Equation field guide
Scale factor S
The scale S is the size of one step on the decoded number line. It must be positive.
Model value r→Integer code q→Decoded value S(q − Z)
A ruler for the integer codes
If S = 0.25, codes one apart represent values 0.25 apart. For Z = 10, code q = 10 means 0, q = 11 means 0.25, and q = 14 means 1.0.
Multiplying q − Z by S changes an integer step count into the model’s numerical scale. S is chosen during quantization or calibration; it is not recalculated from each individual code.
Precision and range
A smaller S puts representable points closer together, which reduces rounding error near those points. With a fixed number of integer codes it also narrows the total real-value interval. A larger S spreads the points farther apart and covers more range.