FFT二分蝶计算
G-Spider @2011 初始版。
void butterfly(unsigned int l,int flag,double *x,double *y)
{
//flag=1 ,fft
//flag=-1,ifft
unsigned int i,j,r,tmpi,m1,m2,m3,m4,m5,N,N0,k1,k2;
double N_1,u,v,tmptheta;
N=(unsigned int)1<<l;
N0=N>>2;
N_1=1.0/(double)N;
tmptheta=_2PI*N_1;
if(flag==-1)
{
for(i=0;i<N;i++)
{
y[i]=-y[i];
}
}
//======================================================
//得到正余弦表
Arrsin[0]=0.0;
Arrcos[0]=1.0;
Arrsin[1]=sin(tmptheta);
Arrcos[1]=cos(tmptheta);
if(l>1)
{
for(i=2;i<=N0;i+=2)
{//i=2,4,6,....
tmpi=i>>1;
Arrsin[i]= 2.0* Arrsin[tmpi] * Arrcos[tmpi];
Arrcos[i]=1.0- 2.0* Arrsin[tmpi] * Arrsin[tmpi];
//======================================================
Arrsin[i+1]= Arrcos[i] * Arrsin[1] + Arrsin[i] * Arrcos[1];
Arrcos[i+1]=-Arrsin[i] * Arrsin[1] + Arrcos[i] * Arrcos[1];
//printf("%18.16lf %18.16lf/n",Arrsin[i],Arrcos[i]);
}
N0<<=1;
for(;i<N0;i+=2)
{//i=N0'+2,N0'+4,N0'+6,....,N0 (N0'=N0/2)
//sin(pi/2 -x)=cos(x); sin(N0-i)=cos(i);
//cos(pi/2-x)=sin(x); cos(N0-i)=sin(i);
tmpi=N0-i;
Arrsin[i]=Arrcos[tmpi];
Arrcos[i]=Arrsin[tmpi];
//======================================================
tmpi--;
Arrsin[i+1]=Arrcos[tmpi];
Arrcos[i+1]=Arrsin[tmpi];
}
}
//======================================================
//二分蝶计算
for(j=0;j<l;)
{
m1=(unsigned int)1<<j++;
m2=m1<<1;
m3=N>>j;
m4=0;
for(i=0;i<m3;i++)
{
m5=0;
for(r=0;r<=(m1>>1);r++)
{
k1=m4+r;
k2=k1+m1;
u=x[k2]*Arrcos[m5]+y[k2]*Arrsin[m5];
v=y[k2]*Arrcos[m5]-x[k2]*Arrsin[m5];
x[k2]=x[k1]-u;
x[k1]=x[k1]+u;
y[k2]=y[k1]-v;
y[k1]=y[k1]+v;
m5+=m3;
}
m5=m3;
for(;r<m1;r++)
{
k1=m4+r;
k2=k1+m1;
u=y[k2]*Arrcos[m5]-x[k2]*Arrsin[m5];
v=-(y[k2]*Arrsin[m5]+x[k2]*Arrcos[m5]);
x[k2]=x[k1]-u;
x[k1]=x[k1]+u;
y[k2]=y[k1]-v;
y[k1]=y[k1]+v;
m5+=m3;
}
m4+=m2;
}
}
//======================================================
//逆变换
if(flag==-1)
{
for(i=0;i<N;i++)
{
x[i]= x[i]*N_1;
y[i]=-y[i]*N_1;
}
}
}
//======================
//动态分配
void butterfly(unsigned int l,int flag,double *x,double *y)
{
//flag=1 ,fft
//flag=-1,ifft
unsigned int i,j,r,tmpi,m1,m2,m3,m4,m5,N,N0,k1,k2;
double N_1,u,v,tmptheta,*Arrsin=NULL,*Arrcos=NULL;
N=(unsigned int)1<<l;
N0=N>>2;
N_1=1.0/(double)N;
tmptheta=_2PI*N_1;
if(flag==-1)
{
for(i=0;i<N;i++)
{
y[i]=-y[i];
}
}
//======================================================
//得到正余弦表
Arrsin=(double *)malloc( ((N>>1)+1)*sizeof(double) );
Arrcos=(double *)malloc( ((N>>1)+1)*sizeof(double) );
if(Arrsin==NULL || Arrcos==NULL)
printf("Memory Allocated Error/n");
Arrsin[0]=0.0;
Arrcos[0]=1.0;
Arrsin[1]=sin(tmptheta);
Arrcos[1]=cos(tmptheta);
if(l>1)
{
for(i=2;i<=N0;i+=2)
{//i=2,4,6,....
tmpi=i>>1;
Arrsin[i]= 2.0* Arrsin[tmpi] * Arrcos[tmpi];
Arrcos[i]=1.0- 2.0* Arrsin[tmpi] * Arrsin[tmpi];
//======================================================
Arrsin[i+1]= Arrcos[i] * Arrsin[1] + Arrsin[i] * Arrcos[1];
Arrcos[i+1]=-Arrsin[i] * Arrsin[1] + Arrcos[i] * Arrcos[1];
}
N0<<=1;
for(;i<N0;i+=2)
{//i=N0'+2,N0'+4,N0'+6,....,N0 (N0'=N0/2)
//sin(pi/2 -x)=cos(x); sin(N0-i)=cos(i);
//cos(pi/2-x)=sin(x); cos(N0-i)=sin(i);
tmpi=N0-i;
Arrsin[i]=Arrcos[tmpi];
Arrcos[i]=Arrsin[tmpi];
//======================================================
tmpi--;
Arrsin[i+1]=Arrcos[tmpi];
Arrcos[i+1]=Arrsin[tmpi];
}
}
//======================================================
//二分蝶计算
for(j=0;j<l;)
{
m1=(unsigned int)1<<j++;
m2=m1<<1;
m3=N>>j;
m4=0;
for(i=0;i<m3;i++)
{
m5=0;
for(r=0;r<=(m1>>1);r++)
{
k1=m4+r;
k2=k1+m1;
u=x[k2]*Arrcos[m5]+y[k2]*Arrsin[m5];
v=y[k2]*Arrcos[m5]-x[k2]*Arrsin[m5];
x[k2]=x[k1]-u;
x[k1]=x[k1]+u;
y[k2]=y[k1]-v;
y[k1]=y[k1]+v;
m5+=m3;
}
m5=m3;
for(;r<m1;r++)
{
k1=m4+r;
k2=k1+m1;
u=y[k2]*Arrcos[m5]-x[k2]*Arrsin[m5];
v=-(y[k2]*Arrsin[m5]+x[k2]*Arrcos[m5]);
x[k2]=x[k1]-u;
x[k1]=x[k1]+u;
y[k2]=y[k1]-v;
y[k1]=y[k1]+v;
m5+=m3;
}
m4+=m2;
}
}
//======================================================
//逆变换
if(flag==-1)
{
for(i=0;i<N;i++)
{
x[i]= x[i]*N_1;
y[i]=-y[i]*N_1;
}
}
}