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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. After completing all the statements in the loop body, the condition, (x < 5), is checked again, and the loop is executed again, this process repeating until the variable x has the value 5.
The LOOP language, introduced in a 1967 paper by Albert R. Meyer and Dennis M. Ritchie, [10] 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 ...
In these examples, if N < 1 then the body of loop may execute once (with I having value 1) or not at all, depending on the programming language. In many programming languages, only integers can be reliably used in a count-controlled loop. Floating-point numbers are represented imprecisely due to hardware constraints, so a loop such as
A prime sieve works by creating a list of all integers up to a desired limit and progressively removing composite numbers (which it directly generates) until only primes are left. This is the most efficient way to obtain a large range of primes; however, to find individual primes, direct primality tests are more efficient [ citation needed ] .
Input #1: b, the number of bits of the result Input #2: k, the number of rounds of testing to perform Output: a strong probable prime n while True: pick a random odd integer n in the range [2 b−1, 2 b −1] if the Miller–Rabin test with inputs n and k returns “probably prime” then return n
However, infinite loops can sometimes be used purposely, often with an exit from the loop built into the loop implementation for every computer language, but many share the same basic structure and/or concept. The While loop and the For loop are the two most common types of conditional loops in most programming languages.
The LOOP language was formulated in a 1967 paper by Albert R. Meyer and Dennis M. Ritchie. [2] They showed the correspondence between the LOOP language and primitive recursive functions. The language also was the topic of the unpublished PhD thesis of Ritchie. [3] [4] It was also presented by Uwe Schöning, along with GOTO and WHILE. [5]
The first deterministic primality test significantly faster than the naive methods was the cyclotomy test; its runtime can be proven to be O((log n) c log log log n), where n is the number to test for primality and c is a constant independent of n. Many further improvements were made, but none could be proven to have polynomial running time.