Decimal digits vs integer digits

[pier4r]

Reading from time to this posts like this:
http://www.hpmuseum.org/forum/thread-10108.html

let me reflects that for some numbers people have developed quite efficient way to get a lot of decimal digits. Instead the task to get integer digits of a large number, starting from relatively simple approaches (+1) or others (powers, factorial, logs, whathever), is quite hard.

For the little that I know, while we may extract hundreds/thousands of decimal digits for a square root with our calculators, getting the same for an integer number is not always that easy.

Dunno compute 345^678 , this may be a number that would require quite a lot of work for a lot of calculators (maybe not the prime/50g).

My guess is: decimal digits somehow can be extracted with a relatively simple approach (think about the algorithm for the square root) that keeps track of a little leftover to work on after every iteration.

The integer digits, instead, have to use on the entire work done until that point, so the complexity of every iteration just increases.