> Attached, rebased version of the patch that implements the Karatsuba > algorithm in numeric.c's mul_var(). It's one of these areas where Dean Rasheed would be a good match for a review, so adding him in CC. He has been doing a lot of stuff in this area over the years. +#de...
The Karatsuba algorithm was the first multiplication algorithm asymptotically faster than the quadratic "grade school" algorithm. Multiplying large numbers efficiently is an important task; however, the traditional, naive way of multiplying numbers involves multiplying each digit in one number to each ...
configurable): the various numeric functions that use mul_var() are immutable, which means that the results from the Karatsuba algorithm must match those from the schoolbook algorithm exactly, for all inputs. That's not currently the case when computing approximate results with a reduced rscale....
> implementing the Karatsuba algorithm, it is implementing the > schoolbook algorithm in two steps, by splitting the longer input into > two pieces. The surprising realization here is that there are actually (var1ndigits, var2ndigits) combinations where *only* doing mul_var_karatsuba_half() r...
> Dean Rasheed <dean.a.rash...@gmail.com> writes: > > There's another complication though (if the threshold is made > > configurable): the various numeric functions that use mul_var() are > > immutable, which means that the results from the Karatsuba algorithm ...
> immutable, which means that the results from the Karatsuba algorithm > must match those from the schoolbook algorithm exactly, for all > inputs. That seems like an impossible standard to meet. What we'd probably have to do is enable Karatsuba only when mul_var is being asked ...
On Sat, Jun 29, 2024, at 14:22, Dean Rasheed wrote: > However, I really don't like having these magic constants at all, > because in practice the threshold above which the Karatsuba algorithm > is a win can vary depending on a number of factors, such as whether ...
Knuth in his “The Art of Computer Programming”, Volume 2, Seminumerical Algorithms, Third Edition, Addison-Wesley 1998). More on the Karatsuba-style multiplication appears in “Generalizations of the Karatsuba Algorithm for Efficient Implementations” by André Weimerskirch and Christof Paar (http:...
Recently, high-performance elliptic curve cryptography has gained great attention for resource-constrained applications. In this paper, we use (a, b)-way Karatsuba algorithm to derive a new way of k-wdoi:10.1007/978-3-319-23207-2_19Chiou-Yng LeeChe Wun ChiouJim-Min Lin...
The paper using Altera FPGA Quartus II to simulate four different multipliers, 36 x 36, 84 x 84, 126 x 126 and 204 x 204, and implemented on Cyclone II EP2C70F896C8 experimental platform. The experimental results show that the proposed multipliers have lower time complexity than the ...