Abstract: Alignment and normalization are needed in the process of floating point summation in computer. Normalization operation conducts rounding processing which will generate errors. Accumulated operations of floating-point numbers will result in the accumulation of error, the lack of precision of the calculations and even wrong calculation results. This paper discussed the influence of different binding order of floating-point numbers on the error of accumulative sum in the process of single precision floating-point accumulation through experimental methods, and aimed to explore the law of caused calculation errors by the binding sequence, provided a basis for a method of selective binding for computing paradigm and calculating structure as multi-core calculation, GPU computation and multi-processor calculation, and facilitated the advantage of parallel computing.

Key words: single precision floating point number, accumulative sum, error, binding sequence, normalization

摘要： 计算机中进行浮点数加法运算时，需要进行对阶和右规格化操作，该操作会进行舍入处理，这种处理过程会产生误差，浮点数累加运算会造成误差的累积，导致计算结果精度不够甚至计算结果错误。通过实验手段研究单精度浮点数累加过程中不同结合顺序对浮点数累加和误差的影响，探索结合顺序导致计算误差的规律，为多核计算、GPU计算、多处理器计算等计算范型和计算结构提供选择结合方法的依据，便于发挥其并行计算的优势。

关键词: 单精度浮点数, 累加和, 误差, 结合顺序, 右规格化