Design and Implementation of Long-Digit Karatsuba''s Multiplication Algorithm Using Tensor Product Formulation

• Main Authors: Chin-Bou Li, 劉欽寶
• Other Authors: Chua-Huang Huang
• Format: Others
• Language: zh-TW
• Published: 2003
• Online Access: http://ndltd.ncl.edu.tw/handle/e9d9y9

碩士 === 逢甲大學 === 資訊工程所 === 91 === Karatsuba''s multiplication algorithm uses three single-digit multiplications to perform one two-digit multiplication. If we apply Karatsuba''s multiplier recursively, it takes only 3n single-digit multiplications to multiply a pair of 2n -digit numbers. This is a significant improvement compared to 4n single-digit multiplications using grade- school multiplier. In this paper, we will use tensor production formulation to express Karatsuba''s multiplication algorithm in both recursive and iterative form. Usually, Karatsuba''s algorithm is implemented as recursive program. With the iterative tensor product formula of Karatsuba''s algorithm, we can derive an iterative (for loop) program to perform multiplication of long-digit numbers. Furthermore, the 3n single- digit multiplications can be fully parallelized.