Thus, this architecture would be a good candidate to be implemented as a large part of systems like DCT, FFT where high speed multiplications
along with good throughput are required.
By now, DCT only needs 12 multiplications
. Similarly, the inverse transform is
In m-ary method, where m = [2.sup.v], the window size v shall be chosen properly to decline the number of modular multiplications
(n+[n/v] + [2.sup.v]) and memory access ([n/v]+ [2.sup.v]), and the window size v = 6 is employed as it offers the least computational cost and memory access.
The Karatsuba method can be used to reduce the execution time for large operand multiplication
. This method replaces some multiplications
with additions and subtractions.
In this article, Lorraine Jacob and Joanne Mulligan discuss how arrays can be used to promote students' early learning in relation to multiplication
, when implemented using LUTs in FPGA, consumes resources based on the size of operation: bigger multiplications
consume more LUTs.
Proof: Initially, divide the input number [sigma] in to three [sigma]/2 digit numbers each can take three multiplications
of [sigma]/2 digits, which is represented as [sigma]/2 x 3.
Sica, "Double-base number system for multi-scalar multiplications
," in EUROCRYPT 2009, pp.
The straightforward implementations of DCT and IDCT require [N.sup.4] multiplications
for an NxN block, so they are rarely implemented in hardware .
Lastly, the results of some one-digit operations, known as arithmetical facts (mainly multiplications
and small additions), are not calculated each time but are retrieved from long-term memory using a verbal code, as they are usually learned by being repeated aloud.
One can then define "unit north-east" as some number w: so that two multiplications
of w (two acts of turning 45 degrees to the right gives unit east) can be written
The finite field multiplication
is the most frequently studied.