passingsprecision

Passingsprecision is a term used in data processing and numerical analysis to describe the fidelity with which a value is preserved as it passes through a chain of processing steps. It characterizes the cumulative impact of rounding, truncation, and representation errors that occur at interfaces between components, services, or devices in a pipeline.

Formal definition can be stated informally as follows. Suppose a true value x* is represented initially as x0, and after a sequence of passes through transformations T1, T2, ..., Tk we obtain xk. For each intermediate step i, define the relative error ri = |xi − x*| / |x*|, where xi is the value after i passes. A practical single-number metric for passingsprecision is P = floor(−log10(maxi ri)). A larger P indicates that a greater number of significant digits of the original value are preserved across the entire chain. In some contexts, P may be reported as digits of precision retained, or as a percentage loss of precision.

Applications of passingsprecision appear in areas such as sensor data pipelines, financial computations, and distributed systems, where data traverses multiple modules with different numerical representations and rounding behaviors. It helps engineers assess whether a pipeline maintains required accuracy and where to tighten data formats or aggregation rules.

Limitations include the need for a known true value x*, or a reliable reference, to compute ri. In many real-world settings the true value is unavailable or dynamic, making passingsprecision a relative rather than absolute measure. See also error propagation, numerical stability, and floating-point precision.