?? rfft.cpp
字號(hào):
t5.re=x5[0]; s0.re=t0.re+t3.re; s1.re=t0.re-t3.re; s2.re=t1.re+t2.re; s3.re=t1.re-t2.re; s4.re=t4.re+t5.re; s5.re=t4.re-t5.re; y0[ 0]=s0.re+s2.re+s4.re; y1[-1]=s1.re+A*(s3.re-s5.re); y1[ 0]= B*(s2.re-s4.re); y2[-1]=s0.re-A*(s2.re+s4.re); y2[ 0]= B*(s3.re+s5.re); y3[-1]=s1.re-s3.re+s5.re; w.re=omega.re+1.0; w.im=omega.im; for(int k=1;k<(L+1)/2;k++) { t0.re=x0[2*k-1]; t0.im=x0[2*k ]; t1.re=x1[2*k-1]; t1.im=x1[2*k ]; t2.re=x2[2*k-1]; t2.im=x2[2*k ]; t3.re=x3[2*k-1]; t3.im=x3[2*k ]; t4.re=x4[2*k-1]; t4.im=x4[2*k ]; t5.re=x5[2*k-1]; t5.im=x5[2*k ]; w2.re=w.re*w.re-w.im*w.im; w2.im=2.0*w.re*w.im; w3.re=w2.re*w.re-w2.im*w.im; w3.im=w2.re*w.im+w2.im*w.re; w4.re=w3.re*w.re-w3.im*w.im; w4.im=w3.re*w.im+w3.im*w.re; w5.re=w4.re*w.re-w4.im*w.im; w5.im=w4.re*w.im+w4.im*w.re; s0.re=t0.re; s0.im=t0.im; s1.re=t1.re*w.re-t1.im*w.im; s1.im=t1.re*w.im+t1.im*w.re; s2.re=t2.re*w2.re-t2.im*w2.im; s2.im=t2.re*w2.im+t2.im*w2.re; s3.re=t3.re*w3.re-t3.im*w3.im; s3.im=t3.re*w3.im+t3.im*w3.re; s4.re=t4.re*w4.re-t4.im*w4.im; s4.im=t4.re*w4.im+t4.im*w4.re; s5.re=t5.re*w5.re-t5.im*w5.im; s5.im=t5.re*w5.im+t5.im*w5.re; t0.re=s0.re+s3.re; t0.im=s0.im+s3.im; t1.re=s1.re+s2.re+s4.re+s5.re; t1.im=s1.im+s2.im+s4.im+s5.im; t2.re=s1.re-s2.re-s4.re+s5.re; t2.im=s1.im-s2.im-s4.im+s5.im; t3.re=s1.re+s2.re-s4.re-s5.re; t3.im=s1.im+s2.im-s4.im-s5.im; t4.re=s1.re-s2.re+s4.re-s5.re; t4.im=s1.im-s2.im+s4.im-s5.im; t5.re=s0.re-s3.re; t5.im=s0.im-s3.im; s0.re=t0.re+t1.re; s0.im=t0.im+t1.im; s5.re=t5.re-t2.re; s5.im=t5.im-t2.im; s1.re=t5.re+A*t2.re; s1.im=t5.im+A*t2.im; s3.re=B*t3.re; s3.im=B*t3.im; s2.re=t0.re-A*t1.re; s2.im=t0.im-A*t1.im; s4.re=B*t4.re; s4.im=B*t4.im; y0[ 2*k-1] = s0.re; y0[ 2*k ] = s0.im; y1[ 2*k-1] = s1.re-s3.im; y1[ 2*k ] = s1.im+s3.re; y1[-2*k-1] = s1.re+s3.im; y1[-2*k ] =-s1.im+s3.re; y2[ 2*k-1] = s2.re-s4.im; y2[ 2*k ] = s2.im+s4.re; y2[-2*k-1] = s2.re+s4.im; y2[-2*k ] =-s2.im+s4.re; y3[-2*k-1] = s5.re; y3[-2*k ] =-s5.im; z.re=omega.re*w.re-omega.im*w.im+w.re; z.im=omega.re*w.im+omega.im*w.re+w.im; w.re=z.re; w.im=z.im; } if(L%2==0) { t0.re=x0[L-1]; t1.re=x1[L-1]; t2.re=x2[L-1]; t3.re=x3[L-1]; t4.re=x4[L-1]; t5.re=x5[L-1]; w2.re=w.re*w.re-w.im*w.im; w2.im=2.0*w.re*w.im; w3.re=w2.re*w.re-w2.im*w.im; w3.im=w2.re*w.im+w2.im*w.re; w4.re=w3.re*w.re-w3.im*w.im; w4.im=w3.re*w.im+w3.im*w.re; w5.re=w4.re*w.re-w4.im*w.im; w5.im=w4.re*w.im+w4.im*w.re; s0.re=t0.re; s0.im=0.0; s1.re=t1.re*w.re; s1.im=t1.re*w.im; s2.re=t2.re*w2.re; s2.im=t2.re*w2.im; s3.re=t3.re*w3.re; s3.im=t3.re*w3.im; s4.re=t4.re*w4.re; s4.im=t4.re*w4.im; s5.re=t5.re*w5.re; s5.im=t5.re*w5.im; t0.re=s0.re+s3.re; t0.im=s0.im+s3.im; t1.re=s0.re-s3.re; t1.im=s0.im-s3.im; t2.re=s1.re+s2.re; t2.im=s1.im+s2.im; t3.re=s1.re-s2.re; t3.im=s1.im-s2.im; t4.re=s4.re+s5.re; t4.im=s4.im+s5.im; t5.re=s4.re-s5.re; t5.im=s4.im-s5.im; s0.re=t0.re+t2.re+t4.re; s0.im=t0.im+t2.im+t4.im; s1.re=t1.re+A*(t3.re-t5.re)-B*(t2.im-t4.im); s1.im=t1.im+A*(t3.im-t5.im)+B*(t2.re-t4.re); s2.re=t0.re-A*(t2.re+t4.re)-B*(t3.im+t5.im); s2.im=t0.im-A*(t2.im+t4.im)+B*(t3.re+t5.re); y0[L-1] = s0.re; y0[L ] = s0.im; y1[L-1] = s1.re; y1[L ] = s1.im; y2[L-1] = s2.re; y2[L ] = s2.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 rfft::node::synthesis_radix6(real *y,real *x,int L,int N){ complex z,w1,w2,w3,w4,w5; complex t0,t1,t2,t3,t4,t5; complex s0,s1,s2,s3,s4,s5; const real A= 0.5L; const real B=-0.5L*root3; real *x0,*x1,*x2,*x3,*x4,*x5; real *y0,*y1,*y2,*y3; for(int j=0;j<N;j++) { x0=x+j*L; x1=x+j*L+N*L; x2=x+j*L+2*N*L; x3=x+j*L+3*N*L; x4=x+j*L+4*N*L; x5=x+j*L+5*N*L; y0=y+j*6*L; y1=y+j*6*L+2*L; y2=y+j*6*L+4*L; y3=y+j*6*L+6*L; t0.re=y0[ 0]; t1.re=y1[-1]; t1.im=y1[ 0]; t2.re=y2[-1]; t2.im=y2[ 0]; t3.re=y3[-1]; s0.re=t0.re+t3.re; s1.re=2.0*(t1.re+t2.re); s1.im=2.0*(t1.im+t2.im); s2.re=2.0*(t1.re-t2.re); s2.im=2.0*(t1.im-t2.im); s3.re=t0.re-t3.re; s4.re=s3.re+A*s2.re; s4.im=B*s1.im; s5.re=s0.re-A*s1.re; s5.im=B*s2.im; x0[0]=s0.re+s1.re; x1[0]=s4.re+s4.im; x2[0]=s5.re+s5.im; x3[0]=s3.re-s2.re; x4[0]=s5.re-s5.im; x5[0]=s4.re-s4.im; w1.re=omega.re+1.0; w1.im=omega.im; for(int k=1;k<(L+1)/2;k++) { t0.re= y0[ 2*k-1]; t0.im= y0[ 2*k ]; t1.re= y1[ 2*k-1]; t1.im= y1[ 2*k ]; t3.re= y1[-2*k-1]; t3.im=-y1[-2*k ]; t2.re= y2[ 2*k-1]; t2.im= y2[ 2*k ]; t4.re= y2[-2*k-1]; t4.im=-y2[-2*k ]; t5.re= y3[-2*k-1]; t5.im=-y3[-2*k ]; s0.re=t0.re+t5.re; s0.im=t0.im+t5.im; s1.re=t0.re-t5.re; s1.im=t0.im-t5.im; s2.re=t1.re-t2.re+t3.re-t4.re; s2.im=t1.im-t2.im+t3.im-t4.im; s3.re=t1.re+t2.re+t3.re+t4.re; s3.im=t1.im+t2.im+t3.im+t4.im; s4.re=t1.re+t2.re-t3.re-t4.re; s4.im=t1.im+t2.im-t3.im-t4.im; s5.re=t1.re-t2.re-t3.re+t4.re; s5.im=t1.im-t2.im-t3.im+t4.im; t0.re=s0.re+s3.re; t0.im=s0.im+s3.im; t1.re=s1.re+A*s2.re; t1.im=s1.im+A*s2.im; t2.re=s0.re-A*s3.re; t2.im=s0.im-A*s3.im; t3.re=s1.re-s2.re; t3.im=s1.im-s2.im; t4.re=B*s5.re; t4.im=B*s5.im; t5.re=B*s4.re; t5.im=B*s4.im; s0.re=t0.re; s0.im=t0.im; s3.re=t3.re; s3.im=t3.im; s1.re=t1.re+t5.im; s1.im=t1.im-t5.re; s2.re=t2.re+t4.im; s2.im=t2.im-t4.re; s5.re=t1.re-t5.im; s5.im=t1.im+t5.re; s4.re=t2.re-t4.im; s4.im=t2.im+t4.re; 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; x0[2*k-1]=s0.re; x0[2*k ]=s0.im; x1[2*k-1]=s1.re*w1.re+s1.im*w1.im; x1[2*k ]=s1.im*w1.re-s1.re*w1.im; x2[2*k-1]=s2.re*w2.re+s2.im*w2.im; x2[2*k ]=s2.im*w2.re-s2.re*w2.im; x3[2*k-1]=s3.re*w3.re+s3.im*w3.im; x3[2*k ]=s3.im*w3.re-s3.re*w3.im; x4[2*k-1]=s4.re*w4.re+s4.im*w4.im; x4[2*k ]=s4.im*w4.re-s4.re*w4.im; x5[2*k-1]=s5.re*w5.re+s5.im*w5.im; x5[2*k ]=s5.im*w5.re-s5.re*w5.im; z.re=omega.re*w1.re-omega.im*w1.im+w1.re; z.im=omega.re*w1.im+omega.im*w1.re+w1.im; w1.re=z.re; w1.im=z.im; } if(L%2==0) { t0.re=y0[L-1]; t0.im=y0[L ]; t1.re=y1[L-1]; t1.im=y1[L ]; t2.re=y2[L-1]; t2.im=y2[L ]; t5.re= t0.re; t5.im=-t0.im; t4.re= t1.re; t4.im=-t1.im; t3.re= t2.re; t3.im=-t2.im; s0.re=t0.re+t3.re; s0.im=t0.im+t3.im; s1.re=t1.re+t2.re+t4.re+t5.re; s1.im=t1.im+t2.im+t4.im+t5.im; s2.re=t0.re-t3.re; s2.im=t0.im-t3.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+s1.re; t0.im=s0.im+s1.im; t1.re=s2.re+A*s3.re+B*s4.im; t1.im=s2.im+A*s3.im-B*s4.re; t2.re=s0.re-A*s1.re+B*s5.im; t2.im=s0.im-A*s1.im-B*s5.re; t3.re=s2.re-s3.re; t3.im=s2.im-s3.im; t4.re=s0.re-A*s1.re-B*s5.im; t4.im=s0.im-A*s1.im+B*s5.re; t5.re=s2.re+A*s3.re-B*s4.im; t5.im=s2.im+A*s3.im+B*s4.re; 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; x0[L-1]=t0.re; x1[L-1]=t1.re*w1.re+t1.im*w1.im; x2[L-1]=t2.re*w2.re+t2.im*w2.im; x3[L-1]=t3.re*w3.re+t3.im*w3.im; x4[L-1]=t4.re*w4.re+t4.im*w4.im; x5[L-1]=t5.re*w5.re+t5.im*w5.im; } }}/// Internal radix-8 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 rfft::node::analysis_radix8(real *x,real *y,int L,int N){ complex w1,w2,w3,w4,w5,w6,w7; complex s0,s1,s2,s3,s4,s5,s6,s7; complex t0,t1,t2,t3,t4,t5,t6,t7; real *x0,*x1,*x2,*x3,*x4,*x5,*x6,*x7; real *y0,*y1,*y2,*y3,*y4; const real c=0.5L*root2; for(int j=0;j<N;j++) { x0=x+j*L; x1=x0+N*L; x2=x1+N*L; x3=x2+N*L; x4=x3+N*L; x5=x4+N*L; x6=x5+N*L; x7=x6+N*L; y0=y +j*8*L; y1=y+2*L+j*8*L; y2=y+4*L+j*8*L; y3=y+6*L+j*8*L; y4=y+8*L+j*8*L; t0.re=x0[0]; t1.re=x1[0]; t2.re=x2[0]; t3.re=x3[0]; t4.re=x4[0]; t5.re=x5[0]; t6.re=x6[0]; t7.re=x7[0]; s0.re=t0.re+t4.re; s1.re=t2.re+t6.re; s2.re=t1.re+t5.re; s3.re=t3.re+t7.re; s4.re=t0.re-t4.re; s5.re=t2.re-t6.re; s6.re=t1.re-t5.re; s7.re=t3.re-t7.re; t0.re= (s0.re+s1.re); t1.re= (s2.re+s3.re); t2.re= s4.re; t2.im= -s5.re; t3.re=c*(s6.re-s7.re); t3.im=c*(-s6.re-s7.re); t4.re= (s0.re-s1.re); t5.im= -(s2.re-s3.re); t6.re= s4.re; t6.im= s5.re; t7.re=-t3.re; t7.im=t3.im; y0[ 0]=t0.re+t1.re; y1[-1]=t2.re+t3.re; y1[ 0]=t2.im+t3.im; y2[-1]=t4.re; y2[ 0]=t5.im; y3[-1]=t6.re+t7.re; y3[ 0]=t6.im+t7.im; y4[-1]=t0.re-t1.re; w1.re=omega.re+1.0; w1.im=omega.im; for(int k=1;k<(L+1)/2;k++) { 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; w6.re=w5.re*w1.re-w5.im*w1.im; w6.im=w5.re*w1.im+w5.im*w1.re; w7.re=w6.re*w1.re-w6.im*w1.im; w7.im=w6.re*w1.im+w6.im*w1.re; t0.re=x0[2*k-1]; t0.im=x0[2*k ]; s1.re=x1[2*k-1]; s1.im=x1[2*k ]; s2.re=x2[2*k-1]; s2.im=x2[2*k ]; s3.re=x3[2*k-1]; s3.im=x3[2*k ]; s4.re=x4[2*k-1]; s4.im=x4[2*k ]; s5.re=x5[2*k-1]; s5.im=x5[2*k ]; s6.re=x6[2*k-1]; s6.im=x6[2*k ]; s7.re=x7[2*k-1]; s7.im=x7[2*k ]; t1.re=s1.re*w1.re-s1.im*w1.im; t1.im=s1.im*w1.re+s1.re*w1.im; t2.re=s2.re*w2.re-s2.im*w2.im; t2.im=s2.im*w2.re+s2.re*w2.im; t3.re=s3.re*w3.re-s3.im*w3.im; t3.im=s3.im*w3.re+s3.re*w3.im; t4.re=s4.re*w4.re-s4.im*w4.im; t4.im=s4.im*w4.re+s4.re*w4.im; t5.re=s5.re*w5.re-s5.im*w5.im; t5.im=s5.im*w5.re+s5.re*w5.im; t6.re=s6.re*w6.re-s6.im*w6.im; t6.im=s6.im*w6.re+s6.re*w6.im; t7.re=s7.re*w7.re-s7.im*w7.im; t7.im=s7.im*w7.re+s7.re*w7.im; s0.re=t0.re+t4.re; s0.im=t0.im+t4.im; s1.re=t2.re+t6.re; s1.im=t2.im+t6.im; s2.re=t1.re+t5.re; s2.im=t1.im+t5.im; s3.re=t3.re+t7.re; s3.im=t3.im+t7.im; s4.re=t0.re-t4.re; s4.im=t0.im-t4.im; s5.re=t2.re-t6.re; s5.im=t2.im-t6.im; s6.re=t1.re-t5.re; s6.im=t1.im-t5.im; s7.re=t3.re-t7.re; s7.im=t3.im-t7.im; t0.re= (s0.re+s1.re); t0.im= (s0.im+s1.im); t1.re= (s2.re+s3.re); t1.im= (s2.im+s3.im); t2.re= (s4.re+s5.im); t2.im= (s4.im-s5.re); t3.re=c*(s6.re+s6.im-s7.re+s7.im); t3.im=c*(s6.im-s6.re-s7.im-s7.re); t4.re= (s0.re-s1.re); t4.im= (s0.im-s1.im); t5.re= (s2.im-s3.im); t5.im= -(s2.re-s3.re); t6.re= (s4.re-s5.im); t6.im= (s4.im+s5.re); t7.re=c*(-s6.re+s6.im+s7.re+s7.im); t7.im=c*(-s6.im-s6.re+s7.im-s7.re); y0[ 2*k-1]= (t0.re+t1.re); y0[ 2*k ]= (t0.im+t1.im); y1[ 2*k-1]= (t2.re+t3.re); y1[ 2*k ]= (t2.im+t3.im); y2[ 2*k-1]= (t4.re+t5.re); y2[ 2*k ]= (t4.im+t5.im); y3[ 2*k-1]= (t6.re+t7.re); y3[ 2*k ]= (t6.im+t7.im); y1[-2*k-1]= (t6.re-t7.re); y1[-2*k ]=-(t6.im-t7.im); y2[-2*k-1]= (t4.re-t5.re); y2[-2*k ]=-(t4.im-t5.im); y3[-2*k-1]= (t2.re-t3.re); y3[-2*k ]=-(t2.im-t3.im); y4[-2*k-1]= (t0.re-t1.re); y4[-2*k ]=-(t0.im-t1.im); t0.re=omega.re*w1.re-omega.im*w1.im+w1.re; t0.im=omega.re*w1.im+omega.im*w1.re+w1.im; w1.re=t0.re; w1.im=t0.im; } if(L%2==0) { 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; w6.re=w5.re*w1.re-w5.im*w1.im; w6.im=w5.re*w1.im+w5.im*w1.re; w7.re=w6.re*w1.re-w6.im*w1.im; w7.im=w6.re*w1.im+w6.im*w1.re; t0.re=x0[L-1]; t0.im=0.0; t1.re=x1[L-1]*w1.re; t1.im=x1[L-1]*w1.im; t2.re=x2[L-1]*w2.re; t2.im=x2[L-1]*w2.im; t3.re=x3[L-1]*w3.re; t3.im=x3[L-1]*w3.im; t4.re=x4[L-1]*w4.re; t4.im=x4[L-1]*w4.im; t5.re=x5[L-1]*w5.re; t5.im=x5[L-1]*w5.im; t6.re=x6[L-1]*w6.re; t6.im=x6[L-1]*w6.im; t7.re=x7[L-1]*w7.re; t7.im=x7[L-1]*w7.im; s0.re=t0.re+t4.re; s0.im=t0.im+t4.im; s1.re=t2.re+t6.re; s1.im=t2.im+t6.im; s2.re=t1.re+t5.re; s2.im=t1.im+t5.im; s3.re=t3.re+t7.re; s3.im=t3.im+t7.im; s4.re=t0.re-t4.re; s4.im=t0.im-t4.im; s5.re=t2.re-t6.re; s5.im=t2.im-t6.im; s6.re=t1.re-t5.re; s6.im=t1.im-t5.im; s7.re=t3.re-t7.re; s7.im=t3.im-t7.im; t0.re= ( s0.re+s1.re); t0.im= ( s0.im+s1.im); t1.re= ( s2.re+s3.re); t1.im= ( s2.im+s3.im); t2.re= ( s4.re+s5.im); t2.im= ( s4.im-s5.re); t3.re=c*( s6.re+s6.im-s7.re+s7.im); t3.im=c*( s6.im-s6.re-s7.im-s7.re); t4.re= ( s0.re-s1.re); t4.im= ( s0.im-s1.im); t5.re= ( s2.im-s3.im); t5.im= (-s2.re+s3.re); t6.re= ( s4.re-s5.im); t6.im= ( s4.im+s5.re); t7.re=c*(-s6.re+s6.im+s7.re+s7.im); t7.im=c*(-s6.im-s6.re+s7.im-s7.re); y0[L-1] = (t0.re+t1.re); y0[L ] = (t0.im+t1.im); y1[L-1] = (t2.re+t3.re); y1[L ] = (t2.im+t3.im); y2[L-1] = (t4.re+t5.re); y2[L ] = (t4.im+t5.im);
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