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For example, in the languages C, Java, C#, [2] Objective-C, and C++, (which use the same syntax in this case), the code fragment int x = 0 ; while ( x < 5 ) { printf ( "x = %d \n " , x ); x ++ ; } first checks whether x is less than 5, which it is, so then the {loop body} is entered, where the printf function is run and x is incremented by 1.
In the C programming language, Duff's device is a way of manually implementing loop unrolling by interleaving two syntactic constructs of C: the do-while loop and a switch statement. Its discovery is credited to Tom Duff in November 1983, when Duff was working for Lucasfilm and used it to speed up a real-time animation program.
If xxx1 is omitted, we get a loop with the test at the top (a traditional while loop). If xxx2 is omitted, we get a loop with the test at the bottom, equivalent to a do while loop in many languages. If while is omitted, we get an infinite loop. The construction here can be thought of as a do loop with the while check in the middle. Hence this ...
The LOOP language, introduced in a 1967 paper by Albert R. Meyer and Dennis M. Ritchie, [7] is such a language. Its computing power coincides with the primitive recursive functions. A variant of the LOOP language is Douglas Hofstadter's BlooP in Gödel, Escher, Bach. Adding unbounded loops (WHILE, GOTO) makes the language general recursive and ...
Do while loops check the condition after the block of code is executed. This control structure can be known as a post-test loop. This means the do-while loop is an exit-condition loop. However a while loop will test the condition before the code within the block is executed.
A prime sieve or prime number sieve is a fast type of algorithm for finding primes. There are many prime sieves. The simple sieve of Eratosthenes (250s BCE), the sieve of Sundaram (1934), the still faster but more complicated sieve of Atkin [1] (2003), sieve of Pritchard (1979), and various wheel sieves [2] are most common.
A prime number is a natural number that has exactly two distinct natural number divisors: the number 1 and itself. To find all the prime numbers less than or equal to a given integer n by Eratosthenes' method: Create a list of consecutive integers from 2 through n: (2, 3, 4, ..., n). Initially, let p equal 2, the smallest prime number.
Gödel used a system based on prime factorization. He first assigned a unique natural number to each basic symbol in the formal language of arithmetic with which he was dealing. To encode an entire formula, which is a sequence of symbols, Gödel used the following system.