22 September 2017 | 1:20 am

Modern processors come with very powerful instructions that are simply not available in many high-level languages JavaScript or Python. Here are a few examples: Most programming languages allow you to multiply two 64-bit integers and to get the 64-bit results (it is typically written as x = a * b). But the multiplication of two … Continue reading Swift as a low-level programming language?

18 September 2017 | 6:50 pm

Suppose that you want to visit all values in an array exactly once in “random order”. You could do it by shuffling your array but it requires some extra storage. You want your code to use just a tiny bit of memory, and you want the code to be super fast. You do not want … Continue reading Visiting all values in an array exactly once in “random order”

18 September 2017 | 2:43 pm

Given x, its (multiplicative) inverse is another value y such that x y = y x = 1. We all know that the multiplicative inverse of x is 1/x and it exists as long as x is non-zero. That’s for real numbers, or at least, rational numbers. But the idea of a multiplicative inverse is more general. It certainly … Continue reading Computing the inverse of odd integers