Mar 9, 2024 · In mathematics, modular arithmetic refers to the arithmetic of integers that wraps around when a certain value is reached, called the modulus. This becomes particularly crucial when handling large numbers in competitive programming.

May 5, 2010 · There are many ways to do it in O(log n) time for n bits; you can do it with multiplication and you don't have to iterate 1 bit at a time. For example, a mod b = a - floor((a * r)/2^n) * b where. r = 2^n / b

There are two faster ways to calculate the inverse: the extended GCD algorithm, and Fermat's little theorem.

Feb 25, 2025 · Modular arithmetic is a system of arithmetic for numbers where numbers “wrap around” after reaching a certain value, called the modulus. It mainly uses remainders to get the value after wrap around. It is often referred to as “clock arithmetic.

First, make sure you're looking at optimized code before drawing conclusion about what GCC is producing (and make sure this particular expression really needs to be optimized).

Modular arithmetic is a special type of arithmetic that involves only integers. This goal of this article is to explain the basics of modular arithmetic while presenting a progression of more difficult and more interesting problems that are easily solved using modular arithmetic. https://youtu.be/7an5wU9Q5hk?t=777.

Feb 18, 2010 · If you want a mod function that will fulfill -1 mod n == n-1, then, in C, you have to do the following: return (a%b + b) % b; You can then do. to decrement n and have it wrap around to max when n==0. Note that, as for the increment case, this will work for arbitrary step sizes.

Dec 29, 2023 · An Algorithm for Computing Mod. Taking all the things that we proved from the previous section, we can now provide us with some slick identities that will allow us to do fast computations of large modulus.

Modulo operation is an important operation for programming. This operation is usually represented as % or MOD. We meet this operation when the number range of a problem is to large and we need return the real result MOD some value to avoid overflow when performing integer calculation.

This lecture introces the concept of modular arithmetic and presents a fast algorithm to compute the power of a number modulo another number. Constructive algorithms, based on the extended Euclidean algorithm, to compute modular inverses and solve the …