> […] will calculate the 1 000 001st and 1 000 002nd numbers in 4 seconds. Classic version would take much more time, as the program has to operate with multi-t

> […] will calculate the 1 000 001st and 1 000 002nd numbers in 4 seconds. Classic version would take much more time, as the program has to operate with multi-thousand-digit numbers. I'm not sure what classical algorithm of computing Fibonacci numbers OP is mentioning, but using Mathematica on my machine takes about 4 ms to compute the 1,000,001st Fibonacci number exactly… Maybe by classical he means naive, in that case: doesn't it ever get tired to pick as an example an algorithm that will be optimized away by any half-decent compiler?