how to calculate (a times b) divided by c only using 32-bit integer types even if a times b would not fit such a type

Question

Consider the following as a reference implementation:

/* calculates (a * b) / c */
uint32_t muldiv(uint32_t a, uint32_t b, uint32_t c)
{
    uint64_t x = a;
         


        

Answer 1

If b = 3000000000 => qn = 3000000000, qn*2 will be overflowed. So I edit the code of Sven Marnach.

uint32_t muldiv(uint32_t a, uint32_t b, uint32_t c)
{
uint32_t q = 0;              // the quotient
uint32_t r = 0;              // the remainder
uint32_t qn = b / c;
uint32_t rn = b % c;
while (a)
{
    if (a & 1)
    {
        q += qn;
        if (qn >= UINT32_MAX) {
            cout << "CO CO" << endl;
        }
        r += rn;
        if (r >= c)
        {
            q++;
            r -= c;
        }
    }
    a >>= 1;
    qn <<= 1;
    int temp = rn;
    if (rn > INT32_MAX) {
        // rn times 2: overflow
        rn = UINT32_MAX;// rn 
        temp = (temp - INT32_MAX) * 2; // find the compensator mean: rn * 2  = UINT32_MAX + temp
        qn++;
        rn = rn - c + temp;
    }
    else {
        rn <<= 1;
        if (rn >= c)
        {
            qn++;
            rn -= c;
        }
    }


}

//return r;
return q;

}