  Compression of floating-point data will play an important role in
high-performance computing as data bandwidth and storage become dominant costs.
Lossy compression of floating-point data is powerful, but theoretical results
are needed to bound its errors when used to store look-up tables, simulation
results, or even the solution state during the computation. \black{In this
paper, we analyze the round-off error introduced by ZFP, a %state-of-the-art
lossy compression algorithm.} The stopping criteria for ZFP depends on the
compression mode specified by the user; either fixed rate, fixed accuracy, or
fixed precision [P. Lindstrom, Fixed-rate compressed floating-point arrays,
IEEE Transactions on Visualization and Computer Graphics, 2014]. While most of
our discussion is focused on the fixed precision mode of ZFP, we establish a
bound on the error introduced by all three compression modes. In order to
tightly capture the error, we first introduce a vector space that allows us to
work with binary representations of components. Under this vector space, we
define operators that implement each step of the ZFP compression and
decompression to establish a bound on the error caused by ZFP. To conclude,
numerical tests are provided to demonstrate the accuracy of the established
bounds.
