请问我写的快速傅立叶变换的逆变换哪里错了？

正向变换是正确的了，我测试过，但是逆变换出错了？请问问题在哪里？
ComplexNumber是复数的类，实现了复数的加减乘除法以及求倒数的运算。
using System;
using System.Collections.Generic;
using System.Text;
using ComplexNumber;using CN =  ComplexNumber.ComplexNumber;namespace FFT
{
    public class FFT
    {
        
        public static CN[] FastFourierTransformation(CN[] a, bool direct)
        {
            CN[] y=new CN[a.Length];
            if (a.Length == 1)
            {
                y[0] = a[0].Clone();
                return y;
            }
            CN[] y0 = new CN[a.Length / 2];
            CN[] y1 = new CN[a.Length / 2];
            CN[] a0 = new CN[a.Length / 2];
            CN[] a1 = new CN[a.Length / 2];
            for (int i = 0; i < a.Length / 2; i++)
            {
                a0[i] = a[2 * i];
                a1[i] = a[2 * i + 1];
            }
            y0 = FastFourierTransformation(a0,direct);
            y1 = FastFourierTransformation(a1,direct);
            CN wn = CN.GetRootOfUnity(a.Length);
            if (direct == false)
                wn = wn.Invert();
            CN w=(CN)1;
            for (int i = 0; i < a.Length / 2; i++)
            {
                w *= wn;
                y[i] = y0[i] + y1[i] * w;
                y[i + a.Length / 2] = y0[i] - w * y1[i];
            }
            if (direct == false)
            {
                for (int i = 0; i < y.Length; i++)
                    y[i] /= (CN)y.Length;
            }
            return y;        }
    }
}namespace FFT
{
    class Program
    {
        static void Main(string[] args)
        {
            double[] a = { 1, 2, 3, 1 };
            double[] c = { 3, 2, 1, 2 };
            ComplexNumber.ComplexNumber[] b = new ComplexNumber.ComplexNumber[a.Length];
            for (int i = 0; i < a.Length; i++)
                b[i] = (ComplexNumber.ComplexNumber)a[i];
            ComplexNumber.ComplexNumber[] d = new ComplexNumber.ComplexNumber[c.Length];
            for (int i = 0; i < a.Length; i++)
                d[i] = (ComplexNumber.ComplexNumber)c[i];
            ComplexNumber.ComplexNumber[] e = FFT.FastFourierTransformation(b, true);
            ComplexNumber.ComplexNumber[] f = FFT.FastFourierTransformation(d, true);            ComplexNumber.ComplexNumber[] g = FFT.FastFourierTransformation(e, false);
        }
    }
}
下面是ComplexNumber类的实现，也许会用到，不过应该是没有什么问题的：
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;namespace ComplexNumber
{
    public class ComplexNumber
    {
        public static double Error = 1e-20;
        public static ComplexNumber GetRootOfUnity(int n)
        {
            ComplexNumber c = new ComplexNumber(Math.Cos(2*Math.PI / n), Math.Sin(2*Math.PI / n));
            return c;
        }
        double RealPart;
        double ImaginaryPart;
        public ComplexNumber(double pReal, double pImaginary)
        {
            RealPart = pReal;
            ImaginaryPart = pImaginary;
        }        public ComplexNumber()
            : this(0, 0)
        {        }        public double Modulus { get { return Math.Sqrt(RealPart*RealPart + ImaginaryPart*ImaginaryPart); } }
        public static explicit operator ComplexNumber(double d)
        {
            ComplexNumber c = new ComplexNumber(d, 0);
            return c;
        }        public static ComplexNumber operator +(ComplexNumber a, ComplexNumber b)
        {
            ComplexNumber c = new ComplexNumber();
            c.RealPart = a.RealPart + b.RealPart;
            c.ImaginaryPart = a.ImaginaryPart + b.ImaginaryPart;
            return c;
        }
        public static ComplexNumber operator -(ComplexNumber a, ComplexNumber b)
        {
            ComplexNumber c = new ComplexNumber();
            c.RealPart = a.RealPart - b.RealPart;
            c.ImaginaryPart = a.ImaginaryPart - b.ImaginaryPart;
            return c;
        }        public static bool operator ==(ComplexNumber a,double b)
        {
            if (Math.Abs(a.ImaginaryPart) <=Error && Math.Abs(a.RealPart -b)<=Error)
                return true;
            return false;
        }        public static bool operator ==(ComplexNumber a,ComplexNumber b)
        {
            if (Math.Abs(a.ImaginaryPart-b.ImaginaryPart) <= Error && Math.Abs(a.RealPart - b.RealPart) <= Error)
                return true;
            return false;
        }        public static bool operator !=(ComplexNumber a, double b)
        {
            if (a == b)
                return false;
            return true;
        }        public static bool operator !=(ComplexNumber a, ComplexNumber b)
        {
            return !(a == b);
        }        public static ComplexNumber operator *(ComplexNumber a, ComplexNumber b)
        {
            ComplexNumber c = new ComplexNumber();
            c.RealPart = a.RealPart * b.RealPart - a.ImaginaryPart * b.ImaginaryPart;
            c.ImaginaryPart = a.RealPart * b.ImaginaryPart + a.ImaginaryPart * b.RealPart;
            return c;
        }
        public ComplexNumber Invert()
        {
            ComplexNumber a = new ComplexNumber();
            if (Math.Abs(ImaginaryPart) <= Error && Math.Abs(RealPart) <= Error)
                throw (new ArgumentException("0 can not be inverted"));
            a.ImaginaryPart = -ImaginaryPart / (RealPart * RealPart + ImaginaryPart * ImaginaryPart);
            a.RealPart = RealPart / (RealPart * RealPart + ImaginaryPart * ImaginaryPart);
            return a;
        }
        public ComplexNumber Clone()
        {
            ComplexNumber c = new ComplexNumber(RealPart, ImaginaryPart);
            return c;
        }        public static ComplexNumber operator /(ComplexNumber a, ComplexNumber b)
        {
            ComplexNumber c = b.Invert();
            return a*c;
        }       
    }
}