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

I suppose there are reasons you can't do

x = a/c;
x = x*b;

are there? And maybe add

y = b/c;
y = y*a;

if ( x != y )
    return ERROR_VALUE;

Note that, since you're using integer division, a*b/c and a/c*b might lead to different values if c is bigger than a or b. Also, if both a and b are smaller than c it won't work.