add (preliminary) type IV transforms

pocketfft_hdronly.h

@@ -2416,6 +2416,36 @@ template<typename T0> class T_dct3
     size_t length() const { return fftplan.length(); }
   };
 
+template<typename T0> class T_dct4
+  {
+  private:
+    T_dct2<T0> dct2;
+    arr<T0> C;
+
+  public:
+    POCKETFFT_NOINLINE T_dct4(size_t length)
+      : dct2(length), C(length)
+      {
+      constexpr T0 pi = T0(3.141592653589793238462643383279502884197L);
+      for (size_t i=0; i<length; ++i)
+        C[i] = cos(T0(0.5)*pi*(T0(i)+T0(0.5))/T0(length));
+      }
+
+    template<typename T> POCKETFFT_NOINLINE void exec(T c[], T0 fct) const
+      {
+      // FIXME: due to the recurrence below, the algorithm is not very accurate
+      // Trying to find a better one...
+      size_t N = length();
+      for (size_t i=0; i<N; ++i)
+        c[i] *= C[i];
+      dct2.exec(c, fct);
+      for (size_t i=1; i<N; ++i)
+        c[i] = 2*c[i] - c[i-1];
+      }
+
+    size_t length() const { return dct2.length(); }
+  };
+
 template<typename T0> class T_dst1
   {
   private:
@@ -2456,7 +2486,6 @@ template<typename T0> class T_dst2
       {
       size_t N=length();
       if (N==1) { c[0]*=2*fct; return; }
-
       for (size_t k=1; k<N; k+=2)
         c[k] = -c[k];
       dct.exec(c, fct);
@@ -2491,6 +2520,30 @@ template<typename T0> class T_dst3
     size_t length() const { return dct.length(); }
   };
 
+template<typename T0> class T_dst4
+  {
+  private:
+    T_dct4<T0> dct;
+
+  public:
+    POCKETFFT_NOINLINE T_dst4(size_t length)
+      : dct(length) {}
+
+    template<typename T> POCKETFFT_NOINLINE void exec(T c[], T0 fct)
+      {
+      size_t N=length();
+      //if (N==1) { c[0]*=fct; return; }
+      size_t NS2 = N/2;
+      for (size_t k=0, kc=N-1; k<NS2; ++k, --kc)
+        swap(c[k], c[kc]);
+      dct.exec(c, fct);
+      for (size_t k=1; k<N; k+=2)
+        c[k] = -c[k];
+      }
+
+    size_t length() const { return dct.length(); }
+  };
+
 
 //
 // multi-D infrastructure
@@ -3256,6 +3309,8 @@ template<typename T> void r2r_dct(const shape_t &shape,
     general_dcst<T_dct2<T>>(ain, aout, axes, fct, nthreads);
   else if (type==3)
     general_dcst<T_dct3<T>>(ain, aout, axes, fct, nthreads);
+  else if (type==4)
+    general_dcst<T_dct4<T>>(ain, aout, axes, fct, nthreads);
   else
     throw runtime_error("unsupported DCT type");
   }
@@ -3275,6 +3330,8 @@ template<typename T> void r2r_dst(const shape_t &shape,
     general_dcst<T_dst2<T>>(ain, aout, axes, fct, nthreads);
   else if (type==3)
     general_dcst<T_dst3<T>>(ain, aout, axes, fct, nthreads);
+  else if (type==4)
+    general_dcst<T_dst4<T>>(ain, aout, axes, fct, nthreads);
   else
     throw runtime_error("unsupported DST type");
   }

test.py

@@ -221,3 +221,22 @@ def testdcst1D(len, inorm, type):
     _assert_close(a, pypocketfft.r2r_dst(pypocketfft.r2r_dst(c, inorm=inorm, type=type), inorm=2-inorm, type=itype), 2e-18)
     _assert_close(a, pypocketfft.r2r_dst(pypocketfft.r2r_dst(a, inorm=inorm, type=type), inorm=2-inorm, type=itype), 1.5e-15)
     _assert_close(b, pypocketfft.r2r_dst(pypocketfft.r2r_dst(b, inorm=inorm, type=type), inorm=2-inorm, type=itype), 6e-7)
+
+
+# TEMPORARY: separate test for DCT/DST IV, since they are less accurate
+@pmp("len", len1D)
+@pmp("inorm", [0, 1, 2])
+@pmp("type", [4])
+def testdcst1D4(len, inorm, type):
+    a = np.random.rand(len)-0.5
+    b = a.astype(np.float32)
+    c = a.astype(np.float128)
+    itp = (0, 1, 3, 2, 4)
+    itype = itp[type]
+    if type != 1 or len > 1:
+        _assert_close(a, pypocketfft.r2r_dct(pypocketfft.r2r_dct(c, inorm=inorm, type=type), inorm=2-inorm, type=itype), 2e-16)
+        _assert_close(a, pypocketfft.r2r_dct(pypocketfft.r2r_dct(a, inorm=inorm, type=type), inorm=2-inorm, type=itype), 1.5e-13)
+        _assert_close(b, pypocketfft.r2r_dct(pypocketfft.r2r_dct(b, inorm=inorm, type=type), inorm=2-inorm, type=itype), 6e-5)
+    _assert_close(a, pypocketfft.r2r_dst(pypocketfft.r2r_dst(c, inorm=inorm, type=type), inorm=2-inorm, type=itype), 2e-16)
+    _assert_close(a, pypocketfft.r2r_dst(pypocketfft.r2r_dst(a, inorm=inorm, type=type), inorm=2-inorm, type=itype), 1.5e-13)
+    _assert_close(b, pypocketfft.r2r_dst(pypocketfft.r2r_dst(b, inorm=inorm, type=type), inorm=2-inorm, type=itype), 6e-5)