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Computers typically use binary arithmetic, but to make the example easier to read, it will be given in decimal. Suppose we are using six-digit decimal floating-point arithmetic, sum has attained the value 10000.0, and the next two values of input[i] are 3.14159 and 2.71828. The exact result is 10005.85987, which rounds to 10005.9.
Function calls and blocks of code, such as code contained within a loop, are often replaced by a one-line natural language sentence. Depending on the writer, pseudocode may therefore vary widely in style, from a near-exact imitation of a real programming language at one extreme, to a description approaching formatted prose at the other.
*/ /* This implementation does not implement composite functions, functions with a variable number of arguments, or unary operators. */ while there are tokens to be read: read a token if the token is: - a number: put it into the output queue - a function: push it onto the operator stack - an operator o 1: while ( there is an operator o 2 at the ...
In computer programming, the act of swapping two variables refers to mutually exchanging the values of the variables. Usually, this is done with the data in memory. For example, in a program, two variables may be defined thus (in pseudocode): data_item x := 1 data_item y := 0 swap (x, y);
Pairwise summation is the default summation algorithm in NumPy [9] and the Julia technical-computing language, [10] where in both cases it was found to have comparable speed to naive summation (thanks to the use of a large base case).
The number of swaps can be reduced by calculating the position of multiple elements before moving them. For example, if the target position of two elements is calculated before they are moved into the proper position, the number of swaps can be reduced by about 25% for random data. In the extreme case, this variant works similar to merge sort.
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.
When that occurs, that number is the GCD of the original two numbers. By reversing the steps or using the extended Euclidean algorithm, the GCD can be expressed as a linear combination of the two original numbers, that is the sum of the two numbers, each multiplied by an integer (for example, 21 = 5 × 105 + (−2) × 252).