Help me write a binary search for boundary values (extracting sub lists)

vector<double> x(100000);

void subarray(const double a, const double b, vector<double> &sub) {
    ...
}

void subarray(const double a, const double b, vector<double> &sub) {
    for (size_t i = 0; i < data.size(); i++) {
        if (a <= data[i] && data[i] <= b) {
            sub.push_back(data[i]);
        }
    }
}

void subarray(const double a, const double b, vector <double> &sub, vector <int> pn) {
    vector <int>::const_iterator begin, end;
    begin = lower_bound(pn.begin(), pn.end(), a);
    end = upper_bound(pn.begin(), pn.end(), b);
    sub.insert(sub.begin(), begin, end);
}