Research Article
A Convolve-And-MErge Approach for Exact Computations on High-Performance Reconfigurable Computers
Table 1
Computational complexity of arithmetic operations [
18].
| Operation | Input | Output | Algorithm | Complexity |
| Addition | Two n-digit numbers | One -digit number | Basecase/Schoolbook | |
| Subtraction | Two n-digit numbers | One -digit number | Basecase/Schoolbook | |
| Multiplication | Two n-digit numbers | One 2n-digit number | Basecase/Schoolbook | | Karatsuba | | 3-way Toom-Cook | | k-way Toom-Cook | | Mixed-level Toom-Cook | | Schösnhage-Strassen | |
| Note: The complexity of multiplication will be referred to as M(n) in the following |
| Division | Two n-digit numbers | One n-digit number | Basecase/Schoolbook | | Newton’s method | | Goldschmidt | |
| Square root | One n-digit number | One n-digit number | Newton’s method | | Goldschmidt | |
| Polynomial evaluation | n fixed-size polynomial coefficients | One fixed size | Horner’s method | | Direct evaluation | |
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