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Commit fcfd81ff authored by Martin Reinecke's avatar Martin Reinecke
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Merge branch 'develop' into 'master' 

Develop

See merge request !4
parents cef9199e 8a3d6ff7
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Showing with 186 additions and 86 deletions
pocketfft_hdronly.h
View file @ fcfd81ff
......@@ -19,6 +19,7 @@
#include <stdexcept>
#include <memory>
#include <vector>
#include <complex>
#if defined(_WIN32)
#include <malloc.h>
#endif
......@@ -36,6 +37,8 @@ namespace pocketfft {
using shape_t = std::vector<size_t>;
using stride_t = std::vector<ptrdiff_t>;
constexpr bool FORWARD = true,
BACKWARD = false;
namespace detail {
......@@ -156,13 +159,29 @@ template<typename T> void ROTM90(cmplx<T> &a)
template<typename T> class sincos_2pibyn
{
private:
template<typename Ta, typename Tb, bool bigger> struct TypeSelector
{};
template<typename Ta, typename Tb> struct TypeSelector<Ta, Tb, true>
{ using type = Ta; };
template<typename Ta, typename Tb> struct TypeSelector<Ta, Tb, false>
{ using type = Tb; };
using Thigh = typename TypeSelector<T, double, (sizeof(T)>sizeof(double))>::type;
arr<T> data;
// adapted from https://stackoverflow.com/questions/42792939/
// CAUTION: this function only works for arguments in the range
// [-0.25; 0.25]!
void my_sincosm1pi (double a, double *restrict res)
void my_sincosm1pi (Thigh a, Thigh *restrict res)
{
if (sizeof(Thigh)>sizeof(double)) // don't have the code for long double
{
Thigh pi = Thigh(3.141592653589793238462643383279502884197L);
res[1] = sin(pi*a);
auto s = res[1];
res[0] = (s*s)/(-sqrt((1-s)*(1+s))-1);
return;
}
double s = a * a;
/* Approximate cos(pi*x)-1 for x in [-0.25,0.25] */
double r = -1.0369917389758117e-4;
......@@ -194,25 +213,25 @@ template<typename T> class sincos_2pibyn
res[0]=1.; res[1]=0.;
if (n==1) return;
size_t l1 = size_t(sqrt(n));
arr<double> tmp(2*l1);
arr<Thigh> tmp(2*l1);
for (size_t i=1; i<l1; ++i)
{
my_sincosm1pi((2.*i)/den,&tmp[2*i]);
my_sincosm1pi((Thigh(2)*i)/den,&tmp[2*i]);
res[2*i ] = tmp[2*i]+1.;
res[2*i+1] = tmp[2*i+1];
}
size_t start=l1;
while(start<n)
{
double cs[2];
my_sincosm1pi((2.*start)/den,cs);
Thigh cs[2];
my_sincosm1pi((Thigh(2)*start)/den,cs);
res[2*start] = cs[0]+1.;
res[2*start+1] = cs[1];
size_t end = l1;
if (start+end>n) end = n-start;
for (size_t i=1; i<end; ++i)
{
double csx[2]={tmp[2*i], tmp[2*i+1]};
Thigh csx[2]={tmp[2*i], tmp[2*i+1]};
res[2*(start+i)] = ((cs[0]*csx[0] - cs[1]*csx[1] + cs[0]) + csx[0]) + 1.;
res[2*(start+i)+1] = (cs[0]*csx[1] + cs[1]*csx[0]) + cs[1] + csx[1];
}
......@@ -253,7 +272,7 @@ template<typename T> class sincos_2pibyn
void fill_first_quadrant(size_t n, T * restrict res)
{
const double hsqt2 = 0.707106781186547524400844362104849;
constexpr Thigh hsqt2 = Thigh(0.707106781186547524400844362104849L);
size_t quart = n>>2;
if ((n&7)==0)
res[quart] = res[quart+1] = hsqt2;
......@@ -336,7 +355,7 @@ struct util // hack to avoid duplicate symbols
static NOINLINE double cost_guess (size_t n)
{
const double lfp=1.1; // penalty for non-hardcoded larger factors
constexpr double lfp=1.1; // penalty for non-hardcoded larger factors
size_t ni=n;
double result=0.;
while ((n&1)==0)
......@@ -377,6 +396,41 @@ struct util // hack to avoid duplicate symbols
res*=sz;
return res;
}
static NOINLINE void sanity_check(const shape_t &shape,
const stride_t &stride_in, const stride_t &stride_out, bool inplace)
{
auto ndim = shape.size();
if (ndim<1) throw runtime_error("ndim must be >= 1");
if ((stride_in.size()!=ndim) || (stride_out.size()!=ndim))
throw runtime_error("stride dimension mismatch");
for (auto shp: shape)
if (shp<1) throw runtime_error("zero extent detected");
if (inplace && (stride_in!=stride_out))
throw runtime_error("stride mismatch");
}
static NOINLINE void sanity_check(const shape_t &shape,
const stride_t &stride_in, const stride_t &stride_out, bool inplace,
const shape_t &axes)
{
sanity_check(shape, stride_in, stride_out, inplace);
auto ndim = shape.size();
shape_t tmp(ndim,0);
for (auto ax : axes)
{
if (ax>=ndim) throw runtime_error("bad axis number");
if (++tmp[ax]>1) throw runtime_error("axis specified repeatedly");
}
}
static NOINLINE void sanity_check(const shape_t &shape,
const stride_t &stride_in, const stride_t &stride_out, bool inplace,
size_t axis)
{
sanity_check(shape, stride_in, stride_out, inplace);
if (axis>=shape.size()) throw runtime_error("bad axis number");
}
};
#define CH(a,b,c) ch[(a)+ido*((b)+l1*(c))]
......@@ -390,7 +444,6 @@ struct util // hack to avoid duplicate symbols
template<typename T0> class cfftp
{
private:
struct fctdata
{
size_t fct;
......@@ -452,7 +505,8 @@ template<bool bwd, typename T> void pass3 (size_t ido, size_t l1,
const T * restrict cc, T * restrict ch, const cmplx<T0> * restrict wa)
{
constexpr size_t cdim=3;
constexpr T0 tw1r=-0.5, tw1i= (bwd ? 1.: -1.) * 0.86602540378443864676;
constexpr T0 tw1r=-0.5,
tw1i= (bwd ? 1: -1) * T0(0.8660254037844386467637231707529362L);
if (ido==1)
for (size_t k=0; k<l1; ++k)
......@@ -554,10 +608,10 @@ template<bool bwd, typename T> void pass5 (size_t ido, size_t l1,
const T * restrict cc, T * restrict ch, const cmplx<T0> * restrict wa)
{
constexpr size_t cdim=5;
constexpr T0 tw1r= 0.3090169943749474241,
tw1i= (bwd ? 1.: -1.) * 0.95105651629515357212,
tw2r= -0.8090169943749474241,
tw2i= (bwd ? 1.: -1.) * 0.58778525229247312917;
constexpr T0 tw1r= T0(0.3090169943749474241022934171828191L),
tw1i= (bwd ? 1: -1) * T0(0.9510565162951535721164393333793821L),
tw2r= T0(-0.8090169943749474241022934171828191L),
tw2i= (bwd ? 1: -1) * T0(0.5877852522924731291687059546390728L);
if (ido==1)
for (size_t k=0; k<l1; ++k)
......@@ -618,12 +672,12 @@ template<bool bwd, typename T> void pass7(size_t ido, size_t l1,
const T * restrict cc, T * restrict ch, const cmplx<T0> * restrict wa)
{
constexpr size_t cdim=7;
constexpr T0 tw1r= 0.623489801858733530525,
tw1i= (bwd ? 1. : -1.) * 0.7818314824680298087084,
tw2r= -0.222520933956314404289,
tw2i= (bwd ? 1. : -1.) * 0.9749279121818236070181,
tw3r= -0.9009688679024191262361,
tw3i= (bwd ? 1. : -1.) * 0.4338837391175581204758;
constexpr T0 tw1r= T0(0.6234898018587335305250048840042398L),
tw1i= (bwd ? 1 : -1) * T0(0.7818314824680298087084445266740578L),
tw2r= T0(-0.2225209339563144042889025644967948L),
tw2i= (bwd ? 1 : -1) * T0(0.9749279121818236070181316829939312L),
tw3r= T0(-0.9009688679024191262361023195074451L),
tw3i= (bwd ? 1 : -1) * T0(0.433883739117558120475768332848359L);
if (ido==1)
for (size_t k=0; k<l1; ++k)
......@@ -688,17 +742,17 @@ template<bool bwd, typename T> void pass7(size_t ido, size_t l1,
template<bool bwd, typename T> void pass11 (size_t ido, size_t l1,
const T * restrict cc, T * restrict ch, const cmplx<T0> * restrict wa)
{
const size_t cdim=11;
const T0 tw1r = 0.8412535328311811688618,
tw1i = (bwd ? 1. : -1.) * 0.5406408174555975821076,
tw2r = 0.4154150130018864255293,
tw2i = (bwd ? 1. : -1.) * 0.9096319953545183714117,
tw3r = -0.1423148382732851404438,
tw3i = (bwd ? 1. : -1.) * 0.9898214418809327323761,
tw4r = -0.6548607339452850640569,
tw4i = (bwd ? 1. : -1.) * 0.755749574354258283774,
tw5r = -0.9594929736144973898904,
tw5i = (bwd ? 1. : -1.) * 0.2817325568414296977114;
constexpr size_t cdim=11;
constexpr T0 tw1r= T0(0.8412535328311811688618116489193677L),
tw1i= (bwd ? 1 : -1) * T0(0.5406408174555975821076359543186917L),
tw2r= T0(0.4154150130018864255292741492296232L),
tw2i= (bwd ? 1 : -1) * T0(0.9096319953545183714117153830790285L),
tw3r= T0(-0.1423148382732851404437926686163697L),
tw3i= (bwd ? 1 : -1) * T0(0.9898214418809327323760920377767188L),
tw4r= T0(-0.6548607339452850640569250724662936L),
tw4i= (bwd ? 1 : -1) * T0(0.7557495743542582837740358439723444L),
tw5r= T0(-0.9594929736144973898903680570663277L),
tw5i= (bwd ? 1 : -1) * T0(0.2817325568414296977114179153466169L);
if (ido==1)
for (size_t k=0; k<l1; ++k)
......@@ -1035,7 +1089,7 @@ template<typename T> void radf3(size_t ido, size_t l1,
const T * restrict cc, T * restrict ch, const T0 * restrict wa)
{
constexpr size_t cdim=3;
constexpr T0 taur=-0.5, taui=0.86602540378443864676;
constexpr T0 taur=-0.5, taui=T0(0.8660254037844386467637231707529362L);
for (size_t k=0; k<l1; k++)
{
......@@ -1069,7 +1123,7 @@ template<typename T> void radf4(size_t ido, size_t l1,
const T * restrict cc, T * restrict ch, const T0 * restrict wa)
{
constexpr size_t cdim=4;
constexpr T0 hsqt2=0.70710678118654752440;
constexpr T0 hsqt2=T0(0.707106781186547524400844362104849L);
for (size_t k=0; k<l1; k++)
{
......@@ -1110,8 +1164,10 @@ template<typename T> void radf5(size_t ido, size_t l1,
const T * restrict cc, T * restrict ch, const T0 * restrict wa)
{
constexpr size_t cdim=5;
constexpr T0 tr11= 0.3090169943749474241, ti11=0.95105651629515357212,
tr12=-0.8090169943749474241, ti12=0.58778525229247312917;
constexpr T0 tr11= T0(0.3090169943749474241022934171828191L),
ti11= T0(0.9510565162951535721164393333793821L),
tr12= T0(-0.8090169943749474241022934171828191L),
ti12= T0(0.5877852522924731291687059546390728L);
for (size_t k=0; k<l1; k++)
{
......@@ -1335,7 +1391,7 @@ template<typename T> void radb3(size_t ido, size_t l1,
const T * restrict cc, T * restrict ch, const T0 * restrict wa)
{
constexpr size_t cdim=3;
constexpr T0 taur=-0.5, taui=0.86602540378443864676;
constexpr T0 taur=-0.5, taui=T0(0.8660254037844386467637231707529362L);
for (size_t k=0; k<l1; k++)
{
......@@ -1370,7 +1426,7 @@ template<typename T> void radb4(size_t ido, size_t l1,
const T * restrict cc, T * restrict ch, const T0 * restrict wa)
{
constexpr size_t cdim=4;
constexpr T0 sqrt2=1.41421356237309504880;
constexpr T0 sqrt2=T0(1.414213562373095048801688724209698L);
for (size_t k=0; k<l1; k++)
{
......@@ -1416,8 +1472,10 @@ template<typename T> void radb5(size_t ido, size_t l1,
const T * restrict cc, T * restrict ch, const T0 * restrict wa)
{
constexpr size_t cdim=5;
constexpr T0 tr11= 0.3090169943749474241, ti11=0.95105651629515357212,
tr12=-0.8090169943749474241, ti12=0.58778525229247312917;
constexpr T0 tr11= T0(0.3090169943749474241022934171828191L),
ti11= T0(0.9510565162951535721164393333793821L),
tr12= T0(-0.8090169943749474241022934171828191L),
ti12= T0(0.5877852522924731291687059546390728L);
for (size_t k=0; k<l1; k++)
{
......@@ -1825,7 +1883,7 @@ template<typename T0> class fftblue
}
/* initialize the zero-padded, Fourier transformed b_k. Add normalisation. */
T0 xn2 = 1./n2;
T0 xn2 = T0(1)/n2;
bkf[0] = bk[0]*xn2;
for (size_t m=1; m<n; ++m)
bkf[m] = bkf[n2-m] = bk[m]*xn2;
......@@ -1996,10 +2054,9 @@ template<size_t N, typename Ti, typename To> class multi_iter
for (int i=pos.size()-1; i>=0; --i)
{
if (i==int(idim)) continue;
++pos[i];
p_ii += iarr.stride(i);
p_oi += oarr.stride(i);
if (pos[i] < iarr.shape(i))
if (++pos[i] < iarr.shape(i))
return;
pos[i] = 0;
p_ii -= iarr.shape(i)*iarr.stride(i);
......@@ -2039,7 +2096,12 @@ template<size_t N, typename Ti, typename To> class multi_iter
};
#if defined(HAVE_VECSUPPORT)
template<typename T> struct VTYPE{};
template<typename T> struct VTYPE {};
template<> struct VTYPE<long double>
{
using type = long double __attribute__ ((vector_size (sizeof(long double))));
static constexpr int vlen=1;
};
template<> struct VTYPE<double>
{
using type = double __attribute__ ((vector_size (VBYTELEN)));
......@@ -2051,10 +2113,7 @@ template<> struct VTYPE<float>
static constexpr int vlen=VBYTELEN/sizeof(float);
};
#else
template<typename T> struct VTYPE{};
template<> struct VTYPE<double>
{ static constexpr int vlen=1; };
template<> struct VTYPE<float>
template<typename T> struct VTYPE
{ static constexpr int vlen=1; };
#endif
......@@ -2345,52 +2404,99 @@ template<typename T> NOINLINE void general_r(
} // namespace detail
template<typename T> void c2c(const shape_t &shape,
const stride_t &stride_in, const stride_t &stride_out, const shape_t &axes,
bool forward, const void *data_in, void *data_out, T fct)
template<typename T> void c2c(const shape_t &shape, const stride_t &stride_in,
const stride_t &stride_out, const shape_t &axes, bool forward,
const std::complex<T> *data_in, std::complex<T> *data_out, T fct)
{
using namespace detail;
util::sanity_check(shape, stride_in, stride_out, data_in==data_out, axes);
ndarr<cmplx<T>> ain(data_in, shape, stride_in),
aout(data_out, shape, stride_out);
general_c(ain, aout, axes, forward, fct);
}
template<typename T> void r2c(const shape_t &shape,
template<typename T> void r2c(const shape_t &shape_in,
const stride_t &stride_in, const stride_t &stride_out, size_t axis,
const void *data_in, void *data_out, T fct)
const T *data_in, std::complex<T> *data_out, T fct)
{
using namespace detail;
ndarr<T> ain(data_in, shape, stride_in);
ndarr<cmplx<T>> aout(data_out, shape, stride_out);
util::sanity_check(shape_in, stride_in, stride_out, false, axis);
ndarr<T> ain(data_in, shape_in, stride_in);
ndarr<cmplx<T>> aout(data_out, shape_in, stride_out); // FIXME
general_r2c(ain, aout, axis, fct);
}
template<typename T> void c2r(const shape_t &shape, size_t new_size,
template<typename T> void r2c(const shape_t &shape_in,
const stride_t &stride_in, const stride_t &stride_out, const shape_t &axes,
const T *data_in, std::complex<T> *data_out, T fct)
{
using namespace detail;
util::sanity_check(shape_in, stride_in, stride_out, false, axes);
r2c(shape_in, stride_in, stride_out, axes.back(), data_in, data_out, fct);
if (axes.size()==1) return;
shape_t shape_out(shape_in);
shape_out[axes.back()] = shape_in[axes.back()]/2 + 1;
auto newaxes = shape_t{axes.begin(), --axes.end()};
c2c(shape_out, stride_out, stride_out, newaxes, true, data_out, data_out,
T(1));
}
template<typename T> void c2r(const shape_t &shape_out,
const stride_t &stride_in, const stride_t &stride_out, size_t axis,
const void *data_in, void *data_out, T fct)
const std::complex<T> *data_in, T *data_out, T fct)
{
using namespace detail;
shape_t shape_out(shape);
shape_out[axis] = new_size;
ndarr<cmplx<T>> ain(data_in, shape, stride_in);
util::sanity_check(shape_out, stride_in, stride_out, false, axis);
shape_t shape_in(shape_out);
shape_in[axis] = shape_out[axis]/2 + 1;
ndarr<cmplx<T>> ain(data_in, shape_in, stride_in);
ndarr<T> aout(data_out, shape_out, stride_out);
general_c2r(ain, aout, axis, fct);
}
template<typename T> void c2r(const shape_t &shape_out,
const stride_t &stride_in, const stride_t &stride_out, const shape_t &axes,
const std::complex<T> *data_in, T *data_out, T fct)
{
using namespace detail;
if (axes.size()==1)
{
c2r(shape_out, stride_in, stride_out, axes[0], data_in, data_out, fct);
return;
}
util::sanity_check(shape_out, stride_in, stride_out, false, axes);
auto shape_in = shape_out;
shape_in[axes.back()] = shape_out[axes.back()]/2 + 1;
auto nval = util::prod(shape_in);
stride_t stride_inter(shape_in.size());
stride_inter.back() = sizeof(cmplx<T>);
for (int i=shape_in.size()-2; i>=0; --i)
stride_inter[i] = stride_inter[i+1]*shape_in[i+1];
arr<complex<T>> tmp(nval);
auto newaxes = shape_t({axes.begin(), --axes.end()});
c2c(shape_in, stride_in, stride_inter, newaxes, false, data_in, tmp.data(),
T(1));
c2r(shape_out, stride_inter, stride_out, axes.back(), tmp.data(), data_out,
fct);
}
template<typename T> void r2r_fftpack(const shape_t &shape,
const stride_t &stride_in, const stride_t &stride_out, size_t axis,
bool forward, const void *data_in, void *data_out, T fct)
bool forward, const T *data_in, T *data_out, T fct)
{
using namespace detail;
util::sanity_check(shape, stride_in, stride_out, data_in==data_out, axis);
ndarr<T> ain(data_in, shape, stride_in), aout(data_out, shape, stride_out);
general_r(ain, aout, axis, forward, fct);
}
template<typename T> void r2r_hartley(const shape_t &shape,
const stride_t &stride_in, const stride_t &stride_out, const shape_t &axes,
const void *data_in, void *data_out, T fct)
const T *data_in, T *data_out, T fct)
{
using namespace detail;
util::sanity_check(shape, stride_in, stride_out, data_in==data_out, axes);
ndarr<T> ain(data_in, shape, stride_in), aout(data_out, shape, stride_out);
general_hartley(ain, aout, axes, fct);
}
......
pypocketfft.cc
View file @ fcfd81ff
......@@ -26,7 +26,6 @@ namespace {
using namespace std;
using namespace pocketfft;
using namespace pocketfft::detail;
namespace py = pybind11;
......@@ -83,9 +82,9 @@ template<typename T> py::array xfftn_internal(const py::array &in,
{
auto dims(copy_shape(in));
py::array res = inplace ? in : py::array_t<complex<T>>(dims);
ndarr<cmplx<T>> ain(in.data(), dims, copy_strides(in));
ndarr<cmplx<T>> aout(res.mutable_data(), dims, copy_strides(res));
general_c<T>(ain, aout, axes, fwd, fct);
c2c(dims, copy_strides(in), copy_strides(res), axes, fwd,
reinterpret_cast<const complex<T> *>(in.data()),
reinterpret_cast<complex<T> *>(res.mutable_data()), T(fct));
return res;
}
......@@ -108,12 +107,9 @@ template<typename T> py::array rfftn_internal(const py::array &in,
auto dims_in(copy_shape(in)), dims_out(dims_in);
dims_out[axes.back()] = (dims_out[axes.back()]>>1)+1;
py::array res = py::array_t<complex<T>>(dims_out);
ndarr<T> ain(in.data(), dims_in, copy_strides(in));
ndarr<cmplx<T>> aout(res.mutable_data(), dims_out, copy_strides(res));
general_r2c<T>(ain, aout, axes.back(), fct);
if (axes.size()==1) return res;
shape_t axes2(axes.begin(), --axes.end());
general_c<T>(aout, aout, axes2, true, 1.);
r2c(dims_in, copy_strides(in), copy_strides(res), axes,
reinterpret_cast<const T *>(in.data()),
reinterpret_cast<complex<T> *>(res.mutable_data()), T(fct));
return res;
}
py::array rfftn(const py::array &in, py::object axes_, double fct)
......@@ -126,9 +122,9 @@ template<typename T> py::array xrfft_scipy(const py::array &in,
{
auto dims(copy_shape(in));
py::array res = inplace ? in : py::array_t<T>(dims);
ndarr<T> ain(in.data(), dims, copy_strides(in));
ndarr<T> aout(res.mutable_data(), dims, copy_strides(res));
general_r<T>(ain, aout, axis, fwd, fct);
r2r_fftpack(dims, copy_strides(in), copy_strides(res), axis, fwd,
reinterpret_cast<const T *>(in.data()),
reinterpret_cast<T *>(res.mutable_data()), T(fct));
return res;
}
py::array rfft_scipy(const py::array &in, size_t axis, double fct, bool inplace)
......@@ -148,19 +144,16 @@ template<typename T> py::array irfftn_internal(const py::array &in,
py::object axes_, size_t lastsize, T fct)
{
auto axes = makeaxes(in, axes_);
py::array inter = (axes.size()==1) ? in :
xfftn_internal<T>(in, shape_t(axes.begin(), --axes.end()), 1., false, false);
size_t axis = axes.back();
if (lastsize==0) lastsize=2*inter.shape(axis)-1;
if (ptrdiff_t(lastsize/2) + 1 != inter.shape(axis))
shape_t dims_in(copy_shape(in)), dims_out=dims_in;
if (lastsize==0) lastsize=2*dims_in[axis]-1;
if ((lastsize/2) + 1 != dims_in[axis])
throw runtime_error("bad lastsize");
auto dims_out(copy_shape(inter));
dims_out[axis] = lastsize;
py::array res = py::array_t<T>(dims_out);
ndarr<cmplx<T>> ain(inter.data(), copy_shape(inter), copy_strides(inter));
ndarr<T> aout(res.mutable_data(), dims_out, copy_strides(res));
general_c2r<T>(ain, aout, axis, fct);
c2r(dims_in, lastsize, copy_strides(in), copy_strides(res), axes,
reinterpret_cast<const complex<T> *>(in.data()),
reinterpret_cast<T *>(res.mutable_data()), T(fct));
return res;
}
py::array irfftn(const py::array &in, py::object axes_, size_t lastsize,
......@@ -176,9 +169,9 @@ template<typename T> py::array hartley_internal(const py::array &in,
{
auto dims(copy_shape(in));
py::array res = inplace ? in : py::array_t<T>(dims);
ndarr<T> ain(in.data(), copy_shape(in), copy_strides(in));
ndarr<T> aout(res.mutable_data(), copy_shape(res), copy_strides(res));
general_hartley<T>(ain, aout, makeaxes(in, axes_), fct);
r2r_hartley(dims, copy_strides(in), copy_strides(res), makeaxes(in, axes_),
reinterpret_cast<const T *>(in.data()),
reinterpret_cast<T *>(res.mutable_data()), T(fct));
return res;
}
py::array hartley(const py::array &in, py::object axes_, double fct,
......@@ -192,6 +185,7 @@ py::array hartley(const py::array &in, py::object axes_, double fct,
template<typename T>py::array complex2hartley(const py::array &in,
const py::array &tmp, py::object axes_, bool inplace)
{
using namespace pocketfft::detail;
int ndim = in.ndim();
auto dims_out(copy_shape(in));
py::array out = inplace ? in : py::array_t<T>(dims_out);
......
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