int main(){
int k, n, N, p, q, r;
double *y_r, *y_i, *x_r, *x_i, w_r, w_i;
printf("Please input p q r=");
scanf("%d %d %d", &p, &q, &r);
N = Generate_N(p, q, r);
printf("N=2^%d 3^%d 5^%d = %d\n",p,q,r,N);
x_r = (double *) malloc(N*sizeof(double));
x_i = (double *) malloc(N*sizeof(double));
y_r = (double *) malloc(N*sizeof(double));
y_i = (double *) malloc(N*sizeof(double));
Initial(x_r, x_i, N);
FFTv3(x_r, x_i, y_r, y_i, N);
/*
for(int i=0;i<N;++i){
printf("%f\n",y_r[i]);
}
*/
Print_Complex_Vector(y_r, y_i, N);
return 0;
}
int main()
{
int k, n, p, q, r, N;
double *y_r, *y_i, *x_r, *x_i, w_r, w_i;
clock_t t1, t2;
printf("Please input p q r=");
scanf("%d %d %d", &p, &q, &r);
N = Generate_N(p, q, r);
printf("N=2^%d 3^%d 5^%d = %d\n",p,q,r,N);
x_r = (double *) malloc(N*sizeof(double));
x_i = (double *) malloc(N*sizeof(double));
y_r = (double *) malloc(N*sizeof(double));
y_i = (double *) malloc(N*sizeof(double));
Initial(x_r, x_i, N);
t1 = clock();
FFTr3(x_r, x_i, y_r, y_i, N);
t2 = clock();
printf("Fast FT3: %f secs\n", 1.0*(t2-t1)/CLOCKS_PER_SEC);
// Print_Complex_Vector(y_r, y_i, N);
return 0;
}
int main()
{
int i, k, n, p, q, r, N;
double *y_r, *y_i, *x_r, *x_i, *z_r, *z_i, w_r, w_i, everage, *t;
clock_t t1, t2;
printf("Please input p q r=");
scanf("%d %d %d", &p, &q, &r);
N = Generate_N(p, q, r);
printf("N=2^%d 3^%d 5^%d = %d\n",p,q,r,N);
z_r = (double *) malloc(N*sizeof(double));
z_i = (double *) malloc(N*sizeof(double));
x_r = (double *) malloc(N*sizeof(double));
x_i = (double *) malloc(N*sizeof(double));
y_r = (double *) malloc(N*sizeof(double));
y_i = (double *) malloc(N*sizeof(double));
t = (double *) malloc(20*sizeof(double));
Initial(x_r, x_i, N);
int m=20;
for(i=0;i<m;i++)
{
t1 = clock();
FFT(x_r, x_i, y_r, y_i, z_r, z_i, p, q, r);
t2 = clock();
t[i] = 1.0*(t2-t1)/CLOCKS_PER_SEC;
printf("Fast FTT: %f secs\n", 1.0*(t2-t1)/CLOCKS_PER_SEC);
}
everage = 0;
for(i=0;i<m;i++)
{
everage = everage + t[i];
}
everage = everage / m;
printf("everage time: %f \n", everage);
// Print_Complex_Vector(y_r, y_i, N);
return 0;
}
int FFT(double *x_r, double *x_i, double *y_r, double *y_i,double *z_r, double *z_i, int p, int q, int r)
{
//bit-reverse
int i, j, pp, qq, bse, N, M;
N = 1;
N = Generate_N(p, q, r);
for(i=0;i<N;i++)
{
y_r[i]=x_r[i];
y_i[i]=x_i[i];
}
for(i=0;i<N;i++)
{
z_r[i]=y_r[i];
z_i[i]=y_i[i];
}
j=0;
for(i=1;i<N;i++)
{
M=N;
if(p==0)
{
if(q==0)
{
//(0,0,r)
j = j + M/5;
while(j >= M & M > 1)
{
j=j-M;
M=M/5;
j=j+M/5;
}
}
else
{
if(r==0)
{
//(0,q,0)
j=j+M/3;
while(j>=M)
{
j=j-M;
M=M/3;
j=j+M/3;
}
}
else
{
//(0,q,r);
bse=3;
qq=q;
j=j+M/bse;
while(j>=M)
{
j=j-M;
M=M/bse;
qq=qq-1;
if(qq==0) bse=5;
j=j+M/bse;
}
}
}
}
else
{
if(q==0)
{
if(r==0)
{
//(p,0,0)
j=j+M/2;
while(j>=M)
{
j=j-M;
M=M/2;
j=j+M/2;
}
}
else
{
//(p,0,r)
bse=2;
pp=p;
j=j+M/bse;
while(j>=M)
{
j=j-M;
M=M/bse;
pp=pp-1;
if(pp==0) bse=5;
j=j+M/bse;
}
}
}
else
{
if(r==0)
{
//(p,q,0)
bse=2;
pp=p;
j=j+M/bse;
while(j>=M)
{
j=j-M;
M=M/bse;
pp=pp-1;
if(pp==0) bse=3;
j=j+M/bse;
}
}
else
{
//(p,q,r)
pp=p;
qq=q;
j=j+M/2;
while(j>=M)
{
j=j-M;
M=M/2;
pp=pp-1;
if(pp>0) j=j+M/2;
else
{
j=j+M/3;
while(j>=M)
{
j=j-M;
M=M/3;
qq=qq-1;
if(qq>0) j=j+M/3;
else
{
j=j+M/5;
while(j>=M)
{
j=j-M;
M=M/3;
j=j+M/5;
}
}
}
}
}
}
}
}
y_r[i]=z_r[j];
y_i[i]=z_i[j];
}
//Butterfly structure
int P, Q, R;
P = pow(2,p);
Q = pow(3,q);
//p != 0
if(p > 0)
{
double theta, w_br, w_bi, a_r, a_i;
int k, n, pp;
pp = 0;
n = 2;
while(pp < p & p > 0)
{
for(k=0;k<n/2;k++)
{
theta = -2.0*k*M_PI/n;
w_br = cos(theta);
w_bi = sin(theta);
for(i=k;i<N;i+=n)
{
j = i + n/2;
a_r = w_br * y_r[j] - w_bi * y_i[j];
a_i = w_br * y_i[j] + w_bi * y_r[j];
y_r[j] = y_r[i] - a_r;
y_i[j] = y_i[i] - a_i;
y_r[i] = y_r[i] + a_r;
y_i[i] = y_i[i] + a_i;
}
}
n = n * 2;
pp = pp + 1;
}
}
// q != 0
if(q > 0)
{
double theta, w_br, w_bi, w_cr, w_ci, a_r, a_i, b_r, b_i, c_r, c_i, s;
int l, k, n, m, qq;
qq = 0;
n = 3*P;
s = sqrt(3)/2;
while(qq < q & q > 0)
{
for(k=0;k<n/3;k++)
{
theta = -2.0*k*M_PI/n;
w_br = cos(theta);
w_bi = sin(theta);
w_cr = cos(2*theta);
w_ci = sin(2*theta);
for(i=k;i<N;i+=n)
{
j = i + n/3;
l = j + n/3;
a_r = y_r[i];
a_i = y_i[i];
b_r = w_br * y_r[j] - w_bi * y_i[j];
b_i = w_br * y_i[j] + w_bi * y_r[j];
c_r = w_cr * y_r[l] - w_ci * y_i[l];
c_i = w_cr * y_i[l] + w_ci * y_r[l];
y_r[i] = a_r + b_r + c_r;
y_i[i] = a_i + b_i + c_i;
y_r[j] = a_r - (b_r + c_r)/2 + (b_i - c_i) * s;
y_i[j] = a_i - (b_i + c_i)/2 - (b_r - c_r) * s;
y_r[l] = a_r - (b_r + c_r)/2 - (b_i - c_i) * s;
y_i[l] = a_i - (b_i + c_i)/2 + (b_r - c_r) * s;
}
}
n = n * 3;
qq = qq + 1;
}
}
if(r > 0)
{
double a, b, c, d, theta, w_br, w_bi, w_cr, w_ci, w_dr, w_di, w_er, w_ei, a_r, a_i, b_r, b_i, c_r, c_i, d_r, d_i, e_r, e_i;
int f, g, h, n, k, rr;
rr = 0;
n = 5*Q*P;
a = cos(2.0*M_PI/5);
b = sin(2.0*M_PI/5);
c = -cos(4.0*M_PI/5);
d = sin(4.0*M_PI/5);
while(rr < r & r > 0)
{
for(k=0;k<n/5;k++)
{
theta = -2.0*k*M_PI/n;
w_br = cos(theta);
w_bi = sin(theta);
w_cr = cos(2.0*theta);
w_ci = sin(2.0*theta);
w_dr = cos(3.0*theta);
w_di = sin(3.0*theta);
w_er = cos(4.0*theta);
w_ei = sin(4.0*theta);
for(i=k;i<N;i+=n)
{
j = i + n/5;
f = j + n/5;
g = f + n/5;
h = g + n/5;
a_r = y_r[i];
a_i = y_i[i];
b_r = (y_r[j] * w_br - y_i[j] * w_bi);
b_i = (y_r[j] * w_bi + y_i[j] * w_br);
c_r = (y_r[f] * w_cr - y_i[f] * w_ci);
c_i = (y_r[f] * w_ci + y_i[f] * w_cr);
d_r = (y_r[g] * w_dr - y_i[g] * w_di);
d_i = (y_r[g] * w_di + y_i[g] * w_dr);
e_r = (y_r[h] * w_er - y_i[h] * w_ei);
e_i = (y_r[h] * w_ei + y_i[h] * w_er);
y_r[i] = a_r + b_r + c_r + d_r + e_r;
y_i[i] = a_i + b_i + c_i + d_i + e_i;
y_r[j] = a_r + (a * (b_r + e_r) - c * (c_r + d_r)) + (b * (b_i - e_i) + d * (c_i - d_i));
y_i[j] = a_i + (a * (b_i + e_i) - c * (c_i + d_i)) - (b * (b_r - e_r) + d * (c_r - d_r));
y_r[f] = a_r - (c * (b_r + e_r) - a * (c_r + d_r)) + (d * (b_i - e_i) - b * (c_i - d_i));
y_i[f] = a_i - (c * (b_i + e_i) - a * (c_i + d_i)) - (d * (b_r - e_r) - b * (c_r - d_r));
y_r[g] = a_r - (c * (b_r + e_r) - a * (c_r + d_r)) - (d * (b_i - e_i) - b * (c_i - d_i));
y_i[g] = a_i - (c * (b_i + e_i) - a * (c_i + d_i)) + (d * (b_r - e_r) - b * (c_r - d_r));
y_r[h] = a_r + (a * (b_r + e_r) - c * (c_r + d_r)) - (b * (b_i - e_i) + d * (c_i - d_i));
y_i[h] = a_i + (a * (b_i + e_i) - c * (c_i + d_i)) + (b * (b_r - e_r) + d * (c_r - d_r));
}
}
n = n * 5;
rr = rr + 1;
}
}
}
