Why Does std::pow() Produce Unexpected Results in Integer Arithmetic?

Understanding Precision Issues in Integer Math with std::pow

When performing integer arithmetic operations with std::pow(), programmers may encounter unexpected results. This is because std::pow() natively works with floating point numbers, which introduces potential issues due to finite precision.

Consider the following example:

#include <iostream>
#include <cmath>

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

This code attempts to calculate the value of i as 23 1 * 10^2. However, the output is "122" instead of the expected "123." This is because std::pow() operates on floating point numbers, which may result in small inaccuracies in the computed result.

To resolve this issue, it is preferable to use an integer-specific pow function that ensures precise integer-based calculations. One way to achieve this is by creating a custom pow function that performs integer multiplication recursively:

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

This custom function ensures accurate integer calculations without the potential precision issues associated with floating point arithmetic.

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