Efficient Implementations of the Chinese Remainder Theorem for Sign Detection and Residue Decoding
IEEE Transactions on Computers
An improved residue number system digital-to-analog converter
Residue number system arithmetic: modern applications in digital signal processing
Concrete Math
A Library for Parallel Modular Arithmetic
Euro-Par '99 Proceedings of the 5th International Euro-Par Conference on Parallel Processing
Digital/analog arithmetic with continuous-valued residues
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
| Hi-index | 14.98 |
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.