| 摘要 |
The integers involved in the computation are embedded into a modular system whose index (i.e., its modulus) is an integer M that is bigger than all of these integers involved. In other words, these integers are treated not as belonging to ordinary integers anymore, but as "modular integers" belonging to the modular system indexed by M. Having completed the embedding, CRT provides the bridge which connects the single modular system indexed by M (ZM) with a collection of k modular systems indexed by m1,m2, . . . , mk respectively (Zm1, Zm2, . . . , Zmk), where M factorizes as m1*m2*m3* . . . *mk, and where each mi is slightly smaller than single precision. Then, after numbers are manipulated within modular arithmetic, the answer is reconstructed via the algorithm of CRT, also known as CRA. Finally, the present invention introduces the process of dinking that overcomes the major weakness of implementing division with modular arithmetic. Particularly, within a composite modular arithmetic system, any theoretically impossible modular division is altered slightly [dinked] to a theoretical possible modular division whose quotient is closed enough to the true quotient sought, thus allowing all four arithmetic operations of modular arithmetic in high precision computation.
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