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Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
The two examples below, written in Python, present a while loop with an inner for loop and a while loop without an inner loop. Although both have the same terminating condition for their while loops, the first example will finish faster because of the inner for loop. The variable innermax is a fraction of the maxticketno variable in the first ...
Python supports normal floating point numbers, which are created when a dot is used in a literal (e.g. 1.1), when an integer and a floating point number are used in an expression, or as a result of some mathematical operations ("true division" via the / operator, or exponentiation with a negative exponent).
In abstract algebra, given a magma with binary operation ∗ (which could nominally be termed multiplication), left division of b by a (written a \ b) is typically defined as the solution x to the equation a ∗ x = b, if this exists and is unique. Similarly, right division of b by a (written b / a) is the solution y to the equation y ∗ a = b ...
The else clause in the above example is linked to the for statement, and not the inner if statement. Both Python's for and while loops support such an else clause, which is executed only if early exit of the loop has not occurred. Some languages support breaking out of nested loops; in theory circles, these are called multi-level breaks.
For example, a single statement within an outer loop ' for i := 0 to n ' and an inner loop ' for j := 0 to i+2 ' is executed once for each (i, j) pair such that 0 <= i <= n and 0 <= j <= i+2. Once again, a transformation is legal if it preserves the temporal sequence of all dependencies. Estimating the benefits of a transformation, or finding ...
Loop splitting is a compiler optimization technique. It attempts to simplify a loop or eliminate dependencies by breaking it into multiple loops which have the same bodies but iterate over different contiguous portions of the index range.
An orange that has been sliced into two halves. In mathematics, division by two or halving has also been called mediation or dimidiation. [1] The treatment of this as a different operation from multiplication and division by other numbers goes back to the ancient Egyptians, whose multiplication algorithm used division by two as one of its fundamental steps. [2]