pocketfft_hdronly.h 108 KB
Newer Older
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
This file is part of pocketfft.

Copyright (C) 2010-2019 Max-Planck-Society
Author: Martin Reinecke

All rights reserved.

Redistribution and use in source and binary forms, with or without modification,
are permitted provided that the following conditions are met:

* Redistributions of source code must retain the above copyright notice, this
  list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright notice, this
  list of conditions and the following disclaimer in the documentation and/or
  other materials provided with the distribution.
* Neither the name of the copyright holder nor the names of its contributors may
  be used to endorse or promote products derived from this software without
  specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
32 33 34 35

#ifndef POCKETFFT_HDRONLY_H
#define POCKETFFT_HDRONLY_H

36
#ifndef __cplusplus
37
#error This file is C++ and requires a C++ compiler.
38 39
#endif

Martin Reinecke's avatar
sync  
Martin Reinecke committed
40
#if !(__cplusplus >= 201103L || _MSVC_LANG+0L >= 201103L)
41
#error This file requires at least C++11 support.
42 43
#endif

44 45 46 47
#ifndef POCKETFFT_CACHE_SIZE
#define POCKETFFT_CACHE_SIZE 16
#endif

48 49 50 51 52 53
#include <cmath>
#include <cstring>
#include <cstdlib>
#include <stdexcept>
#include <memory>
#include <vector>
Martin Reinecke's avatar
sync  
Martin Reinecke committed
54
#include <complex>
55 56
#if POCKETFFT_CACHE_SIZE!=0
#include <array>
Martin Reinecke's avatar
Martin Reinecke committed
57
#include <mutex>
58
#endif
Martin Reinecke's avatar
Martin Reinecke committed
59 60 61 62
#ifdef POCKETFFT_OPENMP
#include <omp.h>
#endif

63

Martin Reinecke's avatar
Martin Reinecke committed
64
#if defined(__GNUC__)
65 66
#define POCKETFFT_NOINLINE __attribute__((noinline))
#define POCKETFFT_RESTRICT __restrict__
Martin Reinecke's avatar
Martin Reinecke committed
67
#elif defined(_MSC_VER)
68 69
#define POCKETFFT_NOINLINE __declspec(noinline)
#define POCKETFFT_RESTRICT __restrict
70
#else
71 72
#define POCKETFFT_NOINLINE
#define POCKETFFT_RESTRICT
73 74 75 76 77 78
#endif

namespace pocketfft {

namespace detail {

Martin Reinecke's avatar
Martin Reinecke committed
79 80
using namespace std;

Martin Reinecke's avatar
Martin Reinecke committed
81 82 83 84 85 86
using shape_t = vector<size_t>;
using stride_t = vector<ptrdiff_t>;

constexpr bool FORWARD  = true,
               BACKWARD = false;

Martin Reinecke's avatar
sync  
Martin Reinecke committed
87 88 89 90
// only enable vector support for gcc>=5.0 and clang>=5.0
#ifndef POCKETFFT_NO_VECTORS
#define POCKETFFT_NO_VECTORS
#if defined(__INTEL_COMPILER)
91
// do nothing. This is necessary because this compiler also sets __GNUC__.
Martin Reinecke's avatar
sync  
Martin Reinecke committed
92 93 94 95 96 97 98 99 100 101 102
#elif defined(__clang__)
#if __clang__>=5
#undef POCKETFFT_NO_VECTORS
#endif
#elif defined(__GNUC__)
#if __GNUC__>=5
#undef POCKETFFT_NO_VECTORS
#endif
#endif
#endif

Martin Reinecke's avatar
Martin Reinecke committed
103 104
template<typename T> struct VLEN { static constexpr size_t val=1; };

Martin Reinecke's avatar
Martin Reinecke committed
105 106
#ifndef POCKETFFT_NO_VECTORS
#if (defined(__AVX512F__))
Martin Reinecke's avatar
Martin Reinecke committed
107 108
template<> struct VLEN<float> { static constexpr size_t val=16; };
template<> struct VLEN<double> { static constexpr size_t val=8; };
Martin Reinecke's avatar
Martin Reinecke committed
109
#elif (defined(__AVX__))
Martin Reinecke's avatar
Martin Reinecke committed
110 111
template<> struct VLEN<float> { static constexpr size_t val=8; };
template<> struct VLEN<double> { static constexpr size_t val=4; };
Martin Reinecke's avatar
Martin Reinecke committed
112
#elif (defined(__SSE2__))
Martin Reinecke's avatar
Martin Reinecke committed
113 114
template<> struct VLEN<float> { static constexpr size_t val=4; };
template<> struct VLEN<double> { static constexpr size_t val=2; };
Martin Reinecke's avatar
sync  
Martin Reinecke committed
115
#elif (defined(__VSX__))
Martin Reinecke's avatar
Martin Reinecke committed
116 117
template<> struct VLEN<float> { static constexpr size_t val=4; };
template<> struct VLEN<double> { static constexpr size_t val=2; };
Martin Reinecke's avatar
Martin Reinecke committed
118 119 120 121 122
#else
#define POCKETFFT_NO_VECTORS
#endif
#endif

Martin Reinecke's avatar
Martin Reinecke committed
123
template<typename T> class arr
124 125 126 127 128
  {
  private:
    T *p;
    size_t sz;

Martin Reinecke's avatar
Martin Reinecke committed
129
#if defined(POCKETFFT_NO_VECTORS)
130 131 132 133 134
    static T *ralloc(size_t num)
      {
      if (num==0) return nullptr;
      void *res = malloc(num*sizeof(T));
      if (!res) throw bad_alloc();
Martin Reinecke's avatar
Martin Reinecke committed
135 136 137 138 139 140 141 142
      return reinterpret_cast<T *>(res);
      }
    static void dealloc(T *ptr)
      { free(ptr); }
#elif __cplusplus >= 201703L
    static T *ralloc(size_t num)
      {
      if (num==0) return nullptr;
143 144
      void *res = aligned_alloc(64,num*sizeof(T));
      if (!res) throw bad_alloc();
Martin Reinecke's avatar
Martin Reinecke committed
145 146 147 148
      return reinterpret_cast<T *>(res);
      }
    static void dealloc(T *ptr)
      { free(ptr); }
149
#else // portable emulation
Martin Reinecke's avatar
Martin Reinecke committed
150 151 152
    static T *ralloc(size_t num)
      {
      if (num==0) return nullptr;
153 154 155 156 157 158
      void *ptr = malloc(num*sizeof(T)+64);
      if (!ptr) throw bad_alloc();
      T *res = reinterpret_cast<T *>
        ((reinterpret_cast<size_t>(ptr) & ~(size_t(63))) + 64);
      (reinterpret_cast<void**>(res))[-1] = ptr;
      return res;
Martin Reinecke's avatar
Martin Reinecke committed
159 160
      }
    static void dealloc(T *ptr)
161
      { if (ptr) free((reinterpret_cast<void**>(ptr))[-1]); }
Martin Reinecke's avatar
Martin Reinecke committed
162
#endif
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

  public:
    arr() : p(0), sz(0) {}
    arr(size_t n) : p(ralloc(n)), sz(n) {}
    arr(arr &&other)
      : p(other.p), sz(other.sz)
      { other.p=nullptr; other.sz=0; }
    ~arr() { dealloc(p); }

    void resize(size_t n)
      {
      if (n==sz) return;
      dealloc(p);
      p = ralloc(n);
      sz = n;
      }

    T &operator[](size_t idx) { return p[idx]; }
    const T &operator[](size_t idx) const { return p[idx]; }

    T *data() { return p; }
    const T *data() const { return p; }

    size_t size() const { return sz; }
  };

template<typename T> struct cmplx {
  T r, i;
  cmplx() {}
  cmplx(T r_, T i_) : r(r_), i(i_) {}
  void Set(T r_, T i_) { r=r_; i=i_; }
  void Set(T r_) { r=r_; i=T(0); }
  cmplx &operator+= (const cmplx &other)
    { r+=other.r; i+=other.i; return *this; }
  template<typename T2>cmplx &operator*= (T2 other)
    { r*=other; i*=other; return *this; }
199 200 201 202 203 204 205
  template<typename T2>cmplx &operator*= (const cmplx<T2> &other)
    {
    T tmp = r*other.r - i*other.i;
    i = r*other.i + i*other.r;
    r = tmp;
    return *this;
    }
206 207 208 209 210 211 212 213 214 215
  cmplx operator+ (const cmplx &other) const
    { return cmplx(r+other.r, i+other.i); }
  cmplx operator- (const cmplx &other) const
    { return cmplx(r-other.r, i-other.i); }
  template<typename T2> auto operator* (const T2 &other) const
    -> cmplx<decltype(r*other)>
    { return {r*other, i*other}; }
  template<typename T2> auto operator* (const cmplx<T2> &other) const
    -> cmplx<decltype(r+other.r)>
    { return {r*other.r-i*other.i, r*other.i + i*other.r}; }
Martin Reinecke's avatar
Martin Reinecke committed
216
  template<bool fwd, typename T2> auto special_mul (const cmplx<T2> &other) const
217 218
    -> cmplx<decltype(r+other.r)>
    {
Martin Reinecke's avatar
sync  
Martin Reinecke committed
219
    using Tres = cmplx<decltype(r+other.r)>;
Martin Reinecke's avatar
Martin Reinecke committed
220 221
    return fwd ? Tres(r*other.r+i*other.i, i*other.r-r*other.i)
               : Tres(r*other.r-i*other.i, r*other.i+i*other.r);
222 223 224 225 226 227 228 229 230 231
    }
};
template<typename T> void PMC(cmplx<T> &a, cmplx<T> &b,
  const cmplx<T> &c, const cmplx<T> &d)
  { a = c+d; b = c-d; }
template<typename T> cmplx<T> conj(const cmplx<T> &a)
  { return {a.r, -a.i}; }

template<typename T> void ROT90(cmplx<T> &a)
  { auto tmp_=a.r; a.r=-a.i; a.i=tmp_; }
Martin Reinecke's avatar
Martin Reinecke committed
232 233
template<bool fwd, typename T> void ROTX90(cmplx<T> &a)
  { auto tmp_= fwd ? -a.r : a.r; a.r = fwd ? a.i : -a.i; a.i=tmp_; }
234 235 236 237 238 239 240 241

//
// twiddle factor section
//

template<typename T> class sincos_2pibyn
  {
  private:
Martin Reinecke's avatar
cleanup  
Martin Reinecke committed
242
    using Thigh = typename conditional<(sizeof(T)>sizeof(double)), T, double>::type;
243 244
    arr<T> data;

245
    void my_sincosm1pi (Thigh a_, Thigh *POCKETFFT_RESTRICT res)
246
      {
Martin Reinecke's avatar
sync  
Martin Reinecke committed
247 248
      if (sizeof(Thigh)>sizeof(double)) // don't have the code for long double
        {
Martin Reinecke's avatar
sync  
Martin Reinecke committed
249 250 251
        constexpr Thigh pi = Thigh(3.141592653589793238462643383279502884197L);
        auto s = sin(pi*a_);
        res[1] = s;
Martin Reinecke's avatar
sync  
Martin Reinecke committed
252 253 254
        res[0] = (s*s)/(-sqrt((1-s)*(1+s))-1);
        return;
        }
Martin Reinecke's avatar
sync  
Martin Reinecke committed
255 256 257
      // adapted from https://stackoverflow.com/questions/42792939/
      // CAUTION: this function only works for arguments in the range
      //          [-0.25; 0.25]!
Martin Reinecke's avatar
sync  
Martin Reinecke committed
258
      double a = double(a_);
259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282
      double s = a * a;
      /* Approximate cos(pi*x)-1 for x in [-0.25,0.25] */
      double r =     -1.0369917389758117e-4;
      r = fma (r, s,  1.9294935641298806e-3);
      r = fma (r, s, -2.5806887942825395e-2);
      r = fma (r, s,  2.3533063028328211e-1);
      r = fma (r, s, -1.3352627688538006e+0);
      r = fma (r, s,  4.0587121264167623e+0);
      r = fma (r, s, -4.9348022005446790e+0);
      double c = r*s;
      /* Approximate sin(pi*x) for x in [-0.25,0.25] */
      r =             4.6151442520157035e-4;
      r = fma (r, s, -7.3700183130883555e-3);
      r = fma (r, s,  8.2145868949323936e-2);
      r = fma (r, s, -5.9926452893214921e-1);
      r = fma (r, s,  2.5501640398732688e+0);
      r = fma (r, s, -5.1677127800499516e+0);
      s = s * a;
      r = r * s;
      s = fma (a, 3.1415926535897931e+0, r);
      res[0] = c;
      res[1] = s;
      }

283 284
    POCKETFFT_NOINLINE void calc_first_octant(size_t den,
      T * POCKETFFT_RESTRICT res)
285 286 287 288 289
      {
      size_t n = (den+4)>>3;
      if (n==0) return;
      res[0]=1.; res[1]=0.;
      if (n==1) return;
Martin Reinecke's avatar
Martin Reinecke committed
290
      size_t l1 = size_t(sqrt(n));
Martin Reinecke's avatar
sync  
Martin Reinecke committed
291
      arr<Thigh> tmp(2*l1);
292 293
      for (size_t i=1; i<l1; ++i)
        {
Martin Reinecke's avatar
sync  
Martin Reinecke committed
294 295 296
        my_sincosm1pi(Thigh(2*i)/Thigh(den),&tmp[2*i]);
        res[2*i  ] = T(tmp[2*i]+1);
        res[2*i+1] = T(tmp[2*i+1]);
297 298 299 300
        }
      size_t start=l1;
      while(start<n)
        {
Martin Reinecke's avatar
sync  
Martin Reinecke committed
301
        Thigh cs[2];
Martin Reinecke's avatar
sync  
Martin Reinecke committed
302 303 304
        my_sincosm1pi((Thigh(2*start))/Thigh(den),cs);
        res[2*start] = T(cs[0]+1);
        res[2*start+1] = T(cs[1]);
305 306 307 308
        size_t end = l1;
        if (start+end>n) end = n-start;
        for (size_t i=1; i<end; ++i)
          {
Martin Reinecke's avatar
sync  
Martin Reinecke committed
309
          Thigh csx[2]={tmp[2*i], tmp[2*i+1]};
Martin Reinecke's avatar
sync  
Martin Reinecke committed
310 311
          res[2*(start+i)] = T(((cs[0]*csx[0] - cs[1]*csx[1] + cs[0]) + csx[0]) + 1);
          res[2*(start+i)+1] = T((cs[0]*csx[1] + cs[1]*csx[0]) + cs[1] + csx[1]);
312 313 314 315 316
          }
        start += l1;
        }
      }

317
    void calc_first_quadrant(size_t n, T * POCKETFFT_RESTRICT res)
318
      {
319
      T * POCKETFFT_RESTRICT p = res+n;
320 321 322 323 324
      calc_first_octant(n<<1, p);
      size_t ndone=(n+2)>>2;
      size_t i=0, idx1=0, idx2=2*ndone-2;
      for (; i+1<ndone; i+=2, idx1+=2, idx2-=2)
        {
Martin Reinecke's avatar
Martin Reinecke committed
325 326
        res[idx1] = p[2*i  ]; res[idx1+1] = p[2*i+1];
        res[idx2] = p[2*i+3]; res[idx2+1] = p[2*i+2];
327 328
        }
      if (i!=ndone)
Martin Reinecke's avatar
Martin Reinecke committed
329
        { res[idx1] = p[2*i]; res[idx1+1] = p[2*i+1]; }
330 331
      }

332
    void calc_first_half(size_t n, T * POCKETFFT_RESTRICT res)
333
      {
Martin Reinecke's avatar
sync  
Martin Reinecke committed
334
      int ndone=int(n+1)>>1;
335 336
      T * p = res+n-1;
      calc_first_octant(n<<2, p);
Martin Reinecke's avatar
sync  
Martin Reinecke committed
337
      int i4=0, in=int(n), i=0;
338
      for (; i4<=in-i4; ++i, i4+=4) // octant 0
Martin Reinecke's avatar
Martin Reinecke committed
339
        { res[2*i] = p[2*i4]; res[2*i+1] = p[2*i4+1]; }
340
      for (; i4-in <= 0; ++i, i4+=4) // octant 1
Martin Reinecke's avatar
sync  
Martin Reinecke committed
341
        { auto xm = in-i4; res[2*i] = p[2*xm+1]; res[2*i+1] = p[2*xm]; }
342
      for (; i4<=3*in-i4; ++i, i4+=4) // octant 2
Martin Reinecke's avatar
sync  
Martin Reinecke committed
343
        { auto xm = i4-in; res[2*i] = -p[2*xm+1]; res[2*i+1] = p[2*xm]; }
344
      for (; i<ndone; ++i, i4+=4) // octant 3
Martin Reinecke's avatar
sync  
Martin Reinecke committed
345
        { auto xm = 2*in-i4; res[2*i] = -p[2*xm]; res[2*i+1] = p[2*xm+1]; }
346 347
      }

348
    void fill_first_quadrant(size_t n, T * POCKETFFT_RESTRICT res)
349
      {
Martin Reinecke's avatar
sync  
Martin Reinecke committed
350
      constexpr T hsqt2 = T(0.707106781186547524400844362104849L);
351 352 353 354
      size_t quart = n>>2;
      if ((n&7)==0)
        res[quart] = res[quart+1] = hsqt2;
      for (size_t i=2, j=2*quart-2; i<quart; i+=2, j-=2)
Martin Reinecke's avatar
Martin Reinecke committed
355
        { res[j] = res[i+1]; res[j+1] = res[i]; }
356 357
      }

358
    POCKETFFT_NOINLINE void fill_first_half(size_t n, T * POCKETFFT_RESTRICT res)
359 360 361 362
      {
      size_t half = n>>1;
      if ((n&3)==0)
        for (size_t i=0; i<half; i+=2)
Martin Reinecke's avatar
Martin Reinecke committed
363
          { res[i+half] = -res[i+1]; res[i+half+1] = res[i]; }
364 365
      else
        for (size_t i=2, j=2*half-2; i<half; i+=2, j-=2)
Martin Reinecke's avatar
Martin Reinecke committed
366
          { res[j] = -res[i]; res[j+1] = res[i+1]; }
367 368
      }

369
    void fill_second_half(size_t n, T * POCKETFFT_RESTRICT res)
370 371 372 373 374 375
      {
      if ((n&1)==0)
        for (size_t i=0; i<n; ++i)
          res[i+n] = -res[i];
      else
        for (size_t i=2, j=2*n-2; i<n; i+=2, j-=2)
Martin Reinecke's avatar
Martin Reinecke committed
376
          { res[j] = res[i]; res[j+1] = -res[i+1]; }
377 378
      }

379
    POCKETFFT_NOINLINE void sincos_2pibyn_half(size_t n, T * POCKETFFT_RESTRICT res)
380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396
      {
      if ((n&3)==0)
        {
        calc_first_octant(n, res);
        fill_first_quadrant(n, res);
        fill_first_half(n, res);
        }
      else if ((n&1)==0)
        {
        calc_first_quadrant(n, res);
        fill_first_half(n, res);
        }
      else
        calc_first_half(n, res);
      }

  public:
397
    POCKETFFT_NOINLINE sincos_2pibyn(size_t n, bool half)
398 399 400 401 402 403 404 405 406 407 408 409
      : data(2*n)
      {
      sincos_2pibyn_half(n, data.data());
      if (!half) fill_second_half(n, data.data());
      }

    T operator[](size_t idx) const { return data[idx]; }
    const T *rdata() const { return data; }
    const cmplx<T> *cdata() const
      { return reinterpret_cast<const cmplx<T> *>(data.data()); }
  };

Martin Reinecke's avatar
Martin Reinecke committed
410
struct util // hack to avoid duplicate symbols
411
  {
412
  static POCKETFFT_NOINLINE size_t largest_prime_factor (size_t n)
413
    {
Martin Reinecke's avatar
Martin Reinecke committed
414 415 416
    size_t res=1;
    while ((n&1)==0)
      { res=2; n>>=1; }
Martin Reinecke's avatar
Martin Reinecke committed
417 418 419
    for (size_t x=3; x*x<=n; x+=2)
      while ((n%x)==0)
        { res=x; n/=x; }
Martin Reinecke's avatar
Martin Reinecke committed
420 421 422 423
    if (n>1) res=n;
    return res;
    }

424
  static POCKETFFT_NOINLINE double cost_guess (size_t n)
425
    {
Martin Reinecke's avatar
sync  
Martin Reinecke committed
426
    constexpr double lfp=1.1; // penalty for non-hardcoded larger factors
Martin Reinecke's avatar
Martin Reinecke committed
427 428 429 430
    size_t ni=n;
    double result=0.;
    while ((n&1)==0)
      { result+=2; n>>=1; }
Martin Reinecke's avatar
Martin Reinecke committed
431 432 433 434 435 436
    for (size_t x=3; x*x<=n; x+=2)
      while ((n%x)==0)
        {
        result+= (x<=5) ? double(x) : lfp*double(x); // penalize larger prime factors
        n/=x;
        }
Martin Reinecke's avatar
sync  
Martin Reinecke committed
437 438
    if (n>1) result+=(n<=5) ? double(n) : lfp*double(n);
    return result*double(ni);
439 440
    }

Martin Reinecke's avatar
Martin Reinecke committed
441
  /* returns the smallest composite of 2, 3, 5, 7 and 11 which is >= n */
442
  static POCKETFFT_NOINLINE size_t good_size(size_t n)
Martin Reinecke's avatar
Martin Reinecke committed
443 444 445 446 447 448 449 450 451 452 453 454
    {
    if (n<=12) return n;

    size_t bestfac=2*n;
    for (size_t f2=1; f2<bestfac; f2*=2)
      for (size_t f23=f2; f23<bestfac; f23*=3)
        for (size_t f235=f23; f235<bestfac; f235*=5)
          for (size_t f2357=f235; f2357<bestfac; f2357*=7)
            for (size_t f235711=f2357; f235711<bestfac; f235711*=11)
              if (f235711>=n) bestfac=f235711;
    return bestfac;
    }
455

Martin Reinecke's avatar
Martin Reinecke committed
456 457 458 459 460 461 462
  static size_t prod(const shape_t &shape)
    {
    size_t res=1;
    for (auto sz: shape)
      res*=sz;
    return res;
    }
Martin Reinecke's avatar
Martin Reinecke committed
463

464
  static POCKETFFT_NOINLINE void sanity_check(const shape_t &shape,
Martin Reinecke's avatar
Martin Reinecke committed
465 466 467 468 469 470
    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");
Martin Reinecke's avatar
sync  
Martin Reinecke committed
471 472
    if (inplace && (stride_in!=stride_out))
      throw runtime_error("stride mismatch");
Martin Reinecke's avatar
Martin Reinecke committed
473 474
    }

475
  static POCKETFFT_NOINLINE void sanity_check(const shape_t &shape,
Martin Reinecke's avatar
Martin Reinecke committed
476 477 478 479 480 481 482 483
    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)
      {
484 485
      if (ax>=ndim) throw invalid_argument("bad axis number");
      if (++tmp[ax]>1) throw invalid_argument("axis specified repeatedly");
Martin Reinecke's avatar
Martin Reinecke committed
486 487 488
      }
    }

489
  static POCKETFFT_NOINLINE void sanity_check(const shape_t &shape,
Martin Reinecke's avatar
Martin Reinecke committed
490 491 492 493
    const stride_t &stride_in, const stride_t &stride_out, bool inplace,
    size_t axis)
    {
    sanity_check(shape, stride_in, stride_out, inplace);
494
    if (axis>=shape.size()) throw invalid_argument("bad axis number");
Martin Reinecke's avatar
Martin Reinecke committed
495
    }
Martin Reinecke's avatar
Martin Reinecke committed
496 497

#ifdef POCKETFFT_OPENMP
Martin Reinecke's avatar
sync  
Martin Reinecke committed
498 499
    static size_t nthreads() { return size_t(omp_get_num_threads()); }
    static size_t thread_num() { return size_t(omp_get_thread_num()); }
Martin Reinecke's avatar
Martin Reinecke committed
500 501 502 503
    static size_t thread_count (size_t nthreads, const shape_t &shape,
      size_t axis)
      {
      if (nthreads==1) return 1;
Martin Reinecke's avatar
Martin Reinecke committed
504
      if (prod(shape) < 20*shape[axis]) return 1;
Martin Reinecke's avatar
sync  
Martin Reinecke committed
505
      return (nthreads==0) ? size_t(omp_get_max_threads()) : nthreads;
Martin Reinecke's avatar
Martin Reinecke committed
506
      }
Martin Reinecke's avatar
Martin Reinecke committed
507
#else
Martin Reinecke's avatar
Martin Reinecke committed
508 509
    static constexpr size_t nthreads() { return 1; }
    static constexpr size_t thread_num() { return 0; }
Martin Reinecke's avatar
Martin Reinecke committed
510
#endif
Martin Reinecke's avatar
Martin Reinecke committed
511
  };
512 513 514 515 516 517 518 519 520 521 522 523 524 525

//
// complex FFTPACK transforms
//

template<typename T0> class cfftp
  {
  private:
    struct fctdata
      {
      size_t fct;
      cmplx<T0> *tw, *tws;
      };

Martin Reinecke's avatar
Martin Reinecke committed
526
    size_t length;
527
    arr<cmplx<T0>> mem;
Martin Reinecke's avatar
Martin Reinecke committed
528
    vector<fctdata> fact;
529 530

    void add_factor(size_t factor)
Martin Reinecke's avatar
Martin Reinecke committed
531
      { fact.push_back({factor, nullptr, nullptr}); }
532

Martin Reinecke's avatar
Martin Reinecke committed
533
template<bool fwd, typename T> void pass2 (size_t ido, size_t l1,
534 535
  const T * POCKETFFT_RESTRICT cc, T * POCKETFFT_RESTRICT ch,
  const cmplx<T0> * POCKETFFT_RESTRICT wa)
536 537 538
  {
  constexpr size_t cdim=2;

539 540
  auto CH = [ch,ido,l1](size_t a, size_t b, size_t c) -> T&
    { return ch[a+ido*(b+l1*c)]; };
541
  auto CC = [cc,ido,cdim](size_t a, size_t b, size_t c) -> const T&
542 543 544 545
    { return cc[a+ido*(b+cdim*c)]; };
  auto WA = [wa, ido](size_t x, size_t i)
    { return wa[i-1+x*(ido-1)]; };

546 547 548 549 550 551 552 553 554 555 556 557 558 559
  if (ido==1)
    for (size_t k=0; k<l1; ++k)
      {
      CH(0,k,0) = CC(0,0,k)+CC(0,1,k);
      CH(0,k,1) = CC(0,0,k)-CC(0,1,k);
      }
  else
    for (size_t k=0; k<l1; ++k)
      {
      CH(0,k,0) = CC(0,0,k)+CC(0,1,k);
      CH(0,k,1) = CC(0,0,k)-CC(0,1,k);
      for (size_t i=1; i<ido; ++i)
        {
        CH(i,k,0) = CC(i,0,k)+CC(i,1,k);
Martin Reinecke's avatar
Martin Reinecke committed
560
        CH(i,k,1) = (CC(i,0,k)-CC(i,1,k)).template special_mul<fwd>(WA(0,i));
561 562 563 564
        }
      }
  }

565
#define POCKETFFT_PREP3(idx) \
566 567 568
        T t0 = CC(idx,0,k), t1, t2; \
        PMC (t1,t2,CC(idx,1,k),CC(idx,2,k)); \
        CH(idx,k,0)=t0+t1;
569
#define POCKETFFT_PARTSTEP3a(u1,u2,twr,twi) \
570 571 572 573 574 575
        { \
        T ca,cb; \
        ca=t0+t1*twr; \
        cb=t2*twi; ROT90(cb); \
        PMC(CH(0,k,u1),CH(0,k,u2),ca,cb) ;\
        }
576
#define POCKETFFT_PARTSTEP3b(u1,u2,twr,twi) \
577 578 579 580 581
        { \
        T ca,cb,da,db; \
        ca=t0+t1*twr; \
        cb=t2*twi; ROT90(cb); \
        PMC(da,db,ca,cb); \
Martin Reinecke's avatar
Martin Reinecke committed
582 583
        CH(i,k,u1) = da.template special_mul<fwd>(WA(u1-1,i)); \
        CH(i,k,u2) = db.template special_mul<fwd>(WA(u2-1,i)); \
584
        }
Martin Reinecke's avatar
Martin Reinecke committed
585
template<bool fwd, typename T> void pass3 (size_t ido, size_t l1,
586 587
  const T * POCKETFFT_RESTRICT cc, T * POCKETFFT_RESTRICT ch,
  const cmplx<T0> * POCKETFFT_RESTRICT wa)
588 589
  {
  constexpr size_t cdim=3;
Martin Reinecke's avatar
sync  
Martin Reinecke committed
590
  constexpr T0 tw1r=-0.5,
Martin Reinecke's avatar
Martin Reinecke committed
591
               tw1i= (fwd ? -1: 1) * T0(0.8660254037844386467637231707529362L);
592

593 594
  auto CH = [ch,ido,l1](size_t a, size_t b, size_t c) -> T&
    { return ch[a+ido*(b+l1*c)]; };
595
  auto CC = [cc,ido,cdim](size_t a, size_t b, size_t c) -> const T&
596 597 598 599
    { return cc[a+ido*(b+cdim*c)]; };
  auto WA = [wa, ido](size_t x, size_t i)
    { return wa[i-1+x*(ido-1)]; };

600 601 602
  if (ido==1)
    for (size_t k=0; k<l1; ++k)
      {
603 604
      POCKETFFT_PREP3(0)
      POCKETFFT_PARTSTEP3a(1,2,tw1r,tw1i)
605 606 607 608 609
      }
  else
    for (size_t k=0; k<l1; ++k)
      {
      {
610 611
      POCKETFFT_PREP3(0)
      POCKETFFT_PARTSTEP3a(1,2,tw1r,tw1i)
612 613 614
      }
      for (size_t i=1; i<ido; ++i)
        {
615 616
        POCKETFFT_PREP3(i)
        POCKETFFT_PARTSTEP3b(1,2,tw1r,tw1i)
617 618 619 620
        }
      }
  }

621 622 623
#undef POCKETFFT_PARTSTEP3b
#undef POCKETFFT_PARTSTEP3a
#undef POCKETFFT_PREP3
624

Martin Reinecke's avatar
Martin Reinecke committed
625
template<bool fwd, typename T> void pass4 (size_t ido, size_t l1,
626 627
  const T * POCKETFFT_RESTRICT cc, T * POCKETFFT_RESTRICT ch,
  const cmplx<T0> * POCKETFFT_RESTRICT wa)
628 629 630
  {
  constexpr size_t cdim=4;

631 632
  auto CH = [ch,ido,l1](size_t a, size_t b, size_t c) -> T&
    { return ch[a+ido*(b+l1*c)]; };
633
  auto CC = [cc,ido,cdim](size_t a, size_t b, size_t c) -> const T&
634 635 636 637
    { return cc[a+ido*(b+cdim*c)]; };
  auto WA = [wa, ido](size_t x, size_t i)
    { return wa[i-1+x*(ido-1)]; };

638 639 640 641 642 643
  if (ido==1)
    for (size_t k=0; k<l1; ++k)
      {
      T t1, t2, t3, t4;
      PMC(t2,t1,CC(0,0,k),CC(0,2,k));
      PMC(t3,t4,CC(0,1,k),CC(0,3,k));
Martin Reinecke's avatar
Martin Reinecke committed
644
      ROTX90<fwd>(t4);
645 646 647 648 649 650 651 652 653 654
      PMC(CH(0,k,0),CH(0,k,2),t2,t3);
      PMC(CH(0,k,1),CH(0,k,3),t1,t4);
      }
  else
    for (size_t k=0; k<l1; ++k)
      {
      {
      T t1, t2, t3, t4;
      PMC(t2,t1,CC(0,0,k),CC(0,2,k));
      PMC(t3,t4,CC(0,1,k),CC(0,3,k));
Martin Reinecke's avatar
Martin Reinecke committed
655
      ROTX90<fwd>(t4);
656 657 658 659 660 661 662 663 664
      PMC(CH(0,k,0),CH(0,k,2),t2,t3);
      PMC(CH(0,k,1),CH(0,k,3),t1,t4);
      }
      for (size_t i=1; i<ido; ++i)
        {
        T c2, c3, c4, t1, t2, t3, t4;
        T cc0=CC(i,0,k), cc1=CC(i,1,k),cc2=CC(i,2,k),cc3=CC(i,3,k);
        PMC(t2,t1,cc0,cc2);
        PMC(t3,t4,cc1,cc3);
Martin Reinecke's avatar
Martin Reinecke committed
665
        ROTX90<fwd>(t4);
666 667
        PMC(CH(i,k,0),c3,t2,t3);
        PMC(c2,c4,t1,t4);
Martin Reinecke's avatar
Martin Reinecke committed
668 669 670
        CH(i,k,1) = c2.template special_mul<fwd>(WA(0,i));
        CH(i,k,2) = c3.template special_mul<fwd>(WA(1,i));
        CH(i,k,3) = c4.template special_mul<fwd>(WA(2,i));
671 672 673 674
        }
      }
  }

675
#define POCKETFFT_PREP5(idx) \
676 677 678 679 680 681
        T t0 = CC(idx,0,k), t1, t2, t3, t4; \
        PMC (t1,t4,CC(idx,1,k),CC(idx,4,k)); \
        PMC (t2,t3,CC(idx,2,k),CC(idx,3,k)); \
        CH(idx,k,0).r=t0.r+t1.r+t2.r; \
        CH(idx,k,0).i=t0.i+t1.i+t2.i;

682
#define POCKETFFT_PARTSTEP5a(u1,u2,twar,twbr,twai,twbi) \
683 684 685 686 687 688 689 690 691
        { \
        T ca,cb; \
        ca.r=t0.r+twar*t1.r+twbr*t2.r; \
        ca.i=t0.i+twar*t1.i+twbr*t2.i; \
        cb.i=twai*t4.r twbi*t3.r; \
        cb.r=-(twai*t4.i twbi*t3.i); \
        PMC(CH(0,k,u1),CH(0,k,u2),ca,cb); \
        }

692
#define POCKETFFT_PARTSTEP5b(u1,u2,twar,twbr,twai,twbi) \
693 694 695 696 697 698 699
        { \
        T ca,cb,da,db; \
        ca.r=t0.r+twar*t1.r+twbr*t2.r; \
        ca.i=t0.i+twar*t1.i+twbr*t2.i; \
        cb.i=twai*t4.r twbi*t3.r; \
        cb.r=-(twai*t4.i twbi*t3.i); \
        PMC(da,db,ca,cb); \
Martin Reinecke's avatar
Martin Reinecke committed
700 701
        CH(i,k,u1) = da.template special_mul<fwd>(WA(u1-1,i)); \
        CH(i,k,u2) = db.template special_mul<fwd>(WA(u2-1,i)); \
702
        }
Martin Reinecke's avatar
Martin Reinecke committed
703
template<bool fwd, typename T> void pass5 (size_t ido, size_t l1,
704 705
  const T * POCKETFFT_RESTRICT cc, T * POCKETFFT_RESTRICT ch,
  const cmplx<T0> * POCKETFFT_RESTRICT wa)
706 707
  {
  constexpr size_t cdim=5;
Martin Reinecke's avatar
sync  
Martin Reinecke committed
708
  constexpr T0 tw1r= T0(0.3090169943749474241022934171828191L),
Martin Reinecke's avatar
Martin Reinecke committed
709
               tw1i= (fwd ? -1: 1) * T0(0.9510565162951535721164393333793821L),
Martin Reinecke's avatar
sync  
Martin Reinecke committed
710
               tw2r= T0(-0.8090169943749474241022934171828191L),
Martin Reinecke's avatar
Martin Reinecke committed
711
               tw2i= (fwd ? -1: 1) * T0(0.5877852522924731291687059546390728L);
712

713 714
  auto CH = [ch,ido,l1](size_t a, size_t b, size_t c) -> T&
    { return ch[a+ido*(b+l1*c)]; };
715
  auto CC = [cc,ido,cdim](size_t a, size_t b, size_t c) -> const T&
716 717 718 719
    { return cc[a+ido*(b+cdim*c)]; };
  auto WA = [wa, ido](size_t x, size_t i)
    { return wa[i-1+x*(ido-1)]; };

720 721 722
  if (ido==1)
    for (size_t k=0; k<l1; ++k)
      {
723 724 725
      POCKETFFT_PREP5(0)
      POCKETFFT_PARTSTEP5a(1,4,tw1r,tw2r,+tw1i,+tw2i)
      POCKETFFT_PARTSTEP5a(2,3,tw2r,tw1r,+tw2i,-tw1i)
726 727 728 729 730
      }
  else
    for (size_t k=0; k<l1; ++k)
      {
      {
731 732 733
      POCKETFFT_PREP5(0)
      POCKETFFT_PARTSTEP5a(1,4,tw1r,tw2r,+tw1i,+tw2i)
      POCKETFFT_PARTSTEP5a(2,3,tw2r,tw1r,+tw2i,-tw1i)
734 735 736
      }
      for (size_t i=1; i<ido; ++i)
        {
737 738 739
        POCKETFFT_PREP5(i)
        POCKETFFT_PARTSTEP5b(1,4,tw1r,tw2r,+tw1i,+tw2i)
        POCKETFFT_PARTSTEP5b(2,3,tw2r,tw1r,+tw2i,-tw1i)
740 741 742 743
        }
      }
  }

744 745 746
#undef POCKETFFT_PARTSTEP5b
#undef POCKETFFT_PARTSTEP5a
#undef POCKETFFT_PREP5
747

748
#define POCKETFFT_PREP7(idx) \
749 750 751 752 753 754 755
        T t1 = CC(idx,0,k), t2, t3, t4, t5, t6, t7; \
        PMC (t2,t7,CC(idx,1,k),CC(idx,6,k)); \
        PMC (t3,t6,CC(idx,2,k),CC(idx,5,k)); \
        PMC (t4,t5,CC(idx,3,k),CC(idx,4,k)); \
        CH(idx,k,0).r=t1.r+t2.r+t3.r+t4.r; \
        CH(idx,k,0).i=t1.i+t2.i+t3.i+t4.i;

756
#define POCKETFFT_PARTSTEP7a0(u1,u2,x1,x2,x3,y1,y2,y3,out1,out2) \
757 758 759 760 761 762 763 764
        { \
        T ca,cb; \
        ca.r=t1.r+x1*t2.r+x2*t3.r+x3*t4.r; \
        ca.i=t1.i+x1*t2.i+x2*t3.i+x3*t4.i; \
        cb.i=y1*t7.r y2*t6.r y3*t5.r; \
        cb.r=-(y1*t7.i y2*t6.i y3*t5.i); \
        PMC(out1,out2,ca,cb); \
        }
765 766 767
#define POCKETFFT_PARTSTEP7a(u1,u2,x1,x2,x3,y1,y2,y3) \
        POCKETFFT_PARTSTEP7a0(u1,u2,x1,x2,x3,y1,y2,y3,CH(0,k,u1),CH(0,k,u2))
#define POCKETFFT_PARTSTEP7(u1,u2,x1,x2,x3,y1,y2,y3) \
768 769
        { \
        T da,db; \
770
        POCKETFFT_PARTSTEP7a0(u1,u2,x1,x2,x3,y1,y2,y3,da,db) \
Martin Reinecke's avatar
Martin Reinecke committed
771 772
        CH(i,k,u1) = da.template special_mul<fwd>(WA(u1-1,i)); \
        CH(i,k,u2) = db.template special_mul<fwd>(WA(u2-1,i)); \
773 774
        }

Martin Reinecke's avatar
Martin Reinecke committed
775
template<bool fwd, typename T> void pass7(size_t ido, size_t l1,
776 777
  const T * POCKETFFT_RESTRICT cc, T * POCKETFFT_RESTRICT ch,
  const cmplx<T0> * POCKETFFT_RESTRICT wa)
778 779
  {
  constexpr size_t cdim=7;
Martin Reinecke's avatar
sync  
Martin Reinecke committed
780
  constexpr T0 tw1r= T0(0.6234898018587335305250048840042398L),
Martin Reinecke's avatar
Martin Reinecke committed
781
               tw1i= (fwd ? -1 : 1) * T0(0.7818314824680298087084445266740578L),
Martin Reinecke's avatar
sync  
Martin Reinecke committed
782
               tw2r= T0(-0.2225209339563144042889025644967948L),
Martin Reinecke's avatar
Martin Reinecke committed
783
               tw2i= (fwd ? -1 : 1) * T0(0.9749279121818236070181316829939312L),
Martin Reinecke's avatar
sync  
Martin Reinecke committed
784
               tw3r= T0(-0.9009688679024191262361023195074451L),
Martin Reinecke's avatar
Martin Reinecke committed
785
               tw3i= (fwd ? -1 : 1) * T0(0.433883739117558120475768332848359L);
786

787 788
  auto CH = [ch,ido,l1](size_t a, size_t b, size_t c) -> T&
    { return ch[a+ido*(b+l1*c)]; };
789
  auto CC = [cc,ido,cdim](size_t a, size_t b, size_t c) -> const T&
790 791 792 793
    { return cc[a+ido*(b+cdim*c)]; };
  auto WA = [wa, ido](size_t x, size_t i)
    { return wa[i-1+x*(ido-1)]; };

794 795 796
  if (ido==1)
    for (size_t k=0; k<l1; ++k)
      {
797 798 799 800
      POCKETFFT_PREP7(0)
      POCKETFFT_PARTSTEP7a(1,6,tw1r,tw2r,tw3r,+tw1i,+tw2i,+tw3i)
      POCKETFFT_PARTSTEP7a(2,5,tw2r,tw3r,tw1r,+tw2i,-tw3i,-tw1i)
      POCKETFFT_PARTSTEP7a(3,4,tw3r,tw1r,tw2r,+tw3i,-tw1i,+tw2i)
801 802 803 804 805
      }
  else
    for (size_t k=0; k<l1; ++k)
      {
      {
806 807 808 809
      POCKETFFT_PREP7(0)
      POCKETFFT_PARTSTEP7a(1,6,tw1r,tw2r,tw3r,+tw1i,+tw2i,+tw3i)
      POCKETFFT_PARTSTEP7a(2,5,tw2r,tw3r,tw1r,+tw2i,-tw3i,-tw1i)
      POCKETFFT_PARTSTEP7a(3,4,tw3r,tw1r,tw2r,+tw3i,-tw1i,+tw2i)
810 811 812
      }
      for (size_t i=1; i<ido; ++i)
        {
813 814 815 816
        POCKETFFT_PREP7(i)
        POCKETFFT_PARTSTEP7(1,6,tw1r,tw2r,tw3r,+tw1i,+tw2i,+tw3i)
        POCKETFFT_PARTSTEP7(2,5,tw2r,tw3r,tw1r,+tw2i,-tw3i,-tw1i)
        POCKETFFT_PARTSTEP7(3,4,tw3r,tw1r,tw2r,+tw3i,-tw1i,+tw2i)
817 818 819 820
        }
      }
  }

821 822 823 824
#undef POCKETFFT_PARTSTEP7
#undef POCKETFFT_PARTSTEP7a0
#undef POCKETFFT_PARTSTEP7a
#undef POCKETFFT_PREP7
825

Martin Reinecke's avatar
Martin Reinecke committed
826
template <bool fwd, typename T> void ROTX45(T &a)
Martin Reinecke's avatar
sync  
Martin Reinecke committed
827 828
  {
  constexpr T0 hsqt2=T0(0.707106781186547524400844362104849L);
Martin Reinecke's avatar
Martin Reinecke committed
829
  if (fwd)
Martin Reinecke's avatar
sync  
Martin Reinecke committed
830
    { auto tmp_=a.r; a.r=hsqt2*(a.r+a.i); a.i=hsqt2*(a.i-tmp_); }
Martin Reinecke's avatar
Martin Reinecke committed
831 832
  else
    { auto tmp_=a.r; a.r=hsqt2*(a.r-a.i); a.i=hsqt2*(a.i+tmp_); }
Martin Reinecke's avatar
sync  
Martin Reinecke committed
833
  }
Martin Reinecke's avatar
Martin Reinecke committed
834
template <bool fwd, typename T> void ROTX135(T &a)
Martin Reinecke's avatar
sync  
Martin Reinecke committed
835 836
  {
  constexpr T0 hsqt2=T0(0.707106781186547524400844362104849L);
Martin Reinecke's avatar
Martin Reinecke committed
837
  if (fwd)
Martin Reinecke's avatar
sync  
Martin Reinecke committed
838
    { auto tmp_=a.r; a.r=hsqt2*(a.i-a.r); a.i=hsqt2*(-tmp_-a.i); }
Martin Reinecke's avatar
Martin Reinecke committed
839 840
  else
    { auto tmp_=a.r; a.r=hsqt2*(-a.r-a.i); a.i=hsqt2*(tmp_-a.i); }
Martin Reinecke's avatar
sync  
Martin Reinecke committed
841 842 843 844
  }
template<typename T> inline void PMINPLACE(T &a, T &b)
  { T t = a; a.r+=b.r; a.i+=b.i; b.r=t.r-b.r; b.i=t.i-b.i; }

Martin Reinecke's avatar
Martin Reinecke committed
845
template<bool fwd, typename T> void pass8 (size_t ido, size_t l1,
846 847
  const T * POCKETFFT_RESTRICT cc, T * POCKETFFT_RESTRICT ch,
  const cmplx<T0> * POCKETFFT_RESTRICT wa)
Martin Reinecke's avatar
sync  
Martin Reinecke committed
848 849 850
  {
  constexpr size_t cdim=8;

851 852
  auto CH = [ch,ido,l1](size_t a, size_t b, size_t c) -> T&
    { return ch[a+ido*(b+l1*c)]; };
853
  auto CC = [cc,ido,cdim](size_t a, size_t b, size_t c) -> const T&
854 855 856 857
    { return cc[a+ido*(b+cdim*c)]; };
  auto WA = [wa, ido](size_t x, size_t i)
    { return wa[i-1+x*(ido-1)]; };

Martin Reinecke's avatar
sync  
Martin Reinecke committed
858 859 860 861 862 863 864 865
  if (ido==1)
    for (size_t k=0; k<l1; ++k)
      {
      T a0, a1, a2, a3, a4, a5, a6, a7;
      PMC(a0,a4,CC(0,0,k),CC(0,4,k));
      PMC(a1,a5,CC(0,1,k),CC(0,5,k));
      PMC(a2,a6,CC(0,2,k),CC(0,6,k));
      PMC(a3,a7,CC(0,3,k),CC(0,7,k));
Martin Reinecke's avatar
Martin Reinecke committed
866 867
      ROTX90<fwd>(a6);
      ROTX90<fwd>(a7);
Martin Reinecke's avatar
sync  
Martin Reinecke committed
868 869 870 871
      PMINPLACE(a0,a2);
      PMINPLACE(a1,a3);
      PMINPLACE(a4,a6);
      PMINPLACE(a5,a7);
Martin Reinecke's avatar
Martin Reinecke committed
872 873 874
      ROTX45<fwd>(a5);
      ROTX90<fwd>(a3);
      ROTX135<fwd>(a7);
Martin Reinecke's avatar
sync  
Martin Reinecke committed
875 876 877 878 879 880 881 882 883 884 885 886 887
      PMC(CH(0,k,0),CH(0,k,4),a0,a1);
      PMC(CH(0,k,1),CH(0,k,5),a4,a5);
      PMC(CH(0,k,2),CH(0,k,6),a2,a3);
      PMC(CH(0,k,3),CH(0,k,7),a6,a7);
      }
  else
    for (size_t k=0; k<l1; ++k)
      {
      T a0, a1, a2, a3, a4, a5, a6, a7;
      PMC(a0,a4,CC(0,0,k),CC(0,4,k));
      PMC(a1,a5,CC(0,1,k),CC(0,5,k));
      PMC(a2,a6,CC(0,2,k),CC(0,6,k));
      PMC(a3,a7,CC(0,3,k),CC(0,7,k));
Martin Reinecke's avatar
Martin Reinecke committed
888 889
      ROTX90<fwd>(a6);
      ROTX90<fwd>(a7);
Martin Reinecke's avatar
sync  
Martin Reinecke committed
890 891 892 893
      PMINPLACE(a0,a2);
      PMINPLACE(a1,a3);
      PMINPLACE(a4,a6);
      PMINPLACE(a5,a7);
Martin Reinecke's avatar
Martin Reinecke committed
894 895 896
      ROTX45<fwd>(a5);
      ROTX90<fwd>(a3);
      ROTX135<fwd>(a7);
Martin Reinecke's avatar
sync  
Martin Reinecke committed
897 898 899 900 901 902 903 904 905 906 907 908
      PMC(CH(0,k,0),CH(0,k,4),a0,a1);
      PMC(CH(0,k,1),CH(0,k,5),a4,a5);
      PMC(CH(0,k,2),CH(0,k,6),a2,a3);
      PMC(CH(0,k,3),CH(0,k,7),a6,a7);

      for (size_t i=1; i<ido; ++i)
        {
        T a0, a1, a2, a3, a4, a5, a6, a7;
        PMC(a0,a4,CC(i,0,k),CC(i,4,k));
        PMC(a1,a5,CC(i,1,k),CC(i,5,k));
        PMC(a2,a6,CC(i,2,k),CC(i,6,k));
        PMC(a3,a7,CC(i,3,k),CC(i,7,k));
Martin Reinecke's avatar
Martin Reinecke committed
909 910
        ROTX90<fwd>(a6);
        ROTX90<fwd>(a7);
Martin Reinecke's avatar
sync  
Martin Reinecke committed
911 912 913 914
        PMINPLACE(a0,a2);
        PMINPLACE(a1,a3);
        PMINPLACE(a4,a6);
        PMINPLACE(a5,a7);
Martin Reinecke's avatar
Martin Reinecke committed
915 916 917
        ROTX45<fwd>(a5);
        ROTX90<fwd>(a3);
        ROTX135<fwd>(a7);
Martin Reinecke's avatar
sync  
Martin Reinecke committed
918 919 920 921 922
        PMINPLACE(a0,a1);
        PMINPLACE(a2,a3);
        PMINPLACE(a4,a5);
        PMINPLACE(a6,a7);
        CH(i,k,0) = a0;
Martin Reinecke's avatar
Martin Reinecke committed
923 924 925 926 927 928 929
        CH(i,k,1) = a4.template special_mul<fwd>(WA(0,i));
        CH(i,k,2) = a2.template special_mul<fwd>(WA(1,i));
        CH(i,k,3) = a6.template special_mul<fwd>(WA(2,i));
        CH(i,k,4) = a1.template special_mul<fwd>(WA(3,i));
        CH(i,k,5) = a5.template special_mul<fwd>(WA(4,i));
        CH(i,k,6) = a3.template special_mul<fwd>(WA(5,i));
        CH(i,k,7) = a7.template special_mul<fwd>(WA(6,i));
Martin Reinecke's avatar
sync  
Martin Reinecke committed
930 931 932 933 934
        }
      }
   }


935
#define POCKETFFT_PREP11(idx) \
936 937 938 939 940 941 942 943 944
        T t1 = CC(idx,0,k), t2, t3, t4, t5, t6, t7, t8, t9, t10, t11; \
        PMC (t2,t11,CC(idx,1,k),CC(idx,10,k)); \
        PMC (t3,t10,CC(idx,2,k),CC(idx, 9,k)); \
        PMC (t4,t9 ,CC(idx,3,k),CC(idx, 8,k)); \
        PMC (t5,t8 ,CC(idx,4,k),CC(idx, 7,k)); \
        PMC (t6,t7 ,CC(idx,5,k),CC(idx, 6,k)); \
        CH(idx,k,0).r=t1.r+t2.r+t3.r+t4.r+t5.r+t6.r; \
        CH(idx,k,0).i=t1.i+t2.i+t3.i+t4.i+t5.i+t6.i;

945
#define POCKETFFT_PARTSTEP11a0(u1,u2,x1,x2,x3,x4,x5,y1,y2,y3,y4,y5,out1,out2) \
946 947 948 949 950 951 952
        { \
        T ca = t1 + t2*x1 + t3*x2 + t4*x3 + t5*x4 +t6*x5, \
          cb; \
        cb.i=y1*t11.r y2*t10.r y3*t9.r y4*t8.r y5*t7.r; \
        cb.r=-(y1*t11.i y2*t10.i y3*t9.i y4*t8.i y5*t7.i ); \
        PMC(out1,out2,ca,cb); \
        }
953 954 955
#define POCKETFFT_PARTSTEP11a(u1,u2,x1,x2,x3,x4,x5,y1,y2,y3,y4,y5) \
        POCKETFFT_PARTSTEP11a0(u1,u2,x1,x2,x3,x4,x5,y1,y2,y3,y4,y5,CH(0,k,u1),CH(0,k,u2))
#define POCKETFFT_PARTSTEP11(u1,u2,x1,x2,x3,x4,x5,y1,y2,y3,y4,y5) \
956 957
        { \
        T da,db; \
958
        POCKETFFT_PARTSTEP11a0(u1,u2,x1,x2,x3,x4,x5,y1,y2,y3,y4,y5,da,db) \
Martin Reinecke's avatar
Martin Reinecke committed
959 960
        CH(i,k,u1) = da.template special_mul<fwd>(WA(u1-1,i)); \
        CH(i,k,u2) = db.template special_mul<fwd>(WA(u2-1,i)); \
961 962
        }

Martin Reinecke's avatar
Martin Reinecke committed
963
template<bool fwd, typename T> void pass11 (size_t ido, size_t l1,
964 965
  const T * POCKETFFT_RESTRICT cc, T * POCKETFFT_RESTRICT ch,
  const cmplx<T0> * POCKETFFT_RESTRICT wa)
966
  {
Martin Reinecke's avatar
sync  
Martin Reinecke committed
967 968
  constexpr size_t cdim=11;
  constexpr T0 tw1r= T0(0.8412535328311811688618116489193677L),
Martin Reinecke's avatar
Martin Reinecke committed
969
               tw1i= (fwd ? -1 : 1) * T0(0.5406408174555975821076359543186917L),
Martin Reinecke's avatar
sync  
Martin Reinecke committed
970
               tw2r= T0(0.4154150130018864255292741492296232L),
Martin Reinecke's avatar
Martin Reinecke committed
971
               tw2i= (fwd ? -1 : 1) * T0(0.9096319953545183714117153830790285L),
Martin Reinecke's avatar
sync  
Martin Reinecke committed
972
               tw3r= T0(-0.1423148382732851404437926686163697L),
Martin Reinecke's avatar
Martin Reinecke committed
973
               tw3i= (fwd ? -1 : 1) * T0(0.9898214418809327323760920377767188L),
Martin Reinecke's avatar
sync  
Martin Reinecke committed
974
               tw4r= T0(-0.6548607339452850640569250724662936L),
Martin Reinecke's avatar
Martin Reinecke committed
975
               tw4i= (fwd ? -1 : 1) * T0(0.7557495743542582837740358439723444L),
Martin Reinecke's avatar
sync  
Martin Reinecke committed
976
               tw5r= T0(-0.9594929736144973898903680570663277L),
Martin Reinecke's avatar
Martin Reinecke committed
977
               tw5i= (fwd ? -1 : 1) * T0(0.2817325568414296977114179153466169L);
978

979 980
  auto CH = [ch,ido,l1](size_t a, size_t b, size_t c) -> T&
    { return ch[a+ido*(b+l1*c)]; };
981
  auto CC = [cc,ido,cdim](size_t a, size_t b, size_t c) -> const T&
982 983 984 985
    { return cc[a+ido*(b+cdim*c)]; };
  auto WA = [wa, ido](size_t x, size_t i)
    { return wa[i-1+x*(ido-1)]; };

986 987 988
  if (ido==1)
    for (size_t k=0; k<l1; ++k)
      {
989
      POCKETFFT_PREP11(0)
990 991 992 993 994
      POCKETFFT_PARTSTEP11a(1,10,tw1r,tw2r,tw3r,tw4r,tw5r,+tw1i,+tw2i,+tw3i,+tw4i,+tw5i)
      POCKETFFT_PARTSTEP11a(2, 9,tw2r,tw4r,tw5r,tw3r,tw1r,+tw2i,+tw4i,-tw5i,-tw3i,-tw1i)
      POCKETFFT_PARTSTEP11a(3, 8,tw3r,tw5r,tw2r,tw1r,tw4r,+tw3i,-tw5i,-tw2i,+tw1i,+tw4i)
      POCKETFFT_PARTSTEP11a(4, 7,tw4r,tw3r,tw1r,tw5r,tw2r,+tw4i,-tw3i,+tw1i,+tw5i,-tw2i)
      POCKETFFT_PARTSTEP11a(5, 6,tw5r,tw1r,tw4r,tw2r,tw3r,+tw5i,-tw1i,+tw4i,-tw2i,+tw3i)
995 996 997 998 999
      }
  else
    for (size_t k=0; k<l1; ++k)
      {
      {
1000
      POCKETFFT_PREP11(0)
1001 1002 1003 1004 1005
      POCKETFFT_PARTSTEP11a(1,10,tw1r,tw2r,tw3r,tw4r,tw5r,+tw1i,+tw2i,+tw3i,+tw4i,+tw5i)
      POCKETFFT_PARTSTEP11a(2, 9,tw2r,tw4r,tw5r,tw3r,tw1r,+tw2i,+tw4i,-tw5i,-tw3i,-tw1i)
      POCKETFFT_PARTSTEP11a(3, 8,tw3r,tw5r,tw2r,tw1r,tw4r,+tw3i,-tw5i,-tw2i,+tw1i,+tw4i)
      POCKETFFT_PARTSTEP11a(4, 7,tw4r,tw3r,tw1r,tw5r,tw2r,+tw4i,-tw3i,+tw1i,+tw5i,-tw2i)
      POCKETFFT_PARTSTEP11a(5, 6,tw5r,tw1r,tw4r,tw2r,tw3r,+tw5i,-tw1i,+tw4i,-tw2i,+tw3i)
1006 1007 1008
      }
      for (size_t i=1; i<ido; ++i)
        {