Cosft.cin

// cosft.cin is the C++ numerical implementation of the DiscreteCos transform.

// The input is array; z_type is supposed to be defined as complex(double), although other definition (for example, just double or float) also may have sense for some applications; in the old book Numerical recipes in C, the argument is supposed to be array of float variables.

```#define SWAP(a,b) tempr=(a);(a)=(b);(b)=tempr
void zfour1(z_type data[], unsigned long nn, int isign)
{
unsigned long n,mmax,m,j,istep,i;
double wtemp,wr,wpr,wpi,wi,theta;
z_type tempr,tempi;
n=nn << 1;
j=1;
for(i=1;i<n;i+=2){
if(j>i){SWAP(data[j],data[i]);
SWAP(data[j+1],data[i+1]); }
m=n >> 1;
while (m >= 2 && j > m) { j -= m; m >>= 1; }
j += m;
}
mmax=2;
while(n>mmax)
{ istep=mmax << 1;
theta=isign*(6.28318530717959/mmax);
wtemp=sin(0.5*theta);
wpr = -2.0*wtemp*wtemp;
wpi=sin(theta);
wr=1.0;
wi=0.0;
for(m=1;m<mmax;m+=2)
{for (i=m;i<=n;i+=istep)
{j=i+mmax;
tempr=wr*data[j]-wi*data[j+1];
tempi=wr*data[j+1]+wi*data[j];
data[j]=data[i]-tempr;
data[j+1]=data[i+1]-tempi;
data[i] += tempr;
data[i+1] += tempi;
}
wr=(wtemp=wr)*wpr-wi*wpi+wr;
wi=wi*wpr+wtemp*wpi+wi;
}
mmax=istep;
}
}
#undef SWAP
```
```/* #include <math.h>*/
void zrealft(z_type data[], unsigned long n, int isign)
{ /* void zfour1(z_type data[], unsigned long nn, int isign);*/
unsigned long i,i1,i2,i3,i4,np3;
z_type c1=0.5,c2,h1r,h1i,h2r,h2i;
double wr,wi,wpr,wpi,wtemp,theta;
theta=M_PI/(double) (n>>1);
if(isign == 1){ c2 = -(double)0.5; zfour1(data,n>>1,1);}
else { c2 =  (double)0.5; theta = -theta; }
wtemp=sin((double)0.5*theta);
wpr = -(double)2.0*wtemp*wtemp;
wpi=sin(theta);
wr=(double)1.0+wpr;
wi=wpi; np3=n+3;
for(i=2;i<=(n>>2);i++)
{ i4=1+(i3=np3-(i2=1+(i1=i+i-1)));
h1r=c1*(data[i1]+data[i3]);
h1i=c1*(data[i2]-data[i4]);
h2r = -c2*(data[i2]+data[i4]);
h2i=c2*(data[i1]-data[i3]);
data[i1]=h1r+wr*h2r-wi*h2i;
data[i2]=h1i+wr*h2i+wi*h2r;
data[i3]=h1r-wr*h2r+wi*h2i;
data[i4] = -h1i+wr*h2i+wi*h2r;
wr=(wtemp=wr)*wpr-wi*wpi+wr;
wi=wi*wpr+wtemp*wpi+wi;
}
if (isign == 1){ data[1] = (h1r=data[1])+data[2];
data[2] = h1r-data[2];  }
else { data[1]=c1*((h1r=data[1])+data[2]);
data[2]=c1*(h1r-data[2]);
zfour1(data,n>>1,-1); }
}
```
```void zcosft1(z_type y[], int n)
{ /* void zrealft(z_type data[], unsigned long n, int isign);*/
int j,n2;  z_type sum,y1,y2;
double theta,wi=0.0,wpi,wpr,wr=1.0,wtemp;
theta=M_PI/n;
wtemp=sin(0.5*theta);
wpr = -2.0*wtemp*wtemp;
wpi=sin(theta);
sum=0.5*(y[1]-y[n+1]);
y[1]=0.5*(y[1]+y[n+1]);
n2=n+2;
for (j=2;j<=(n>>1);j++) {
wr=(wtemp=wr)*wpr-wi*wpi+wr;
wi=wi*wpr+wtemp*wpi+wi;
y1=0.5*(y[j]+y[n2-j]);
y2=(y[j]-y[n2-j]);
y[j]=y1-wi*y2;
y[n2-j]=y1+wi*y2;
sum += wr*y2;
}
zrealft(y,n,1);
y[n+1]=y[2];
y[2]=sum;
for(j=4;j<=n;j+=2) {sum += y[j]; y[j]=sum;}
}
```
```void cosft(z_type a[], int N){ int n; DB d; zcosft1(a-1,N); d=sqrt(2./N);  DO(n,N) a[n]*=d; }
```