first experiments with DCT/DST type 2/3

pocketfft_hdronly.h

@@ -2276,6 +2276,144 @@ template<typename T0> class pocketfft_r
     size_t length() const { return len; }
   };
 
+
+//
+// sine/cosine transforms
+//
+
+template<typename T0> class T_cosq
+  {
+  private:
+    pocketfft_r<T0> fftplan;
+    vector<T0> twiddle;
+
+  public:
+    POCKETFFT_NOINLINE T_cosq(size_t length)
+      : fftplan(length), twiddle(length)
+      {
+      constexpr T0 pi = T0(3.141592653589793238462643383279502884197L);
+      for (size_t i=0; i<length; ++i)
+        twiddle[i] = T0(cos(0.5*pi*T0(i+1)/T0(length)));
+      }
+
+    template<typename T> POCKETFFT_NOINLINE void backward(T c[], T0 fct)
+      {
+      constexpr T0 sqrt2=T0(1.414213562373095048801688724209698L);
+      size_t N=length();
+      if (N==1) { c[0]*=2*fct; return; }
+      if (N==2)
+        {
+        T x1 = 2*fct*(c[0]+c[1]);
+        c[1] = sqrt2*fct*(c[0]-c[1]);
+        c[0] = x1;
+        return;
+        }
+      size_t NS2 = (N+1)/2;
+      for (size_t i=2; i<N; i+=2)
+        {
+        T xim1 = T0(0.5)*(c[i-1]+c[i]);
+        c[i] = T0(0.5)*(c[i]-c[i-1]);
+        c[i-1] = xim1;
+        }
+//      c[0] *= 2;
+//      if ((N&1)==0)
+//        c[N-1] *= 2;
+      fftplan.backward(c, fct);
+      for (size_t k=1, kc=N-1; k<NS2; ++k, --kc)
+        {
+        T tmp = twiddle[k-1]*c[kc]+twiddle[kc-1]*c[k];
+        c[kc] = twiddle[k-1]*c[k]-twiddle[kc-1]*c[kc];
+        c[k] = tmp;
+        }
+      if ((N&1)==0)
+        c[NS2] = twiddle[NS2-1]*(c[NS2]+c[NS2]);
+      for (size_t k=1, kc=N-1; k<NS2; ++k, --kc)
+        {
+        T tmp = c[k]+c[kc];
+        c[kc] = c[k]-c[kc];
+        c[k] = tmp;
+        }
+      c[0] *= 2;
+      }
+
+    template<typename T> POCKETFFT_NOINLINE void forward(T c[], T0 fct)
+      {
+      constexpr T0 sqrt2=T0(1.414213562373095048801688724209698L);
+      size_t N=length();
+      if (N==1) { c[0]*=fct; return; }
+      if (N==2)
+        {
+        T TSQX = sqrt2*c[1];
+        c[1] = c[0]-TSQX;
+        c[0] = c[0]+TSQX;
+        return;
+        }
+      size_t NS2 = (N+1)/2;
+      for (size_t k=1, kc=N-1; k<NS2; ++k, --kc)
+        {
+        T tmp = c[k]-c[kc];
+        c[k] = c[k]+c[kc];
+        c[kc] = tmp;
+        }
+      if ((N&1)==0)
+        c[NS2] = c[NS2]+c[NS2];
+      for (size_t k=1, kc=N-1; k<NS2; ++k, --kc)
+        {
+        T tmp = twiddle[k-1]*c[k]-twiddle[kc-1]*c[kc];
+        c[k] = twiddle[k-1]*c[kc]+twiddle[kc-1]*c[k];
+        c[kc] = tmp;
+        }
+      if ((N&1)==0)
+        c[NS2] = twiddle[NS2-1]*c[NS2];
+      fftplan.forward(c, fct);
+      for (size_t i=2; i<N; i+=2)
+        {
+        T xim1 = c[i-1]-c[i];
+        c[i] += c[i-1];
+        c[i-1] = xim1;
+        }
+      }
+
+    size_t length() const { return fftplan.length(); }
+  };
+
+template<typename T0> class T_sinq
+  {
+  private:
+    T_cosq<T0> cosq;
+
+  public:
+    POCKETFFT_NOINLINE T_sinq(size_t length)
+      : cosq(length) {}
+
+    template<typename T> POCKETFFT_NOINLINE void backward(T c[], T0 fct)
+      {
+      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];
+      cosq.backward(c, fct);
+      for (size_t k=0, kc=N-1; k<kc; ++k, --kc)
+        swap(c[k], c[kc]);
+      }
+
+    template<typename T> POCKETFFT_NOINLINE void forward(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]);
+      cosq.forward(c, fct);
+      for (size_t k=1; k<N; k+=2)
+        c[k] = -c[k];
+      }
+
+    size_t length() const { return cosq.length(); }
+  };
+
+
 //
 // multi-D infrastructure
 //
@@ -2719,6 +2857,133 @@ template<typename T> POCKETFFT_NOINLINE void general_hartley(
     }
   }
 
+template<typename T> POCKETFFT_NOINLINE void general_dct23(
+  const cndarr<T> &in, ndarr<T> &out, const shape_t &axes, bool forward, T fct,
+  size_t POCKETFFT_NTHREADS)
+  {
+  shared_ptr<T_cosq<T>> plan;
+
+  for (size_t iax=0; iax<axes.size(); ++iax)
+    {
+    constexpr auto vlen = VLEN<T>::val;
+    size_t len=in.shape(axes[iax]);
+    if ((!plan) || (len!=plan->length()))
+      plan = get_plan<T_cosq<T>>(len);
+
+#ifdef POCKETFFT_OPENMP
+#pragma omp parallel num_threads(util::thread_count(nthreads, in.shape(), axes[iax]))
+#endif
+{
+    auto storage = alloc_tmp<T>(in.shape(), len, sizeof(T));
+    const auto &tin(iax==0 ? in : out);
+    multi_iter<vlen> it(tin, out, axes[iax]);
+#ifndef POCKETFFT_NO_VECTORS
+    if (vlen>1)
+      while (it.remaining()>=vlen)
+        {
+        using vtype = typename VTYPE<T>::type;
+        it.advance(vlen);
+        auto tdatav = reinterpret_cast<vtype *>(storage.data());
+        for (size_t i=0; i<len; ++i)
+          for (size_t j=0; j<vlen; ++j)
+            tdatav[i][j] = tin[it.iofs(j,i)];
+        forward ? plan->forward (tdatav, fct) : plan->backward(tdatav, fct);
+        for (size_t i=0; i<len; ++i)
+          for (size_t j=0; j<vlen; ++j)
+            out[it.oofs(j,i)] = tdatav[i][j];
+        }
+#endif
+    while (it.remaining()>0)
+      {
+      it.advance(1);
+      auto tdata = reinterpret_cast<T *>(storage.data());
+      if ((&tin[0]==&out[0]) && (it.stride_out()==sizeof(T))) // fully in-place
+        forward ? plan->forward (&out[it.oofs(0)], fct)
+                : plan->backward(&out[it.oofs(0)], fct);
+      else if (it.stride_out()==sizeof(T)) // compute FFT in output location
+        {
+        for (size_t i=0; i<len; ++i)
+          out[it.oofs(i)] = tin[it.iofs(i)];
+        forward ? plan->forward (&out[it.oofs(0)], fct)
+                : plan->backward(&out[it.oofs(0)], fct);
+        }
+      else
+        {
+        for (size_t i=0; i<len; ++i)
+          tdata[i] = tin[it.iofs(i)];
+        forward ? plan->forward (tdata, fct) : plan->backward(tdata, fct);
+        for (size_t i=0; i<len; ++i)
+          out[it.oofs(i)] = tdata[i];
+        }
+      }
+} // end of parallel region
+    fct = T(1); // factor has been applied, use 1 for remaining axes
+    }
+  }
+template<typename T> POCKETFFT_NOINLINE void general_dst23(
+  const cndarr<T> &in, ndarr<T> &out, const shape_t &axes, bool forward, T fct,
+  size_t POCKETFFT_NTHREADS)
+  {
+  shared_ptr<T_sinq<T>> plan;
+
+  for (size_t iax=0; iax<axes.size(); ++iax)
+    {
+    constexpr auto vlen = VLEN<T>::val;
+    size_t len=in.shape(axes[iax]);
+    if ((!plan) || (len!=plan->length()))
+      plan = get_plan<T_sinq<T>>(len);
+
+#ifdef POCKETFFT_OPENMP
+#pragma omp parallel num_threads(util::thread_count(nthreads, in.shape(), axes[iax]))
+#endif
+{
+    auto storage = alloc_tmp<T>(in.shape(), len, sizeof(T));
+    const auto &tin(iax==0 ? in : out);
+    multi_iter<vlen> it(tin, out, axes[iax]);
+#ifndef POCKETFFT_NO_VECTORS
+    if (vlen>1)
+      while (it.remaining()>=vlen)
+        {
+        using vtype = typename VTYPE<T>::type;
+        it.advance(vlen);
+        auto tdatav = reinterpret_cast<vtype *>(storage.data());
+        for (size_t i=0; i<len; ++i)
+          for (size_t j=0; j<vlen; ++j)
+            tdatav[i][j] = tin[it.iofs(j,i)];
+        forward ? plan->forward (tdatav, fct) : plan->backward(tdatav, fct);
+        for (size_t i=0; i<len; ++i)
+          for (size_t j=0; j<vlen; ++j)
+            out[it.oofs(j,i)] = tdatav[i][j];
+        }
+#endif
+    while (it.remaining()>0)
+      {
+      it.advance(1);
+      auto tdata = reinterpret_cast<T *>(storage.data());
+      if ((&tin[0]==&out[0]) && (it.stride_out()==sizeof(T))) // fully in-place
+        forward ? plan->forward (&out[it.oofs(0)], fct)
+                : plan->backward(&out[it.oofs(0)], fct);
+      else if (it.stride_out()==sizeof(T)) // compute FFT in output location
+        {
+        for (size_t i=0; i<len; ++i)
+          out[it.oofs(i)] = tin[it.iofs(i)];
+        forward ? plan->forward (&out[it.oofs(0)], fct)
+                : plan->backward(&out[it.oofs(0)], fct);
+        }
+      else
+        {
+        for (size_t i=0; i<len; ++i)
+          tdata[i] = tin[it.iofs(i)];
+        forward ? plan->forward (tdata, fct) : plan->backward(tdata, fct);
+        for (size_t i=0; i<len; ++i)
+          out[it.oofs(i)] = tdata[i];
+        }
+      }
+} // end of parallel region
+    fct = T(1); // factor has been applied, use 1 for remaining axes
+    }
+  }
+
 template<typename T> POCKETFFT_NOINLINE void general_r2c(
   const cndarr<T> &in, ndarr<cmplx<T>> &out, size_t axis, bool forward, T fct,
   size_t POCKETFFT_NTHREADS)
@@ -2963,6 +3228,28 @@ template<typename T> void c2c(const shape_t &shape, const stride_t &stride_in,
   general_c(ain, aout, axes, forward, fct, nthreads);
   }
 
+template<typename T> void r2r_dct23(const shape_t &shape,
+  const stride_t &stride_in, const stride_t &stride_out, const shape_t &axes,
+  bool forward, const T *data_in, T *data_out, T fct, size_t nthreads=1)
+  {
+  if (util::prod(shape)==0) return;
+  util::sanity_check(shape, stride_in, stride_out, data_in==data_out, axes);
+  cndarr<T> ain(data_in, shape, stride_in);
+  ndarr<T> aout(data_out, shape, stride_out);
+  general_dct23(ain, aout, axes, forward, fct, nthreads);
+  }
+
+template<typename T> void r2r_dst23(const shape_t &shape,
+  const stride_t &stride_in, const stride_t &stride_out, const shape_t &axes,
+  bool forward, const T *data_in, T *data_out, T fct, size_t nthreads=1)
+  {
+  if (util::prod(shape)==0) return;
+  util::sanity_check(shape, stride_in, stride_out, data_in==data_out, axes);
+  cndarr<T> ain(data_in, shape, stride_in);
+  ndarr<T> aout(data_out, shape, stride_out);
+  general_dst23(ain, aout, axes, forward, fct, nthreads);
+  }
+
 template<typename T> void r2c(const shape_t &shape_in,
   const stride_t &stride_in, const stride_t &stride_out, size_t axis,
   bool forward, const T *data_in, complex<T> *data_out, T fct,
@@ -3069,6 +3356,8 @@ using detail::c2r;
 using detail::r2c;
 using detail::r2r_fftpack;
 using detail::r2r_separable_hartley;
+using detail::r2r_dct23;
+using detail::r2r_dst23;
 
 } // namespace pocketfft
 

pypocketfft.cc

@@ -226,6 +226,60 @@ py::array r2r_fftpack(const py::array &in, const py::object &axes_,
     real2hermitian, forward, inorm, out_, nthreads))
   }
 
+template<typename T> py::array r2r_dct23_internal(const py::array &in,
+  const py::object &axes_, bool forward, int inorm, py::object &out_,
+  size_t nthreads)
+  {
+  auto axes = makeaxes(in, axes_);
+  auto dims(copy_shape(in));
+  py::array res = prepare_output<T>(out_, dims);
+  auto s_in=copy_strides(in);
+  auto s_out=copy_strides(res);
+  auto d_in=reinterpret_cast<const T *>(in.data());
+  auto d_out=reinterpret_cast<T *>(res.mutable_data());
+  {
+  py::gil_scoped_release release;
+  T fct = norm_fct<T>(inorm, dims, axes);
+  pocketfft::r2r_dct23(dims, s_in, s_out, axes, forward, d_in, d_out, fct,
+    nthreads);
+  }
+  return res;
+  }
+
+py::array r2r_dct23(const py::array &in, const py::object &axes_,
+  bool forward, int inorm, py::object &out_, size_t nthreads)
+  {
+  DISPATCH(in, f64, f32, flong, r2r_dct23_internal, (in, axes_,
+    forward, inorm, out_, nthreads))
+  }
+
+template<typename T> py::array r2r_dst23_internal(const py::array &in,
+  const py::object &axes_, bool forward, int inorm, py::object &out_,
+  size_t nthreads)
+  {
+  auto axes = makeaxes(in, axes_);
+  auto dims(copy_shape(in));
+  py::array res = prepare_output<T>(out_, dims);
+  auto s_in=copy_strides(in);
+  auto s_out=copy_strides(res);
+  auto d_in=reinterpret_cast<const T *>(in.data());
+  auto d_out=reinterpret_cast<T *>(res.mutable_data());
+  {
+  py::gil_scoped_release release;
+  T fct = norm_fct<T>(inorm, dims, axes);
+  pocketfft::r2r_dst23(dims, s_in, s_out, axes, forward, d_in, d_out, fct,
+    nthreads);
+  }
+  return res;
+  }
+
+py::array r2r_dst23(const py::array &in, const py::object &axes_,
+  bool forward, int inorm, py::object &out_, size_t nthreads)
+  {
+  DISPATCH(in, f64, f32, flong, r2r_dst23_internal, (in, axes_,
+    forward, inorm, out_, nthreads))
+  }
+
 template<typename T> py::array c2r_internal(const py::array &in,
   const py::object &axes_, size_t lastsize, bool forward, int inorm,
   py::object &out_, size_t nthreads)
@@ -543,4 +597,8 @@ PYBIND11_MODULE(pypocketfft, m)
     "axes"_a=None, "inorm"_a=0, "out"_a=None, "nthreads"_a=1);
   m.def("genuine_hartley", genuine_hartley, genuine_hartley_DS, "a"_a,
     "axes"_a=None, "inorm"_a=0, "out"_a=None, "nthreads"_a=1);
+  m.def("r2r_dct23", r2r_dct23, /*r2r_dct23_DS,*/ "a"_a,
+    "axes"_a=None, "forward"_a, "inorm"_a=0, "out"_a=None, "nthreads"_a=1);
+  m.def("r2r_dst23", r2r_dst23, /*r2r_dst23_DS,*/ "a"_a,
+    "axes"_a=None, "forward"_a, "inorm"_a=0, "out"_a=None, "nthreads"_a=1);
   }