Xu Qun, Wang Xianchao, Xu Chao
Appl Opt. 2017 Jun 1;56(16):4661-4669. doi: 10.1364/AO.56.004661.
Multiplication with traditional electronic computers is faced with a low calculating accuracy and a long computation time delay. To overcome these problems, the modified signed digit (MSD) multiplication routine is established based on the MSD system and the carry-free adder. Also, its parallel algorithm and optimization techniques are studied in detail. With the help of a ternary optical computer's characteristics, the structured data processor is designed especially for the multiplication routine. Several ternary optical operators are constructed to perform M transformations and summations in parallel, which has accelerated the iterative process of multiplication. In particular, the routine allocates data bits of the ternary optical processor based on digits of multiplication input, so the accuracy of the calculation results can always satisfy the users. Finally, the routine is verified by simulation experiments, and the results are in full compliance with the expectations. Compared with an electronic computer, the MSD multiplication routine is not only good at dealing with large-value data and high-precision arithmetic, but also maintains lower power consumption and fewer calculating delays.
传统电子计算机进行乘法运算时面临计算精度低和计算时延长的问题。为克服这些问题，基于修正符号数（MSD）系统和无进位加法器建立了MSD乘法程序。此外，还对其并行算法和优化技术进行了详细研究。借助三值光计算机的特性，专门为乘法程序设计了结构化数据处理器。构造了几个三值光算子来并行执行M变换和求和，加速了乘法的迭代过程。特别是，该程序根据乘法输入的数位分配三值光处理器的数据位，因此计算结果的精度总能满足用户需求。最后，通过仿真实验对该程序进行了验证，结果完全符合预期。与电子计算机相比，MSD乘法程序不仅擅长处理大数值数据和高精度运算，而且功耗更低，计算延迟更少。
