These quantities define the tolerable error on individual values or multidimensional fields of data from a given datatype.
The definition is mostly based on the notion of the term error, which is the residual when subtracting the (lossy) compressed value (d) from the true value (v).
Absolute error tolerance: is the maximum amount of the residual error in the calculations; abs(v-d) < absolute error
Relative error tolerance is a measure of absolute error compared to the size of the calculations.
Relative error with finest absolute tolerance is a combination of two quantities. With a relative tolerance, small numbers around 0 are problematic for compressors, e.g. 1% relative error for the data value 0.01 results in the compressed accuracy of 0.01±0.0001. The finest absolute tolerance limits the smallest relative error. In our example, setting a relative error finest absolute tolerance of 0.01 would result in an error of ±0.01f or small numbers, while for large numbers their relative error is considered. Thus, it is the lower bound and guaranteed error for relative error bounds, where as the absolute tolerance is the guaranteed resolution for all data points.
Precision bits and precision digits indicates how much bits or decimal digits are required to represent the array values.
Mean squared error (MSE) is the arithmetic mean of squared errors between uncompressed and original values;
Standard deviation is the square root of the mean squared error.
Average absolute deviation summarises the statistical dispersion or variability.
Peak signal-to-noise ratio (PSNR) is the ratio between the maximum possible power of a signal and the power of corrupting noise that affects the fidelity of its representation.
Preserved values , which must be preserved literally, i.e., they cannot be changed and must be preserved, i.e., only lossless compression can be applied to those values.