I'm heaving an (big) array of floats, each float takes 4 bytes.
Is there a way, given the fact that my floats are ranged between 0 and 255, to store each float in less than 4 bytes?
I can do any amount of computation on the whole array.
I'm using C.
The absolute range of your data doesn't really matter that much, it's the amount of precision you need. If you can get away with e.g. 6 digits of precision, then you only need as much storage as would be required to store the integers from 1-1000000, and that's 20 bits. So, supposing this, what you can do is:
1) Shift your data so that the smallest element has value 0. I.e. subtract a single value from every element. Record this shift.
2) Scale (multiply) your data by a number just large enough so that after truncation to an integer, you will not lose any precision you need.
3) Now this might be tricky unless you can pack your data into convenient 8- or 16-bit units--pack the data into successive unsigned integers. Each one of your data values needs 20 bits in this example, so value 1 takes up the first 20 bits of integer 1, value 2 takes up the remaining 12 bits of integer 1 and the first 8 bits of integer 2, and so on. In this hypothetical case you end up saving ~40%.
4) Now, 'decrypting'. Unpack the values (you have saved the # of bits in each one), un-scale, and un-shift.
So, this will do it, and might be faster and more compact than standard compression algorithms, as they aren't allowed to make assumptions about how much precision you need, but you are.