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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.
Adding 4 hours to 9 o'clock gives 1 o'clock, since 13 is congruent to 1 modulo 12. In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones ...
C++ also contains the type conversion operators const_cast, static_cast, dynamic_cast, and reinterpret_cast. The formatting of these operators means that their precedence level is unimportant. Most of the operators available in C and C++ are also available in other C-family languages such as C#, D, Java, Perl, and PHP with the same precedence ...
Euclidean division, and algorithms to compute it, are fundamental for many questions concerning integers, such as the Euclidean algorithm for finding the greatest common divisor of two integers, [1] and modular arithmetic, for which only remainders are considered. [2] The operation consisting of computing only the remainder is called the modulo ...
The most important optimization consists in using larger accumulators and delaying the relatively costly modulo operation for as long as it can be proven that no overflow will occur. Further benefit can be derived from replacing the modulo operator with an equivalent function tailored to this specific case—for instance, a simple compare-and ...
The congruence relation, modulo m, partitions the set of integers into m congruence classes. Operations of addition and multiplication can be defined on these m objects in the following way: To either add or multiply two congruence classes, first pick a representative (in any way) from each class, then perform the usual operation for integers on the two representatives and finally take the ...
C, C++: modulo power of two: undefined behavior C#: modulo power of 2 in unchecked context; System.OverflowException is raised in checked context [10] Java: modulo power of two (char is the only unsigned primitive type in Java) modulo power of two JavaScript: all numbers are double-precision floating-point except the new BigInt: MATLAB: Builtin ...
Primitive root modulo. n. In modular arithmetic, a number g is a primitive root modulo n if every number a coprime to n is congruent to a power of g modulo n. That is, g is a primitive root modulo n if for every integer a coprime to n, there is some integer k for which gk ≡ a (mod n). Such a value k is called the index or discrete logarithm ...