基于一种新的公共子表达式消除算法的分圆FFT
Cyclotomic FFTs with Reduced Additive Complexities Based on a Novel Common Subexpression Elimination Algorithm
摘要：
在本文中，我们首先提出了一种新的公共子表达式消除（CSE）算法的矩阵向量乘法特征2域。相对于以前提出的CSE算法，它通常侧重于复杂性的节省，由于递归的子表达式，我们的CSE算法实现了两种类型的复杂性降低，差分储蓄和递归储蓄，利用特征2字段的取消属性。使用我们的CSE算法，我们减少了分圆快速傅里叶变换（CFFT）的加法复杂度。使用乘法和加法的数量的加权和作为度量，我们的CFFT实现了比以前提出的CFFT和其他FFT更小的总复杂度，在许多情况下需要更少的乘法和更少的加法。
英文摘要：
In this paper, we first propose a novel common subexpression elimination (CSE) algorithm for matrix-vector multiplications over characteristic-2 fields. As opposed to previously proposed CSE algorithms, which usually focus on complexity savings due to recurrences of subexpressions, our CSE algorithm achieves two types of complexity reductions, differential savings and recurrence savings, by taking advantage of the cancelation property of characteristic-2 fields. Using our CSE algorithm, we reduce the additive complexities of cyclotomic fast Fourier transforms (CFFTs). Using a weighted sum of the numbers of multiplications and additions as a metric, our CFFTs achieve smaller total complexities than previously proposed CFFTs and other FFTs, requiring both fewer multiplications and fewer additions in many cases.
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