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.

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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';
}

"best performance possible" - given you insert elements in increasing order, you can push_back/emplace_back them into a std::vector then use std::lower_bound - you'll get better cache utilisation because the data will be packed into contiguous address space.

You could of course use lower_bound and upper_bound, which are logarithmic in runtime. And they should do what you want.

std::map<double,double>::iterator close_low;
//... your_map ...
close_low=your_map.lower_bound (current_length);

This should give you an iterator to the the first map element whose key is < current length. Do likewise with upper_bound and you have your time surrounded.