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Another method of multiplication is called Toom–Cook or Toom-3. The Toom–Cook method splits each number to be multiplied into multiple parts. The Toom–Cook method is one of the generalizations of the Karatsuba method. A three-way Toom–Cook can do a size-3N multiplication for the cost of five size-N multiplications. This accelerates the ...
[52] [53] While Python 2.7 and older versions are officially unsupported, a different unofficial Python implementation, PyPy, continues to support Python 2, i.e. "2.7.18+" (plus 3.10), with the plus meaning (at least some) "backported security updates". [54] Python 3.0 was released on 3 December 2008, with some new semantics and changed syntax.
Python aims to be simple and consistent in the design of its syntax, encapsulated in the mantra "There should be one— and preferably only one —obvious way to do it", from the Zen of Python. [ 2 ] This mantra is deliberately opposed to the Perl and Ruby mantra, " there's more than one way to do it ".
The predecessor program changes the variable x 2, which might be in use elsewhere. To expand the statement x 0 := x 1 ∸ 1, one could initialize the variables x n, x n+1 and x n+2 (for a big enough n) to 0, x 1 and 0 respectively, run the code on these variables and copy the result (x n) to x 0. A compiler can do this.
Maple has two forms of for-loop, one for iterating over a range of values, and the other for iterating over the contents of a container. The value range form is as follows: for i from f by b to t while w do # loop body od; All parts except do and od are optional. The for I part, if present, must come first.
The macro is unhygienic: it declares a new variable in the existing scope which remains after the loop. One foreach macro cannot be defined that works with different collection types (e.g., array and linked list) or that is extensible to user types. C string as a collection of char
Applied to a function with one variable, the Y combinator usually does not terminate. More interesting results are obtained by applying the Y combinator to functions of two or more variables. The additional variables may be used as a counter, or index. The resulting function behaves like a while or a for loop in an imperative language.
The definition of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries = =. From this, a simple algorithm can be constructed which loops over the indices i from 1 through n and j from 1 through p, computing the above using a nested loop: