Fusion sorting algorithm

[firebird1]

Is this the correct way to implement a function that uses the fusion sorting algorithm to sort a vector of doubles?

#include <iostream>
#include <vector>
using namespace std;

vector<double> fusion(const vector<double>& v1, const vector<double>& v2) {
    vector<double> aux(v1.size() + v2.size());
    int i, j, k;
    i = j = k = 0;
    while(i < v1.size() and j < v2.size()) {
        if(v1[i] <= v2[j]) {
            aux[k] = v1[i];
            ++i;
        }
        else {
            aux[k] = v2[j];
            ++j;
        }
        ++k;
    }
    while(i < v1.size()) {
        aux[k] = v1[i];
        ++k;
        ++i;
    }
    while(j < v2.size()) {
        aux[k] = v2[j];
        ++k;
        ++j;
    }
    return aux;
}

void fusion_sort(vector<double>& v) {
    int m = v.size()/2;
    if(m != 0) {
        vector<double> aux1(m);
        for(int i = 0; i < aux1.size(); ++i) {
            aux1[i] = v[i];
        }
        vector<double> aux2(v.size()-aux1.size());
        for(int i = 0; i < aux2.size(); ++i) {
            aux1[i] = v[aux1.size()+i];
        }
        fusion_sort(aux1);
        fusion_sort(aux2);
        v = fusion(aux1, aux2);
    }
}