that much precision. Your very question asks an impossibility. You have two choices: store the value in something other than a floating point value, or throw away some precision before you convert.
Or describe more completely what you're trying to accomplish.
EDITING:
Based on your additional information, I am even more certain that converting to floating point is not what you want to do. If you want to reduce the storage size to something more efficient, convert to a vector of bytes (uint8), which is as dense as you can get. Just split the binary string into N rows of 8 digits each, using reshape. This seems to be an accepted approach for biological data.
str = char((rand(1, 100)>0.5) + '0'); % test data
data = uint8(bin2dec(reshape(str(1:end-mod(end,8)), [], 8)));
In this code, I toss any bits that don't divide evenly into 8. Or, skip the uint8 step and just perform your processing on the resulting vector, where each double-precision float represents one 8-bit word from your sequence.

Answer 2

You could roll your own implementation:
len = 60;
string = [];
for i = 1:len
string = [string sprintf('%d', randi([0 1]))];
end
% error
% bin2dec(string);
% roll your own...
value = 0;
for i = length(string):-1:1
value = value + str2num(string(i))*2^(length(string)-i);
end
I'm just looping through the string and adding to some value. At the end, value will contain the decimal value of the string. Does this work for you?
Note: This solution is slow. You can speed it up a bit by preallocating the string, which I did on my own machine. Also, it's going to have issues if your number gets up to 1e6 digits. At that point, you need variable precision arithmetic to keep track of it. And adding that to the calculation really slowed things down. If I were you, I'd strongly consider compiling this from a .mex file if you need the functionality in MATLAB.

Answer 3

credits due to #aardvarkk, but here's a sped up version of his algorithm (+- 100x faster):
N=100;
strbin = char(randi(2,1,N)+'0'-1);
pows2 = 2.^(N-1:-1:0);
value=pows2*(strbin-'0')';
double's range goes only up to 1.79769e+308 which is 2^1024 give or take. From there on, value will be Inf or NaN. So you still need to find another way storing the resulting number.
A final pro on this algorithm: you can cache pows2 for a large number and then use a piece of it for any new strbin of length N:
Nmax = 1e8; % already 700MB for pows2, watch out!
pows2 = 2.^(Nmax-1:-1:0);
and then use
value = pows2(Nmax-N+1:end)*(strbin-'0')';
Solution to matlab's numeric upper bound
There's a tool on the File Exchange called vpi: http://www.mathworks.com/matlabcentral/fileexchange/22725
It allows you to use really big integers (2^5000? no prob). It's only slower (a lot) in calculating everything, I don't suggest using my method above with this. But hey, you can't have everything!
Download the package, addpath it and the following might work:
N=3000;
strbin = char(randi(2,1,N)+'0'-1);
binvals=strbin-'0';
val=0;
twopow=vpi(1);
for ii=1:N
val=val+twopow*binvals(N-ii+1);
twopow=twopow*2;
end