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To create factorial codes, Horace Barlow and co-workers suggested to minimize the sum of the bit entropies of the code components of binary codes (1989). Jürgen Schmidhuber (1992) re-formulated the problem in terms of predictors and binary feature detectors , each receiving the raw data as an input.
The code above will execute at run time to determine the factorial value of the literals 0 and 4. By using template metaprogramming and template specialization to provide the ending condition for the recursion, the factorials used in the program—ignoring any factorial not used—can be calculated at compile time by this code:
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:
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.
function factorial (n is a non-negative integer) if n is 0 then return 1 [by the convention that 0! = 1] else if n is in lookup-table then return lookup-table-value-for-n else let x = factorial(n – 1) times n [recursively invoke factorial with the parameter 1 less than n] store x in lookup-table in the n th slot [remember the result of n! for ...
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
In C++ templates, compile-time cases were historically performed by pattern matching over the template arguments. For example, the template base class in the Factorial example below is implemented by matching 0 rather than with an inequality test, which was previously unavailable.
First the code within the block is executed. Then the condition is evaluated. If the condition is true the code within the block is executed again. This repeats until the condition becomes false. 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 ...