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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 ) .
dc: "Desktop Calculator" arbitrary-precision RPN calculator that comes standard on most Unix-like systems. KCalc, Linux based scientific calculator; Maxima: a computer algebra system which bignum integers are directly inherited from its implementation language Common Lisp. In addition, it supports arbitrary-precision floating-point numbers ...
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 ...
For multi-way partitioning, when c=ceiling(n/k) and each of the k subsets must contain either ceiling(n/k) or floor(n/k) items, the approximation ratio of BLDM for the minimum largest sum is exactly 4/3 for c=3, 19/12 for c=4, 103/60 for c=5, 643/360 for c=6, and 4603/2520 for c=7. The ratios were found by solving a mixed integer linear program.
Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations.
Some programming languages such as Lisp, Python, Perl, Haskell, Ruby and Raku use, or have an option to use, arbitrary-precision numbers for all integer arithmetic. Although this reduces performance, it eliminates the possibility of incorrect results (or exceptions) due to simple overflow.
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.