Why Does `std::pow()` Produce Incorrect Results with Integer Math?

Integer Math with std::pow() Yields Incorrect Results

In the provided code snippet:

int i = 23;
int j = 1;
int base = 10;
int k = 2;
i += j * pow(base, k);
std::cout << i << std::endl;

the expected output should be "123" but instead, "122" is printed.

Reason for Incorrect Output

The issue lies in the use of std::pow(). This function is designed to work with floating-point numbers, which lack infinite precision. Despite this being a potential implementation flaw in g 4.7.2 (MinGW, Windows XP), the root cause is the limited precision of floating-point calculations.

Solution: Integer Power Function

To resolve this issue, an integer power function can be implemented for accurate results with integers. In C 11 and later, this function can be defined as a constexpr, allowing it to potentially compute the result at compile-time if possible:

constexpr int int_pow(int b, int e)
{
    return (e == 0) ? 1 : b * int_pow(b, e - 1);
}

Alternative Tail-Recursive Form

This function can also be implemented in a tail-recursive form, which is more efficient in some circumstances:

constexpr int int_pow(int b, int e, int res = 1)
{
    return (e == 0) ? res : int_pow(b, e - 1, b * res);
}

By using these integer power functions in place of std::pow(), the code will produce the correct output, "123", without the precision issues associated with floating-point calculations.

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