In this video, we delve into the fascinating world of big number multiplication and explore how computers perform this task ...

You wouldn’t use this algorithm when calculating a tip, but when it comes to multiplying large numbers, Karatsuba’s method was a big advance. And once Karatsuba opened the door to faster ...

See all Abstractions blog Even more important, the multiplication algorithm is part of a class of nearly ubiquitous algorithms in computer science. Gidney expects that his new technique will allow ...

High-performance matrix multiplication remains a cornerstone of numerical computing, underpinning a wide array of applications from scientific simulations to machine learning. Researchers ...

By transforming operands into a Montgomery domain, these algorithms enable efficient modular multiplication and exponentiation, which are crucial for public-key cryptosystems.

Those algorithms run up to 20% faster than existing matrix multiplication methods, according to the Alphabet unit.

The second (and much more difficult) part of their conjecture is that N log (N) should be the fundamental speed limit—that no possible multiplication algorithm could do better than this.

To help you understand the algorithm, the video shows a simple two-digit by two-digit multiplication. You can see that the first and last digits are essentially the result of one multiplication.

Karatsuba’s divide-and-conquer multiplication algorithm takes advantage of this saving. Consider a multiplication algorithm that parallels the way multiplication of complex numbers works.

The ancient Egyptians created an algorithm to multiply two numbers without requiring a multiplication table, and Greek mathematician Euclid described an algorithm to compute the greatest common ...