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Showing content from https://en.cppreference.com/w/cpp/language/../memory/shared_ptr/../../types/size_t.html below:

std::size_t - cppreference.com

typedef /* implementation-defined */ size_t;

std::size_t is the unsigned integer type of the result of the following operators:

If a program attempts to form an oversized type (i.e., the number of bytes in its object representation exceeds the maximum value representable in std::size_t), the program is ill-formed.

The bit width of std::size_t is not less than 16.

(since C++11) [edit] Notes

std::size_t can store the maximum size of a theoretically possible object of any type (including array). On many platforms (an exception is systems with segmented addressing) std::size_t can safely store the value of any non-member pointer, in which case it is synonymous with std::uintptr_t.

std::size_t is commonly used for array indexing and loop counting. Programs that use other types, such as unsigned int, for array indexing may fail on, e.g. 64-bit systems when the index exceeds UINT_MAX or if it relies on 32-bit modular arithmetic.

When indexing C++ containers, such as std::string, std::vector, etc, the appropriate type is the nested type size_type provided by such containers. It is usually defined as a synonym for std::size_t.

It is unspecified whether the declaration of std::size_t is available in any other standard library header. An implementation may avoid introducing this name even when the standard requires std::size_t to be used.

The integer literal suffix for std::size_t is any combination of z or Z with u or U (i.e. zu, zU, Zu, ZU, uz, uZ, Uz, or UZ).

(since C++23) [edit] Possible implementation

using size_t = decltype(sizeof 0);

[edit] Example
#include <array>
#include <cstddef>
#include <iostream>
 
int main()
{
    std::array<std::size_t, 10> a;
 
    // Example with C++23 std::size_t literal
    for (auto i = 0uz; i != a.size(); ++i)
        std::cout << (a[i] = i) << ' ';
    std::cout << '\n';
 
    // Example of decrementing loop
    for (std::size_t i = a.size(); i--;)
        std::cout << a[i] << ' ';
    std::cout << '\n';
 
    // Note the naive decrementing loop:
    //  for (std::size_t i = a.size() - 1; i >= 0; --i) ...
    // is an infinite loop, because unsigned numbers are always non-negative
}

Output:

0 1 2 3 4 5 6 7 8 9
9 8 7 6 5 4 3 2 1 0
[edit] Defect reports

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

DR Applied to Behavior as published Correct behavior CWG 1122 C++98 std::size_t was circularly defined[1] it is implementation-defined CWG 1464 C++98 object size might be not representable in std::size_t such type is ill-formed
  1. ↑ The definition of std::size_t was exactly the same as the definition of size_t in C, which is “the result type of sizeof”. There is no circular definition in C because the result type of sizeof in C is an implementation-defined unsigned integer type.
[edit] References
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