Research On High-Performance Arithmetic For Floating-point Division And The Elementary Functions

With development of VLSI technology, the processors for all aspects of applications have been produced, especially for DSP, MMP. These processors requirement for performance make it possible the elementary function as the independently arithmetic component. Meantime, the performance of these elementary function components is one of the important factors for the performance of the total computer system. All those different processors have various requirements for the speed, area, and power. Of course, those requirements can affect the designs of the elementary function components.There are two kinds of common algorithms to implement the elementary functions, which include the digital recurrence algorithm and the function iteration algorithm. The digital recurrence algorithm based on subtractive method produces a quotient number each iteration; and the function iteration algorithm based on multiplicative method obtains the approximation value of the real quotient.For the digital recurrence algorithm, the delay of the implementations can decide the frequency of the processors; and the cycle number required by the implementations can impact the performance of the processors. So, reducing the delay with the same cycle number or decreasing the cycle number obviously at the expense of a little delay (the total delay should be less than the delay constraint of the total processor), will contribute to increase the performance of the processors significantly. As for the previously published methods and architectures for SRT algorithm, this dissertation gives out the two optimized architectures. One can reduce the delay of the critical path of SRT implementation; the other can reduce the cycle number of SRT-4 implementation, which is often used as the algorithm for the division or square root component in the modern processors.For the function iteration algorithm including Newton-Raphson and Goldschmid, the very important aspect for the performance of that algorithm is the length of the seed value. If the length is longer, the required iteration number is less; if the length is shorter, the required iteration number is more numerous. As for how to obtain the seed value, there are many methods published previously. Among those methods, there are mostly two kinds of methods. One is based on the muti-tables addition methods, which is which is suitable for obtaining the approximation value for the seed value with the short length; the other is based on polynomial approximation methods, which is suitable for obtaining the approximation value for the seed value with long length. This dissertation gives out our approximation methods for those two...