pypocketfft.cc 23.7 KB
Newer Older
Martin Reinecke's avatar
Martin Reinecke committed
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
/*
 * This file is part of pocketfft.
 * Licensed under a 3-clause BSD style license - see LICENSE.md
 */

/*
 *  Python interface.
 *
 *  Copyright (C) 2019 Max-Planck-Society
 *  Copyright (C) 2019 Peter Bell
 *  \author Martin Reinecke
 *  \author Peter Bell
 */

#include <pybind11/pybind11.h>
#include <pybind11/numpy.h>
#include <pybind11/stl.h>

#include "mr_util/fft.h"

namespace {

using mr::shape_t;
using mr::stride_t;
using std::size_t;
using std::ptrdiff_t;

namespace py = pybind11;

// Only instantiate long double transforms if they offer more precision
using ldbl_t = typename std::conditional<
  sizeof(long double)==sizeof(double), double, long double>::type;

using c64 = std::complex<float>;
using c128 = std::complex<double>;
using clong = std::complex<ldbl_t>;
using f32 = float;
using f64 = double;
using flong = ldbl_t;
auto None = py::none();

shape_t copy_shape(const py::array &arr)
  {
  shape_t res(size_t(arr.ndim()));
  for (size_t i=0; i<res.size(); ++i)
    res[i] = size_t(arr.shape(int(i)));
  return res;
  }

stride_t copy_strides(const py::array &arr)
  {
  stride_t res(size_t(arr.ndim()));
  for (size_t i=0; i<res.size(); ++i)
    res[i] = arr.strides(int(i));
  return res;
  }

shape_t makeaxes(const py::array &in, const py::object &axes)
  {
  if (axes.is_none())
    {
    shape_t res(size_t(in.ndim()));
    for (size_t i=0; i<res.size(); ++i)
      res[i]=i;
    return res;
    }
  auto tmp=axes.cast<std::vector<ptrdiff_t>>();
  auto ndim = in.ndim();
  if ((tmp.size()>size_t(ndim)) || (tmp.size()==0))
    throw std::runtime_error("bad axes argument");
  for (auto& sz: tmp)
    {
    if (sz<0)
      sz += ndim;
    if ((sz>=ndim) || (sz<0))
      throw std::invalid_argument("axes exceeds dimensionality of output");
    }
  return shape_t(tmp.begin(), tmp.end());
  }

#define DISPATCH(arr, T1, T2, T3, func, args) \
  { \
  if (py::isinstance<py::array_t<T1>>(arr)) return func<double> args; \
  if (py::isinstance<py::array_t<T2>>(arr)) return func<float> args;  \
  if (py::isinstance<py::array_t<T3>>(arr)) return func<ldbl_t> args; \
  throw std::runtime_error("unsupported data type"); \
  }

template<typename T> T norm_fct(int inorm, size_t N)
  {
  if (inorm==0) return T(1);
  if (inorm==2) return T(1/ldbl_t(N));
  if (inorm==1) return T(1/sqrt(ldbl_t(N)));
  throw std::invalid_argument("invalid value for inorm (must be 0, 1, or 2)");
  }

template<typename T> T norm_fct(int inorm, const shape_t &shape,
  const shape_t &axes, size_t fct=1, int delta=0)
  {
  if (inorm==0) return T(1);
  size_t N(1);
  for (auto a: axes)
    N *= fct * size_t(int64_t(shape[a])+delta);
  return norm_fct<T>(inorm, N);
  }

template<typename T> py::array_t<T> prepare_output(py::object &out_,
  shape_t &dims)
  {
  if (out_.is_none()) return py::array_t<T>(dims);
  auto tmp = out_.cast<py::array_t<T>>();
  if (!tmp.is(out_)) // a new object was created during casting
    throw std::runtime_error("unexpected data type for output array");
  return tmp;
  }

template<typename T> py::array c2c_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));
  auto res = prepare_output<std::complex<T>>(out_, dims);
  auto s_in=copy_strides(in);
  auto s_out=copy_strides(res);
  auto d_in=reinterpret_cast<const std::complex<T> *>(in.data());
  auto d_out=reinterpret_cast<std::complex<T> *>(res.mutable_data());
  {
  py::gil_scoped_release release;
  T fct = norm_fct<T>(inorm, dims, axes);
  mr::c2c(dims, s_in, s_out, axes, forward, d_in, d_out, fct, nthreads);
  }
  return move(res);
  }

template<typename T> py::array c2c_sym_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));
  auto res = prepare_output<std::complex<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<std::complex<T> *>(res.mutable_data());
  {
  py::gil_scoped_release release;
  T fct = norm_fct<T>(inorm, dims, axes);
  mr::r2c(dims, s_in, s_out, axes, forward, d_in, d_out, fct, nthreads);
  // now fill in second half
  using namespace mr::detail_fft;
  ndarr<std::complex<T>> ares(res.mutable_data(), dims, s_out);
  rev_iter iter(ares, axes);
  while(iter.remaining()>0)
    {
    auto v = ares[iter.ofs()];
    ares[iter.rev_ofs()] = conj(v);
    iter.advance();
    }
  }
  return move(res);
  }

py::array c2c(const py::array &a, const py::object &axes_, bool forward,
  int inorm, py::object &out_, size_t nthreads)
  {
  if (a.dtype().kind() == 'c')
    DISPATCH(a, c128, c64, clong, c2c_internal, (a, axes_, forward,
             inorm, out_, nthreads))

  DISPATCH(a, f64, f32, flong, c2c_sym_internal, (a, axes_, forward,
           inorm, out_, nthreads))
  }

template<typename T> py::array r2c_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_in(copy_shape(in)), dims_out(dims_in);
  dims_out[axes.back()] = (dims_out[axes.back()]>>1)+1;
  py::array res = prepare_output<std::complex<T>>(out_, dims_out);
  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<std::complex<T> *>(res.mutable_data());
  {
  py::gil_scoped_release release;
  T fct = norm_fct<T>(inorm, dims_in, axes);
  mr::r2c(dims_in, s_in, s_out, axes, forward, d_in, d_out, fct,
    nthreads);
  }
  return res;
  }

py::array r2c(const py::array &in, const py::object &axes_, bool forward,
  int inorm, py::object &out_, size_t nthreads)
  {
  DISPATCH(in, f64, f32, flong, r2c_internal, (in, axes_, forward, inorm, out_,
    nthreads))
  }

template<typename T> py::array r2r_fftpack_internal(const py::array &in,
  const py::object &axes_, bool real2hermitian, 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);
  mr::r2r_fftpack(dims, s_in, s_out, axes, real2hermitian, forward,
    d_in, d_out, fct, nthreads);
  }
  return res;
  }

py::array r2r_fftpack(const py::array &in, const py::object &axes_,
  bool real2hermitian, bool forward, int inorm, py::object &out_,
  size_t nthreads)
  {
  DISPATCH(in, f64, f32, flong, r2r_fftpack_internal, (in, axes_,
    real2hermitian, forward, inorm, out_, nthreads))
  }

template<typename T> py::array dct_internal(const py::array &in,
  const py::object &axes_, int type, 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 = (type==1) ? norm_fct<T>(inorm, dims, axes, 2, -1)
                    : norm_fct<T>(inorm, dims, axes, 2);
  bool ortho = inorm == 1;
  mr::dct(dims, s_in, s_out, axes, type, d_in, d_out, fct, ortho,
    nthreads);
  }
  return res;
  }

py::array dct(const py::array &in, int type, const py::object &axes_,
  int inorm, py::object &out_, size_t nthreads)
  {
  if ((type<1) || (type>4)) throw std::invalid_argument("invalid DCT type");
  DISPATCH(in, f64, f32, flong, dct_internal, (in, axes_, type, inorm, out_,
    nthreads))
  }

template<typename T> py::array dst_internal(const py::array &in,
  const py::object &axes_, int type, 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 = (type==1) ? norm_fct<T>(inorm, dims, axes, 2, 1)
                    : norm_fct<T>(inorm, dims, axes, 2);
  bool ortho = inorm == 1;
  mr::dst(dims, s_in, s_out, axes, type, d_in, d_out, fct, ortho,
    nthreads);
  }
  return res;
  }

py::array dst(const py::array &in, int type, const py::object &axes_,
  int inorm, py::object &out_, size_t nthreads)
  {
  if ((type<1) || (type>4)) throw std::invalid_argument("invalid DST type");
  DISPATCH(in, f64, f32, flong, dst_internal, (in, axes_, type, 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)
  {
  auto axes = makeaxes(in, axes_);
  size_t axis = axes.back();
  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 std::invalid_argument("bad lastsize");
  dims_out[axis] = lastsize;
  py::array res = prepare_output<T>(out_, dims_out);
  auto s_in=copy_strides(in);
  auto s_out=copy_strides(res);
  auto d_in=reinterpret_cast<const std::complex<T> *>(in.data());
  auto d_out=reinterpret_cast<T *>(res.mutable_data());
  {
  py::gil_scoped_release release;
  T fct = norm_fct<T>(inorm, dims_out, axes);
  mr::c2r(dims_out, s_in, s_out, axes, forward, d_in, d_out, fct,
    nthreads);
  }
  return res;
  }

py::array c2r(const py::array &in, const py::object &axes_, size_t lastsize,
  bool forward, int inorm, py::object &out_, size_t nthreads)
  {
  DISPATCH(in, c128, c64, clong, c2r_internal, (in, axes_, lastsize, forward,
    inorm, out_, nthreads))
  }

template<typename T> py::array separable_hartley_internal(const py::array &in,
  const py::object &axes_, int inorm, py::object &out_, size_t nthreads)
  {
  auto dims(copy_shape(in));
  py::array res = prepare_output<T>(out_, dims);
  auto axes = makeaxes(in, axes_);
  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);
  mr::r2r_separable_hartley(dims, s_in, s_out, axes, d_in, d_out, fct,
    nthreads);
  }
  return res;
  }

py::array separable_hartley(const py::array &in, const py::object &axes_,
  int inorm, py::object &out_, size_t nthreads)
  {
  DISPATCH(in, f64, f32, flong, separable_hartley_internal, (in, axes_, inorm,
    out_, nthreads))
  }

template<typename T> py::array genuine_hartley_internal(const py::array &in,
  const py::object &axes_, int inorm, py::object &out_, size_t nthreads)
  {
  auto dims(copy_shape(in));
  py::array res = prepare_output<T>(out_, dims);
  auto axes = makeaxes(in, axes_);
  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);
  mr::r2r_genuine_hartley(dims, s_in, s_out, axes, d_in, d_out, fct,
    nthreads);
  }
  return res;
  }

py::array genuine_hartley(const py::array &in, const py::object &axes_,
  int inorm, py::object &out_, size_t nthreads)
  {
  DISPATCH(in, f64, f32, flong, genuine_hartley_internal, (in, axes_, inorm,
    out_, nthreads))
  }

// Export good_size in raw C-API to reduce overhead (~4x faster)
PyObject * good_size(PyObject * /*self*/, PyObject * args)
  {
  Py_ssize_t n_ = -1;
  int real = false;
  if (!PyArg_ParseTuple(args, "n|p:good_size", &n_, &real))
    return nullptr;

  if (n_<0)
    {
    PyErr_SetString(PyExc_ValueError, "Target length must be positive");
    return nullptr;
    }
  if ((n_-1) > static_cast<Py_ssize_t>(std::numeric_limits<size_t>::max() / 11))
    {
    PyErr_Format(PyExc_ValueError,
                 "Target length is too large to perform an FFT: %zi", n_);
    return nullptr;
    }
  const auto n = static_cast<size_t>(n_);
  using namespace mr::detail_fft;
  return PyLong_FromSize_t(
    real ? util::good_size_real(n) : util::good_size_cmplx(n));
  }

const char *pypocketfft_DS = R"""(Fast Fourier and Hartley transforms.

This module supports
- single, double, and long double precision
- complex and real-valued transforms
- multi-dimensional transforms

For two- and higher-dimensional transforms the code will use SSE2 and AVX
vector instructions for faster execution if these are supported by the CPU and
were enabled during compilation.
)""";

const char *c2c_DS = R"""(Performs a complex FFT.

Parameters
----------
a : numpy.ndarray (any complex or real type)
    The input data. If its type is real, a more efficient real-to-complex
    transform will be used.
axes : list of integers
    The axes along which the FFT is carried out.
    If not set, all axes will be transformed.
forward : bool
    If `True`, a negative sign is used in the exponent, else a positive one.
inorm : int
    Normalization type
      0 : no normalization
      1 : divide by sqrt(N)
      2 : divide by N
    where N is the product of the lengths of the transformed axes.
out : numpy.ndarray (same shape as `a`, complex type with same accuracy as `a`)
    May be identical to `a`, but if it isn't, it must not overlap with `a`.
    If None, a new array is allocated to store the output.
nthreads : int
    Number of threads to use. If 0, use the system default (typically governed
    by the `OMP_NUM_THREADS` environment variable).

Returns
-------
numpy.ndarray (same shape as `a`, complex type with same accuracy as `a`)
    The transformed data.
)""";

const char *r2c_DS = R"""(Performs an FFT whose input is strictly real.

Parameters
----------
a : numpy.ndarray (any real type)
    The input data
axes : list of integers
    The axes along which the FFT is carried out.
    If not set, all axes will be transformed in ascending order.
forward : bool
    If `True`, a negative sign is used in the exponent, else a positive one.
inorm : int
    Normalization type
      0 : no normalization
      1 : divide by sqrt(N)
      2 : divide by N
    where N is the product of the lengths of the transformed input axes.
out : numpy.ndarray (complex type with same accuracy as `a`)
    For the required shape, see the `Returns` section.
    Must not overlap with `a`.
    If None, a new array is allocated to store the output.
nthreads : int
    Number of threads to use. If 0, use the system default (typically governed
    by the `OMP_NUM_THREADS` environment variable).

Returns
-------
numpy.ndarray (complex type with same accuracy as `a`)
    The transformed data. The shape is identical to that of the input array,
    except for the axis that was transformed last. If the length of that axis
    was n on input, it is n//2+1 on output.
)""";

const char *c2r_DS = R"""(Performs an FFT whose output is strictly real.

Parameters
----------
a : numpy.ndarray (any complex type)
    The input data
axes : list of integers
    The axes along which the FFT is carried out.
    If not set, all axes will be transformed in ascending order.
lastsize : the output size of the last axis to be transformed.
    If the corresponding input axis has size n, this can be 2*n-2 or 2*n-1.
forward : bool
    If `True`, a negative sign is used in the exponent, else a positive one.
inorm : int
    Normalization type
      0 : no normalization
      1 : divide by sqrt(N)
      2 : divide by N
    where N is the product of the lengths of the transformed output axes.
out : numpy.ndarray (real type with same accuracy as `a`)
    For the required shape, see the `Returns` section.
    Must not overlap with `a`.
    If None, a new array is allocated to store the output.
nthreads : int
    Number of threads to use. If 0, use the system default (typically governed
    by the `OMP_NUM_THREADS` environment variable).

Returns
-------
numpy.ndarray (real type with same accuracy as `a`)
    The transformed data. The shape is identical to that of the input array,
    except for the axis that was transformed last, which has now `lastsize`
    entries.
)""";

const char *r2r_fftpack_DS = R"""(Performs a real-valued FFT using the FFTPACK storage scheme.

Parameters
----------
a : numpy.ndarray (any real type)
    The input data
axes : list of integers
    The axes along which the FFT is carried out.
    If not set, all axes will be transformed.
real2hermitian : bool
    if True, the input is purely real and the output will have Hermitian
    symmetry and be stored in FFTPACK's halfcomplex ordering, otherwise the
    opposite.
forward : bool
    If `True`, a negative sign is used in the exponent, else a positive one.
inorm : int
    Normalization type
      0 : no normalization
      1 : divide by sqrt(N)
      2 : divide by N
    where N is the length of `axis`.
out : numpy.ndarray (same shape and data type as `a`)
    May be identical to `a`, but if it isn't, it must not overlap with `a`.
    If None, a new array is allocated to store the output.
nthreads : int
    Number of threads to use. If 0, use the system default (typically governed
    by the `OMP_NUM_THREADS` environment variable).

Returns
-------
numpy.ndarray (same shape and data type as `a`)
    The transformed data. The shape is identical to that of the input array.
)""";

const char *separable_hartley_DS = R"""(Performs a separable Hartley transform.
For every requested axis, a 1D forward Fourier transform is carried out, and
the real and imaginary parts of the result are added before the next axis is
processed.

Parameters
----------
a : numpy.ndarray (any real type)
    The input data
axes : list of integers
    The axes along which the transform is carried out.
    If not set, all axes will be transformed.
inorm : int
    Normalization type
      0 : no normalization
      1 : divide by sqrt(N)
      2 : divide by N
    where N is the product of the lengths of the transformed axes.
out : numpy.ndarray (same shape and data type as `a`)
    May be identical to `a`, but if it isn't, it must not overlap with `a`.
    If None, a new array is allocated to store the output.
nthreads : int
    Number of threads to use. If 0, use the system default (typically governed
    by the `OMP_NUM_THREADS` environment variable).

Returns
-------
numpy.ndarray (same shape and data type as `a`)
    The transformed data
)""";

const char *genuine_hartley_DS = R"""(Performs a full Hartley transform.
A full Fourier transform is carried out over the requested axes, and the
sum of real and imaginary parts of the result is stored in the output
array. For a single transformed axis, this is identical to `separable_hartley`,
but when transforming multiple axes, the results are different.

Parameters
----------
a : numpy.ndarray (any real type)
    The input data
axes : list of integers
    The axes along which the transform is carried out.
    If not set, all axes will be transformed.
inorm : int
    Normalization type
      0 : no normalization
      1 : divide by sqrt(N)
      2 : divide by N
    where N is the product of the lengths of the transformed axes.
out : numpy.ndarray (same shape and data type as `a`)
    May be identical to `a`, but if it isn't, it must not overlap with `a`.
    If None, a new array is allocated to store the output.
nthreads : int
    Number of threads to use. If 0, use the system default (typically governed
    by the `OMP_NUM_THREADS` environment variable).

Returns
-------
numpy.ndarray (same shape and data type as `a`)
    The transformed data
)""";

const char *dct_DS = R"""(Performs a discrete cosine transform.

Parameters
----------
a : numpy.ndarray (any real type)
    The input data
type : integer
    the type of DCT. Must be in [1; 4].
axes : list of integers
    The axes along which the transform is carried out.
    If not set, all axes will be transformed.
inorm : int
    Normalization type
      0 : no normalization
      1 : make transform orthogonal and divide by sqrt(N)
      2 : divide by N
    where N is the product of n_i for every transformed axis i.
    n_i is 2*(<axis_length>-1 for type 1 and 2*<axis length>
    for types 2, 3, 4.
    Making the transform orthogonal involves the following additional steps
    for every 1D sub-transform:
      Type 1 : multiply first and last input value by sqrt(2)
               divide first and last output value by sqrt(2)
      Type 2 : divide first output value by sqrt(2)
      Type 3 : multiply first input value by sqrt(2)
      Type 4 : nothing
out : numpy.ndarray (same shape and data type as `a`)
    May be identical to `a`, but if it isn't, it must not overlap with `a`.
    If None, a new array is allocated to store the output.
nthreads : int
    Number of threads to use. If 0, use the system default (typically governed
    by the `OMP_NUM_THREADS` environment variable).

Returns
-------
numpy.ndarray (same shape and data type as `a`)
    The transformed data
)""";

const char *dst_DS = R"""(Performs a discrete sine transform.

Parameters
----------
a : numpy.ndarray (any real type)
    The input data
type : integer
    the type of DST. Must be in [1; 4].
axes : list of integers
    The axes along which the transform is carried out.
    If not set, all axes will be transformed.
inorm : int
    Normalization type
      0 : no normalization
      1 : make transform orthogonal and divide by sqrt(N)
      2 : divide by N
    where N is the product of n_i for every transformed axis i.
    n_i is 2*(<axis_length>+1 for type 1 and 2*<axis length>
    for types 2, 3, 4.
    Making the transform orthogonal involves the following additional steps
    for every 1D sub-transform:
      Type 1 : nothing
      Type 2 : divide first output value by sqrt(2)
      Type 3 : multiply first input value by sqrt(2)
      Type 4 : nothing
out : numpy.ndarray (same shape and data type as `a`)
    May be identical to `a`, but if it isn't, it must not overlap with `a`.
    If None, a new array is allocated to store the output.
nthreads : int
    Number of threads to use. If 0, use the system default (typically governed
    by the `OMP_NUM_THREADS` environment variable).

Returns
-------
numpy.ndarray (same shape and data type as `a`)
    The transformed data
)""";

const char * good_size_DS = R"""(Returns a good length to pad an FFT to.

Parameters
----------
n : int
    Minimum transform length
real : bool, optional
    True if either input or output of FFT should be fully real.

Returns
-------
out : int
    The smallest fast size >= n

)""";

} // unnamed namespace

PYBIND11_MODULE(pypocketfft, m)
  {
  using namespace pybind11::literals;

  m.doc() = pypocketfft_DS;
  m.def("c2c", c2c, c2c_DS, "a"_a, "axes"_a=None, "forward"_a=true,
    "inorm"_a=0, "out"_a=None, "nthreads"_a=1);
  m.def("r2c", r2c, r2c_DS, "a"_a, "axes"_a=None, "forward"_a=true,
    "inorm"_a=0, "out"_a=None, "nthreads"_a=1);
  m.def("c2r", c2r, c2r_DS, "a"_a, "axes"_a=None, "lastsize"_a=0,
    "forward"_a=true, "inorm"_a=0, "out"_a=None, "nthreads"_a=1);
  m.def("r2r_fftpack", r2r_fftpack, r2r_fftpack_DS, "a"_a, "axes"_a,
    "real2hermitian"_a, "forward"_a, "inorm"_a=0, "out"_a=None, "nthreads"_a=1);
  m.def("separable_hartley", separable_hartley, separable_hartley_DS, "a"_a,
    "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("dct", dct, dct_DS, "a"_a, "type"_a, "axes"_a=None, "inorm"_a=0,
    "out"_a=None, "nthreads"_a=1);
  m.def("dst", dst, dst_DS, "a"_a, "type"_a, "axes"_a=None, "inorm"_a=0,
    "out"_a=None, "nthreads"_a=1);

  static PyMethodDef good_size_meth[] =
    {{"good_size", good_size, METH_VARARGS, good_size_DS}, {0}};
  PyModule_AddFunctions(m.ptr(), good_size_meth);
  }