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Using the XOR swap algorithm to exchange nibbles between variables without the use of temporary storage. In computer programming, the exclusive or swap (sometimes shortened to XOR swap) is an algorithm that uses the exclusive or bitwise operation to swap the values of two variables without using the temporary variable which is normally required.
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.
For 8-bit integers the table of quarter squares will have 2 9 −1=511 entries (one entry for the full range 0..510 of possible sums, the differences using only the first 256 entries in range 0..255) or 2 9 −1=511 entries (using for negative differences the technique of 2-complements and 9-bit masking, which avoids testing the sign of ...
Computing the carry-less product. The carry-less product of two binary numbers is the result of carry-less multiplication of these numbers. This operation conceptually works like long multiplication except for the fact that the carry is discarded instead of applied to the more significant position.
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 ]
By using the Chinese remainder theorem, after splitting M into smaller different types of N, one can find the answer of multiplication xy [10] Fermat numbers and Mersenne numbers are just two types of numbers, in something called generalized Fermat Mersenne number (GSM); with formula: [11]
To compute the product of 12345 and 6789, where B = 10, choose m = 3. We use m right shifts for decomposing the input operands using the resulting base (B m = 1000), as: 12345 = 12 · 1000 + 345 6789 = 6 · 1000 + 789. Only three multiplications, which operate on smaller integers, are used to compute three partial results: z 2 = 12 × 6 = 72 z ...
A similar complex multiplication algorithm multiplies two complex numbers using 3 real multiplications instead of 4 Toom-Cook algorithm , a faster generalization of the Karatsuba algorithm that permits recursive divide-and-conquer decomposition into more than 2 blocks at a time