mixed radix fast fourier transform FFT radix-5*radix-3*radix-2*radix-4 for N=120 points example c++

//mixed radix fast fourier transform FFT radix-5*radix-3*radix-2*radix-4 for N=120 points example c++


void fun_fourier_transform_FFT_mixedradix_N_120(int N,std::complex<double> tab[])
{
 //source:
//Rabiner L.R., Gold B. Theory and application of digital signal processing p 378
    const double pi=3.141592653589793238462;
    std::complex<double>  tab2[4096]={};    // tab2[]==N
    std::complex<double>  w1[1]={{1,0}};
    std::complex<double>  w2[1]={{1,0}};
    std::complex<double>  w3[1]={{1,0}};
    std::complex<double>  w4[1]={{1,0}};
    std::complex<double>  w40[1]={{1,0}};
    std::complex<double>  w5[1]={{1,0}};
    std::complex<double>  w6[1]={{1,0}};
    std::complex<double>  w50[1]={{1,0}};
    std::complex<double>  w60[1]={{1,0}};
    std::complex<double>  w7[1]={{1,0}};
    std::complex<double>  w11[1]={{1,0}};
    std::complex<double>  w12[1]={{1,0}};
    std::complex<double>  w13[1]={{1,0}};
    std::complex<double>  w14[1]={{1,0}};
    std::complex<double>  w15[1]={{1,0}};
    std::complex<double>  w16[1]={{1,0}};
    std::complex<double>  w17[1]={{1,0}};
    std::complex<double>  w18[1]={{1,0}};
    std::complex<double>  w19[1]={{1,0}};
    std::complex<double>  w20[1]={{1,0}};
    std::complex<double> tmp1,tmp2,tmp3,tmp4,tmp11;
    double tmp5;
    double tmp6;
    double tmp7;
    double tmp8;


    tmp5=2*pi/(N/1);
    tmp6=2*pi/(N/1);
    tmp7=2*pi/(3/1);
    tmp8=2*pi/(5/1);

//radix 3 fundament
          w4[0].real()=cos(0*tmp7);
          w4[0].imag()=-sin(0*tmp7);
          w5[0].real()=cos(1*tmp7);
          w5[0].imag()=-sin(1*tmp7);
          w6[0].real()=cos(2*tmp7);
          w6[0].imag()=-sin(2*tmp7);
          w7[0].real()=cos(4*tmp7);
          w7[0].imag()=-sin(4*tmp7);


//radix 5 fundament
          w11[0].real()=cos(0*tmp8);
          w11[0].imag()=-sin(0*tmp8);
          w12[0].real()=cos(1*tmp8);
          w12[0].imag()=-sin(1*tmp8);
          w13[0].real()=cos(2*tmp8);
          w13[0].imag()=-sin(2*tmp8);
          w14[0].real()=cos(3*tmp8);
          w14[0].imag()=-sin(3*tmp8);
          w15[0].real()=cos(4*tmp8);
          w15[0].imag()=-sin(4*tmp8);
          w16[0].real()=cos(6*tmp8);
          w16[0].imag()=-sin(6*tmp8);
          w17[0].real()=cos(8*tmp8);
          w17[0].imag()=-sin(8*tmp8);
          w18[0].real()=cos(9*tmp8);
          w18[0].imag()=-sin(9*tmp8);
          w19[0].real()=cos(12*tmp8);
          w19[0].imag()=-sin(12*tmp8);
          w20[0].real()=cos(16*tmp8);
          w20[0].imag()=-sin(16*tmp8);


//stage 1  radix-5
          w1[0].real()=cos(0);
          w1[0].imag()=-sin(0);
          w2[0].real()=cos(0);
          w2[0].imag()=-sin(0);
          w3[0].real()=cos(0);
          w3[0].imag()=-sin(0);
          w4[0].real()=cos(0);
          w4[0].imag()=-sin(0);
          w40[0].real()=cos(0);
          w40[0].imag()=-sin(0);
        for(int i=0;i<24;i++)
        {
          tmp1=w1[0]*tab[i+0];
          tmp2=w2[0]*tab[i+24];
          tmp3=w3[0]*tab[i+48];
          tmp4=w4[0]*tab[i+72];
          tmp11=w40[0]*tab[i+96];
         //radix-5
          tab2[i]      =w11[0]*tmp1+w11[0]*tmp2+w11[0]*tmp3+w11[0]*tmp4+w11[0]*tmp11;
          tab2[i+24]   =w11[0]*tmp1+w12[0]*tmp2+w13[0]*tmp3+w14[0]*tmp4+w15[0]*tmp11;
          tab2[i+48]   =w11[0]*tmp1+w13[0]*tmp2+w15[0]*tmp3+w16[0]*tmp4+w17[0]*tmp11;
          tab2[i+72]   =w11[0]*tmp1+w14[0]*tmp2+w16[0]*tmp3+w18[0]*tmp4+w19[0]*tmp11;
          tab2[i+96]   =w11[0]*tmp1+w15[0]*tmp2+w17[0]*tmp3+w19[0]*tmp4+w20[0]*tmp11;
        }

//stage 2 radix-3
    int b=0;
    for(int i=0;i<5;i=i+1,b++)
    {
        for(int j=0;j<8;j=j+1)
        {
          w1[0].real()=cos(b*(0+j)*tmp6);
          w1[0].imag()=-sin(b*(0+j)*tmp6);
          w2[0].real()=cos(b*(8+j)*tmp6);
          w2[0].imag()=-sin(b*(8+j)*tmp6);
          w3[0].real()=cos(b*(16+j)*tmp6);
          w3[0].imag()=-sin(b*(16+j)*tmp6);

          tmp1=w1[0]*tab2[i*24+0+j];
          tmp2=w2[0]*tab2[i*24+8+j];
          tmp3=w3[0]*tab2[i*24+16+j];
         //radix-3
          tab[i*24+0+j]   =w4[0]*tmp1+w4[0]*tmp2+w4[0]*tmp3;
          tab[i*24+8+j]   =w4[0]*tmp1+w5[0]*tmp2+w6[0]*tmp3;
          tab[i*24+16+j]  =w4[0]*tmp1+w6[0]*tmp2+w7[0]*tmp3;
        }
    }

//stage 3 radix-2

    for(int i=0;i<5*3;i=i+1,b++)
    {
        if(b>=3){b=0;}
        for(int j=0;j<4;j=j+1)
        {
            w1[0].real()= cos(5*b*(0+j)*tmp5);
            w1[0].imag()=-sin(5*b*(0+j)*tmp5);
            w2[0].real()= cos(5*b*(4+j)*tmp5);
            w2[0].imag()=-sin(5*b*(4+j)*tmp5);
            tmp1=w1[0]*tab[0+i*8+j];
            tmp2=w2[0]*tab[4+i*8+j];
            tab2[0+i*8+j]=tmp1+tmp2;
            tab2[4+i*8+j]=tmp1-tmp2;
        }
    }

//stage 4 radix-4

    w50[0].real()=0;
    w50[0].imag()=-1;
    w60[0].real()=0;
    w60[0].imag()=1;

    for(int i=0;i<5*3*2;i=i+1,b++)
    {
        if(b>=2){b=0;}
        for(int j=0;j<1;j=j+1)
        {
          w1[0].real()=cos(0*tmp5);
          w1[0].imag()=-sin(0*tmp5);
          w2[0].real()=cos(5*3*b*(1)*tmp5);
          w2[0].imag()=-sin(5*3*b*(1)*tmp5);
          w3[0].real()=cos(5*3*b*(2)*tmp5);
          w3[0].imag()=-sin(5*3*b*(2)*tmp5);
          w4[0].real()=cos(5*3*b*(3)*tmp5);
          w4[0].imag()=-sin(5*3*b*(3)*tmp5);

            tmp1=w1[0]*tab2[i*4+0];
            tmp2=w2[0]*tab2[i*4+1];
            tmp3=w3[0]*tab2[i*4+2];
            tmp4=w4[0]*tab2[i*4+3];
            //radix-4
            tab[i*4]       =tmp1+tmp2+tmp3+tmp4;
            tab[i*4+1]   =tmp1-tmp3+w50[0]*(tmp2-tmp4);
            tab[i*4+2]   =tmp1-tmp2+tmp3-tmp4;
            tab[i*4+3] =tmp1-tmp3+w60[0]*(tmp2-tmp4);
        }
    }
   
//new
    for(int j=0;j<N;j++)
    {
     tab[j].real() =tab[j].real()*2/N;
     tab[j].imag() =tab[j].imag()*2/N;
    }
}