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The Metacode extension to C++ (Vandevoorde 2003) [1] was an early experimental system to allow compile-time function evaluation (CTFE) and code injection as an improved syntax for C++ template metaprogramming. In earlier versions of C++, template metaprogramming is often used to compute values at compile time, such as:
The global optimum of this objective function corresponds to a factorial code represented in a distributed fashion across the outputs of the feature detectors. Painsky, Rosset and Feder (2016, 2017) further studied this problem in the context of independent component analysis over finite alphabet sizes. Through a series of theorems they show ...
In C++11 and C++20, constexpr and consteval were introduced to let the compiler execute code. Using constexpr and consteval, one can use the usual recursive factorial definition with the non-templated syntax.
program FactorialProg integer:: counter = 5 integer:: factorial = 1 factorial = factorial * counter counter = counter-1 do while (counter > 0)! Truth value is tested before the loop factorial = factorial * counter counter = counter - 1 end do print * , factorial end program FactorialProg
Dim counter As Integer = 5 ' init variable and set value Dim factorial As Integer = 1 ' initialize factorial variable Do While counter > 0 factorial = factorial * counter counter = counter-1 Loop ' program goes here, until counter = 0 'Debug.Print factorial ' Console.WriteLine(factorial) in Visual Basic .NET
For example, in the factorial function, properly the base case is 0! = 1, while immediately returning 1 for 1! is a short circuit, and may miss 0; this can be mitigated by a wrapper function. The box shows C code to shortcut factorial cases 0 and 1.
The word "factorial" (originally French: factorielle) was first used in 1800 by Louis François Antoine Arbogast, [18] in the first work on Faà di Bruno's formula, [19] but referring to a more general concept of products of arithmetic progressions. The "factors" that this name refers to are the terms of the product formula for the factorial. [20]
factorial := 1 counter := 1 while counter < 5 counter := counter + 1 factorial := factorial * counter print counter + "! equals " + factorial As demonstrated by the output of the variables. Timeline of the for-loop syntax in various programming languages