Research And Implementation Of The Prefix Model For The Leading 0 Prediction In Floating Point Operation

With the development of computer system,many methods have been proposed to represent the real numbers,but the most widely used method is floating point representation.Thus any number can be expressed as the number of floating point.With the consideration of the fixed point number,the index number is used by the floating number to make the position of the decimal point up and down according to the need,so it can be more flexible to express the real number.Actually the floating point arithmetic is real arithmetic,for that the computer can only store an integer,the real numbers are approximate ones,thus the speed of the floating-point arithmetic is very slow and there will be errors.It can be seen that the study of floating point arithmetic is very important.For the problem of how to improve the operation speed,the floating point arithmetic is considered as the research object.Based on the full understanding and analysis of the existing floating point addition,it is found that the leading-0-prediction(LOP)module is always considered as the critical path,and the improvement of the LOP(leading-one-prediction)module's performance can make the overall performance improve.First of all,in this paper,considering from the perspective of the prefix computation,a series of definitions and theorems are proved that the leading-0-detection algorithms can be essentially attributed to the prefix computation problem,thus such a system could apply to recursive solution method.Secondly,applying the prefix computation theory to the leading-0-prediction and considering from it,doing subtraction of “Borrow Retirement” for the two addition operation,thus translating the prediction problem of two operation to feature detection problem based on a series of numbers of {1,0,-1},so then it is possible to apply the method to solve the dichotomy recursive problem.Thirdly,through the careful analysis,using the re-encoding technology of continuous elimination of the string of “-1”,it presents a unified form of bit strings to predict the digit of leading-0-prediction,and devises a recursive identification method composed of a set of bit string and a recursive method to judge of the digit of the leading-0-prediction.Finally,the precoding algorithm,the weight encoding algorithm and the two recursive algorithm are all designed.Based on the Quartus II platform,the design of the electric circuit is verified by verilog hardware programming language or drawing the schematic diagram directly.