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In number theory, Kaprekar's routine is an iterative algorithm named after its inventor, Indian mathematician D. R. Kaprekar. [1] [2] Each iteration starts with a four digit random number, sorts the digits into descending and ascending order, and calculates the difference between the two new numbers.
[1] [2] All functions use floating-point numbers in one manner or another. Different C standards provide different, albeit backwards-compatible, sets of functions. Most of these functions are also available in the C++ standard library, though in different headers (the C headers are included as well, but only as a deprecated compatibility feature).
because the argument to f must be a variable integer, but i is a constant integer. This matching is a form of program correctness, and is known as const-correctness.This allows a form of programming by contract, where functions specify as part of their type signature whether they modify their arguments or not, and whether their return value is modifiable or not.
Even functions can be const in C++. The meaning here is that only a const function may be called for an object instantiated as const; a const function doesn't change any non-mutable data. C# has both a const and a readonly qualifier; its const is only for compile-time constants, while readonly can be used in constructors and other runtime ...
One disadvantage of a prime modulus is that the modular reduction requires a double-width product and an explicit reduction step. Often a prime just less than a power of 2 is used (the Mersenne primes 2 31 −1 and 2 61 −1 are popular), so that the reduction modulo m = 2 e − d can be computed as (ax mod 2 e) + d ⌊ ax/2 e ⌋.
The number of subtractions is limited to ad/m, which can be easily limited to one if d is small and a < m/d is chosen. (This condition also ensures that d ⌊ ax/2 e ⌋ is a single-width product; if it is violated, a double-width product must be computed.) When the modulus is a Mersenne prime (d = 1), the procedure is particularly simple.
^g ALGOL 68G's runtime option --precision "number" can set precision for long long ints to the required "number" significant digits. The standard constants long long int width and long long max int can be used to determine actual precision.
In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called factors.For example, 21 is the product of 3 and 7 (the result of multiplication), and (+) is the product of and (+) (indicating that the two factors should be multiplied together).