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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.
Download QR code; Print/export Download as PDF; ... the factorial of a non-negative integer ... [74] and the Boost C++ library. ...
Download QR code; Print/export Download as PDF; Printable version ... The following is an incomplete list of some arbitrary-precision arithmetic libraries for C++ ...
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 ...
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.
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
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: