don't store second half of unit circle

pocketfft_hdronly.h

@@ -438,6 +438,7 @@ template<typename T> class sincos_2pibyn
   {
   private:
     using Thigh = typename conditional<(sizeof(T)>sizeof(double)), T, double>::type;
+    size_t sz;
     arr<cmplx<T>> data;
 
     POCKETFFT_NOINLINE void calc_first_octant(size_t den,
@@ -474,8 +475,8 @@ template<typename T> class sincos_2pibyn
 
     void calc_first_quadrant(size_t n, cmplx<T> * POCKETFFT_RESTRICT res)
       {
-      cmplx<T> * POCKETFFT_RESTRICT p = res+n/2; // n is always even here
-      calc_first_octant(n<<1, p);
+      arr<cmplx<T>> p(n/2); // n is always even here
+      calc_first_octant(n<<1, p.data());
       size_t ndone=(n+2)>>2;
       size_t i=0, idx1=0, idx2=ndone-1;
       for (; i+1<ndone; i+=2, ++idx1, --idx2)
@@ -490,8 +491,8 @@ template<typename T> class sincos_2pibyn
     void calc_first_half(size_t n, cmplx<T> * POCKETFFT_RESTRICT res)
       {
       int ndone=int(n+1)>>1;
-      cmplx<T> * p = res+(n-1)/2; // n is always odd here
-      calc_first_octant(n<<2, p);
+      arr<cmplx<T>> p((n+1)/2); // n is always odd here
+      calc_first_octant(n<<2, p.data());
       int i4=0, in=int(n), i=0;
       for (; i4<=in-i4; ++i, i4+=4) // octant 0
         res[i] = p[i4];
@@ -522,16 +523,7 @@ template<typename T> class sincos_2pibyn
       else
         for (size_t i=1, j=half-1; 2*i<half; ++i, --j)
           res[j].Set(-res[i].r, res[i].i);
-      }
-
-    void fill_second_half(size_t n, cmplx<T> * POCKETFFT_RESTRICT res)
-      {
-      if ((n&1)==0)
-        for (size_t i=0; i<n/2; ++i)
-          res[i+n/2].Set(-res[i].r, -res[i].i);
-      else
-        for (size_t i=1, j=n-1; 2*i<n; ++i, --j)
-          res[j].Set(res[i].r, -res[i].i);
+      res[half].Set(T(-1),T(0));
       }
 
     POCKETFFT_NOINLINE void sincos_2pibyn_half(size_t n, cmplx<T> * POCKETFFT_RESTRICT res)
@@ -552,14 +544,18 @@ template<typename T> class sincos_2pibyn
       }
 
   public:
-    POCKETFFT_NOINLINE sincos_2pibyn(size_t n, bool half)
-      : data(n)
+    POCKETFFT_NOINLINE sincos_2pibyn(size_t n)
+      : sz(n), data(n/2+1)
+      { sincos_2pibyn_half(n, data.data()); }
+
+    cmplx<T> operator[](size_t idx) const
       {
-      sincos_2pibyn_half(n, data.data());
-      if (!half) fill_second_half(n, data.data());
+      if (idx<data.size())
+        return data[idx];
+      auto c = data[sz-idx];
+      c.i = -c.i;
+      return c;
       }
-
-    cmplx<T> operator[](size_t idx) const { return data[idx]; }
   };
 
 struct util // hack to avoid duplicate symbols
@@ -1613,7 +1609,7 @@ template<bool fwd, typename T> void pass_all(T c[], T0 fct) const
 
     void comp_twiddle()
       {
-      sincos_2pibyn<T0> twiddle(length, false);
+      sincos_2pibyn<T0> twiddle(length);
       size_t l1=1;
       size_t memofs=0;
       for (size_t k=0; k<fact.size(); ++k)
@@ -2421,7 +2417,7 @@ template<typename T> void radbg(size_t ido, size_t ip, size_t l1,
 
     void comp_twiddle()
       {
-      sincos_2pibyn<T0> twid(length, true);
+      sincos_2pibyn<T0> twid(length);
       size_t l1=1;
       T0 *ptr=mem.data();
       for (size_t k=0; k<fact.size(); ++k)
@@ -2515,7 +2511,7 @@ template<typename T0> class fftblue
         bk(mem.data()), bkf(mem.data()+n)
       {
       /* initialize b_k */
-      sincos_2pibyn<T0> tmp(2*n, false);
+      sincos_2pibyn<T0> tmp(2*n);
       bk[0].Set(1, 0);
 
       size_t coeff=0;