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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:
Finding minimum entropy codes. Neural Computation, 1:412-423, 1989. Jürgen Schmidhuber. Learning factorial codes by predictability minimization. Neural Computation, 4(6):863-879, 1992; J. Schmidhuber and M. Eldracher and B. Foltin. Semilinear predictability minimization produces well-known feature detectors. Neural Computation, 8(4):773-786, 1996
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:
Indeed, n * factorial(n - 1) wraps the call to factorial. But it can be transformed into a tail-recursive definition by adding an argument a called an accumulator. [8] This Julia program gives a tail-recursive definition fact_iter of the factorial:
Download QR code; Print/export Download as PDF; ... the factorial of a non-negative integer ... [74] and the Boost C++ library. ...
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 ...
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 code contains a number of equations, not imperative assignments, that describe ("declare") the behavioral relationships. When a model is expressed in this formalism, a computer is able to perform algebraic manipulations to best formulate the solution algorithm.