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Several programming languages and libraries provide functions for fast and vectorized clamping. In Python, the pandas library offers the Series.clip [1] and DataFrame.clip [2] methods. The NumPy library offers the clip [3] function. In the Wolfram Language, it is implemented as Clip [x, {minimum, maximum}]. [4]
m ← Ceiling(√ n) For all j where 0 ≤ j < m: Compute α j and store the pair (j, α j) in a table. (See § In practice) Compute α −m. γ ← β. (set γ = β) For all i where 0 ≤ i < m: Check to see if γ is the second component (α j) of any pair in the table. If so, return im + j. If not, γ ← γ • α −m.
Given real numbers x and y, integers m and n and the set of integers, floor and ceiling may be defined by the equations ⌊ ⌋ = {}, ⌈ ⌉ = {}. Since there is exactly one integer in a half-open interval of length one, for any real number x, there are unique integers m and n satisfying the equation
The term closure is often used as a synonym for anonymous function, though strictly, an anonymous function is a function literal without a name, while a closure is an instance of a function, a value, whose non-local variables have been bound either to values or to storage locations (depending on the language; see the lexical environment section below).
Variable binding relates three things: a variable v, a location a for that variable in an expression and a non-leaf node n of the form Q(v, P). Note: we define a location in an expression as a leaf node in the syntax tree. Variable binding occurs when that location is below the node n. In the lambda calculus, x is a bound variable in the term M ...
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The binding site for a variable n is the nth binder it is in the scope of, starting from the innermost binder. The most primitive operation on λ-terms is substitution: replacing free variables in a term with other terms. In the β-reduction (λ M) N, for example, we must
For example, in the snippet of Python code on the right, two functions are defined: square and sum_of_squares. square computes the square of a number; sum_of_squares computes the sum of all squares up to a number. (For example, square(4) is 4 2 = 16, and sum_of_squares(4) is 0 2 + 1 2 + 2 2 + 3 2 + 4 2 = 30.)