采用算术变换验证泰勒级数表达的定点数电路

对于不精确的电路,误差是不可避免的,因此设计出的电路只在一定程度上实现了描述,研究它们之间的误差是非常必要的。传统计算误差的方法主要是依靠仿真,但是过长的计算时间往往导致不可行。为了克服仿真的缺陷,首先分析了多项式表达的数据通道中误差的来源,主要包括函数近似误差、输入变量量化误差、常系数量化误差和输出变量量化误差等,然后采用中间生成的算术变换多项式作为精密分析量化(位宽)和近似值来源的分析手段,提出一个高效的算法来计算各种不同类型的误差,检查泰勒级数或实值多项式的电路实现是否满足给定的误差边界。

Verification of fixed point circuits specified by Taylor series using arithmetic transform

For imprecise circuits, error is unavoidable, so implementations can only realize specifications to some extent. Investigation of their difference is necessary. The traditional method relies on simulation, but long execution time usually results in infeasibility. To overcome disadvantages of simulation, this paper first analyzes error source of imprecise datapath represented by polynomials including function approximation, quantizations of input variables, coefficients and output variables, then intermediate arithmetic transform polynomials are used as an analytical apparatus suitable to precision analysis for both the quantization (bit-width) and approximation sources, and an efficient algorithm is proposed to compute each different type error and check an existing implementation of Taylor series or real-valued polynomials whether satisfying the given error bound.