Why does the implementation of std::to_string create a buffer 4 times the size of the type?

Question

C++11 introduces std::to_string, so I took a look at one implementation: it calls vsnprintf internally. Okay, but why does it always set the size parameter as 4 times the size of the type?

 inline string
 to_string(int __val)
 { return __gnu_cxx::__to_xstring<string>(&std::vsnprintf, 4 * sizeof(int),
                                          "%d", __val); }

 inline string
 to_string(unsigned __val)
 { return __gnu_cxx::__to_xstring<string>(&std::vsnprintf,
                                          4 * sizeof(unsigned),
                                          "%u", __val); }

 inline string
 to_string(long __val)
 { return __gnu_cxx::__to_xstring<string>(&std::vsnprintf, 4 * sizeof(long),
                                          "%ld", __val); }

Answer 1

The maximal number of binary digits of a N-decimal value is the ceil value of (N * log(10) / log(2)). A single decimal digit needs ceil(3.32) binary digits, That is 4.

For sizes of 8 bits it is:

Decimals = ceil(8 * Size / 3.32) = ceil(2.41 * Size).

For the sign (overhead and allocation) you get:

Decimals = 4 * Size.

Note: A conversion with snprintf of a single signed char needs 5 bytes (including the sign and the terminating zero). For values with a size greater than one byte, Decimals = 4 * Size provides a result, which is big enough.