Error analysis of approximate Chinese-remainder-theorem decoding

Approximate Chinese-remainder-theorem decoding of residue numbers is a useful operation in residue arithmetic. The decoding yields an approximation to (X mod M)M, in the range [0, 1), where X is the input number and M is the product of all moduli. We show the error distribution and worst-case errors for both the truncation and rounding versions of the approximate decoding procedure. We also prove that, contrary to some published accounts, limiting the dynamic range is ineffective in reducing the maximal error