A formula that guarantees that f(ULLONG_MAX) * f(ULLONG_MAX) is not more than ULLONG_MAX

Question

I'm making a container class and I want to specify that its maximum size, if multiplied by itself, should not be more than the maximum value of unsigned long long (specifically, std::numeric_limits::max()).

Assuming that ULLONG_MAX is 2⁶⁴-1, how safe is this calculation and how can I improve it if necessary?

typedef unsigned long long size_type;
size_type max_size = size_type(std::sqrt(ULLONG_MAX)) - 1;

user_1774667 · Answer

2³² squared is 2⁶⁴, too big.

2³² - 1 squared is 2⁶⁴-2³³+1.

So just use 2³²-1.

In general (static_cast(1) << static_cast(sizeof(T)*4)) - 1 gets you the largest squarable unsigned value of type T, if T is an unsigned integral type.

A formula that guarantees that f(ULLONG_MAX) * f(ULLONG_MAX) is not more than ULLONG_MAX

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