Floating point is quite adequate for financial computations -- if the programmer understands how it works.
According to the IEEE floating-point standard, that is used by all major makers since the 1980s, a double-precision float can represent all integers up to 2^53 exactly, with no rounding. It turns out that 21 million BTC is just below 2^51 satoshis. That means it is safe to store BTC amounts as doubles, and even do simple math on them, if one stores them internally as satoshi amounts, rather than fractional BTC amounts.
(The only theory I know for why Satoshi limited the max issuance to 21 million BTC is that he knew this fact, and was aware that Excel, Awk, Python, Matlab, and many other languages and formats used IEEE doubles for all numbers, integer or real. Een though he did not use floating point in the bitcoin protocol, he must have felt necessary to accommodate those languages.)
Based on the above, should there be any attack vectors or exploit for altcoins like dogecoin, which went beyond 2^53, issuing in the hundreds of millions or billions? (Litecoin should be slightly below 2^53). If they are just cloning code that wasn't meant for their use case, perhaps vulnerabilities exist or arise at some point (?).
Doge isn't actually internally referencing total coint count anywhere though, so it doesn't matter. All Doge does is say, this block we will unload a dump truck of Doges of whatever size on your doorstep, then the algorithm will gradually decrease the size of the dump truck until reaching a minimum of 10,000. Maybe if a single block reward exceeded 2^53 you might run into some issues, but no coins do that. It's all for external systems to deal with.
The Bitcoin coin count is modeled more around value of 1 satoshi should it become a world reserve currency than other issues like this that can be side stepped. It was decided going vastly lower granularity than 1 penny wouldn't be needed or desired in regards to dust, so this put coin count + initial decimal places around a certain range. Who wants to purchase something and then type in 10 decimal places for the bill afterwards, all of which have no actual value?
Doge also has it's own anthropic principle. The coin granularity looks almost like it was designed by god himself with magic numbers to benefit strong arm market manipulators. So is Wolong a product of Doge, or is Doge designed for people like Wolong.
