The function\'s shift task is to shift a letter of the alphabet by x amount. Fun

Question

The function's shift task is to shift a letter of the alphabet by x amount.
Function’s prototype is
char shift(int shift_amount, char original);
However, function has a logic error.
**Find the logic error, repair it, so that the code has no logic errors.**
This is what I have so far:

#include
#include
using namespace std;

const string empty_string = "";

char shift(int shift_amount, char original);
string shift(int shift_amount, const string& original);

int main()
{
string original = "Of all things, never to have been born is best!";
for(int shift_amount = 0; shift_amount <= 26; shift_amount++)
{
string shifted = shift(shift_amount, original);
cout << shifted << endl;
}

system("pause");
return 0;
}
char shift(int shift_amount, char original)
{
char shifted;

static const int ALPHA_SIZE = 26;
static const int upper_base_code = static_cast('A');
static const int lower_base_code = static_cast('a');

shift_amount = shift_amount % ALPHA_SIZE;
if(shift_amount < 0)
shift_amount += ALPHA_SIZE;

int base_code;
if(isupper(original))
base_code = upper_base_code;
else
base_code = lower_base_code;

int original_code = static_cast(original);
int original_offset = original_code - base_code;
int shifted_offset = (original_offset + shift_amount) % ALPHA_SIZE;
int shifted_code = shifted_offset + base_code;
shifted = static_cast(shifted_code);
return shifted;
}
string shift(int shift_amount, const string& original)
{
string shifted = empty_string;
int length = original.length();
for(int index = 0; index < length; index++)
shifted += shift(shift_amount, original[index]);
return shifted;
}

Explanation / Answer

#include <iostream>
#include <string>
using namespace std;

const string empty_string = "";

char shift(int shift_amount, char original);
string shift(int shift_amount, const string& original);

int main()
{
string original = "Of all things, never to have been born is best!";
for(int shift_amount = 0; shift_amount <= 26; shift_amount++)
{
string shifted = shift(shift_amount, original);
cout << shifted << endl;
}

system("pause");
return 0;
}
char shift(int shift_amount, char original)
{
char shifted;

static const int ALPHA_SIZE = 26;
static const int upper_base_code = static_cast<int>('A');
static const int lower_base_code = static_cast<int>('a');

shift_amount = shift_amount % ALPHA_SIZE;
if(shift_amount < 0)
shift_amount += ALPHA_SIZE;

int base_code;
if(isupper(original))
base_code = upper_base_code;
else
base_code = lower_base_code;

int original_code = static_cast<int>(original);
int original_offset = original_code - base_code;
int shifted_offset = (original_offset + shift_amount) % ALPHA_SIZE;
int shifted_code = shifted_offset + base_code;
shifted = static_cast<char>(shifted_code);
return shifted;
}
string shift(int shift_amount, const string& original)
{
string shifted = empty_string;
int length = original.length();

for(int index = 0; index < length; index++)
shifted += shift(shift_amount, original[index]);

return shifted;
}

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