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Pseudocode is commonly used in textbooks and scientific publications related to computer science and numerical computation to describe algorithms in a way that is accessible to programmers regardless of their familiarity with specific programming languages.
This algorithm can also be rewritten to use the Fast2Sum algorithm: [7] function KahanSum2(input) // Prepare the accumulator. var sum = 0.0 // A running compensation for lost low-order bits. var c = 0.0 // The array input has elements indexed for i = 1 to input.length do // c is zero the first time around.
A carry-save adder [1] [2] [nb 1] is a type of digital adder, used to efficiently compute the sum of three or more binary numbers. It differs from other digital adders in that it outputs two (or more) numbers, and the answer of the original summation can be achieved by adding these outputs together.
A typical example of carry is in the following pencil-and-paper addition: 1 27 + 59 ---- 86 7 + 9 = 16, and the digit 1 is the carry. The opposite is a borrow, as in −1 47 − 19 ---- 28 Here, 7 − 9 = −2, so try (10 − 9) + 7 = 8, and the 10 is got by taking ("borrowing") 1 from the next digit to the left. There are two ways in which ...
In pseudocode, this method can be performed the following way: function modular_pow(base, exponent, modulus) is if modulus = 1 then return 0 c := 1 for e_prime = 0 to exponent-1 do c := (c * base) mod modulus return c
In addition, swapping two variables in object-oriented languages such as C++ may involve one call to the class constructor and destructor for the temporary variable, and three calls to the copy constructor. Some classes may allocate memory in the constructor and deallocate it in the destructor, thus creating expensive calls to the system.
For example, if the polynomial used to define the finite field GF(2 8) is p = x 8 + x 4 + x 3 + x + 1, and a = x 6 + x 4 + x + 1 is the element whose inverse is desired, then performing the algorithm results in the computation described in the following table. Let us recall that in fields of order 2 n, one has −z = z and z + z = 0 for every ...
The basic principle of Karatsuba's algorithm is divide-and-conquer, using a formula that allows one to compute the product of two large numbers and using three multiplications of smaller numbers, each with about half as many digits as or , plus some additions and digit shifts.