Simplestring::AtoI()

Move PlatformSpecificAtoI() to SimpleString.
Not really sure what you mean? How is 'pushing them down' more C++ style?

I can declare sign where I first use it. That would be okay.

I don't see much point in pushing down result - I can't declare it inside the loop, because it's used outside the loop. I guess under the circumstances I would need a better reason.