#include <stdio.h>
#include <math.h>

float yreal(float a1, float b1, float c1, float d1, float theta2);
float yimaginary(float a1, float b1, float c1, float d1, float theta2);
int shuffleinorder (float a[8], float b[8], float c[8], float d[8]);

struct complex
{
float real;
float imag;

} ; 



complex MultiplybyTwiddleFactor (float a, float b, int k, int N)
{

struct complex returned;
float Realpart, Imagpart;
float c, d;
float PI= 3.1415926;


c= cos(-k*2.0*PI/N); /* Found a error on July 24, 2014 and corrected */
d= sin(-k*2.0*PI/N);

/* (a + bJ)*(c+ dJ)        */

Realpart= a*c - b*d;
Imagpart= a*d+ b*c;
returned.real= Realpart;
returned.imag= Imagpart;

return (returned);

}

complex complexmult(complex a, complex b)
{

complex product;

product.real=  a.real* b.real- a.real* b.imag;
product.imag=  a.real* b.imag+ a.imag* b.real;

return(product)	;
	
}

int combo32(complex x1[16], complex x2[16])
{

float a[32], b[32];
float e1[32], f1[32];
float theta1;

int i;

for (i= 0; i < 16; i++)
{
printf("x1[%i]=%f\n", i, x1[i].real);
printf("x1[%i]=%f\n", i, x1[i].imag);

}

for (i= 0; i < 16; i++)
{
printf("x2[%i]=%f\n", i, x2[i].real);
printf("x2[%i]=%f\n", i, x2[i].imag);

}



for (i= 0 ; i< 16 ; i++ )
{

theta1 = - 2 * 3.1415926/32* i;

a[i]= yreal(x1[i].real, x1[i].imag, x2[i].real, x2[i].imag, theta1);
b[i]= yimaginary(x1[i].real, x1[i].imag, x2[i].real, x2[i].imag, theta1);



theta1 =  - 2 * 3.1415926/32* i + 3.141592;
/* Output is in linear form , As well */
a[i+16]= yreal(x1[i].real, x1[i].imag, x2[i].real, x2[i].imag, theta1);
b[i+16]= yimaginary(x1[i].real, x1[i].imag, x2[i].real, x2[i].imag, theta1);

}


for (i= 0; i < 32; i++)
{
printf("a[%i]=%f\n", i, a[i]);
printf("b[%i]=%f\n", i, b[i]);

}

printf("decoupled so\n");



printf("real\n");
for (i=0; i< 32; i++)
{
  
printf ("%f\n",a[i]);
}

printf("imaginary\n");
for (i=0; i< 32; i++)
{
  
printf("%f\n",b[i]);
}
}

int backend (float c6[32], float d6[32], float x[32], float y[32])
{




int i,j,N;

int m;

float c1[64];
complex d1[32][4];
float twiddlefactorcoeff;
complex number;

complex Y2[32];
complex sum[32];

complex c[32], d[8][4];
complex s[64];


for (i=0; i< 32; i++)
{
c[i].real=c6[i];
c[i].imag=d6[i];
}

for (i=0; i< 32; i++)
{
printf("c=%f\n", c[i].real);
printf("c=%f\n", c[i].imag);
}






for (m=0; m< 8; m++)

{

for (i=0; i< 4; i++)
{

d[m][i].real=c[8*i+m].real;
d[m][i].imag= c[8*i+m].imag;

}
}


for (m=0; m<8; m++)
{

for (i=0; i< 4; i++)
{
printf("d=%f\n", d[m][i].real);
printf("d=%f\n", d[m][i].imag);
}
}

for (m= 0; m< 8; m++)
{

for (i=0; i< 4; i++)
{

twiddlefactorcoeff= (m*i )%32;
number=  MultiplybyTwiddleFactor( d[m][i].real, d[m][i].imag, twiddlefactorcoeff, 32);
d1[m][i].real= number.real;
d1[m][i].imag= number.imag;
}
}



for (m= 8; m< 16; m++)
{

for (i=0; i< 4; i++)
{

twiddlefactorcoeff= (m*i )%32;
number=  MultiplybyTwiddleFactor( d[m-8][i].real, d[m-8][i].imag, twiddlefactorcoeff, 32);
d1[m][i].real= number.real;
d1[m][i].imag= number.imag;
}
}

for (m=16; m< 24; m++)
{

for (i=0; i< 4; i++)
{
twiddlefactorcoeff= (m*i) %32;
number=  MultiplybyTwiddleFactor( d[m-16][i].real, d[m-16][i].imag, twiddlefactorcoeff, 32);
d1[m][i].real= number.real;
d1[m][i].imag= number.imag;
}
}

for (m=24; m<32; m++)
{

for (i=0; i< 4; i++)
{
twiddlefactorcoeff= (m*i )%32;
number=  MultiplybyTwiddleFactor( d[m-24][i].real, d[m-24][i].imag, twiddlefactorcoeff, 32);
d1[m][i].real= number.real;
d1[m][i].imag= number.imag;
}
}



for (m=0; m< 32; m++)
{

for (i=0; i< 4; i++)
{
printf("d1[%i][%i]= %f\n", m, i, d1[m][i].real);
printf("d1[%i][%i]= %f\n", m, i, d1[m][i].imag);	
}
}

for (m=0; m< 32; m++)
{
sum[m].real= 0.0;
sum[m].imag= 0.0;   
}

for (m=0; m< 32; m++)
{

for (i= 0; i< 4; i++)
{
sum[m].real=d1[m][i].real+ sum[m].real;
sum[m].imag=d1[m][i].imag+ sum[m].imag;
}
}



for (m=0; m< 32; m++)
{

Y2[m].real= sum[m].real;
Y2[m].imag= sum[m].imag;
}





for (m=0; m< 32; m++)
{
printf("Y2[%i].real= %f\n", m, Y2[m].real);
printf("Y2[%i].imag= %f\n", m, Y2[m].imag);

}


 for (m=0; m< 32; m++)
{
x[m]= Y2[m].real;
y[m]= Y2[m].imag;
}

return(3);

}


int combo(complex x1[8], complex x2[8], complex z[16])
{

float a[16], b[16];
float e1[16], f1[16];
float theta1;

int i;

for (i= 0; i < 8; i++)
{
printf("x1[%i]=%f\n", i, x1[i].real);
printf("x1[%i]=%f\n", i, x1[i].imag);

}

for (i= 0; i < 8; i++)
{
printf("x2[%i]=%f\n", i, x2[i].real);
printf("x2[%i]=%f\n", i, x2[i].imag);

}



for (i= 0 ; i< 8 ; i++ )
{

theta1 = - 2 * 3.1415926/16* i;

a[i]= yreal(x1[i].real, x1[i].imag, x2[i].real, x2[i].imag, theta1);
b[i]= yimaginary(x1[i].real, x1[i].imag, x2[i].real, x2[i].imag, theta1);



theta1 =  - 2 * 3.1415926/16* i + 3.141592;
/* Output is in linear form , As well */
a[i+8]= yreal(x1[i].real, x1[i].imag, x2[i].real, x2[i].imag, theta1);
b[i+8]= yimaginary(x1[i].real, x1[i].imag, x2[i].real, x2[i].imag, theta1);

}


for (i= 0; i < 16; i++)
{
printf("a[%i]=%f\n", i, a[i]);
printf("b[%i]=%f\n", i, b[i]);

}

for (i=0; i< 16; i++)
{
z[i].real= a[i];
z[i].imag= b[i];		
}

printf("decoupled so\n");



printf("real\n");
for (i=0; i< 16; i++)
{
  
printf ("%f\n",a[i]);
}

printf("imaginary\n");
for (i=0; i< 16; i++)
{
  
printf("%f\n",b[i]);
}
}


main()
{
      

int i;
float a1[32], b1[32], a2[32], b2[32];
float e1[8], f1[8];
float a[8], b[8];
float a4[32], b4[32];
float x[32], y[32];
int count;
int i1;
int j;
complex x2[8], y2[8], x3[8], y3[8];
FILE *sombrero;

float theta2;

complex z2[16], z3[16];

 
sombrero= fopen( "Card23.IN", "r");



for (i= 0; i< 32; i++)
{
fscanf(sombrero, "%f\n", &a2[i]);
fscanf(sombrero, "%f\n", &b2[i]);

}

fclose(sombrero);



for (i=0; i< 32; i++)
{
printf("a2[%i]= %f\n", i, a2[i]);
printf("b2[%i]= %f\n", i, b2[i]);
	
}

count=0;

for (i=0; i< 16; i++)
{

a1[i]= a2[2*i];
b1[i]= b2[2*i];
}

for (i=0; i< 16; i++)
{

a1[i+16]= a2[2*i+1];
b1[i+16]= b2[2*i+1];
}


/* first shuffle even over odds */



for (i=0; i< 8; i++)
{

a2[i]= a1[2*i];
b2[i]= b1[2*i];
}

for (i=0; i< 8; i++)
{

a2[i+8]= a1[2*i+1];
b2[i+8]= b1[2*i+1];
}
for (i=0; i< 8; i++)
{

a2[i+16]= a1[2*i+16];
b2[i+16]= b1[2*i+16];
}

for (i=0; i< 8; i++)
{

a2[i+24]= a1[2*i+1+16];
b2[i+24]= b1[2*i+1+16];
}




while (count <4)
{

i1= count;

{

e1[0]= a2[0+8*i1];
f1[0]= b2[0+8*i1];
e1[1]= a2[4+8*i1];
f1[1]= b2[4+8*i1];
e1[2]= a2[2+8*i1];
f1[2]= b2[2+8*i1];
e1[3]= a2[6+8*i1];
f1[3]= b2[6+8*i1];
e1[4]= a2[1+8*i1];
f1[4]= b2[1+8*i1];
e1[5]= a2[5+8*i1];
f1[5]= b2[5+8*i1];
e1[6]= a2[3+8*i1];
f1[6]= b2[3+8*i1];
e1[7]= a2[7+8*i1];
f1[7]= b2[7+8*i1];
}

shuffleinorder(e1, f1, a, b);

for (i=0; i< 8; i++)
{

a4[8*i1+i]= a[i];
b4[8*i1+i]= b[i];
}
count= count +1;
}






for (i=0; i< 32; i++)
{
printf("a4[%i]= %f\n", i, a4[i]);
printf("b4[%i]= %f\n", i, b4[i]);
}    


for (i=0; i< 8; i++)
{
x2[i].real= a4[i];
x2[i].imag= b4[i];
y2[i].real= a4[i+8];
y2[i].imag= b4[i+8];
}

for (i=0; i< 8; i++)
{
x3[i].real= a4[i+16];
x3[i].imag= b4[i+16];
y3[i].real= a4[i+8+16];
y3[i].imag= b4[i+8+16];
}



j=combo(x2, y2, z2);
j=combo(x3, y3, z3);

j= combo32(z2, z3);


/*
j= backend(a4, b4, x, y);

for (i=0; i< 32; i++)
{
printf("X[%i].real=%f\n", i, x[i]);
printf("X[%i].imag=%f\n", i, y[i]);
	
}

*/
}

float yreal(float a, float b, float c, float d, float theta1)
{
float sum1;
sum1=0.0;            

sum1= a+ c*cos(theta1)-d*sin(theta1);

return sum1;      
}


float yimaginary(float a, float b, float c, float d, float theta1)
{      
float sum2;
sum2=0.0;       


sum2=b+d*cos(theta1)+c*sin(theta1);


return sum2;      
}


int shuffleinorder (float a[8], float b[8], float c[8], float d[8])


{

float theta1;
int i, j;
float e1[8], f1[8], e[8], f[8];

float y0real, y0imaginary;
float increment, increment2, increment3;

increment= -2* 3.1415926/2.0;
increment2= -2*3.141592/4.0;
increment3= -2* 3.141592/8.0;

for (i=0; i< 8; i++)
{
e1[i]= a[i];
f1[i]= b[i];

}

printf("Input values\n");
for (i= 0; i< 8; i++)
{
printf("e1[%i]=%f\n", i, e1[i]);
printf("f1[%i]=%f\n", i, f1[i]);
}

printf("\n");
for (i= 0; i< 8; i++)
{
e[i]=e1[i];
f[i]=f1[i];

}

for (i= 0; i< 4; i++)

{
theta1=0.0;
y0real=yreal(e[2*i],f[2*i],e[2*i+1],f[2*i+1], theta1);
y0imaginary=yimaginary(e[2*i],f[2*i],e[2*i+1],f[2*i+1], theta1);

e1[2*i]= y0real;
f1[2*i]= y0imaginary;

theta1=increment;
y0real=yreal(e[2*i],f[2*i],e[2*i+1],f[2*i+1], theta1);
y0imaginary=yimaginary(e[2*i],f[2*i],e[2*i+1],f[2*i+1], theta1);

e1[2*i+1]= y0real;
f1[2*i+1]= y0imaginary;
}


printf("After the First Round\n");

for (i=0; i< 8; i++)
{
printf ("e1[%i] = %f\n", i, e1[i]);
printf ("f1[%i] = %f\n", i, f1[i]);
}
printf("\n");

e[0]= e1[0];
f[0]= f1[0];
e[1]= e1[2];
f[1]= f1[2];

e[2]= e1[1];
f[2]= f1[1];
e[3]= e1[3];
f[3]= f1[3];

e[4]= e1[4];
f[4]= f1[4];
e[5]= e1[6];
f[5]= f1[6];

e[6]= e1[5];
f[6]= f1[5];
e[7]= e1[7];
f[7]= f1[7];





for (i=0; i< 2; i++)
{
for(j=0; j< 2; j++)

{

theta1=j*increment2;
y0real=yreal(e[4*i+2*j],f[4*i+2*j],e[4*i+2*j+1],f[4*i+2*j+1], theta1);
y0imaginary=yimaginary(e[4*i+2*j],f[4*i+2*j],e[4*i+2*j+1],f[4*i+2*j+1], theta1);
e1[4*i+2*j]= y0real;
f1[4*i+2*j]= y0imaginary;


theta1=(j+2)*increment2;
y0real=yreal(e[4*i+2*j],f[4*i+2*j],e[4*i+2*j+1],f[4*i+2*j+1], theta1);
y0imaginary=yimaginary(e[4*i+2*j],f[4*i+2*j],e[4*i+2*j+1],f[4*i+2*j+1], theta1);
e1[4*i+2*j+1]= y0real;
f1[4*i+2*j+1]= y0imaginary;
}
}

printf("After the 2nd Round\n");

for (i=0; i< 8; i++)
{
printf ("e1[%i] = %f\n", i, e1[i]);
printf ("f1[%i] = %f\n", i, f1[i]);
}

printf("\n");


e[0]= e1[0];
f[0]= f1[0];
e[1]= e1[2];
f[1]= f1[2];

e[2]= e1[1];
f[2]= f1[1];
e[3]= e1[3];
f[3]= f1[3];

e[4]= e1[4];
f[4]= f1[4];
e[5]= e1[6];
f[5]= f1[6];

e[6]= e1[5];
f[6]= f1[5];
e[7]= e1[7];
f[7]= f1[7];

printf("\n");
printf("Shuffle into linear order \n");
for (i=0; i< 8; i++)
{
printf ("e[%i] = %f\n", i, e[i]);
printf ("f[%i] = %f\n", i, f[i]);
}

printf("\n");


e1[0]= e[0];
f1[0]= f[0];
e1[1]= e[4];
f1[1]= f[4];

e1[2]= e[1];
f1[2]= f[1];
e1[3]= e[5];
f1[3]= f[5];

e1[4]= e[2];
f1[4]= f[2];
e1[5]= e[6];
f1[5]= f[6];

e1[6]= e[3];
f1[6]= f[3];
e1[7]= e[7];
f1[7]= f[7];

for (i=0; i< 4; i++)

{
theta1= i*increment3;

y0real=yreal(e1[2*i],f1[2*i],e1[2*i+1],f1[2*i+1], theta1);
y0imaginary=yimaginary(e1[2*i],f1[2*i],e1[2*i+1],f1[2*i+1], theta1);
e[2*i]= y0real;
f[2*i]= y0imaginary;

theta1= (i+4)*increment3;

y0real=yreal(e1[2*i],f1[2*i],e1[2*i+1],f1[2*i+1], theta1);
y0imaginary=yimaginary(e1[2*i],f1[2*i],e1[2*i+1],f1[2*i+1], theta1);
e[2*i+1]= y0real;
f[2*i+1]= y0imaginary;
}


for (i=0; i< 8; i++)
{
printf ("e[%i] = %f\n", i, e[i]);
printf ("f[%i] = %f\n", i, f[i]);
}

for (i=0; i< 4; i++)
{

c[i]= e[2*i];
d[i]= f[2*i];

c[i+4]= e[2*i+1];
d[i+4]= f[2*i+1];

}

}