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In computer programming, a bitwise operation operates on a bit string, a bit array or a binary numeral (considered as a bit string) at the level of its individual bits. It is a fast and simple action, basic to the higher-level arithmetic operations and directly supported by the processor. Most bitwise operations are presented as two-operand ...
Karatsuba multiplication of az+b and cz+d (boxed), and 1234 and 567 with z=100. Magenta arrows denote multiplication, amber denotes addition, silver denotes subtraction and cyan denotes left shift. (A), (B) and (C) show recursion with z=10 to obtain intermediate values. The Karatsuba algorithm is a fast multiplication algorithm.
Multiplication by a constant and division by a constant can be implemented using a sequence of shifts and adds or subtracts. For example, there are several ways to multiply by 10 using only bit-shift and addition. (
Intrinsic functions are often used to explicitly implement vectorization and parallelization in languages which do not address such constructs. Some application programming interfaces (API), for example, AltiVec and OpenMP, use intrinsic functions to declare, respectively, vectorizable and multiprocessing-aware operations during compiling.
In computer science and mathematical logic, satisfiability modulo theories (SMT) is the problem of determining whether a mathematical formula is satisfiable.It generalizes the Boolean satisfiability problem (SAT) to more complex formulas involving real numbers, integers, and/or various data structures such as lists, arrays, bit vectors, and strings.
Booth's multiplication algorithm is a multiplication algorithm that multiplies two signed binary numbers in two's complement notation. The algorithm was invented by Andrew Donald Booth in 1950 while doing research on crystallography at Birkbeck College in Bloomsbury, London. [1] Booth's algorithm is of interest in the study of computer ...
With the example in view, a number of details can be discussed. The most important is the choice of the representation of the big number. In this case, only integer values are required for digits, so an array of fixed-width integers is adequate. It is convenient to have successive elements of the array represent higher powers of the base.
For example, to construct the smallest B(2,4) de Bruijn sequence of length 2 4 = 16, repeat the alphabet (ab) 8 times yielding w=abababababababab. Sort the characters in w, yielding w ′ =aaaaaaaabbbbbbbb. Position w ′ above w as shown, and map each element in w ′ to the corresponding element in w by drawing a line. Number the columns as ...