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?? cfft.cpp

?? The Spectral Toolkit is a C++ spectral transform library written by Rodney James and Chuck Panaccion
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      x2=x1+L*N;      x3=x2+L*N;      y0=y+4*L*j;      y1=y0+L;      y2=y1+L;      y3=y2+L;      t0.re=x0[0].re;      t0.im=x0[0].im;      t1.re=x1[0].re;      t1.im=x1[0].im;      t2.re=x2[0].re;      t2.im=x2[0].im;      t3.re=x3[0].re;      t3.im=x3[0].im;      s0.re=t0.re+t2.re;      s0.im=t0.im+t2.im;      s1.re=t0.re-t2.re;      s1.im=t0.im-t2.im;      s2.re=t1.re+t3.re;      s2.im=t1.im+t3.im;      s3.re=t1.re-t3.re;      s3.im=t1.im-t3.im;      y0[0].re = s0.re+s2.re;      y0[0].im = s0.im+s2.im;      y1[0].re = s1.re-s3.im;      y1[0].im = s1.im+s3.re;      y2[0].re = s0.re-s2.re;      y2[0].im = s0.im-s2.im;      y3[0].re = s1.re+s3.im;      y3[0].im = s1.im-s3.re;      w1.re=omega.re+1.0;      w1.im=-omega.im;      for(int i=1;i<L;i++)        {	  w2.re=w1.re*w1.re-w1.im*w1.im;	  w2.im=2.0*w1.re*w1.im;	  w3.re=w2.re*w1.re-w2.im*w1.im;	  w3.im=w2.re*w1.im+w2.im*w1.re; 	  t0.re=x0[i].re;	  t0.im=x0[i].im;	  t1.re=w1.re*x1[i].re-w1.im*x1[i].im;	  t1.im=w1.re*x1[i].im+w1.im*x1[i].re;	  t2.re=w2.re*x2[i].re-w2.im*x2[i].im;	  t2.im=w2.re*x2[i].im+w2.im*x2[i].re;	  t3.re=w3.re*x3[i].re-w3.im*x3[i].im;	  t3.im=w3.re*x3[i].im+w3.im*x3[i].re;	  s0.re=t0.re+t2.re;	  s0.im=t0.im+t2.im;	  s1.re=t0.re-t2.re;	  s1.im=t0.im-t2.im;	  s2.re=t1.re+t3.re;	  s2.im=t1.im+t3.im;	  s3.re=t1.re-t3.re;	  s3.im=t1.im-t3.im;	  y0[i].re = s0.re+s2.re;	  y0[i].im = s0.im+s2.im;	  y1[i].re = s1.re-s3.im;	  y1[i].im = s1.im+s3.re;	  y2[i].re = s0.re-s2.re;	  y2[i].im = s0.im-s2.im;	  y3[i].re = s1.re+s3.im;	  y3[i].im = s1.im-s3.re;	  t1.re=omega.re*w1.re+w1.im*omega.im+w1.re;	  t1.im=omega.re*w1.im-w1.re*omega.im+w1.im;	  w1.re=t1.re;	  w1.im=t1.im;        }    }}  /// Internal radix-5 butterfly forward transform./// \param x input array/// \param y output array/// \param L accumulation product of previous factors/// \param N remaining sequence length from node downvoid cfft::node::analysis_radix5(complex *x,complex *y,int L,int N){  complex w1,w2,w3,w4;  complex t0,t1,t2,t3,t4;  complex s0,s1,s2,s3,s4;  complex *x0,*x1,*x2,*x3,*x4;  complex *y0,*y1,*y2,*y3,*y4;  const real a1=0.3090169943749474241022934171830L;  // cos(-2*pi/5)  const real b1=-0.9510565162951535721164393333793L; // sin(-2*pi/5)  const real a2=-0.8090169943749474241022934171825L; // cos(-4*pi/5)  const real b2=-0.5877852522924731291687059546394L; // sin(-2*pi/5)      for(int j=0;j<N;j++)    {       x0=x+j*L;      x1=x0+L*N;      x2=x1+L*N;      x3=x2+L*N;      x4=x3+L*N;      y0=y+5*L*j;      y1=y0+L;      y2=y1+L;      y3=y2+L;      y4=y3+L;      t0.re=x0[0].re;      t0.im=x0[0].im;      t1.re=x1[0].re;      t1.im=x1[0].im;      t2.re=x2[0].re;      t2.im=x2[0].im;      t3.re=x3[0].re;      t3.im=x3[0].im;      t4.re=x4[0].re;      t4.im=x4[0].im;      s0.re=t0.re;      s0.im=t0.im;      s1.re=t1.re+t4.re;      s1.im=t1.im+t4.im;      s2.re=t2.re+t3.re;      s2.im=t2.im+t3.im;      s3.re=t1.re-t4.re;      s3.im=t1.im-t4.im;      s4.re=t2.re-t3.re;      s4.im=t2.im-t3.im;      t0.re=s0.re+s1.re+s2.re;      t0.im=s0.im+s1.im+s2.im;      t1.re=s0.re+a1*s1.re+a2*s2.re;      t1.im=s0.im+a1*s1.im+a2*s2.im;      t2.re=s0.re+a2*s1.re+a1*s2.re;      t2.im=s0.im+a2*s1.im+a1*s2.im;      t3.re=b1*s3.re+b2*s4.re;      t3.im=b1*s3.im+b2*s4.im;      t4.re=b2*s3.re-b1*s4.re;      t4.im=b2*s3.im-b1*s4.im;      y0[0].re=t0.re;      y0[0].im=t0.im;      y1[0].re=t1.re-t3.im;      y1[0].im=t1.im+t3.re;      y2[0].re=t2.re-t4.im;      y2[0].im=t2.im+t4.re;      y3[0].re=t2.re+t4.im;      y3[0].im=t2.im-t4.re;      y4[0].re=t1.re+t3.im;      y4[0].im=t1.im-t3.re;      w1.re=omega.re+1.0;      w1.im=omega.im;      for(int i=1;i<L;i++)        {	  w2.re = w1.re*w1.re-w1.im*w1.im;	  w2.im = 2.0*w1.re*w1.im;	  w3.re = w2.re*w1.re-w2.im*w1.im;	  w3.im = w2.re*w1.im+w2.im*w1.re; 	  w4.re = w3.re*w1.re-w3.im*w1.im;	  w4.im = w3.re*w1.im+w3.im*w1.re; 	  t0.re=x0[i].re;	  t0.im=x0[i].im;	  t1.re = w1.re*x1[i].re-w1.im*x1[i].im;	  t1.im = w1.re*x1[i].im+w1.im*x1[i].re;	  t2.re = w2.re*x2[i].re-w2.im*x2[i].im;	  t2.im = w2.re*x2[i].im+w2.im*x2[i].re;	  t3.re = w3.re*x3[i].re-w3.im*x3[i].im;	  t3.im = w3.re*x3[i].im+w3.im*x3[i].re;	  t4.re = w4.re*x4[i].re-w4.im*x4[i].im;	  t4.im = w4.re*x4[i].im+w4.im*x4[i].re;	  s0.re=t0.re;	  s0.im=t0.im;	  s1.re=t1.re+t4.re;	  s1.im=t1.im+t4.im;	  s2.re=t2.re+t3.re;	  s2.im=t2.im+t3.im;	  s3.re=t1.re-t4.re;	  s3.im=t1.im-t4.im;	  s4.re=t2.re-t3.re;	  s4.im=t2.im-t3.im;	  t0.re=s0.re+s1.re+s2.re;	  t0.im=s0.im+s1.im+s2.im;	  t1.re=s0.re+a1*s1.re+a2*s2.re;	  t1.im=s0.im+a1*s1.im+a2*s2.im;	  t2.re=s0.re+a2*s1.re+a1*s2.re;	  t2.im=s0.im+a2*s1.im+a1*s2.im;	  t3.re=b1*s3.re+b2*s4.re;	  t3.im=b1*s3.im+b2*s4.im;	  t4.re=b2*s3.re-b1*s4.re;	  t4.im=b2*s3.im-b1*s4.im;	  y0[i].re=t0.re;	  y0[i].im=t0.im;	  y1[i].re=t1.re-t3.im;	  y1[i].im=t1.im+t3.re;	  y2[i].re=t2.re-t4.im;	  y2[i].im=t2.im+t4.re;	  y3[i].re=t2.re+t4.im;	  y3[i].im=t2.im-t4.re;	  y4[i].re=t1.re+t3.im;	  y4[i].im=t1.im-t3.re;	  t1.re=omega.re*w1.re-w1.im*omega.im+w1.re;	  t1.im=omega.re*w1.im+w1.re*omega.im+w1.im;	  w1.re=t1.re;	  w1.im=t1.im;        }    }}  /// Internal radix-5 butterfly backward transform./// \param x input array/// \param y output array/// \param L accumulation product of previous factors/// \param N remaining sequence length from node downvoid cfft::node::synthesis_radix5(complex *x,complex *y,int L,int N){  complex w1,w2,w3,w4;  complex t0,t1,t2,t3,t4;  complex s0,s1,s2,s3,s4;  complex *x0,*x1,*x2,*x3,*x4;  complex *y0,*y1,*y2,*y3,*y4;  const real a1=0.3090169943749474241022934171830L;  const real b1=-0.9510565162951535721164393333793L;  const real a2=-0.8090169943749474241022934171825L;  const real b2=-0.5877852522924731291687059546394L;      for(int j=0;j<N;j++)    {       x0=x+j*L;      x1=x0+L*N;      x2=x1+L*N;      x3=x2+L*N;      x4=x3+L*N;      y0=y+5*L*j;      y1=y0+L;      y2=y1+L;      y3=y2+L;      y4=y3+L;      t0.re=x0[0].re;      t0.im=x0[0].im;      t1.re=x1[0].re;      t1.im=x1[0].im;      t2.re=x2[0].re;      t2.im=x2[0].im;      t3.re=x3[0].re;      t3.im=x3[0].im;      t4.re=x4[0].re;      t4.im=x4[0].im;      s0.re=t0.re;      s0.im=t0.im;      s1.re=t1.re+t4.re;      s1.im=t1.im+t4.im;      s2.re=t2.re+t3.re;      s2.im=t2.im+t3.im;      s3.re=t1.re-t4.re;      s3.im=t1.im-t4.im;      s4.re=t2.re-t3.re;      s4.im=t2.im-t3.im;      t0.re=s0.re+s1.re+s2.re;      t0.im=s0.im+s1.im+s2.im;      t1.re=s0.re+a1*s1.re+a2*s2.re;      t1.im=s0.im+a1*s1.im+a2*s2.im;      t2.re=s0.re+a2*s1.re+a1*s2.re;      t2.im=s0.im+a2*s1.im+a1*s2.im;      t3.re=b1*s3.re+b2*s4.re;      t3.im=b1*s3.im+b2*s4.im;      t4.re=b2*s3.re-b1*s4.re;      t4.im=b2*s3.im-b1*s4.im;      y0[0].re=t0.re;      y0[0].im=t0.im;      y1[0].re=t1.re+t3.im;      y1[0].im=t1.im-t3.re;      y2[0].re=t2.re+t4.im;      y2[0].im=t2.im-t4.re;      y3[0].re=t2.re-t4.im;      y3[0].im=t2.im+t4.re;      y4[0].re=t1.re-t3.im;      y4[0].im=t1.im+t3.re;      w1.re=omega.re+1.0;      w1.im=-omega.im;      for(int i=1;i<L;i++)        {	  w2.re = w1.re*w1.re-w1.im*w1.im;	  w2.im = 2.0*w1.re*w1.im;	  w3.re = w2.re*w1.re-w2.im*w1.im;	  w3.im = w2.re*w1.im+w2.im*w1.re; 	  w4.re = w3.re*w1.re-w3.im*w1.im;	  w4.im = w3.re*w1.im+w3.im*w1.re; 	  t0.re=x0[i].re;	  t0.im=x0[i].im;	  t1.re = w1.re*x1[i].re-w1.im*x1[i].im;	  t1.im = w1.re*x1[i].im+w1.im*x1[i].re;	  t2.re = w2.re*x2[i].re-w2.im*x2[i].im;	  t2.im = w2.re*x2[i].im+w2.im*x2[i].re;	  t3.re = w3.re*x3[i].re-w3.im*x3[i].im;	  t3.im = w3.re*x3[i].im+w3.im*x3[i].re;	  t4.re = w4.re*x4[i].re-w4.im*x4[i].im;	  t4.im = w4.re*x4[i].im+w4.im*x4[i].re;	  s0.re=t0.re;	  s0.im=t0.im;	  s1.re=t1.re+t4.re;	  s1.im=t1.im+t4.im;	  s2.re=t2.re+t3.re;	  s2.im=t2.im+t3.im;	  s3.re=t1.re-t4.re;	  s3.im=t1.im-t4.im;	  s4.re=t2.re-t3.re;	  s4.im=t2.im-t3.im;	  t0.re=s0.re+s1.re+s2.re;	  t0.im=s0.im+s1.im+s2.im;	  t1.re=s0.re+a1*s1.re+a2*s2.re;	  t1.im=s0.im+a1*s1.im+a2*s2.im;	  t2.re=s0.re+a2*s1.re+a1*s2.re;	  t2.im=s0.im+a2*s1.im+a1*s2.im;	  t3.re=b1*s3.re+b2*s4.re;	  t3.im=b1*s3.im+b2*s4.im;	  t4.re=b2*s3.re-b1*s4.re;	  t4.im=b2*s3.im-b1*s4.im;	  y0[i].re=t0.re;	  y0[i].im=t0.im;	  y1[i].re=t1.re+t3.im;	  y1[i].im=t1.im-t3.re;	  y2[i].re=t2.re+t4.im;	  y2[i].im=t2.im-t4.re;	  y3[i].re=t2.re-t4.im;	  y3[i].im=t2.im+t4.re;	  y4[i].re=t1.re-t3.im;	  y4[i].im=t1.im+t3.re;	  t1.re=omega.re*w1.re+w1.im*omega.im+w1.re;	  t1.im=omega.re*w1.im-w1.re*omega.im+w1.im;	  w1.re=t1.re;	  w1.im=t1.im;        }    }}  /// Internal radix-6 butterfly forward transform./// \param x input array/// \param y output array/// \param L accumulation product of previous factors/// \param N remaining sequence length from node downvoid cfft::node::analysis_radix6(complex *x,complex *y,int L,int N){  complex w1,w2,w3,w4,w5;  complex t0,t1,t2,t3,t4,t5;  complex s0,s1,s2,s3,s4,s5;  complex *x0,*x1,*x2,*x3,*x4,*x5;  complex *y0,*y1,*y2,*y3,*y4,*y5;  const real a= 0.5L;  const real b=-0.5L*root3;      for(int j=0;j<N;j++)    {       x0=x+j*L;      x1=x0+L*N;      x2=x1+L*N;      x3=x2+L*N;      x4=x3+L*N;      x5=x4+L*N;      y0=y+6*L*j;      y1=y0+L;      y2=y1+L;      y3=y2+L;      y4=y3+L;      y5=y4+L;      t0.re=x0[0].re;      t0.im=x0[0].im;      t1.re=x1[0].re;      t1.im=x1[0].im;      t2.re=x2[0].re;      t2.im=x2[0].im;      t3.re=x3[0].re;      t3.im=x3[0].im;      t4.re=x4[0].re;      t4.im=x4[0].im;      t5.re=x5[0].re;      t5.im=x5[0].im;      s0.re=t0.re+t3.re;      s0.im=t0.im+t3.im;      s1.re=t0.re-t3.re;      s1.im=t0.im-t3.im;      s2.re=t1.re+t2.re+t4.re+t5.re;      s2.im=t1.im+t2.im+t4.im+t5.im;      s3.re=t1.re-t2.re-t4.re+t5.re;      s3.im=t1.im-t2.im-t4.im+t5.im;      s4.re=t1.re+t2.re-t4.re-t5.re;      s4.im=t1.im+t2.im-t4.im-t5.im;      s5.re=t1.re-t2.re+t4.re-t5.re;      s5.im=t1.im-t2.im+t4.im-t5.im;      t0.re=s0.re+s2.re;      t0.im=s0.im+s2.im;      t1.re=s1.re+a*s3.re;      t1.im=s1.im+a*s3.im;      t2.re=s0.re-a*s2.re;      t2.im=s0.im-a*s2.im;      t3.re=s1.re-s3.re;      t3.im=s1.im-s3.im;      t4.re=b*s4.re;      t4.im=b*s4.im;      t5.re=b*s5.re;      t5.im=b*s5.im;      y0[0].re=t0.re;      y0[0].im=t0.im;      y1[0].re=t1.re-t4.im;      y1[0].im=t1.im+t4.re;      y2[0].re=t2.re-t5.im;      y2[0].im=t2.im+t5.re;      y3[0].re=t3.re;      y3[0].im=t3.im;      y4[0].re=t2.re+t5.im;      y4[0].im=t2.im-t5.re;      y5[0].re=t1.re+t4.im;      y5[0].im=t1.im-t4.re;      w1.re=omega.re+1.0;      w1.im=omega.im;      for(int i=1;i<L;i++)        {	  w2.re = w1.re*w1.re-w1.im*w1.im;	  w2.im = 2.0*w1.re*w1.im;	  w3.re = w2.re*w1.re-w2.im*w1.im;	  w3.im = w2.re*w1.im+w2.im*w1.re; 	  w4.re = w2.re*w2.re-w2.im*w2.im;	  w4.im = 2.0*w2.re*w2.im;	  w5.re = w4.re*w1.re-w4.im*w1.im;	  w5.im = w4.re*w1.im+w4.im*w1.re; 	  t0.re = x0[i].re;	  t0.im = x0[i].im;	  t1.re = w1.re*x1[i].re-w1.im*x1[i].im;	  t1.im = w1.re*x1[i].im+w1.im*x1[i].re;	  t2.re = w2.re*x2[i].re-w2.im*x2[i].im;	  t2.im = w2.re*x2[i].im+w2.im*x2[i].re;	  t3.re = w3.re*x3[i].re-w3.im*x3[i].im;	  t3.im = w3.re*x3[i].im+w3.im*x3[i].re;	  t4.re = w4.re*x4[i].re-w4.im*x4[i].im;	  t4.im = w4.re*x4[i].im+w4.im*x4[i].re;	  t5.re = w5.re*x5[i].re-w5.im*x5[i].im;	  t5.im = w5.re*x5[i].im+w5.im*x5[i].re;	  s0.re=t0.re+t3.re;	  s0.im=t0.im+t3.im;	  s1.re=t0.re-t3.re;	  s1.im=t0.im-t3.im;	  s2.re=t1.re+t2.re+t4.re+t5.re;	  s2.im=t1.im+t2.im+t4.im+t5.im;	  s3.re=t1.re-t2.re-t4.re+t5.re;	  s3.im=t1.im-t2.im-t4.im+t5.im;	  s4.re=t1.re+t2.re-t4.re-t5.re;	  s4.im=t1.im+t2.im-t4.im-t5.im;	  s5.re=t1.re-t2.re+t4.re-t5.re;	  s5.im=t1.im-t2.im+t4.im-t5.im;	  t0.re=s0.re+s2.re;	  t0.im=s0.im+s2.im;	  t1.re=s1.re+a*s3.re;	  t1.im=s1.im+a*s3.im;	  t2.re=s0.re-a*s2.re;	  t2.im=s0.im-a*s2.im;	  t3.re=s1.re-s3.re;	  t3.im=s1.im-s3.im;	  t4.re=b*s4.re;	  t4.im=b*s4.im;	  t5.re=b*s5.re;	  t5.im=b*s5.im;	  y0[i].re=t0.re;	  y0[i].im=t0.im;	  y1[i].re=t1.re-t4.im;	  y1[i].im=t1.im+t4.re;	  y2[i].re=t2.re-t5.im;	  y2[i].im=t2.im+t5.re;	  y3[i].re=t3.re;	  y3[i].im=t3.im;	  y4[i].re=t2.re+t5.im;	  y4[i].im=t2.im-t5.re;	  y5[i].re=t1.re+t4.im;	  y5[i].im=t1.im-t4.re;	  t1.re=omega.re*w1.re-w1.im*omega.im+w1.re;	  t1.im=omega.re*w1.im+w1.re*omega.im+w1.im;	  w1.re=t1.re;	  w1.im=t1.im;                    }    }}  /// Internal radix-6 butterfly backward transform./// \param x input array/// \param y output array/// \param L accumulation product of previous factors/// \param N remaining sequence length from node downvoid cfft::node::synthesis_radix6(complex *x,complex *y,int L,int N){  complex w1,w2,w3,w4,w5;  complex t0,t1,t2,t3,t4,t5;  complex s0,s1,s2,s3,s4,s5;  complex *x0,*x1,*x2,*x3,*x4,*x5;  complex *y0,*y1,*y2,*y3,*y4,*y5;  const real a= 0.5L;  const real b=-0.5L*root3;      for(int j=0;j<N;j++)    {       x0=x+j*L;      x1=x0+L*N;      x2=x1+L*N;      x3=x2+L*N;      x4=x3+L*N;      x5=x4+L*N;      y0=y+6*L*j;      y1=y0+L;      y2=y1+L;      y3=y2+L;      y4=y3+L;      y5=y4+L;      t0.re=x0[0].re;      t0.im=x0[0].im;      t1.re=x1[0].re;      t1.im=x1[0].im;      t2.re=x2[0].re;      t2.im=x2[0].im;      t3.re=x3[0].re;      t3.im=x3[0].im;      t4.re=x4[0].re;      t4.im=x4[0].im;      t5.re=x5[0].re;      t5.im=x5[0].im;      s0.re=t0.re+t3.re;      s0.im=t0.im+t3.im;      s1.re=t0.re-t3.re;      s1.im=t0.im-t3.im;      s2.re=t1.re+t2.re+t4.re+t5.re;      s2.im=t1.im+t2.im+t4.im+t5.im;      s3.re=t1.re-t2.re-t4.re+t5.re;      s3.im=t1.im-t2.im-t4.im+t5.im;      s4.re=t1.re+t2.re-t4.re-t5.re;      s4.im=t1.im+t2.im-t4.im-t5.im;      s5.re=t1.re-t2.re+t4.re-t5.re;      s5.im=t1.im-t2.im+t4.im-t5.im;      t0.re=s0.re+s2.re;      t0.im=s0.im+s2.im;      t1.re=s1.re+a*s3.re;      t1.im=s1.im+a*s3.im;      t2.re=s0.re-a*s2.re;      t2.im=s0.im-a*s2.im;      t3.re=s1.re-s3.re;      t3.im=s1.im-s3.im;      t4.re=b*s4.re;      t4.im=b*s4.im;      t5.re=b*s5.re;      t5.im=b*s5.im;      y0[0].re=t0.re;      y0[0].im=t0.im;      y1[0].re=t1.re+t4.im;      y1[0].im=t1.im-t4.re;      y2[0].re=t2.re+t5.im;      y2[0].im=t2.im-t5.re;      y3[0].re=t3.re;      y3[0].im=t3.im;      y4[0].re=t2.re-t5.im;      y4[0].im=t2.im+t5.re;      y5[0].re=t1.re-t4.im;      y5[0].im=t1.im+t4.re;      w1.re=omega.re+1.0;      w1.im=-omega.im;      for(int i=1;i<L;i++)        {	  w2.re = w1.re*w1.re-w1.im*w1.im;	  w2.im = 2.0*w1.re*w1.im;	  w3.re = w2.re*w1.re-w2.im*w1.im;	  w3.im = w2.re*w1.im+w2.im*w1.re; 	  w4.re = w3.re*w1.re-w3.im*w1.im;	  w4.im = w3.re*w1.im+w3.im*w1.re; 	  w5.re = w4.re*w1.re-w4.im*w1.im;	  w5.im = w4.re*w1.im+w4.im*w1.re; 	  t0.re=x0[i].re;	  t0.im=x0[i].im;

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