diff --git a/unsupported/Eigen/src/FFT/ei_kissfft_impl.h b/unsupported/Eigen/src/FFT/ei_kissfft_impl.h
index 9bdc012dd..303f85f13 100644
--- a/unsupported/Eigen/src/FFT/ei_kissfft_impl.h
+++ b/unsupported/Eigen/src/FFT/ei_kissfft_impl.h
@@ -25,16 +25,47 @@ struct kiss_cpx_fft
   std::vector<Complex> m_scratchBuf;
   bool m_inverse;
 
-  inline
-    void make_twiddles(int nfft,bool inverse)
+  inline void make_twiddles(int nfft, bool inverse)
+  {
+    using numext::sin;
+    using numext::cos;
+    m_inverse = inverse;
+    m_twiddles.resize(nfft);
+    double phinc =  0.25 * EIGEN_PI / nfft;
+    Scalar flip = inverse ? Scalar(1) : Scalar(-1);
+    m_twiddles[0] = Complex(Scalar(1), Scalar(0));
+    if ((nfft&1)==0)
+      m_twiddles[nfft/2] = Complex(Scalar(-1), Scalar(0));
+    int i=1;
+    for (;i*8<nfft;++i)
     {
-      using std::acos;
-      m_inverse = inverse;
-      m_twiddles.resize(nfft);
-      Scalar phinc =  (inverse?2:-2)* acos( (Scalar) -1)  / nfft;
-      for (int i=0;i<nfft;++i)
-        m_twiddles[i] = exp( Complex(0,i*phinc) );
+      Scalar c = Scalar(cos(i*8*phinc));
+      Scalar s = Scalar(sin(i*8*phinc));
+      m_twiddles[i] = Complex(c, s*flip);
+      m_twiddles[nfft-i] = Complex(c, -s*flip);
     }
+    for (;i*4<nfft;++i)
+    {
+      Scalar c = Scalar(cos((2*nfft-8*i)*phinc));
+      Scalar s = Scalar(sin((2*nfft-8*i)*phinc));
+      m_twiddles[i] = Complex(s, c*flip);
+      m_twiddles[nfft-i] = Complex(s, -c*flip);
+    }
+    for (;i*8<3*nfft;++i)
+    {
+      Scalar c = Scalar(cos((8*i-2*nfft)*phinc));
+      Scalar s = Scalar(sin((8*i-2*nfft)*phinc));
+      m_twiddles[i] = Complex(-s, c*flip);
+      m_twiddles[nfft-i] = Complex(-s, -c*flip);
+    }
+    for (;i*2<nfft;++i)
+    {
+      Scalar c = Scalar(cos((4*nfft-8*i)*phinc));
+      Scalar s = Scalar(sin((4*nfft-8*i)*phinc));
+      m_twiddles[i] = Complex(-c, s*flip);
+      m_twiddles[nfft-i] = Complex(-c, -s*flip);
+    }
+  }
 
   void factorize(int nfft)
   {