seekg() does not set eofbit when reaching EOF of a stream. Is it by design?

I try to detect EOF of an std::istream by advancing the input pointer with 1 step by calling

seekg( 1, std::ios_base::cur )

However seekg() moves 1 position beyond EOF, when it sets the failbit of the stream. The eofbit is never set. See the output of this test program:

#include <iostream>
#include <sstream>

using namespace std;

void info( int aRelativePos, istream& aStream )
{
    cout << "POS=" << aRelativePos <<
            " input pos=" << aStream.tellg() <<
            " char=" << aStream.peek() <<
            "\tGood: " << aStream.good() <<
            " Eof: " << aStream.eof() <<
            " Bad: " << aStream.bad() <<
            " Fail: " << aStream.fail() << "\n";
}

int main()
{
    istringstream   input ("12");

    int i=0;
    while ( input.good() )
    {
        info( i, input );
        input.seekg( 1, std::ios_base::cur ); //advance 1 step forward
        ++i;
    }
    info ( i, input );

    return 0;
}

Output:

POS=0 input pos=0 char=49   Good: 1 Eof: 0 Bad: 0 Fail: 0
POS=1 input pos=1 char=50   Good: 1 Eof: 0 Bad: 0 Fail: 0
POS=2 input pos=-1 char=-1  Good: 1 Eof: 0 Bad: 0 Fail: 0
POS=3 input pos=-1 char=-1  Good: 0 Eof: 0 Bad: 0 Fail: 1

(Compiled by gcc 5.2 with -std=c++11. You can run this code here: http://ift.tt/1OwXXcg )

Moreover MS document on seekg ( http://ift.tt/1S3qRaM ) says that relative positioning in text files is not supported by the C++ Standard.

But I could not find such info in the Standard... Can you please give me the reference?