packetmath.cpp
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1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
5 // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
6 //
7 // This Source Code Form is subject to the terms of the Mozilla
8 // Public License v. 2.0. If a copy of the MPL was not distributed
9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
10 
11 #include "packetmath_test_shared.h"
13 
14 template <typename T>
15 inline T REF_ADD(const T& a, const T& b) {
16  return a + b;
17 }
18 template <typename T>
19 inline T REF_SUB(const T& a, const T& b) {
20  return a - b;
21 }
22 template <typename T>
23 inline T REF_MUL(const T& a, const T& b) {
24  return a * b;
25 }
26 template <typename T>
27 inline T REF_DIV(const T& a, const T& b) {
28  return a / b;
29 }
30 template <typename T>
31 inline T REF_ABS_DIFF(const T& a, const T& b) {
32  return a > b ? a - b : b - a;
33 }
34 
35 // Specializations for bool.
36 template <>
37 inline bool REF_ADD(const bool& a, const bool& b) {
38  return a || b;
39 }
40 template <>
41 inline bool REF_SUB(const bool& a, const bool& b) {
42  return a ^ b;
43 }
44 template <>
45 inline bool REF_MUL(const bool& a, const bool& b) {
46  return a && b;
47 }
48 
49 template <typename T>
50 inline T REF_FREXP(const T& x, T& exp) {
51  int iexp;
52  EIGEN_USING_STD(frexp)
53  const T out = static_cast<T>(frexp(x, &iexp));
54  exp = static_cast<T>(iexp);
55  return out;
56 }
57 
58 template <typename T>
59 inline T REF_LDEXP(const T& x, const T& exp) {
60  EIGEN_USING_STD(ldexp)
61  return static_cast<T>(ldexp(x, static_cast<int>(exp)));
62 }
63 
64 // Uses pcast to cast from one array to another.
65 template <typename SrcPacket, typename TgtPacket, int SrcCoeffRatio, int TgtCoeffRatio>
66 struct pcast_array;
67 
68 template <typename SrcPacket, typename TgtPacket, int TgtCoeffRatio>
69 struct pcast_array<SrcPacket, TgtPacket, 1, TgtCoeffRatio> {
72  static void cast(const SrcScalar* src, size_t size, TgtScalar* dst) {
73  static const int SrcPacketSize = internal::unpacket_traits<SrcPacket>::size;
74  static const int TgtPacketSize = internal::unpacket_traits<TgtPacket>::size;
75  size_t i;
76  for (i = 0; i < size && i + SrcPacketSize <= size; i += TgtPacketSize) {
77  internal::pstoreu(dst + i, internal::pcast<SrcPacket, TgtPacket>(internal::ploadu<SrcPacket>(src + i)));
78  }
79  // Leftovers that cannot be loaded into a packet.
80  for (; i < size; ++i) {
81  dst[i] = static_cast<TgtScalar>(src[i]);
82  }
83  }
84 };
85 
86 template <typename SrcPacket, typename TgtPacket>
87 struct pcast_array<SrcPacket, TgtPacket, 2, 1> {
88  static void cast(const typename internal::unpacket_traits<SrcPacket>::type* src, size_t size,
90  static const int SrcPacketSize = internal::unpacket_traits<SrcPacket>::size;
91  static const int TgtPacketSize = internal::unpacket_traits<TgtPacket>::size;
92  for (size_t i = 0; i < size; i += TgtPacketSize) {
93  SrcPacket a = internal::ploadu<SrcPacket>(src + i);
94  SrcPacket b = internal::ploadu<SrcPacket>(src + i + SrcPacketSize);
95  internal::pstoreu(dst + i, internal::pcast<SrcPacket, TgtPacket>(a, b));
96  }
97  }
98 };
99 
100 template <typename SrcPacket, typename TgtPacket>
101 struct pcast_array<SrcPacket, TgtPacket, 4, 1> {
102  static void cast(const typename internal::unpacket_traits<SrcPacket>::type* src, size_t size,
104  static const int SrcPacketSize = internal::unpacket_traits<SrcPacket>::size;
105  static const int TgtPacketSize = internal::unpacket_traits<TgtPacket>::size;
106  for (size_t i = 0; i < size; i += TgtPacketSize) {
107  SrcPacket a = internal::ploadu<SrcPacket>(src + i);
108  SrcPacket b = internal::ploadu<SrcPacket>(src + i + SrcPacketSize);
109  SrcPacket c = internal::ploadu<SrcPacket>(src + i + 2 * SrcPacketSize);
110  SrcPacket d = internal::ploadu<SrcPacket>(src + i + 3 * SrcPacketSize);
111  internal::pstoreu(dst + i, internal::pcast<SrcPacket, TgtPacket>(a, b, c, d));
112  }
113  }
114 };
115 
116 template <typename SrcPacket, typename TgtPacket>
117 struct pcast_array<SrcPacket, TgtPacket, 8, 1> {
118  static void cast(const typename internal::unpacket_traits<SrcPacket>::type* src, size_t size,
120  static const int SrcPacketSize = internal::unpacket_traits<SrcPacket>::size;
121  static const int TgtPacketSize = internal::unpacket_traits<TgtPacket>::size;
122  for (size_t i = 0; i < size; i += TgtPacketSize) {
123  SrcPacket a = internal::ploadu<SrcPacket>(src + i);
124  SrcPacket b = internal::ploadu<SrcPacket>(src + i + SrcPacketSize);
125  SrcPacket c = internal::ploadu<SrcPacket>(src + i + 2 * SrcPacketSize);
126  SrcPacket d = internal::ploadu<SrcPacket>(src + i + 3 * SrcPacketSize);
127  SrcPacket e = internal::ploadu<SrcPacket>(src + i + 4 * SrcPacketSize);
128  SrcPacket f = internal::ploadu<SrcPacket>(src + i + 5 * SrcPacketSize);
129  SrcPacket g = internal::ploadu<SrcPacket>(src + i + 6 * SrcPacketSize);
130  SrcPacket h = internal::ploadu<SrcPacket>(src + i + 7 * SrcPacketSize);
131  internal::pstoreu(dst + i, internal::pcast<SrcPacket, TgtPacket>(a, b, c, d, e, f, g, h));
132  }
133  }
134 };
135 
136 template <typename SrcPacket, typename TgtPacket, int SrcCoeffRatio, int TgtCoeffRatio, bool CanCast = false>
138 
139 template <typename SrcPacket, typename TgtPacket, int SrcCoeffRatio, int TgtCoeffRatio>
140 struct test_cast_helper<SrcPacket, TgtPacket, SrcCoeffRatio, TgtCoeffRatio, false> {
141  static void run() {}
142 };
143 
144 template <typename SrcPacket, typename TgtPacket, int SrcCoeffRatio, int TgtCoeffRatio>
145 struct test_cast_helper<SrcPacket, TgtPacket, SrcCoeffRatio, TgtCoeffRatio, true> {
146  static void run() {
147  typedef typename internal::unpacket_traits<SrcPacket>::type SrcScalar;
148  typedef typename internal::unpacket_traits<TgtPacket>::type TgtScalar;
149  static const int SrcPacketSize = internal::unpacket_traits<SrcPacket>::size;
150  static const int TgtPacketSize = internal::unpacket_traits<TgtPacket>::size;
151  static const int BlockSize = SrcPacketSize * SrcCoeffRatio;
152  eigen_assert(BlockSize == TgtPacketSize * TgtCoeffRatio && "Packet sizes and cast ratios are mismatched.");
153 
154  static const int DataSize = 10 * BlockSize;
155  EIGEN_ALIGN_MAX SrcScalar data1[DataSize];
156  EIGEN_ALIGN_MAX TgtScalar data2[DataSize];
157  EIGEN_ALIGN_MAX TgtScalar ref[DataSize];
158 
159  // Construct a packet of scalars that will not overflow when casting
160  for (int i = 0; i < DataSize; ++i) {
162  }
163 
164  for (int i = 0; i < DataSize; ++i) {
165  ref[i] = static_cast<const TgtScalar>(data1[i]);
166  }
167 
169 
170  VERIFY(test::areApprox(ref, data2, DataSize) && "internal::pcast<>");
171  }
172 };
173 
174 template <typename SrcPacket, typename TgtPacket>
175 struct test_cast {
176  static void run() {
177  typedef typename internal::unpacket_traits<SrcPacket>::type SrcScalar;
178  typedef typename internal::unpacket_traits<TgtPacket>::type TgtScalar;
179  typedef typename internal::type_casting_traits<SrcScalar, TgtScalar> TypeCastingTraits;
180  static const int SrcCoeffRatio = TypeCastingTraits::SrcCoeffRatio;
181  static const int TgtCoeffRatio = TypeCastingTraits::TgtCoeffRatio;
182  static const int SrcPacketSize = internal::unpacket_traits<SrcPacket>::size;
183  static const int TgtPacketSize = internal::unpacket_traits<TgtPacket>::size;
184  static const bool HasCast =
185  internal::unpacket_traits<SrcPacket>::vectorizable && internal::unpacket_traits<TgtPacket>::vectorizable &&
186  TypeCastingTraits::VectorizedCast && (SrcPacketSize * SrcCoeffRatio == TgtPacketSize * TgtCoeffRatio);
188  }
189 };
190 
191 template <typename SrcPacket, typename TgtScalar,
192  typename TgtPacket = typename internal::packet_traits<TgtScalar>::type,
193  bool Vectorized = internal::packet_traits<TgtScalar>::Vectorizable,
194  bool HasHalf = !internal::is_same<typename internal::unpacket_traits<TgtPacket>::half, TgtPacket>::value>
196 
197 template <typename SrcPacket, typename TgtScalar, typename TgtPacket>
198 struct test_cast_runner<SrcPacket, TgtScalar, TgtPacket, true, false> {
200 };
201 
202 template <typename SrcPacket, typename TgtScalar, typename TgtPacket>
203 struct test_cast_runner<SrcPacket, TgtScalar, TgtPacket, true, true> {
204  static void run() {
207  }
208 };
209 
210 template <typename SrcPacket, typename TgtScalar, typename TgtPacket>
211 struct test_cast_runner<SrcPacket, TgtScalar, TgtPacket, false, false> {
212  static void run() {}
213 };
214 
215 template <typename Scalar, typename Packet, typename EnableIf = void>
217  static void run() {
233  }
234 };
235 
236 // Only some types support cast from std::complex<>.
237 template <typename Scalar, typename Packet>
238 struct packetmath_pcast_ops_runner<Scalar, Packet, typename internal::enable_if<NumTraits<Scalar>::IsComplex>::type> {
239  static void run() {
244  }
245 };
246 
247 template <typename Scalar, typename Packet>
249  const int PacketSize = internal::unpacket_traits<Packet>::size;
250  const int size = 2 * PacketSize;
251  EIGEN_ALIGN_MAX Scalar data1[size];
252  EIGEN_ALIGN_MAX Scalar data2[size];
254 
255  for (int i = 0; i < size; ++i) {
256  data1[i] = internal::random<Scalar>();
257  }
260  for (int i = 0; i < PacketSize; ++i) {
261  data1[i] = Scalar(i);
262  data1[i + PacketSize] = internal::random<bool>() ? data1[i] : Scalar(0);
263  }
264 
266 
267  //Test (-0) == (0) for signed operations
268  for (int i = 0; i < PacketSize; ++i) {
269  data1[i] = Scalar(-0.0);
270  data1[i + PacketSize] = internal::random<bool>() ? data1[i] : Scalar(0);
271  }
273 
274  //Test NaN
275  for (int i = 0; i < PacketSize; ++i) {
276  data1[i] = NumTraits<Scalar>::quiet_NaN();
277  data1[i + PacketSize] = internal::random<bool>() ? data1[i] : Scalar(0);
278  }
280 }
281 
282 template <typename Scalar, typename Packet>
284  const int PacketSize = internal::unpacket_traits<Packet>::size;
285  const int size = 2 * PacketSize;
286  EIGEN_ALIGN_MAX Scalar data1[size];
287  EIGEN_ALIGN_MAX Scalar data2[size];
289 
290  for (int i = 0; i < PacketSize; ++i) {
291  data1[i] = internal::random<Scalar>();
292  data1[i + PacketSize] = internal::random<bool>() ? data1[i] : Scalar(0);
293  }
294 
296 
297  //Test (-0) <=/< (0) for signed operations
298  for (int i = 0; i < PacketSize; ++i) {
299  data1[i] = Scalar(-0.0);
300  data1[i + PacketSize] = internal::random<bool>() ? data1[i] : Scalar(0);
301  }
303 
304  //Test NaN
305  for (int i = 0; i < PacketSize; ++i) {
306  data1[i] = NumTraits<Scalar>::quiet_NaN();
307  data1[i + PacketSize] = internal::random<bool>() ? data1[i] : Scalar(0);
308  }
310 }
311 
312 template <typename Scalar, typename Packet>
314  const int PacketSize = internal::unpacket_traits<Packet>::size;
315  const int size = 2 * PacketSize;
316  EIGEN_ALIGN_MAX Scalar data1[size];
317  EIGEN_ALIGN_MAX Scalar data2[size];
319 
320  for (int i = 0; i < PacketSize; ++i) {
321  data1[i] = internal::random<Scalar>();
322  data1[i + PacketSize] = internal::random<bool>() ? data1[i] : Scalar(0);
323  }
324 
327 
328  //Test (-0) <=/< (0) for signed operations
329  for (int i = 0; i < PacketSize; ++i) {
330  data1[i] = Scalar(-0.0);
331  data1[i + PacketSize] = internal::random<bool>() ? data1[i] : Scalar(0);
332  }
335 
336  //Test NaN
337  for (int i = 0; i < PacketSize; ++i) {
338  data1[i] = NumTraits<Scalar>::quiet_NaN();
339  data1[i + PacketSize] = internal::random<bool>() ? data1[i] : Scalar(0);
340  }
343 }
344 
345 // Packet16b representing bool does not support ptrue, pandnot or pcmp_eq, since the scalar path
346 // (for some compilers) compute the bitwise and with 0x1 of the results to keep the value in [0,1].
347 template<>
349 template<>
351 
352 template <typename Scalar, typename Packet>
354  const int PacketSize = internal::unpacket_traits<Packet>::size;
355  const int size = 2 * PacketSize;
356  EIGEN_ALIGN_MAX Scalar data1[size];
357  EIGEN_ALIGN_MAX Scalar data2[size];
359 
360  for (int i = 0; i < PacketSize; ++i) {
361  data1[i] = Scalar(-0.0);
362  data1[i + PacketSize] = Scalar(-0.0);
363  }
364  CHECK_CWISE2_IF(internal::packet_traits<Scalar>::HasAdd, REF_ADD, internal::padd);
365 }
366 
367 // Ensure optimization barrier compiles and doesn't modify contents.
368 // Only applies to raw types, so will not work for std::complex, Eigen::half
369 // or Eigen::bfloat16. For those you would need to refer to an underlying
370 // storage element.
371 template<typename Packet, typename EnableIf = void>
373  static void run() {}
374 };
375 
376 template<typename Packet>
377 struct eigen_optimization_barrier_test<Packet, typename internal::enable_if<
378  !NumTraits<Packet>::IsComplex &&
379  !internal::is_same<Packet, Eigen::half>::value &&
380  !internal::is_same<Packet, Eigen::bfloat16>::value
381  >::type> {
382  static void run() {
384  Scalar s = internal::random<Scalar>();
385  Packet barrier = internal::pset1<Packet>(s);
387  eigen_assert(s == internal::pfirst(barrier) && "EIGEN_OPTIMIZATION_BARRIER");
388  }
389 };
390 
391 template <typename Scalar, typename Packet>
392 void packetmath() {
393  typedef internal::packet_traits<Scalar> PacketTraits;
394  const int PacketSize = internal::unpacket_traits<Packet>::size;
395  typedef typename NumTraits<Scalar>::Real RealScalar;
396 
397  if (g_first_pass)
398  std::cerr << "=== Testing packet of type '" << typeid(Packet).name() << "' and scalar type '"
399  << typeid(Scalar).name() << "' and size '" << PacketSize << "' ===\n";
400 
401  const int max_size = PacketSize > 4 ? PacketSize : 4;
402  const int size = PacketSize * max_size;
403  EIGEN_ALIGN_MAX Scalar data1[size];
404  EIGEN_ALIGN_MAX Scalar data2[size];
405  EIGEN_ALIGN_MAX Scalar data3[size];
407  RealScalar refvalue = RealScalar(0);
408 
411 
412  for (int i = 0; i < size; ++i) {
413  data1[i] = internal::random<Scalar>() / RealScalar(PacketSize);
414  data2[i] = internal::random<Scalar>() / RealScalar(PacketSize);
415  refvalue = (std::max)(refvalue, numext::abs(data1[i]));
416  }
417 
418  internal::pstore(data2, internal::pload<Packet>(data1));
419  VERIFY(test::areApprox(data1, data2, PacketSize) && "aligned load/store");
420 
421  for (int offset = 0; offset < PacketSize; ++offset) {
422  internal::pstore(data2, internal::ploadu<Packet>(data1 + offset));
423  VERIFY(test::areApprox(data1 + offset, data2, PacketSize) && "internal::ploadu");
424  }
425 
426  for (int offset = 0; offset < PacketSize; ++offset) {
427  internal::pstoreu(data2 + offset, internal::pload<Packet>(data1));
428  VERIFY(test::areApprox(data1, data2 + offset, PacketSize) && "internal::pstoreu");
429  }
430 
431  if (internal::unpacket_traits<Packet>::masked_load_available) {
432  test::packet_helper<internal::unpacket_traits<Packet>::masked_load_available, Packet> h;
433  unsigned long long max_umask = (0x1ull << PacketSize);
434 
435  for (int offset = 0; offset < PacketSize; ++offset) {
436  for (unsigned long long umask = 0; umask < max_umask; ++umask) {
437  h.store(data2, h.load(data1 + offset, umask));
438  for (int k = 0; k < PacketSize; ++k) data3[k] = ((umask & (0x1ull << k)) >> k) ? data1[k + offset] : Scalar(0);
439  VERIFY(test::areApprox(data3, data2, PacketSize) && "internal::ploadu masked");
440  }
441  }
442  }
443 
444  if (internal::unpacket_traits<Packet>::masked_store_available) {
445  test::packet_helper<internal::unpacket_traits<Packet>::masked_store_available, Packet> h;
446  unsigned long long max_umask = (0x1ull << PacketSize);
447 
448  for (int offset = 0; offset < PacketSize; ++offset) {
449  for (unsigned long long umask = 0; umask < max_umask; ++umask) {
450  internal::pstore(data2, internal::pset1<Packet>(Scalar(0)));
451  h.store(data2, h.loadu(data1 + offset), umask);
452  for (int k = 0; k < PacketSize; ++k) data3[k] = ((umask & (0x1ull << k)) >> k) ? data1[k + offset] : Scalar(0);
453  VERIFY(test::areApprox(data3, data2, PacketSize) && "internal::pstoreu masked");
454  }
455  }
456  }
457 
458  VERIFY((!PacketTraits::Vectorizable) || PacketTraits::HasAdd);
459  VERIFY((!PacketTraits::Vectorizable) || PacketTraits::HasSub);
460  VERIFY((!PacketTraits::Vectorizable) || PacketTraits::HasMul);
461 
462  CHECK_CWISE2_IF(PacketTraits::HasAdd, REF_ADD, internal::padd);
463  CHECK_CWISE2_IF(PacketTraits::HasSub, REF_SUB, internal::psub);
464  CHECK_CWISE2_IF(PacketTraits::HasMul, REF_MUL, internal::pmul);
465  CHECK_CWISE2_IF(PacketTraits::HasDiv, REF_DIV, internal::pdiv);
466 
467  if (PacketTraits::HasNegate) CHECK_CWISE1(internal::negate, internal::pnegate);
469 
470  for (int offset = 0; offset < 3; ++offset) {
471  for (int i = 0; i < PacketSize; ++i) ref[i] = data1[offset];
472  internal::pstore(data2, internal::pset1<Packet>(data1[offset]));
473  VERIFY(test::areApprox(ref, data2, PacketSize) && "internal::pset1");
474  }
475 
476  {
477  for (int i = 0; i < PacketSize * 4; ++i) ref[i] = data1[i / PacketSize];
478  Packet A0, A1, A2, A3;
479  internal::pbroadcast4<Packet>(data1, A0, A1, A2, A3);
480  internal::pstore(data2 + 0 * PacketSize, A0);
481  internal::pstore(data2 + 1 * PacketSize, A1);
482  internal::pstore(data2 + 2 * PacketSize, A2);
483  internal::pstore(data2 + 3 * PacketSize, A3);
484  VERIFY(test::areApprox(ref, data2, 4 * PacketSize) && "internal::pbroadcast4");
485  }
486 
487  {
488  for (int i = 0; i < PacketSize * 2; ++i) ref[i] = data1[i / PacketSize];
489  Packet A0, A1;
490  internal::pbroadcast2<Packet>(data1, A0, A1);
491  internal::pstore(data2 + 0 * PacketSize, A0);
492  internal::pstore(data2 + 1 * PacketSize, A1);
493  VERIFY(test::areApprox(ref, data2, 2 * PacketSize) && "internal::pbroadcast2");
494  }
495 
496  VERIFY(internal::isApprox(data1[0], internal::pfirst(internal::pload<Packet>(data1))) && "internal::pfirst");
497 
498  if (PacketSize > 1) {
499  // apply different offsets to check that ploaddup is robust to unaligned inputs
500  for (int offset = 0; offset < 4; ++offset) {
501  for (int i = 0; i < PacketSize / 2; ++i) ref[2 * i + 0] = ref[2 * i + 1] = data1[offset + i];
502  internal::pstore(data2, internal::ploaddup<Packet>(data1 + offset));
503  VERIFY(test::areApprox(ref, data2, PacketSize) && "ploaddup");
504  }
505  }
506 
507  if (PacketSize > 2) {
508  // apply different offsets to check that ploadquad is robust to unaligned inputs
509  for (int offset = 0; offset < 4; ++offset) {
510  for (int i = 0; i < PacketSize / 4; ++i)
511  ref[4 * i + 0] = ref[4 * i + 1] = ref[4 * i + 2] = ref[4 * i + 3] = data1[offset + i];
512  internal::pstore(data2, internal::ploadquad<Packet>(data1 + offset));
513  VERIFY(test::areApprox(ref, data2, PacketSize) && "ploadquad");
514  }
515  }
516 
517  ref[0] = Scalar(0);
518  for (int i = 0; i < PacketSize; ++i) ref[0] += data1[i];
519  VERIFY(test::isApproxAbs(ref[0], internal::predux(internal::pload<Packet>(data1)), refvalue) && "internal::predux");
520 
521  if (!internal::is_same<Packet, typename internal::unpacket_traits<Packet>::half>::value) {
522  int HalfPacketSize = PacketSize > 4 ? PacketSize / 2 : PacketSize;
523  for (int i = 0; i < HalfPacketSize; ++i) ref[i] = Scalar(0);
524  for (int i = 0; i < PacketSize; ++i) ref[i % HalfPacketSize] += data1[i];
525  internal::pstore(data2, internal::predux_half_dowto4(internal::pload<Packet>(data1)));
526  VERIFY(test::areApprox(ref, data2, HalfPacketSize) && "internal::predux_half_dowto4");
527  }
528 
529  ref[0] = Scalar(1);
530  for (int i = 0; i < PacketSize; ++i) ref[0] = REF_MUL(ref[0], data1[i]);
531  VERIFY(internal::isApprox(ref[0], internal::predux_mul(internal::pload<Packet>(data1))) && "internal::predux_mul");
532 
533  for (int i = 0; i < PacketSize; ++i) ref[i] = data1[PacketSize - i - 1];
534  internal::pstore(data2, internal::preverse(internal::pload<Packet>(data1)));
535  VERIFY(test::areApprox(ref, data2, PacketSize) && "internal::preverse");
536 
537  internal::PacketBlock<Packet> kernel;
538  for (int i = 0; i < PacketSize; ++i) {
539  kernel.packet[i] = internal::pload<Packet>(data1 + i * PacketSize);
540  }
541  ptranspose(kernel);
542  for (int i = 0; i < PacketSize; ++i) {
543  internal::pstore(data2, kernel.packet[i]);
544  for (int j = 0; j < PacketSize; ++j) {
545  VERIFY(test::isApproxAbs(data2[j], data1[i + j * PacketSize], refvalue) && "ptranspose");
546  }
547  }
548 
549  // GeneralBlockPanelKernel also checks PacketBlock<Packet,(PacketSize%4)==0?4:PacketSize>;
550  if (PacketSize > 4 && PacketSize % 4 == 0) {
551  internal::PacketBlock<Packet, PacketSize%4==0?4:PacketSize> kernel2;
552  for (int i = 0; i < 4; ++i) {
553  kernel2.packet[i] = internal::pload<Packet>(data1 + i * PacketSize);
554  }
555  ptranspose(kernel2);
556  int data_counter = 0;
557  for (int i = 0; i < PacketSize; ++i) {
558  for (int j = 0; j < 4; ++j) {
559  data2[data_counter++] = data1[j*PacketSize + i];
560  }
561  }
562  for (int i = 0; i < 4; ++i) {
563  internal::pstore(data3, kernel2.packet[i]);
564  for (int j = 0; j < PacketSize; ++j) {
565  VERIFY(test::isApproxAbs(data3[j], data2[i*PacketSize + j], refvalue) && "ptranspose");
566  }
567  }
568  }
569 
570  if (PacketTraits::HasBlend) {
571  Packet thenPacket = internal::pload<Packet>(data1);
572  Packet elsePacket = internal::pload<Packet>(data2);
573  EIGEN_ALIGN_MAX internal::Selector<PacketSize> selector;
574  for (int i = 0; i < PacketSize; ++i) {
575  selector.select[i] = i;
576  }
577 
578  Packet blend = internal::pblend(selector, thenPacket, elsePacket);
580  internal::pstore(result, blend);
581  for (int i = 0; i < PacketSize; ++i) {
582  VERIFY(test::isApproxAbs(result[i], (selector.select[i] ? data1[i] : data2[i]), refvalue));
583  }
584  }
585 
586  {
587  for (int i = 0; i < PacketSize; ++i) {
588  // "if" mask
589  unsigned char v = internal::random<bool>() ? 0xff : 0;
590  char* bytes = (char*)(data1 + i);
591  for (int k = 0; k < int(sizeof(Scalar)); ++k) {
592  bytes[k] = v;
593  }
594  // "then" packet
595  data1[i + PacketSize] = internal::random<Scalar>();
596  // "else" packet
597  data1[i + 2 * PacketSize] = internal::random<Scalar>();
598  }
600  }
601 
602  for (int i = 0; i < size; ++i) {
603  data1[i] = internal::random<Scalar>();
604  }
609 
610  packetmath_boolean_mask_ops<Scalar, Packet>();
612  packetmath_minus_zero_add<Scalar, Packet>();
613 
614  for (int i = 0; i < size; ++i) {
615  data1[i] = numext::abs(internal::random<Scalar>());
616  }
617  CHECK_CWISE1_IF(PacketTraits::HasSqrt, numext::sqrt, internal::psqrt);
618  CHECK_CWISE1_IF(PacketTraits::HasRsqrt, numext::rsqrt, internal::prsqrt);
619 }
620 
621 // Notice that this definition works for complex types as well.
622 // c++11 has std::log2 for real, but not for complex types.
623 template <typename Scalar>
625  return Scalar(EIGEN_LOG2E) * std::log(x);
626 }
627 
628 template <typename Scalar, typename Packet>
630  typedef internal::packet_traits<Scalar> PacketTraits;
631  const int PacketSize = internal::unpacket_traits<Packet>::size;
632 
633  const int size = PacketSize * 4;
634  EIGEN_ALIGN_MAX Scalar data1[PacketSize * 4];
635  EIGEN_ALIGN_MAX Scalar data2[PacketSize * 4];
636  EIGEN_ALIGN_MAX Scalar ref[PacketSize * 4];
637 
638  for (int i = 0; i < size; ++i) {
639  data1[i] = Scalar(internal::random<double>(0, 1) * std::pow(10., internal::random<double>(-6, 6)));
640  data2[i] = Scalar(internal::random<double>(0, 1) * std::pow(10., internal::random<double>(-6, 6)));
641  }
642 
643  if (internal::random<float>(0, 1) < 0.1f) data1[internal::random<int>(0, PacketSize)] = Scalar(0);
644 
645  CHECK_CWISE1_IF(PacketTraits::HasLog, std::log, internal::plog);
646  CHECK_CWISE1_IF(PacketTraits::HasLog, log2, internal::plog2);
647  CHECK_CWISE1_IF(PacketTraits::HasRsqrt, numext::rsqrt, internal::prsqrt);
648 
649  for (int i = 0; i < size; ++i) {
650  data1[i] = Scalar(internal::random<double>(-1, 1) * std::pow(10., internal::random<double>(-3, 3)));
651  data2[i] = Scalar(internal::random<double>(-1, 1) * std::pow(10., internal::random<double>(-3, 3)));
652  }
653  CHECK_CWISE1_IF(PacketTraits::HasSin, std::sin, internal::psin);
654  CHECK_CWISE1_IF(PacketTraits::HasCos, std::cos, internal::pcos);
655  CHECK_CWISE1_IF(PacketTraits::HasTan, std::tan, internal::ptan);
656 
657  CHECK_CWISE1_EXACT_IF(PacketTraits::HasRound, numext::round, internal::pround);
658  CHECK_CWISE1_EXACT_IF(PacketTraits::HasCeil, numext::ceil, internal::pceil);
659  CHECK_CWISE1_EXACT_IF(PacketTraits::HasFloor, numext::floor, internal::pfloor);
660  CHECK_CWISE1_EXACT_IF(PacketTraits::HasRint, numext::rint, internal::print);
661 
662  packetmath_boolean_mask_ops_real<Scalar,Packet>();
663 
664  // Rounding edge cases.
665  if (PacketTraits::HasRound || PacketTraits::HasCeil || PacketTraits::HasFloor || PacketTraits::HasRint) {
666  typedef typename internal::make_integer<Scalar>::type IntType;
667  // Start with values that cannot fit inside an integer, work down to less than one.
668  Scalar val = numext::mini(
669  Scalar(2) * static_cast<Scalar>(NumTraits<IntType>::highest()),
671  std::vector<Scalar> values;
672  while (val > Scalar(0.25)) {
673  // Cover both even and odd, positive and negative cases.
674  values.push_back(val);
675  values.push_back(val + Scalar(0.3));
676  values.push_back(val + Scalar(0.5));
677  values.push_back(val + Scalar(0.8));
678  values.push_back(val + Scalar(1));
679  values.push_back(val + Scalar(1.3));
680  values.push_back(val + Scalar(1.5));
681  values.push_back(val + Scalar(1.8));
682  values.push_back(-val);
683  values.push_back(-val - Scalar(0.3));
684  values.push_back(-val - Scalar(0.5));
685  values.push_back(-val - Scalar(0.8));
686  values.push_back(-val - Scalar(1));
687  values.push_back(-val - Scalar(1.3));
688  values.push_back(-val - Scalar(1.5));
689  values.push_back(-val - Scalar(1.8));
690  values.push_back(Scalar(-1.5) + val); // Bug 1785.
691  val = val / Scalar(2);
692  }
693  values.push_back(NumTraits<Scalar>::infinity());
694  values.push_back(-NumTraits<Scalar>::infinity());
696 
697  for (size_t k=0; k<values.size(); ++k) {
698  data1[0] = values[k];
699  CHECK_CWISE1_EXACT_IF(PacketTraits::HasRound, numext::round, internal::pround);
700  CHECK_CWISE1_EXACT_IF(PacketTraits::HasCeil, numext::ceil, internal::pceil);
701  CHECK_CWISE1_EXACT_IF(PacketTraits::HasFloor, numext::floor, internal::pfloor);
702  CHECK_CWISE1_EXACT_IF(PacketTraits::HasRint, numext::rint, internal::print);
703  }
704  }
705 
706  for (int i = 0; i < size; ++i) {
707  data1[i] = Scalar(internal::random<double>(-1, 1));
708  data2[i] = Scalar(internal::random<double>(-1, 1));
709  }
710  CHECK_CWISE1_IF(PacketTraits::HasASin, std::asin, internal::pasin);
711  CHECK_CWISE1_IF(PacketTraits::HasACos, std::acos, internal::pacos);
712 
713  for (int i = 0; i < size; ++i) {
714  data1[i] = Scalar(internal::random<double>(-87, 88));
715  data2[i] = Scalar(internal::random<double>(-87, 88));
716  }
717  CHECK_CWISE1_IF(PacketTraits::HasExp, std::exp, internal::pexp);
718 
719  CHECK_CWISE1_BYREF1_IF(PacketTraits::HasExp, REF_FREXP, internal::pfrexp);
720  if (PacketTraits::HasExp) {
721  // Check denormals:
722  for (int j=0; j<3; ++j) {
723  data1[0] = Scalar(std::ldexp(1, NumTraits<Scalar>::min_exponent()-j));
724  CHECK_CWISE1_BYREF1_IF(PacketTraits::HasExp, REF_FREXP, internal::pfrexp);
725  data1[0] = -data1[0];
726  CHECK_CWISE1_BYREF1_IF(PacketTraits::HasExp, REF_FREXP, internal::pfrexp);
727  }
728 
729  // zero
730  data1[0] = Scalar(0);
731  CHECK_CWISE1_BYREF1_IF(PacketTraits::HasExp, REF_FREXP, internal::pfrexp);
732 
733  // inf and NaN only compare output fraction, not exponent.
734  test::packet_helper<PacketTraits::HasExp,Packet> h;
735  Packet pout;
736  Scalar sout;
737  Scalar special[] = { NumTraits<Scalar>::infinity(),
740  for (int i=0; i<3; ++i) {
741  data1[0] = special[i];
742  ref[0] = Scalar(REF_FREXP(data1[0], ref[PacketSize]));
743  h.store(data2, internal::pfrexp(h.load(data1), h.forward_reference(pout, sout)));
744  VERIFY(test::areApprox(ref, data2, 1) && "internal::pfrexp");
745  }
746  }
747 
748  for (int i = 0; i < PacketSize; ++i) {
749  data1[i] = Scalar(internal::random<double>(-1, 1));
750  data2[i] = Scalar(internal::random<double>(-1, 1));
751  }
752  for (int i = 0; i < PacketSize; ++i) {
753  data1[i+PacketSize] = Scalar(internal::random<int>(-4, 4));
754  data2[i+PacketSize] = Scalar(internal::random<double>(-4, 4));
755  }
756  CHECK_CWISE2_IF(PacketTraits::HasExp, REF_LDEXP, internal::pldexp);
757  if (PacketTraits::HasExp) {
758  data1[0] = Scalar(-1);
759  // underflow to zero
760  data1[PacketSize] = Scalar(NumTraits<Scalar>::min_exponent()-55);
761  CHECK_CWISE2_IF(PacketTraits::HasExp, REF_LDEXP, internal::pldexp);
762  // overflow to inf
763  data1[PacketSize] = Scalar(NumTraits<Scalar>::max_exponent()+10);
764  CHECK_CWISE2_IF(PacketTraits::HasExp, REF_LDEXP, internal::pldexp);
765  // NaN stays NaN
766  data1[0] = NumTraits<Scalar>::quiet_NaN();
767  CHECK_CWISE2_IF(PacketTraits::HasExp, REF_LDEXP, internal::pldexp);
768  VERIFY((numext::isnan)(data2[0]));
769  // inf stays inf
770  data1[0] = NumTraits<Scalar>::infinity();
771  data1[PacketSize] = Scalar(NumTraits<Scalar>::min_exponent()-10);
772  CHECK_CWISE2_IF(PacketTraits::HasExp, REF_LDEXP, internal::pldexp);
773  // zero stays zero
774  data1[0] = Scalar(0);
775  data1[PacketSize] = Scalar(NumTraits<Scalar>::max_exponent()+10);
776  CHECK_CWISE2_IF(PacketTraits::HasExp, REF_LDEXP, internal::pldexp);
777  // Small number big exponent.
778  data1[0] = Scalar(std::ldexp(Scalar(1.0), NumTraits<Scalar>::min_exponent()-1));
779  data1[PacketSize] = Scalar(-NumTraits<Scalar>::min_exponent()
781  CHECK_CWISE2_IF(PacketTraits::HasExp, REF_LDEXP, internal::pldexp);
782  // Big number small exponent.
783  data1[0] = Scalar(std::ldexp(Scalar(1.0), NumTraits<Scalar>::max_exponent()-1));
784  data1[PacketSize] = Scalar(+NumTraits<Scalar>::min_exponent()
786  CHECK_CWISE2_IF(PacketTraits::HasExp, REF_LDEXP, internal::pldexp);
787  }
788 
789  for (int i = 0; i < size; ++i) {
790  data1[i] = Scalar(internal::random<double>(-1, 1) * std::pow(10., internal::random<double>(-6, 6)));
791  data2[i] = Scalar(internal::random<double>(-1, 1) * std::pow(10., internal::random<double>(-6, 6)));
792  }
793  data1[0] = Scalar(1e-20);
794  CHECK_CWISE1_IF(PacketTraits::HasTanh, std::tanh, internal::ptanh);
795  if (PacketTraits::HasExp && PacketSize >= 2) {
796  const Scalar small = NumTraits<Scalar>::epsilon();
797  data1[0] = NumTraits<Scalar>::quiet_NaN();
798  data1[1] = small;
799  test::packet_helper<PacketTraits::HasExp, Packet> h;
800  h.store(data2, internal::pexp(h.load(data1)));
801  VERIFY((numext::isnan)(data2[0]));
802  // TODO(rmlarsen): Re-enable for bfloat16.
804  VERIFY_IS_APPROX(std::exp(small), data2[1]);
805  }
806 
807  data1[0] = -small;
808  data1[1] = Scalar(0);
809  h.store(data2, internal::pexp(h.load(data1)));
810  // TODO(rmlarsen): Re-enable for bfloat16.
812  VERIFY_IS_APPROX(std::exp(-small), data2[0]);
813  }
814  VERIFY_IS_EQUAL(std::exp(Scalar(0)), data2[1]);
815 
816  data1[0] = (std::numeric_limits<Scalar>::min)();
817  data1[1] = -(std::numeric_limits<Scalar>::min)();
818  h.store(data2, internal::pexp(h.load(data1)));
821 
822  data1[0] = std::numeric_limits<Scalar>::denorm_min();
823  data1[1] = -std::numeric_limits<Scalar>::denorm_min();
824  h.store(data2, internal::pexp(h.load(data1)));
825  VERIFY_IS_APPROX(std::exp(std::numeric_limits<Scalar>::denorm_min()), data2[0]);
826  VERIFY_IS_APPROX(std::exp(-std::numeric_limits<Scalar>::denorm_min()), data2[1]);
827  }
828 
829  if (PacketTraits::HasTanh) {
830  // NOTE this test migh fail with GCC prior to 6.3, see MathFunctionsImpl.h for details.
831  data1[0] = NumTraits<Scalar>::quiet_NaN();
832  test::packet_helper<internal::packet_traits<Scalar>::HasTanh, Packet> h;
833  h.store(data2, internal::ptanh(h.load(data1)));
834  VERIFY((numext::isnan)(data2[0]));
835  }
836 
837  if (PacketTraits::HasExp) {
838  internal::scalar_logistic_op<Scalar> logistic;
839  for (int i = 0; i < size; ++i) {
840  data1[i] = Scalar(internal::random<double>(-20, 20));
841  }
842 
843  test::packet_helper<PacketTraits::HasExp, Packet> h;
844  h.store(data2, logistic.packetOp(h.load(data1)));
845  for (int i = 0; i < PacketSize; ++i) {
846  VERIFY_IS_APPROX(data2[i], logistic(data1[i]));
847  }
848  }
849 
850 #if EIGEN_HAS_C99_MATH && (EIGEN_COMP_CXXVER >= 11)
851  data1[0] = NumTraits<Scalar>::infinity();
852  data1[1] = Scalar(-1);
853  CHECK_CWISE1_IF(PacketTraits::HasLog1p, std::log1p, internal::plog1p);
854  data1[0] = NumTraits<Scalar>::infinity();
855  data1[1] = -NumTraits<Scalar>::infinity();
856  CHECK_CWISE1_IF(PacketTraits::HasExpm1, std::expm1, internal::pexpm1);
857 #endif
858 
859  if (PacketSize >= 2) {
860  data1[0] = NumTraits<Scalar>::quiet_NaN();
861  data1[1] = NumTraits<Scalar>::epsilon();
862  if (PacketTraits::HasLog) {
863  test::packet_helper<PacketTraits::HasLog, Packet> h;
864  h.store(data2, internal::plog(h.load(data1)));
865  VERIFY((numext::isnan)(data2[0]));
866  // TODO(cantonios): Re-enable for bfloat16.
868  VERIFY_IS_APPROX(std::log(data1[1]), data2[1]);
869  }
870 
871  data1[0] = -NumTraits<Scalar>::epsilon();
872  data1[1] = Scalar(0);
873  h.store(data2, internal::plog(h.load(data1)));
874  VERIFY((numext::isnan)(data2[0]));
875  VERIFY_IS_EQUAL(std::log(Scalar(0)), data2[1]);
876 
877  data1[0] = (std::numeric_limits<Scalar>::min)();
878  data1[1] = -(std::numeric_limits<Scalar>::min)();
879  h.store(data2, internal::plog(h.load(data1)));
880  // TODO(cantonios): Re-enable for bfloat16.
883  }
884  VERIFY((numext::isnan)(data2[1]));
885 
886  // Note: 32-bit arm always flushes denorms to zero.
887 #if !EIGEN_ARCH_ARM
888  if (std::numeric_limits<Scalar>::has_denorm == std::denorm_present) {
889  data1[0] = std::numeric_limits<Scalar>::denorm_min();
890  data1[1] = -std::numeric_limits<Scalar>::denorm_min();
891  h.store(data2, internal::plog(h.load(data1)));
892  // TODO(rmlarsen): Reenable.
893  // VERIFY_IS_EQUAL(std::log(std::numeric_limits<Scalar>::denorm_min()), data2[0]);
894  VERIFY((numext::isnan)(data2[1]));
895  }
896 #endif
897 
898  data1[0] = Scalar(-1.0f);
899  h.store(data2, internal::plog(h.load(data1)));
900  VERIFY((numext::isnan)(data2[0]));
901 
902  data1[0] = NumTraits<Scalar>::infinity();
903  h.store(data2, internal::plog(h.load(data1)));
904  VERIFY((numext::isinf)(data2[0]));
905  }
906  if (PacketTraits::HasLog1p) {
907  test::packet_helper<PacketTraits::HasLog1p, Packet> h;
908  data1[0] = Scalar(-2);
909  data1[1] = -NumTraits<Scalar>::infinity();
910  h.store(data2, internal::plog1p(h.load(data1)));
911  VERIFY((numext::isnan)(data2[0]));
912  VERIFY((numext::isnan)(data2[1]));
913  }
914  if (PacketTraits::HasSqrt) {
915  test::packet_helper<PacketTraits::HasSqrt, Packet> h;
916  data1[0] = Scalar(-1.0f);
917  if (std::numeric_limits<Scalar>::has_denorm == std::denorm_present) {
918  data1[1] = -std::numeric_limits<Scalar>::denorm_min();
919  } else {
920  data1[1] = -NumTraits<Scalar>::epsilon();
921  }
922  h.store(data2, internal::psqrt(h.load(data1)));
923  VERIFY((numext::isnan)(data2[0]));
924  VERIFY((numext::isnan)(data2[1]));
925  }
926  // TODO(rmlarsen): Re-enable for half and bfloat16.
927  if (PacketTraits::HasCos
930  test::packet_helper<PacketTraits::HasCos, Packet> h;
931  for (Scalar k = Scalar(1); k < Scalar(10000) / NumTraits<Scalar>::epsilon(); k *= Scalar(2)) {
932  for (int k1 = 0; k1 <= 1; ++k1) {
933  data1[0] = Scalar((2 * double(k) + k1) * double(EIGEN_PI) / 2 * internal::random<double>(0.8, 1.2));
934  data1[1] = Scalar((2 * double(k) + 2 + k1) * double(EIGEN_PI) / 2 * internal::random<double>(0.8, 1.2));
935  h.store(data2, internal::pcos(h.load(data1)));
936  h.store(data2 + PacketSize, internal::psin(h.load(data1)));
937  VERIFY(data2[0] <= Scalar(1.) && data2[0] >= Scalar(-1.));
938  VERIFY(data2[1] <= Scalar(1.) && data2[1] >= Scalar(-1.));
939  VERIFY(data2[PacketSize + 0] <= Scalar(1.) && data2[PacketSize + 0] >= Scalar(-1.));
940  VERIFY(data2[PacketSize + 1] <= Scalar(1.) && data2[PacketSize + 1] >= Scalar(-1.));
941 
942  VERIFY_IS_APPROX(data2[0], std::cos(data1[0]));
943  VERIFY_IS_APPROX(data2[1], std::cos(data1[1]));
944  VERIFY_IS_APPROX(data2[PacketSize + 0], std::sin(data1[0]));
945  VERIFY_IS_APPROX(data2[PacketSize + 1], std::sin(data1[1]));
946 
947  VERIFY_IS_APPROX(numext::abs2(data2[0]) + numext::abs2(data2[PacketSize + 0]), Scalar(1));
948  VERIFY_IS_APPROX(numext::abs2(data2[1]) + numext::abs2(data2[PacketSize + 1]), Scalar(1));
949  }
950  }
951 
952  data1[0] = NumTraits<Scalar>::infinity();
953  data1[1] = -NumTraits<Scalar>::infinity();
954  h.store(data2, internal::psin(h.load(data1)));
955  VERIFY((numext::isnan)(data2[0]));
956  VERIFY((numext::isnan)(data2[1]));
957 
958  h.store(data2, internal::pcos(h.load(data1)));
959  VERIFY((numext::isnan)(data2[0]));
960  VERIFY((numext::isnan)(data2[1]));
961 
962  data1[0] = NumTraits<Scalar>::quiet_NaN();
963  h.store(data2, internal::psin(h.load(data1)));
964  VERIFY((numext::isnan)(data2[0]));
965  h.store(data2, internal::pcos(h.load(data1)));
966  VERIFY((numext::isnan)(data2[0]));
967 
968  data1[0] = -Scalar(0.);
969  h.store(data2, internal::psin(h.load(data1)));
970  VERIFY(internal::biteq(data2[0], data1[0]));
971  h.store(data2, internal::pcos(h.load(data1)));
972  VERIFY_IS_EQUAL(data2[0], Scalar(1));
973  }
974  }
975 }
976 
977 #define CAST_CHECK_CWISE1_IF(COND, REFOP, POP, SCALAR, REFTYPE) if(COND) { \
978  test::packet_helper<COND,Packet> h; \
979  for (int i=0; i<PacketSize; ++i) \
980  ref[i] = SCALAR(REFOP(static_cast<REFTYPE>(data1[i]))); \
981  h.store(data2, POP(h.load(data1))); \
982  VERIFY(test::areApprox(ref, data2, PacketSize) && #POP); \
983 }
984 
985 template <typename Scalar>
987  if ((numext::isnan)(a)) return a;
988  if ((numext::isnan)(b)) return b;
989  return (numext::maxi)(a,b);
990 }
991 
992 template <typename Scalar>
994  if ((numext::isnan)(a)) return a;
995  if ((numext::isnan)(b)) return b;
996  return (numext::mini)(a,b);
997 }
998 
999 template <typename Scalar>
1001  if ((numext::isnan)(a)) return b;
1002  if ((numext::isnan)(b)) return a;
1003  return (numext::maxi)(a,b);
1004 }
1005 
1006 template <typename Scalar>
1008  if ((numext::isnan)(a)) return b;
1009  if ((numext::isnan)(b)) return a;
1010  return (numext::mini)(a,b);
1011 }
1012 
1013 template <typename Scalar, typename Packet>
1015  typedef internal::packet_traits<Scalar> PacketTraits;
1016  const int PacketSize = internal::unpacket_traits<Packet>::size;
1017 
1018  EIGEN_ALIGN_MAX Scalar data1[PacketSize * 4];
1019  EIGEN_ALIGN_MAX Scalar data2[PacketSize * 4];
1020  EIGEN_ALIGN_MAX Scalar ref[PacketSize * 4];
1021 
1022  Array<Scalar, Dynamic, 1>::Map(data1, PacketSize * 4).setRandom();
1023 
1024  VERIFY((!PacketTraits::Vectorizable) || PacketTraits::HasMin);
1025  VERIFY((!PacketTraits::Vectorizable) || PacketTraits::HasMax);
1026 
1027  CHECK_CWISE2_IF(PacketTraits::HasMin, (std::min), internal::pmin);
1028  CHECK_CWISE2_IF(PacketTraits::HasMax, (std::max), internal::pmax);
1029 
1030  CHECK_CWISE2_IF(PacketTraits::HasMin, propagate_number_min, internal::pmin<PropagateNumbers>);
1031  CHECK_CWISE2_IF(PacketTraits::HasMax, propagate_number_max, internal::pmax<PropagateNumbers>);
1033  CHECK_CWISE2_IF(PacketTraits::HasAbsDiff, REF_ABS_DIFF, internal::pabsdiff);
1034 
1035  ref[0] = data1[0];
1036  for (int i = 0; i < PacketSize; ++i) ref[0] = internal::pmin(ref[0], data1[i]);
1037  VERIFY(internal::isApprox(ref[0], internal::predux_min(internal::pload<Packet>(data1))) && "internal::predux_min");
1038  ref[0] = data1[0];
1039  for (int i = 0; i < PacketSize; ++i) ref[0] = internal::pmax(ref[0], data1[i]);
1040  VERIFY(internal::isApprox(ref[0], internal::predux_max(internal::pload<Packet>(data1))) && "internal::predux_max");
1041 
1042  for (int i = 0; i < PacketSize; ++i) ref[i] = data1[0] + Scalar(i);
1043  internal::pstore(data2, internal::plset<Packet>(data1[0]));
1044  VERIFY(test::areApprox(ref, data2, PacketSize) && "internal::plset");
1045 
1046  {
1047  unsigned char* data1_bits = reinterpret_cast<unsigned char*>(data1);
1048  // predux_all - not needed yet
1049  // for (unsigned int i=0; i<PacketSize*sizeof(Scalar); ++i) data1_bits[i] = 0xff;
1050  // VERIFY(internal::predux_all(internal::pload<Packet>(data1)) && "internal::predux_all(1111)");
1051  // for(int k=0; k<PacketSize; ++k)
1052  // {
1053  // for (unsigned int i=0; i<sizeof(Scalar); ++i) data1_bits[k*sizeof(Scalar)+i] = 0x0;
1054  // VERIFY( (!internal::predux_all(internal::pload<Packet>(data1))) && "internal::predux_all(0101)");
1055  // for (unsigned int i=0; i<sizeof(Scalar); ++i) data1_bits[k*sizeof(Scalar)+i] = 0xff;
1056  // }
1057 
1058  // predux_any
1059  for (unsigned int i = 0; i < PacketSize * sizeof(Scalar); ++i) data1_bits[i] = 0x0;
1060  VERIFY((!internal::predux_any(internal::pload<Packet>(data1))) && "internal::predux_any(0000)");
1061  for (int k = 0; k < PacketSize; ++k) {
1062  for (unsigned int i = 0; i < sizeof(Scalar); ++i) data1_bits[k * sizeof(Scalar) + i] = 0xff;
1063  VERIFY(internal::predux_any(internal::pload<Packet>(data1)) && "internal::predux_any(0101)");
1064  for (unsigned int i = 0; i < sizeof(Scalar); ++i) data1_bits[k * sizeof(Scalar) + i] = 0x00;
1065  }
1066  }
1067 
1068 
1069  // Test NaN propagation.
1071  // Test reductions with no NaNs.
1072  ref[0] = data1[0];
1073  for (int i = 0; i < PacketSize; ++i) ref[0] = internal::pmin<PropagateNumbers>(ref[0], data1[i]);
1074  VERIFY(internal::isApprox(ref[0], internal::predux_min<PropagateNumbers>(internal::pload<Packet>(data1))) && "internal::predux_min<PropagateNumbers>");
1075  ref[0] = data1[0];
1076  for (int i = 0; i < PacketSize; ++i) ref[0] = internal::pmin<PropagateNaN>(ref[0], data1[i]);
1077  VERIFY(internal::isApprox(ref[0], internal::predux_min<PropagateNaN>(internal::pload<Packet>(data1))) && "internal::predux_min<PropagateNaN>");
1078  ref[0] = data1[0];
1079  for (int i = 0; i < PacketSize; ++i) ref[0] = internal::pmax<PropagateNumbers>(ref[0], data1[i]);
1080  VERIFY(internal::isApprox(ref[0], internal::predux_max<PropagateNumbers>(internal::pload<Packet>(data1))) && "internal::predux_max<PropagateNumbers>");
1081  ref[0] = data1[0];
1082  for (int i = 0; i < PacketSize; ++i) ref[0] = internal::pmax<PropagateNaN>(ref[0], data1[i]);
1083  VERIFY(internal::isApprox(ref[0], internal::predux_max<PropagateNaN>(internal::pload<Packet>(data1))) && "internal::predux_max<PropagateNumbers>");
1084  // A single NaN.
1085  const size_t index = std::numeric_limits<size_t>::quiet_NaN() % PacketSize;
1086  data1[index] = NumTraits<Scalar>::quiet_NaN();
1087  VERIFY(PacketSize==1 || !(numext::isnan)(internal::predux_min<PropagateNumbers>(internal::pload<Packet>(data1))));
1088  VERIFY((numext::isnan)(internal::predux_min<PropagateNaN>(internal::pload<Packet>(data1))));
1089  VERIFY(PacketSize==1 || !(numext::isnan)(internal::predux_max<PropagateNumbers>(internal::pload<Packet>(data1))));
1090  VERIFY((numext::isnan)(internal::predux_max<PropagateNaN>(internal::pload<Packet>(data1))));
1091  // All NaNs.
1092  for (int i = 0; i < 4 * PacketSize; ++i) data1[i] = NumTraits<Scalar>::quiet_NaN();
1093  VERIFY((numext::isnan)(internal::predux_min<PropagateNumbers>(internal::pload<Packet>(data1))));
1094  VERIFY((numext::isnan)(internal::predux_min<PropagateNaN>(internal::pload<Packet>(data1))));
1095  VERIFY((numext::isnan)(internal::predux_max<PropagateNumbers>(internal::pload<Packet>(data1))));
1096  VERIFY((numext::isnan)(internal::predux_max<PropagateNaN>(internal::pload<Packet>(data1))));
1097 
1098  // Test NaN propagation for coefficient-wise min and max.
1099  for (int i = 0; i < PacketSize; ++i) {
1100  data1[i] = internal::random<bool>() ? NumTraits<Scalar>::quiet_NaN() : Scalar(0);
1101  data1[i + PacketSize] = internal::random<bool>() ? NumTraits<Scalar>::quiet_NaN() : Scalar(0);
1102  }
1103  // Note: NaN propagation is implementation defined for pmin/pmax, so we do not test it here.
1104  CHECK_CWISE2_IF(PacketTraits::HasMin, propagate_number_min, (internal::pmin<PropagateNumbers>));
1105  CHECK_CWISE2_IF(PacketTraits::HasMax, propagate_number_max, internal::pmax<PropagateNumbers>);
1106  CHECK_CWISE2_IF(PacketTraits::HasMin, propagate_nan_min, (internal::pmin<PropagateNaN>));
1107  CHECK_CWISE2_IF(PacketTraits::HasMax, propagate_nan_max, internal::pmax<PropagateNaN>);
1108  }
1109 
1110  packetmath_boolean_mask_ops_notcomplex<Scalar, Packet>();
1111 }
1112 
1113 template <typename Scalar, typename Packet, bool ConjLhs, bool ConjRhs>
1114 void test_conj_helper(Scalar* data1, Scalar* data2, Scalar* ref, Scalar* pval) {
1115  const int PacketSize = internal::unpacket_traits<Packet>::size;
1116 
1117  internal::conj_if<ConjLhs> cj0;
1118  internal::conj_if<ConjRhs> cj1;
1119  internal::conj_helper<Scalar, Scalar, ConjLhs, ConjRhs> cj;
1120  internal::conj_helper<Packet, Packet, ConjLhs, ConjRhs> pcj;
1121 
1122  for (int i = 0; i < PacketSize; ++i) {
1123  ref[i] = cj0(data1[i]) * cj1(data2[i]);
1124  VERIFY(internal::isApprox(ref[i], cj.pmul(data1[i], data2[i])) && "conj_helper pmul");
1125  }
1126  internal::pstore(pval, pcj.pmul(internal::pload<Packet>(data1), internal::pload<Packet>(data2)));
1127  VERIFY(test::areApprox(ref, pval, PacketSize) && "conj_helper pmul");
1128 
1129  for (int i = 0; i < PacketSize; ++i) {
1130  Scalar tmp = ref[i];
1131  ref[i] += cj0(data1[i]) * cj1(data2[i]);
1132  VERIFY(internal::isApprox(ref[i], cj.pmadd(data1[i], data2[i], tmp)) && "conj_helper pmadd");
1133  }
1135  pval, pcj.pmadd(internal::pload<Packet>(data1), internal::pload<Packet>(data2), internal::pload<Packet>(pval)));
1136  VERIFY(test::areApprox(ref, pval, PacketSize) && "conj_helper pmadd");
1137 }
1138 
1139 template <typename Scalar, typename Packet>
1141  typedef internal::packet_traits<Scalar> PacketTraits;
1142  typedef typename Scalar::value_type RealScalar;
1143  const int PacketSize = internal::unpacket_traits<Packet>::size;
1144 
1145  const int size = PacketSize * 4;
1146  EIGEN_ALIGN_MAX Scalar data1[PacketSize * 4];
1147  EIGEN_ALIGN_MAX Scalar data2[PacketSize * 4];
1148  EIGEN_ALIGN_MAX Scalar ref[PacketSize * 4];
1149  EIGEN_ALIGN_MAX Scalar pval[PacketSize * 4];
1150 
1151  for (int i = 0; i < size; ++i) {
1152  data1[i] = internal::random<Scalar>() * Scalar(1e2);
1153  data2[i] = internal::random<Scalar>() * Scalar(1e2);
1154  }
1155 
1156  test_conj_helper<Scalar, Packet, false, false>(data1, data2, ref, pval);
1157  test_conj_helper<Scalar, Packet, false, true>(data1, data2, ref, pval);
1158  test_conj_helper<Scalar, Packet, true, false>(data1, data2, ref, pval);
1159  test_conj_helper<Scalar, Packet, true, true>(data1, data2, ref, pval);
1160 
1161  // Test pcplxflip.
1162  {
1163  for (int i = 0; i < PacketSize; ++i) ref[i] = Scalar(std::imag(data1[i]), std::real(data1[i]));
1164  internal::pstore(pval, internal::pcplxflip(internal::pload<Packet>(data1)));
1165  VERIFY(test::areApprox(ref, pval, PacketSize) && "pcplxflip");
1166  }
1167 
1168  if (PacketTraits::HasSqrt) {
1169  for (int i = 0; i < size; ++i) {
1170  data1[i] = Scalar(internal::random<RealScalar>(), internal::random<RealScalar>());
1171  }
1173 
1174  // Test misc. corner cases.
1175  const RealScalar zero = RealScalar(0);
1176  const RealScalar one = RealScalar(1);
1177  const RealScalar inf = std::numeric_limits<RealScalar>::infinity();
1178  const RealScalar nan = std::numeric_limits<RealScalar>::quiet_NaN();
1179  data1[0] = Scalar(zero, zero);
1180  data1[1] = Scalar(-zero, zero);
1181  data1[2] = Scalar(one, zero);
1182  data1[3] = Scalar(zero, one);
1184  data1[0] = Scalar(-one, zero);
1185  data1[1] = Scalar(zero, -one);
1186  data1[2] = Scalar(one, one);
1187  data1[3] = Scalar(-one, -one);
1189  data1[0] = Scalar(inf, zero);
1190  data1[1] = Scalar(zero, inf);
1191  data1[2] = Scalar(-inf, zero);
1192  data1[3] = Scalar(zero, -inf);
1194  data1[0] = Scalar(inf, inf);
1195  data1[1] = Scalar(-inf, inf);
1196  data1[2] = Scalar(inf, -inf);
1197  data1[3] = Scalar(-inf, -inf);
1199  data1[0] = Scalar(nan, zero);
1200  data1[1] = Scalar(zero, nan);
1201  data1[2] = Scalar(nan, one);
1202  data1[3] = Scalar(one, nan);
1204  data1[0] = Scalar(nan, nan);
1205  data1[1] = Scalar(inf, nan);
1206  data1[2] = Scalar(nan, inf);
1207  data1[3] = Scalar(-inf, nan);
1209  }
1210 }
1211 
1212 template <typename Scalar, typename Packet>
1214  typedef typename NumTraits<Scalar>::Real RealScalar;
1215  const int PacketSize = internal::unpacket_traits<Packet>::size;
1216  EIGEN_ALIGN_MAX Scalar data1[PacketSize];
1217  RealScalar refvalue = RealScalar(0);
1218  for (int i = 0; i < PacketSize; ++i) {
1219  data1[i] = internal::random<Scalar>() / RealScalar(PacketSize);
1220  }
1221 
1222  int stride = internal::random<int>(1, 20);
1223 
1224  // Buffer of zeros.
1225  EIGEN_ALIGN_MAX Scalar buffer[PacketSize * 20] = {};
1226 
1227  Packet packet = internal::pload<Packet>(data1);
1228  internal::pscatter<Scalar, Packet>(buffer, packet, stride);
1229 
1230  for (int i = 0; i < PacketSize * 20; ++i) {
1231  if ((i % stride) == 0 && i < stride * PacketSize) {
1232  VERIFY(test::isApproxAbs(buffer[i], data1[i / stride], refvalue) && "pscatter");
1233  } else {
1234  VERIFY(test::isApproxAbs(buffer[i], Scalar(0), refvalue) && "pscatter");
1235  }
1236  }
1237 
1238  for (int i = 0; i < PacketSize * 7; ++i) {
1239  buffer[i] = internal::random<Scalar>() / RealScalar(PacketSize);
1240  }
1241  packet = internal::pgather<Scalar, Packet>(buffer, 7);
1242  internal::pstore(data1, packet);
1243  for (int i = 0; i < PacketSize; ++i) {
1244  VERIFY(test::isApproxAbs(data1[i], buffer[i * 7], refvalue) && "pgather");
1245  }
1246 }
1247 
1248 namespace Eigen {
1249 namespace test {
1250 
1251 template <typename Scalar, typename PacketType>
1252 struct runall<Scalar, PacketType, false, false> { // i.e. float or double
1253  static void run() {
1254  packetmath<Scalar, PacketType>();
1255  packetmath_scatter_gather<Scalar, PacketType>();
1256  packetmath_notcomplex<Scalar, PacketType>();
1257  packetmath_real<Scalar, PacketType>();
1258  }
1259 };
1260 
1261 template <typename Scalar, typename PacketType>
1262 struct runall<Scalar, PacketType, false, true> { // i.e. int
1263  static void run() {
1264  packetmath<Scalar, PacketType>();
1265  packetmath_scatter_gather<Scalar, PacketType>();
1266  packetmath_notcomplex<Scalar, PacketType>();
1267  }
1268 };
1269 
1270 template <typename Scalar, typename PacketType>
1271 struct runall<Scalar, PacketType, true, false> { // i.e. complex
1272  static void run() {
1273  packetmath<Scalar, PacketType>();
1274  packetmath_scatter_gather<Scalar, PacketType>();
1275  packetmath_complex<Scalar, PacketType>();
1276  }
1277 };
1278 
1279 } // namespace test
1280 } // namespace Eigen
1281 
1283  g_first_pass = true;
1284  for (int i = 0; i < g_repeat; i++) {
1295  CALL_SUBTEST_11(test::runner<std::complex<float> >::run());
1296  CALL_SUBTEST_12(test::runner<std::complex<double> >::run());
1300  g_first_pass = false;
1301  }
1302 }
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autogenerated on Sat Nov 16 2024 04:03:14