How do I convert to ppm to bmp in c++?

Question

I am trying to implement a ray tracer in c++. I've found a code which makes a ppm file. However I am trying to do a bmp file. How can I directly convert ppm to a bmp in c++ code? I've tried this function however my reflections aren't quite accurate so I am trying to find a function to directly convert it.

void savebmp (const char *filename, int w, int h, int dpi, Vec3f *data) {
    FILE *f;
    int k = w*h;
    int s = 4*k;
    int filesize = 54 + s;

    double factor = 39.375;
    int m = static_cast<int>(factor);

    int ppm = dpi*m;

    unsigned char bmpfileheader[14] = {'B','M', 0,0,0,0, 0,0,0,0, 54,0,0,0};
    unsigned char bmpinfoheader[40] = {40,0,0,0, 0,0,0,0, 0,0,0,0, 1,0,24,0};

    bmpfileheader[ 2] = (unsigned char)(filesize);
    bmpfileheader[ 3] = (unsigned char)(filesize>>8);
    bmpfileheader[ 4] = (unsigned char)(filesize>>16);
    bmpfileheader[ 5] = (unsigned char)(filesize>>24);

    bmpinfoheader[ 4] = (unsigned char)(w);
    bmpinfoheader[ 5] = (unsigned char)(w>>8);
    bmpinfoheader[ 6] = (unsigned char)(w>>16);
    bmpinfoheader[ 7] = (unsigned char)(w>>24);

    bmpinfoheader[ 8] = (unsigned char)(h);
    bmpinfoheader[ 9] = (unsigned char)(h>>8);
    bmpinfoheader[10] = (unsigned char)(h>>16);
    bmpinfoheader[11] = (unsigned char)(h>>24);

    bmpinfoheader[21] = (unsigned char)(s);
    bmpinfoheader[22] = (unsigned char)(s>>8);
    bmpinfoheader[23] = (unsigned char)(s>>16);
    bmpinfoheader[24] = (unsigned char)(s>>24);

    bmpinfoheader[25] = (unsigned char)(ppm);
    bmpinfoheader[26] = (unsigned char)(ppm>>8);
    bmpinfoheader[27] = (unsigned char)(ppm>>16);
    bmpinfoheader[28] = (unsigned char)(ppm>>24);

    bmpinfoheader[29] = (unsigned char)(ppm);
    bmpinfoheader[30] = (unsigned char)(ppm>>8);
    bmpinfoheader[31] = (unsigned char)(ppm>>16);
    bmpinfoheader[32] = (unsigned char)(ppm>>24);

    f = fopen(filename,"wb");

    fwrite(bmpfileheader,1,14,f);
    fwrite(bmpinfoheader,1,40,f);


    while (k>0) {
        for (int i=0; i<w; i++){
        double red = (data[k-w+i].x)*255;
        double green = (data[k-w+i].y)*255;
        double blue = (data[k-w+i].z)*255;

        unsigned char color[3] = {(int)floor(blue),(int)floor(green),(int)floor(red)};

        fwrite(color,1,3,f);
        }
        k=k-w;
    }

    fclose(f);
}