#include <math.h>
#define pi 3.141592653589793238462643383279502884197

module PhasePi8 ( qbit bit ) {
    /* PhasePi8 matrix:
       [ [ 1 0    ]
         [ 0 e^i*pi/8 ] ]

	Notes: Can be decomposed as Rz(-pi/8)*[ [e^i*pi/16 0] 
											[0 e^i*pi/16] ]

	 */

	 Rz(bit, pi/8);
}

module cT ( qbit ctrl, qbit target ) {
    /* cT identity matrix:
       [ [ 1 0 0     0    ]
         [ 0 1 0     0    ]
         [ 0 0 1     0    ]
         [ 0 0 0 e^i*pi/4 ] ]
    */

	PhasePi8(ctrl);
	Rz(target,pi/8);
	CNOT(ctrl, target);
	Rz(target,-1*pi/8);
	CNOT(ctrl, target);	
	
}

module cS ( qbit ctrl, qbit target ) {
    /* cS identity matrix:
       [ [ 1 0 0 0 ]
         [ 0 1 0 0 ]
         [ 0 0 1 0 ]
         [ 0 0 0 i ] ]
    */
	
	T(ctrl);
	Rz(target,pi/4);
	CNOT(ctrl, target);
	Rz(target,-1*pi/4);
	CNOT(ctrl, target);
	
}

module cRz ( qbit ctrl, qbit target, const double angle ) {
    /* cRz identity matrix:
       [ [ 1 0 0     			0     ]
         [ 0 1 0     			0     ]
         [ 0 0 e^(-i*angle/2)   0     ]
         [ 0 0 0 				e^(i*angle/2) ] ]
    */

	Rz(target,-1*angle/2);
	CNOT(ctrl, target);
	Rz(target,angle/2);
	CNOT(ctrl, target);
	
}


module qft5 ( qbit bit[5] ) {
    H   ( bit[0] );
    cS  ( bit[0], bit[1] );
    H   ( bit[1] );
    cT  ( bit[0], bit[2] );
    cS  ( bit[1], bit[2] );
    H   ( bit[2] );
    cRz ( bit[0], bit[3], pi/8 );
    cT  ( bit[1], bit[3] );
    cS  ( bit[2], bit[3] );
    H   ( bit[3] );
    cRz ( bit[0], bit[4], pi/16 );
    cRz ( bit[1], bit[4], pi/8 );
    cT  ( bit[2], bit[4] );
    cS  ( bit[3], bit[4] );
    H   ( bit[4] );
}

int main () {
    qbit reg[5];
    cbit out[5];
    int i;

    for ( i = 0; i < 5; i++ ) {
        PrepZ( reg[i],0 );
    }
    qft5( reg );
    for ( i = 0; i < 5; i++ ) {
	H(reg[i]);
        out[i] = MeasZ( reg[i] );
    }
    return 0;
}