Compare a 32 bit float and a 32 bit integer withou

I have a 32 bit floating point f number (known to be positive) that I need to convert to 32 bit unsigned integer. It's magnitude might be too large to fit. Furthermore, there is downstream computation that requires some headroom. I can compute the maximum acceptable value m as a 32 bit integer. How do I efficiently determine in C++11 on a constrained 32 bit machine (ARM M4F) if f <= m mathematically. Note that the types of the two values don't match. The following three approaches each have their issues:

static_cast<uint32_t>(f) <= m: I think this triggers undefined behaviour if f doesn't fit the 32 bit integer
f <= static_cast<float>(m): if m is too large to be converted exactly, the converted value could be larger than m such that the subsequent comparison will produce the wrong result in certain edge cases
static_cast<double>(f) <= static_cast<double>(m): is mathematically correct, but requires casting to, and working with double, which I'd like to avoid for efficiency reasons

Surely there must be a way to convert an integer to a float directly with specified rounding direction, i.e. guaranteeing the result not to exceed the input in magnitude. I'd prefer a C++11 standard solution, but in the worst case platform intrinsics could qualify as well.

I think your best bet is to be a bit platform specific. 2³² can be represented precisely in floating point. Check if f is too large to fit at all, and then convert to unsigned and check against m.

const float unsigned_limit = 4294967296.0f;
bool ok = false;
if (f < unsigned_limit)
{
    const auto uf = static_cast<unsigned int>(f);
    if (uf <= m)
    {
        ok = true;
    }
}

Not fond of the double comparison, but it's clear.

If f is usually significantly less than m (or usually significantly greater), one can test against float(m)*0.99f (respectively float(m)*1.01f), and then do the exact comparison in the unusual case. That is probably only worth doing if profiling shows that the performance gain is worth the extra complexity.