二元运算的错数
首发时间:2019-10-08
摘要:误差的积累与传播机制是个挑战性难题. 针对加减乘除四则运算以及对数与幂指数函数, 本文定量讨论了它们的计算结果中错误有效数字数量的变化规律, 从而证明加减运算与对数、幂指数函数均可能产生错误有效数字, 并给出了其错误有效数字数量的计算方法. 上述理论有助于理解复杂模型的计算过程中错误有效数字的积累与传播机制, 并对浮点程序的静态分析具有一定的指导意义.
关键词: 误差的积累与传播 错数 相减相消 舍入误差 截断误差 有效数字 浮点误差
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CuoShu of six binary basic elementary operations and functions
Abstract:Accumulation and propagation mechanism of errors is a challenging problem. For addition, subtraction, multiplication, division and logarithmic and exponential functions, this paper quantitatively discusses the variation rule of the number of erroneous significant digits in their calculation results, thus proving that addition and subtraction operations and logarithmic and exponential functions may produce erroneous significant digits, and gives the calculation method of the number of wrong significant figures. The above theory is helpful to understand the accumulation and propagation mechanism of erroneous significant digits in the calculation process of complex models, and has certain guiding significance to the static analysis of floating-point programs.
Keywords: Accumulation and propagation mechanism of error CuoShu cancellation rounding error truncation error significant digit representation error
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