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Number Conversions between RNS and Mixed-Radix Number System Based on Modulo (2p - 1) Signed-Digit Arithmetic

机译:基于模(2p-1)有符号数字算法的RNS与混合基数系统之间的数字转换

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In this paper, new hardware algorithms converting the numbers of a residue number system (RNS) into and from the mixed-radix number system(MRNS) using a radix-two signed-digit (SD) arithmetic circuits are presented. In each residue digit of the RNS integers mi = (2 p i - 1) are used as the moduli and the modulo m i addition and multiplication can be performed by an end-around-carry SD adder and a binary modulo mi SD adder tree, respectively. Therefore, the modulo mi addition time is independent of the word length of operands, and the modulo mi multiplication can be performed in a time proportional to log2 pi. An efficient method for calculating a multiplicative inverse number of a modulus is also presented by using the SD arithmetic. By the use of the fast SD arithmetic circuits, number converters of RNS-to-MRNS and MRNS-to-RNS can be implemented with shorter delay time than that using a binary number system
机译:在本文中,提出了一种新的硬件算法,该算法使用一个基数两个符号数字(SD)运算电路将残数系统(RNS)的编号转换为混合基数系统(MRNS)的编号,或将其从混合基数系统(MRNS)转换出来。在RNS的每个残数中,整数m i =(2 p i -1)用作模,模m i 加法和乘法可以分别通过一个端到端SD加法器和一个二进制模m i SD加法器树来执行。因此,模m i 的加法时间与操作数的字长无关,并且模m i 的乘积可以在与log 2成比例的时间内执行 p i 。通过使用SD算法,还提出了一种计算模数乘法逆数的有效方法。通过使用快速SD算术电路,可以实现RNS-to-MRNS和MRNS-to-RNS的数字转换器,其延迟时间比使用二进制数字系统的延迟时间短。

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