I have two integers n and d. These can be exactly represented by double dn(n) and double dd(d). Is there a reliable way in C++ to check if
double result = dn/dd
contains a rounding error? If it was just an integer-division checking if (n/d) * d==n would work but doing that with double precision arithmetic could hide rounding errors.
Edit: Shortly after posting this it struck me that changing the rounding mode to round_down would make the (n/d)*d==n test work for double. But if there is a simpler solution, I'd still like to hear it.
If you ignore overflow and underflow (which you should be able to do unless the integer types representing d and n are very wide), then the (binary) floating-point division dn/dd is exact iff d is a divisor of n times a power of two.
An algorithm to check for this may look like:
assert(d != 0);
while (d & 1 == 0) d >>= 1; // extract largest odd divisor of d
int exact = n % d == 0;
This is cheaper than changing the FPU rounding mode if you want the rounding mode to be “to nearest” the rest of the time, and there probably exist bit-twiddling tricks that can speed up the extraction of the largest odd divisor of d.