Two vectors A and B. how to get a quaternion representing the rotation from A to B?

FromeTwoVector.cc

Template typename<T>
struct quaternion{
 T w,x,y,z;
};
struct _vec3{
  T x,y,z;
};
typedef quaternion quat ;
typedef _vec3 vec3;

quat FromTwoVector(vec3 A, vec3 B)
{
  vec3 delta = (A - B).normalize();
  float dot = dot( A, B);
  vec3 half = (A + B).normalize();
  quat dq;
  if(dot>=1.0f) dq = quat(1,0.0,0.0,0.0);//that means A = B that is colinear but diffient direction, 
  else if(dot <1e-6f - 1.0f)
  {
    	// that means two vector A = - B, colinear but diffient direction
	float c = dot(A, vec3(1, 0, 0));
	if (c < 1e-6f - 1.0f)
	{
		dq = quat(0,cross(A, vec3(0, 1, 0)));
	}
	dq = quat(0,cross(A, vec3(1, 0, 0)));
  }
  else
  {
    dq = quat(dot(from, half), cross(from, half));
  }
}

Two vectors from and to. how to get a quaternion representing the rotation from A to B?
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