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In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor(x). Similarly, the ceiling function maps x to the least integer greater than or equal to x , denoted ⌈ x ⌉ or ceil( x ) .
In Python 3, x / y performs "true division", meaning that it always returns a float, even if both x and y are integers that divide evenly. >>> 4 / 2 2.0 and // performs integer division or floor division , returning the floor of the quotient as an integer.
The +, -, and * operators for mathematical addition, subtraction, and multiplication are similar to other languages, but the behavior of division differs. There are two types of divisions in Python: floor division (or integer division) // and floating-point / division. [97] Python uses the ** operator for exponentiation.
In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation.. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor.
This page was last edited on 12 March 2021, at 23:29 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may ...
However, division can be expensive and, in cryptographic settings, might not be a constant-time instruction on some CPUs, subjecting the operation to a timing attack. Thus Barrett reduction approximates 1 / n {\displaystyle 1/n} with a value m / 2 k {\displaystyle m/2^{k}} because division by 2 k {\displaystyle 2^{k}} is just a right-shift, and ...
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Truncation of positive real numbers can be done using the floor function. Given a number x ∈ R + {\displaystyle x\in \mathbb {R} _{+}} to be truncated and n ∈ N 0 {\displaystyle n\in \mathbb {N} _{0}} , the number of elements to be kept behind the decimal point, the truncated value of x is