Finding the closest or exact key in a std::map

For this, you can use either std::map::lower_bound

Returns an iterator pointing to the first element that is not less than key.

or std::map::equal_range

Returns a range containing all elements with the given key in the container.

In your case, if you want the closest entry, you need to check both the returned entry and the one before and compare the differences. Something like this might work

std::map<double, double>::iterator low, prev;
double pos = 3.0;
low = map.lower_bound(pos);
if (low == map.end()) {
    // nothing found, maybe use rbegin()
} else if (low == map.begin()) {
    std::cout << "low=" << low->first << '\n';
} else {
    prev = std::prev(low);
    if ((pos - prev->first) < (low->first - pos))
        std::cout << "prev=" << prev->first << '\n';
    else
        std::cout << "low=" << low->first << '\n';
}