Here's one interesting application of a digit-count function. The naive implementation of an integer-to-string conversion involves writing the number backwards

Here's one interesting application of a digit-count function. The naive implementation of an integer-to-string conversion involves writing the number backwards, starting from the least significant digit, and then reversing the string at the end. In a 2017 talk titled "Fastware"[1], Andrei Alexandrescu showed that it's faster to start by counting the number of digits you're going to print, and then you can print by working backwards from the least significant digit. It comes out in the correct order without any need to reverse at the end. His implementation of the digit count was itself interesting, since it does 4 comparisons per loop and then a divide by 10000, instead of the naive single comparison and divide by 10. uint32_t digits10(uint64_t v) { uint32_t result = 1; for (;;) { if (v < 10) return result; if (v < 100) return result + 1; if (v < 1000) return result + 2; if (v < 10000) return result + 3; v /= 10000U; result += 4; } } IIRC, his insight was that smaller numbers tend to occur more often in the real world, so most calls to this function will not end up doing any divisions. [1] https://www.youtube.com/watch?v=o4-CwDo2zpg https://www.youtube.com/watch?v=o4-CwDo2zpg