pocketfft_hdronly.h 94.2 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
#define NOINLINE __attribute__((noinline))
Martin Reinecke's avatar
updates  
Martin Reinecke committed
66
#define RESTRICT __restrict__
Martin Reinecke's avatar
Martin Reinecke committed
67 68
#elif defined(_MSC_VER)
#define NOINLINE __declspec(noinline)
Martin Reinecke's avatar
updates  
Martin Reinecke committed
69
#define RESTRICT __restrict
70 71
#else
#define NOINLINE
Martin Reinecke's avatar
updates  
Martin Reinecke committed
72
#define 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
163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208

  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; }
  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
209
  template<bool fwd, typename T2> auto special_mul (const cmplx<T2> &other) const
210 211
    -> cmplx<decltype(r+other.r)>
    {
Martin Reinecke's avatar
sync  
Martin Reinecke committed
212
    using Tres = cmplx<decltype(r+other.r)>;
Martin Reinecke's avatar
Martin Reinecke committed
213 214
    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);
215 216 217 218 219 220 221 222 223 224
    }
};
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
225 226
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_; }
227 228 229 230 231 232 233 234

//
// twiddle factor section
//

template<typename T> class sincos_2pibyn
  {
  private:
Martin Reinecke's avatar
sync  
Martin Reinecke committed
235 236 237 238 239 240 241 242
    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;
243 244
    arr<T> data;

Martin Reinecke's avatar
updates  
Martin Reinecke committed
245
    void my_sincosm1pi (Thigh a_, Thigh *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;
      }

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

Martin Reinecke's avatar
updates  
Martin Reinecke committed
316
    void calc_first_quadrant(size_t n, T * RESTRICT res)
317
      {
Martin Reinecke's avatar
updates  
Martin Reinecke committed
318
      T * RESTRICT p = res+n;
319 320 321 322 323
      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
324 325
        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];
326 327
        }
      if (i!=ndone)
Martin Reinecke's avatar
Martin Reinecke committed
328
        { res[idx1] = p[2*i]; res[idx1+1] = p[2*i+1]; }
329 330
      }

Martin Reinecke's avatar
updates  
Martin Reinecke committed
331
    void calc_first_half(size_t n, T * RESTRICT res)
332
      {
Martin Reinecke's avatar
sync  
Martin Reinecke committed
333
      int ndone=int(n+1)>>1;
334 335
      T * p = res+n-1;
      calc_first_octant(n<<2, p);
Martin Reinecke's avatar
sync  
Martin Reinecke committed
336
      int i4=0, in=int(n), i=0;
337
      for (; i4<=in-i4; ++i, i4+=4) // octant 0
Martin Reinecke's avatar
Martin Reinecke committed
338
        { res[2*i] = p[2*i4]; res[2*i+1] = p[2*i4+1]; }
339
      for (; i4-in <= 0; ++i, i4+=4) // octant 1
Martin Reinecke's avatar
sync  
Martin Reinecke committed
340
        { auto xm = in-i4; res[2*i] = p[2*xm+1]; res[2*i+1] = p[2*xm]; }
341
      for (; i4<=3*in-i4; ++i, i4+=4) // octant 2
Martin Reinecke's avatar
sync  
Martin Reinecke committed
342
        { auto xm = i4-in; res[2*i] = -p[2*xm+1]; res[2*i+1] = p[2*xm]; }
343
      for (; i<ndone; ++i, i4+=4) // octant 3
Martin Reinecke's avatar
sync  
Martin Reinecke committed
344
        { auto xm = 2*in-i4; res[2*i] = -p[2*xm]; res[2*i+1] = p[2*xm+1]; }
345 346
      }

Martin Reinecke's avatar
updates  
Martin Reinecke committed
347
    void fill_first_quadrant(size_t n, T * RESTRICT res)
348
      {
Martin Reinecke's avatar
sync  
Martin Reinecke committed
349
      constexpr T hsqt2 = T(0.707106781186547524400844362104849L);
350 351 352 353
      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
354
        { res[j] = res[i+1]; res[j+1] = res[i]; }
355 356
      }

Martin Reinecke's avatar
updates  
Martin Reinecke committed
357
    NOINLINE void fill_first_half(size_t n, T * RESTRICT res)
358 359 360 361
      {
      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
362
          { res[i+half] = -res[i+1]; res[i+half+1] = res[i]; }
363 364
      else
        for (size_t i=2, j=2*half-2; i<half; i+=2, j-=2)
Martin Reinecke's avatar
Martin Reinecke committed
365
          { res[j] = -res[i]; res[j+1] = res[i+1]; }
366 367
      }

Martin Reinecke's avatar
updates  
Martin Reinecke committed
368
    void fill_second_half(size_t n, T * RESTRICT res)
369 370 371 372 373 374
      {
      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
375
          { res[j] = res[i]; res[j+1] = -res[i+1]; }
376 377
      }

Martin Reinecke's avatar
updates  
Martin Reinecke committed
378
    NOINLINE void sincos_2pibyn_half(size_t n, T * RESTRICT res)
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
      {
      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:
    NOINLINE sincos_2pibyn(size_t n, bool half)
      : 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
409
struct util // hack to avoid duplicate symbols
410
  {
Martin Reinecke's avatar
Martin Reinecke committed
411
  static NOINLINE size_t largest_prime_factor (size_t n)
412
    {
Martin Reinecke's avatar
Martin Reinecke committed
413 414 415
    size_t res=1;
    while ((n&1)==0)
      { res=2; n>>=1; }
Martin Reinecke's avatar
Martin Reinecke committed
416 417 418
    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
419 420 421 422 423
    if (n>1) res=n;
    return res;
    }

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

Martin Reinecke's avatar
Martin Reinecke committed
440 441 442 443 444 445 446 447 448 449 450 451 452 453
  /* returns the smallest composite of 2, 3, 5, 7 and 11 which is >= n */
  static NOINLINE size_t good_size(size_t n)
    {
    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;
    }
454

Martin Reinecke's avatar
Martin Reinecke committed
455 456 457 458 459 460 461
  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
462 463 464 465 466 467 468 469

  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");
Martin Reinecke's avatar
sync  
Martin Reinecke committed
470 471
    if (inplace && (stride_in!=stride_out))
      throw runtime_error("stride mismatch");
Martin Reinecke's avatar
Martin Reinecke committed
472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494
    }

  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");
    }
Martin Reinecke's avatar
Martin Reinecke committed
495 496

#ifdef POCKETFFT_OPENMP
Martin Reinecke's avatar
sync  
Martin Reinecke committed
497 498
    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
499 500 501 502
    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
503
      if (prod(shape) < 20*shape[axis]) return 1;
Martin Reinecke's avatar
sync  
Martin Reinecke committed
504
      return (nthreads==0) ? size_t(omp_get_max_threads()) : nthreads;
Martin Reinecke's avatar
Martin Reinecke committed
505
      }
Martin Reinecke's avatar
Martin Reinecke committed
506
#else
Martin Reinecke's avatar
Martin Reinecke committed
507 508
    static constexpr size_t nthreads() { return 1; }
    static constexpr size_t thread_num() { return 0; }
Martin Reinecke's avatar
Martin Reinecke committed
509
#endif
Martin Reinecke's avatar
Martin Reinecke committed
510
  };
511 512 513 514 515 516 517 518 519 520 521 522 523 524

//
// 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
525
    size_t length;
526
    arr<cmplx<T0>> mem;
Martin Reinecke's avatar
Martin Reinecke committed
527
    vector<fctdata> fact;
528 529

    void add_factor(size_t factor)
Martin Reinecke's avatar
Martin Reinecke committed
530
      { fact.push_back({factor, nullptr, nullptr}); }
531

Martin Reinecke's avatar
Martin Reinecke committed
532
template<bool fwd, typename T> void pass2 (size_t ido, size_t l1,
Martin Reinecke's avatar
updates  
Martin Reinecke committed
533
  const T * RESTRICT cc, T * RESTRICT ch, const cmplx<T0> * RESTRICT wa)
534 535 536
  {
  constexpr size_t cdim=2;

537 538 539 540 541 542 543
  auto CH = [ch,ido,l1](size_t a, size_t b, size_t c) -> T&
    { return ch[a+ido*(b+l1*c)]; };
  auto CC = [cc,ido,cdim](size_t a, size_t b, size_t c) -> const T&
    { return cc[a+ido*(b+cdim*c)]; };
  auto WA = [wa, ido](size_t x, size_t i)
    { return wa[i-1+x*(ido-1)]; };

544 545 546 547 548 549 550 551 552 553 554 555 556 557
  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
558
        CH(i,k,1) = (CC(i,0,k)-CC(i,1,k)).template special_mul<fwd>(WA(0,i));
559 560 561 562
        }
      }
  }

563
#define POCKETFFT_PREP3(idx) \
564 565 566
        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;
567
#define POCKETFFT_PARTSTEP3a(u1,u2,twr,twi) \
568 569 570 571 572 573
        { \
        T ca,cb; \
        ca=t0+t1*twr; \
        cb=t2*twi; ROT90(cb); \
        PMC(CH(0,k,u1),CH(0,k,u2),ca,cb) ;\
        }
574
#define POCKETFFT_PARTSTEP3b(u1,u2,twr,twi) \
575 576 577 578 579
        { \
        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
580 581
        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)); \
582
        }
Martin Reinecke's avatar
Martin Reinecke committed
583
template<bool fwd, typename T> void pass3 (size_t ido, size_t l1,
Martin Reinecke's avatar
updates  
Martin Reinecke committed
584
  const T * RESTRICT cc, T * RESTRICT ch, const cmplx<T0> * RESTRICT wa)
585 586
  {
  constexpr size_t cdim=3;
Martin Reinecke's avatar
sync  
Martin Reinecke committed
587
  constexpr T0 tw1r=-0.5,
Martin Reinecke's avatar
Martin Reinecke committed
588
               tw1i= (fwd ? -1: 1) * T0(0.8660254037844386467637231707529362L);
589

590 591 592 593 594 595 596
  auto CH = [ch,ido,l1](size_t a, size_t b, size_t c) -> T&
    { return ch[a+ido*(b+l1*c)]; };
  auto CC = [cc,ido,cdim](size_t a, size_t b, size_t c) -> const T&
    { return cc[a+ido*(b+cdim*c)]; };
  auto WA = [wa, ido](size_t x, size_t i)
    { return wa[i-1+x*(ido-1)]; };

597 598 599
  if (ido==1)
    for (size_t k=0; k<l1; ++k)
      {
600 601
      POCKETFFT_PREP3(0)
      POCKETFFT_PARTSTEP3a(1,2,tw1r,tw1i)
602 603 604 605 606
      }
  else
    for (size_t k=0; k<l1; ++k)
      {
      {
607 608
      POCKETFFT_PREP3(0)
      POCKETFFT_PARTSTEP3a(1,2,tw1r,tw1i)
609 610 611
      }
      for (size_t i=1; i<ido; ++i)
        {
612 613
        POCKETFFT_PREP3(i)
        POCKETFFT_PARTSTEP3b(1,2,tw1r,tw1i)
614 615 616 617
        }
      }
  }

618 619 620
#undef POCKETFFT_PARTSTEP3b
#undef POCKETFFT_PARTSTEP3a
#undef POCKETFFT_PREP3
621

Martin Reinecke's avatar
Martin Reinecke committed
622
template<bool fwd, typename T> void pass4 (size_t ido, size_t l1,
Martin Reinecke's avatar
updates  
Martin Reinecke committed
623
  const T * RESTRICT cc, T * RESTRICT ch, const cmplx<T0> * RESTRICT wa)
624 625 626
  {
  constexpr size_t cdim=4;

627 628 629 630 631 632 633
  auto CH = [ch,ido,l1](size_t a, size_t b, size_t c) -> T&
    { return ch[a+ido*(b+l1*c)]; };
  auto CC = [cc,ido,cdim](size_t a, size_t b, size_t c) -> const T&
    { return cc[a+ido*(b+cdim*c)]; };
  auto WA = [wa, ido](size_t x, size_t i)
    { return wa[i-1+x*(ido-1)]; };

634 635 636 637 638 639
  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
640
      ROTX90<fwd>(t4);
641 642 643 644 645 646 647 648 649 650
      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
651
      ROTX90<fwd>(t4);
652 653 654 655 656 657 658 659 660
      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
661
        ROTX90<fwd>(t4);
662 663
        PMC(CH(i,k,0),c3,t2,t3);
        PMC(c2,c4,t1,t4);
Martin Reinecke's avatar
Martin Reinecke committed
664 665 666
        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));
667 668 669 670
        }
      }
  }

671
#define POCKETFFT_PREP5(idx) \
672 673 674 675 676 677
        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;

678
#define POCKETFFT_PARTSTEP5a(u1,u2,twar,twbr,twai,twbi) \
679 680 681 682 683 684 685 686 687
        { \
        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); \
        }

688
#define POCKETFFT_PARTSTEP5b(u1,u2,twar,twbr,twai,twbi) \
689 690 691 692 693 694 695
        { \
        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
696 697
        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)); \
698
        }
Martin Reinecke's avatar
Martin Reinecke committed
699
template<bool fwd, typename T> void pass5 (size_t ido, size_t l1,
Martin Reinecke's avatar
updates  
Martin Reinecke committed
700
  const T * RESTRICT cc, T * RESTRICT ch, const cmplx<T0> * RESTRICT wa)
701 702
  {
  constexpr size_t cdim=5;
Martin Reinecke's avatar
sync  
Martin Reinecke committed
703
  constexpr T0 tw1r= T0(0.3090169943749474241022934171828191L),
Martin Reinecke's avatar
Martin Reinecke committed
704
               tw1i= (fwd ? -1: 1) * T0(0.9510565162951535721164393333793821L),
Martin Reinecke's avatar
sync  
Martin Reinecke committed
705
               tw2r= T0(-0.8090169943749474241022934171828191L),
Martin Reinecke's avatar
Martin Reinecke committed
706
               tw2i= (fwd ? -1: 1) * T0(0.5877852522924731291687059546390728L);
707

708 709 710 711 712 713 714
  auto CH = [ch,ido,l1](size_t a, size_t b, size_t c) -> T&
    { return ch[a+ido*(b+l1*c)]; };
  auto CC = [cc,ido,cdim](size_t a, size_t b, size_t c) -> const T&
    { return cc[a+ido*(b+cdim*c)]; };
  auto WA = [wa, ido](size_t x, size_t i)
    { return wa[i-1+x*(ido-1)]; };

715 716 717
  if (ido==1)
    for (size_t k=0; k<l1; ++k)
      {
718 719 720
      POCKETFFT_PREP5(0)
      POCKETFFT_PARTSTEP5a(1,4,tw1r,tw2r,+tw1i,+tw2i)
      POCKETFFT_PARTSTEP5a(2,3,tw2r,tw1r,+tw2i,-tw1i)
721 722 723 724 725
      }
  else
    for (size_t k=0; k<l1; ++k)
      {
      {
726 727 728
      POCKETFFT_PREP5(0)
      POCKETFFT_PARTSTEP5a(1,4,tw1r,tw2r,+tw1i,+tw2i)
      POCKETFFT_PARTSTEP5a(2,3,tw2r,tw1r,+tw2i,-tw1i)
729 730 731
      }
      for (size_t i=1; i<ido; ++i)
        {
732 733 734
        POCKETFFT_PREP5(i)
        POCKETFFT_PARTSTEP5b(1,4,tw1r,tw2r,+tw1i,+tw2i)
        POCKETFFT_PARTSTEP5b(2,3,tw2r,tw1r,+tw2i,-tw1i)
735 736 737 738
        }
      }
  }

739 740 741
#undef POCKETFFT_PARTSTEP5b
#undef POCKETFFT_PARTSTEP5a
#undef POCKETFFT_PREP5
742

743
#define POCKETFFT_PREP7(idx) \
744 745 746 747 748 749 750
        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;

751
#define POCKETFFT_PARTSTEP7a0(u1,u2,x1,x2,x3,y1,y2,y3,out1,out2) \
752 753 754 755 756 757 758 759
        { \
        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); \
        }
760 761 762
#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) \
763 764
        { \
        T da,db; \
765
        POCKETFFT_PARTSTEP7a0(u1,u2,x1,x2,x3,y1,y2,y3,da,db) \
Martin Reinecke's avatar
Martin Reinecke committed
766 767
        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)); \
768 769
        }

Martin Reinecke's avatar
Martin Reinecke committed
770
template<bool fwd, typename T> void pass7(size_t ido, size_t l1,
Martin Reinecke's avatar
updates  
Martin Reinecke committed
771
  const T * RESTRICT cc, T * RESTRICT ch, const cmplx<T0> * RESTRICT wa)
772 773
  {
  constexpr size_t cdim=7;
Martin Reinecke's avatar
sync  
Martin Reinecke committed
774
  constexpr T0 tw1r= T0(0.6234898018587335305250048840042398L),
Martin Reinecke's avatar
Martin Reinecke committed
775
               tw1i= (fwd ? -1 : 1) * T0(0.7818314824680298087084445266740578L),
Martin Reinecke's avatar
sync  
Martin Reinecke committed
776
               tw2r= T0(-0.2225209339563144042889025644967948L),
Martin Reinecke's avatar
Martin Reinecke committed
777
               tw2i= (fwd ? -1 : 1) * T0(0.9749279121818236070181316829939312L),
Martin Reinecke's avatar
sync  
Martin Reinecke committed
778
               tw3r= T0(-0.9009688679024191262361023195074451L),
Martin Reinecke's avatar
Martin Reinecke committed
779
               tw3i= (fwd ? -1 : 1) * T0(0.433883739117558120475768332848359L);
780

781 782 783 784 785 786 787
  auto CH = [ch,ido,l1](size_t a, size_t b, size_t c) -> T&
    { return ch[a+ido*(b+l1*c)]; };
  auto CC = [cc,ido,cdim](size_t a, size_t b, size_t c) -> const T&
    { return cc[a+ido*(b+cdim*c)]; };
  auto WA = [wa, ido](size_t x, size_t i)
    { return wa[i-1+x*(ido-1)]; };

788 789 790
  if (ido==1)
    for (size_t k=0; k<l1; ++k)
      {
791 792 793 794
      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)
795 796 797 798 799
      }
  else
    for (size_t k=0; k<l1; ++k)
      {
      {
800 801 802 803
      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)
804 805 806
      }
      for (size_t i=1; i<ido; ++i)
        {
807 808 809 810
        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)
811 812 813 814
        }
      }
  }

815 816 817 818
#undef POCKETFFT_PARTSTEP7
#undef POCKETFFT_PARTSTEP7a0
#undef POCKETFFT_PARTSTEP7a
#undef POCKETFFT_PREP7
819

Martin Reinecke's avatar
Martin Reinecke committed
820
template <bool fwd, typename T> void ROTX45(T &a)
Martin Reinecke's avatar
sync  
Martin Reinecke committed
821 822
  {
  constexpr T0 hsqt2=T0(0.707106781186547524400844362104849L);
Martin Reinecke's avatar
Martin Reinecke committed
823
  if (fwd)
Martin Reinecke's avatar
sync  
Martin Reinecke committed
824
    { auto tmp_=a.r; a.r=hsqt2*(a.r+a.i); a.i=hsqt2*(a.i-tmp_); }
Martin Reinecke's avatar
Martin Reinecke committed
825 826
  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
827
  }
Martin Reinecke's avatar
Martin Reinecke committed
828
template <bool fwd, typename T> void ROTX135(T &a)
Martin Reinecke's avatar
sync  
Martin Reinecke committed
829 830
  {
  constexpr T0 hsqt2=T0(0.707106781186547524400844362104849L);
Martin Reinecke's avatar
Martin Reinecke committed
831
  if (fwd)
Martin Reinecke's avatar
sync  
Martin Reinecke committed
832
    { auto tmp_=a.r; a.r=hsqt2*(a.i-a.r); a.i=hsqt2*(-tmp_-a.i); }
Martin Reinecke's avatar
Martin Reinecke committed
833 834
  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
835 836 837 838
  }
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
839
template<bool fwd, typename T> void pass8 (size_t ido, size_t l1,
Martin Reinecke's avatar
updates  
Martin Reinecke committed
840
  const T * RESTRICT cc, T * RESTRICT ch, const cmplx<T0> * RESTRICT wa)
Martin Reinecke's avatar
sync  
Martin Reinecke committed
841 842 843
  {
  constexpr size_t cdim=8;

844 845 846 847 848 849 850
  auto CH = [ch,ido,l1](size_t a, size_t b, size_t c) -> T&
    { return ch[a+ido*(b+l1*c)]; };
  auto CC = [cc,ido,cdim](size_t a, size_t b, size_t c) -> const T&
    { 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
851 852 853 854 855 856 857 858
  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
859 860
      ROTX90<fwd>(a6);
      ROTX90<fwd>(a7);
Martin Reinecke's avatar
sync  
Martin Reinecke committed
861 862 863 864
      PMINPLACE(a0,a2);
      PMINPLACE(a1,a3);
      PMINPLACE(a4,a6);
      PMINPLACE(a5,a7);
Martin Reinecke's avatar
Martin Reinecke committed
865 866 867
      ROTX45<fwd>(a5);
      ROTX90<fwd>(a3);
      ROTX135<fwd>(a7);
Martin Reinecke's avatar
sync  
Martin Reinecke committed
868 869 870 871 872 873 874 875 876 877 878 879 880
      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
881 882
      ROTX90<fwd>(a6);
      ROTX90<fwd>(a7);
Martin Reinecke's avatar
sync  
Martin Reinecke committed
883 884 885 886
      PMINPLACE(a0,a2);
      PMINPLACE(a1,a3);
      PMINPLACE(a4,a6);
      PMINPLACE(a5,a7);
Martin Reinecke's avatar
Martin Reinecke committed
887 888 889
      ROTX45<fwd>(a5);
      ROTX90<fwd>(a3);
      ROTX135<fwd>(a7);
Martin Reinecke's avatar
sync  
Martin Reinecke committed
890 891 892 893 894 895 896 897 898 899 900 901
      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
902 903
        ROTX90<fwd>(a6);
        ROTX90<fwd>(a7);
Martin Reinecke's avatar
sync  
Martin Reinecke committed
904 905 906 907
        PMINPLACE(a0,a2);
        PMINPLACE(a1,a3);
        PMINPLACE(a4,a6);
        PMINPLACE(a5,a7);
Martin Reinecke's avatar
Martin Reinecke committed
908 909 910
        ROTX45<fwd>(a5);
        ROTX90<fwd>(a3);
        ROTX135<fwd>(a7);
Martin Reinecke's avatar
sync  
Martin Reinecke committed
911 912 913 914 915
        PMINPLACE(a0,a1);
        PMINPLACE(a2,a3);
        PMINPLACE(a4,a5);
        PMINPLACE(a6,a7);
        CH(i,k,0) = a0;
Martin Reinecke's avatar
Martin Reinecke committed
916 917 918 919 920 921 922
        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
923 924 925 926 927
        }
      }
   }


928
#define POCKETFFT_PREP11(idx) \
929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951
        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;

#define PARTSTEP11a0(u1,u2,x1,x2,x3,x4,x5,y1,y2,y3,y4,y5,out1,out2) \
        { \
        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); \
        }
#define PARTSTEP11a(u1,u2,x1,x2,x3,x4,x5,y1,y2,y3,y4,y5) \
        PARTSTEP11a0(u1,u2,x1,x2,x3,x4,x5,y1,y2,y3,y4,y5,CH(0,k,u1),CH(0,k,u2))
#define PARTSTEP11(u1,u2,x1,x2,x3,x4,x5,y1,y2,y3,y4,y5) \
        { \
        T da,db; \
        PARTSTEP11a0(u1,u2,x1,x2,x3,x4,x5,y1,y2,y3,y4,y5,da,db) \
Martin Reinecke's avatar
Martin Reinecke committed
952 953
        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)); \
954 955
        }

Martin Reinecke's avatar
Martin Reinecke committed
956
template<bool fwd, typename T> void pass11 (size_t ido, size_t l1,
Martin Reinecke's avatar
updates  
Martin Reinecke committed
957
  const T * RESTRICT cc, T * RESTRICT ch, const cmplx<T0> * RESTRICT wa)
958
  {
Martin Reinecke's avatar
sync  
Martin Reinecke committed
959 960
  constexpr size_t cdim=11;
  constexpr T0 tw1r= T0(0.8412535328311811688618116489193677L),
Martin Reinecke's avatar
Martin Reinecke committed
961
               tw1i= (fwd ? -1 : 1) * T0(0.5406408174555975821076359543186917L),
Martin Reinecke's avatar
sync  
Martin Reinecke committed
962
               tw2r= T0(0.4154150130018864255292741492296232L),
Martin Reinecke's avatar
Martin Reinecke committed
963
               tw2i= (fwd ? -1 : 1) * T0(0.9096319953545183714117153830790285L),
Martin Reinecke's avatar
sync  
Martin Reinecke committed
964
               tw3r= T0(-0.1423148382732851404437926686163697L),
Martin Reinecke's avatar
Martin Reinecke committed
965
               tw3i= (fwd ? -1 : 1) * T0(0.9898214418809327323760920377767188L),
Martin Reinecke's avatar
sync  
Martin Reinecke committed
966
               tw4r= T0(-0.6548607339452850640569250724662936L),
Martin Reinecke's avatar
Martin Reinecke committed
967
               tw4i= (fwd ? -1 : 1) * T0(0.7557495743542582837740358439723444L),
Martin Reinecke's avatar
sync  
Martin Reinecke committed
968
               tw5r= T0(-0.9594929736144973898903680570663277L),
Martin Reinecke's avatar
Martin Reinecke committed
969
               tw5i= (fwd ? -1 : 1) * T0(0.2817325568414296977114179153466169L);
970

971 972 973 974 975 976 977
  auto CH = [ch,ido,l1](size_t a, size_t b, size_t c) -> T&
    { return ch[a+ido*(b+l1*c)]; };
  auto CC = [cc,ido,cdim](size_t a, size_t b, size_t c) -> const T&
    { return cc[a+ido*(b+cdim*c)]; };
  auto WA = [wa, ido](size_t x, size_t i)
    { return wa[i-1+x*(ido-1)]; };

978 979 980
  if (ido==1)
    for (size_t k=0; k<l1; ++k)
      {
981
      POCKETFFT_PREP11(0)
982 983 984 985 986 987 988 989 990 991
      PARTSTEP11a(1,10,tw1r,tw2r,tw3r,tw4r,tw5r,+tw1i,+tw2i,+tw3i,+tw4i,+tw5i)
      PARTSTEP11a(2, 9,tw2r,tw4r,tw5r,tw3r,tw1r,+tw2i,+tw4i,-tw5i,-tw3i,-tw1i)
      PARTSTEP11a(3, 8,tw3r,tw5r,tw2r,tw1r,tw4r,+tw3i,-tw5i,-tw2i,+tw1i,+tw4i)
      PARTSTEP11a(4, 7,tw4r,tw3r,tw1r,tw5r,tw2r,+tw4i,-tw3i,+tw1i,+tw5i,-tw2i)
      PARTSTEP11a(5, 6,tw5r,tw1r,tw4r,tw2r,tw3r,+tw5i,-tw1i,+tw4i,-tw2i,+tw3i)
      }
  else
    for (size_t k=0; k<l1; ++k)
      {
      {
992
      POCKETFFT_PREP11(0)
993 994 995 996 997 998 999 1000
      PARTSTEP11a(1,10,tw1r,tw2r,tw3r,tw4r,tw5r,+tw1i,+tw2i,+tw3i,+tw4i,+tw5i)
      PARTSTEP11a(2, 9,tw2r,tw4r,tw5r,tw3r,tw1r,+tw2i,+tw4i,-tw5i,-tw3i,-tw1i)
      PARTSTEP11a(3, 8,tw3r,tw5r,tw2r,tw1r,tw4r,+tw3i,-tw5i,-tw2i,+tw1i,+tw4i)
      PARTSTEP11a(4, 7,tw4r,tw3r,tw1r,tw5r,tw2r,+tw4i,-tw3i,+tw1i,+tw5i,-tw2i)
      PARTSTEP11a(5, 6,tw5r,tw1r,tw4r,tw2r,tw3r,+tw5i,-tw1i,+tw4i,-tw2i,+tw3i)
      }
      for (size_t i=1; i<ido; ++i)
        {
1001
        POCKETFFT_PREP11(i)
1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013
        PARTSTEP11(1,10,tw1r,tw2r,tw3r,tw4r,tw5r,+tw1i,+tw2i,+tw3i,+tw4i,+tw5i)
        PARTSTEP11(2, 9,tw2r,tw4r,tw5r,tw3r,tw1r,+tw2i,+tw4i,-tw5i,-tw3i,-tw1i)
        PARTSTEP11(3, 8,tw3r,tw5r,tw2r,tw1r,tw4r,+tw3i,-tw5i,-tw2i,+tw1i,+tw4i)
        PARTSTEP11(4, 7,tw4r,tw3r,tw1r,tw5r,tw2r,+tw4i,-tw3i,+tw1i,+tw5i,-tw2i)
        PARTSTEP11(5, 6,tw5r,tw1r,tw4r,tw2r,tw3r,+tw5i,-tw1i,+tw4i,-tw2i,+tw3i)
        }
      }
  }

#undef PARTSTEP11
#undef PARTSTEP11a0
#undef PARTSTEP11a
1014
#undef POCKETFFT_PREP11
1015

Martin Reinecke's avatar
Martin Reinecke committed
1016
template<bool fwd, typename T> void passg (size_t ido, size_t ip,
Martin Reinecke's avatar
updates  
Martin Reinecke committed
1017 1018
  size_t l1, T * RESTRICT cc, T * RESTRICT ch, const cmplx<T0> * RESTRICT wa,
  const cmplx<T0> * RESTRICT csarr)
1019 1020 1021 1022 1023
  {
  const size_t cdim=ip;
  size_t ipph = (ip+1)/2;
  size_t idl1 = ido*l1;

1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034
  auto CH = [ch,ido,l1](size_t a, size_t b, size_t c) -> T&
    { return ch[a+ido*(b+l1*c)]; };
  auto CC = [cc,ido,cdim](size_t a, size_t b, size_t c) -> const T&
    { return cc[a+ido*(b+cdim*c)]; };
  auto CX = [cc, ido, l1](size_t a, size_t b, size_t c) -> T&
    { return cc[a+ido*(b+l1*c)]; };
  auto CX2 = [cc, idl1](size_t a, size_t b) -> T&
    { return cc[a+idl1*b]; };
  auto CH2 = [ch, idl1](size_t a, size_t b) -> const T&
    { return ch[a+idl1*b]; };

1035 1036 1037
  arr<cmplx<T0>> wal(ip);
  wal[0] = cmplx<T0>(1., 0.);
  for (size_t i=1; i<ip; ++i)
Martin Reinecke's avatar
Martin Reinecke committed
1038
    wal[i]=cmplx<T0>(csarr[i].r,fwd ? -csarr[i].i : csarr[i].i);
1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115

  for (size_t k=0; k<l1; ++k)
    for (size_t i=0; i<ido; ++i)
      CH(i,k,0) = CC(i,0,k);
  for (size_t j=1, jc=ip-1;