The simple beauty of XOR floating point compression
Clemens Winter discusses compression in a list of floating point numbers.
I recently implemented a small program to visualize the inner workings of a scheme that compresses floating point time series by XORing subsequent values. The resulting visualizations are quite neat and made it much easier for me to understand this beautiful algorithm than any of the explanations that I had previously encountered.
The algorithm is simple. We start by writing out the first floating point number in full. All subsequent numbers are XORed with the previous number and then encoded in one of three ways:
We write a single 0 bit. This indicates that the number is identical to the previous number.
We write the two bit sequence 11. We write a 5 bit integer that indicates the number of leading zeros in the XORed value. We write a 6 bit integer that indicates the number of bits in the subsequence that starts at the first 1 bit and includes and ends at the last 1 bit. We then write out this subsequence, omitting all leading and trailing zeros.
We write the two bit sequence 10. We then immediately write out the subsequence of the XORed value that has the same starting index and length as the last subsequence we wrote.
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