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In computing, a roundoff error, [1] also called rounding error, [2] is the difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounded arithmetic. [3]
Integer overflow can be demonstrated through an odometer overflowing, a mechanical version of the phenomenon. All digits are set to the maximum 9 and the next increment of the white digit causes a cascade of carry-over additions setting all digits to 0, but there is no higher digit (1,000,000s digit) to change to a 1, so the counter resets to zero.
Rounding to a specified power is very different from rounding to a specified multiple; for example, it is common in computing to need to round a number to a whole power of 2. The steps, in general, to round a positive number x to a power of some positive number b other than 1, are:
Python provides a round function for rounding a float to the nearest integer. For tie-breaking, Python 3 uses round to even: round(1.5) and round(2.5) both produce 2. [124] Versions before 3 used round-away-from-zero: round(0.5) is 1.0, round(-0.5) is −1.0. [125] Python allows Boolean expressions with multiple equality relations in a manner ...
Several programming languages (e.g., Ada, D, C++11, Smalltalk, PHP, Perl, Object Pascal, Java, C#, MATLAB, Visual Basic, Ruby, Python, JavaScript, Fortran 95 and later) have special constructs which allow implicit looping through all elements of an array, or all members of a set or collection.
An array data structure can be mathematically modeled as an abstract data structure (an abstract array) with two operations get(A, I): the data stored in the element of the array A whose indices are the integer tuple I. set(A, I, V): the array that results by setting the value of that element to V. These operations are required to satisfy the ...
This functionality is also available in wider versions in the SSE2 and AVX2 integer instruction sets. It is also available in ARM NEON instruction set. Saturation arithmetic for integers has also been implemented in software for a number of programming languages including C , C++ , such as the GNU Compiler Collection , [ 2 ] LLVM IR, and Eiffel .
In computer science, integer sorting is the algorithmic problem of sorting a collection of data values by integer keys. Algorithms designed for integer sorting may also often be applied to sorting problems in which the keys are floating point numbers, rational numbers , or text strings. [ 1 ]