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[citation needed] In base two, long multiplication is sometimes called "shift and add", because the algorithm simplifies and just consists of shifting left (multiplying by powers of two) and adding. Most currently available microprocessors implement this or other similar algorithms (such as Booth encoding ) for various integer and floating ...
Download QR code; Print/export Download as PDF; Printable version; In other projects Wikidata item; Appearance. ... Pages in category "Shift-and-add algorithms"
This includes algorithms for multiplication and division, as well as algorithms for the efficient evaluation of mathematical constants and special functions to high precision. See also Category:Number theoretic algorithms for arbitrary-precision integer and cryptography algorithms.
CORDIC is part of the class of "shift-and-add" algorithms, as are the logarithm and exponential algorithms derived from Henry Briggs' work. Another shift-and-add algorithm which can be used for computing many elementary functions is the BKM algorithm , which is a generalization of the logarithm and exponential algorithms to the complex plane.
In binary (base-2) math, multiplication by a power of 2 is merely a register shift operation. Thus, multiplying by 2 is calculated in base-2 by an arithmetic shift. The factor (2 −1) is a right arithmetic shift, a (0) results in no operation (since 2 0 = 1 is the multiplicative identity element), and a (2 1) results in a left arithmetic shift ...
The BKM algorithm is a shift-and-add algorithm for computing elementary functions, first published in 1994 by Jean-Claude Bajard, Sylvanus Kla, and Jean-Michel Muller. BKM is based on computing complex logarithms (L-mode) and exponentials (E-mode) using a method similar to the algorithm Henry Briggs used to compute logarithms. By using a ...
For an n-bit multiplier, this will take n clock cycles (where each cycle does either a shift or a shift-and-add). To convert this into an algorithm for modular multiplication, with a modulus r, it is necessary to subtract r conditionally at each stage: Double the contents of the accumulator. If the result is greater than or equal to r, subtract r.
Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations.