cart-elc

Source code for CART-ELC
git clone git://git.laack.co/cart-elc.git
Log | Files | Refs | README | LICENSE

packetmath.cpp (55436B)


      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"
     12 #include "random_without_cast_overflow.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> {
     70   typedef typename internal::unpacket_traits<SrcPacket>::type SrcScalar;
     71   typedef typename internal::unpacket_traits<TgtPacket>::type TgtScalar;
     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,
     89                    typename internal::unpacket_traits<TgtPacket>::type* dst) {
     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,
    103                    typename internal::unpacket_traits<TgtPacket>::type* dst) {
    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,
    119                    typename internal::unpacket_traits<TgtPacket>::type* dst) {
    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>
    137 struct test_cast_helper;
    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) {
    161       data1[i] = internal::random_without_cast_overflow<SrcScalar, TgtScalar>::value();
    162     }
    163 
    164     for (int i = 0; i < DataSize; ++i) {
    165       ref[i] = static_cast<const TgtScalar>(data1[i]);
    166     }
    167 
    168     pcast_array<SrcPacket, TgtPacket, SrcCoeffRatio, TgtCoeffRatio>::cast(data1, DataSize, data2);
    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);
    187     test_cast_helper<SrcPacket, TgtPacket, SrcCoeffRatio, TgtCoeffRatio, HasCast>::run();
    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>
    195 struct test_cast_runner;
    196 
    197 template <typename SrcPacket, typename TgtScalar, typename TgtPacket>
    198 struct test_cast_runner<SrcPacket, TgtScalar, TgtPacket, true, false> {
    199   static void run() { test_cast<SrcPacket, TgtPacket>::run(); }
    200 };
    201 
    202 template <typename SrcPacket, typename TgtScalar, typename TgtPacket>
    203 struct test_cast_runner<SrcPacket, TgtScalar, TgtPacket, true, true> {
    204   static void run() {
    205     test_cast<SrcPacket, TgtPacket>::run();
    206     test_cast_runner<SrcPacket, TgtScalar, typename internal::unpacket_traits<TgtPacket>::half>::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>
    216 struct packetmath_pcast_ops_runner {
    217   static void run() {
    218     test_cast_runner<Packet, float>::run();
    219     test_cast_runner<Packet, double>::run();
    220     test_cast_runner<Packet, int8_t>::run();
    221     test_cast_runner<Packet, uint8_t>::run();
    222     test_cast_runner<Packet, int16_t>::run();
    223     test_cast_runner<Packet, uint16_t>::run();
    224     test_cast_runner<Packet, int32_t>::run();
    225     test_cast_runner<Packet, uint32_t>::run();
    226     test_cast_runner<Packet, int64_t>::run();
    227     test_cast_runner<Packet, uint64_t>::run();
    228     test_cast_runner<Packet, bool>::run();
    229     test_cast_runner<Packet, std::complex<float> >::run();
    230     test_cast_runner<Packet, std::complex<double> >::run();
    231     test_cast_runner<Packet, half>::run();
    232     test_cast_runner<Packet, bfloat16>::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() {
    240     test_cast_runner<Packet, std::complex<float> >::run();
    241     test_cast_runner<Packet, std::complex<double> >::run();
    242     test_cast_runner<Packet, half>::run();
    243     test_cast_runner<Packet, bfloat16>::run();
    244   }
    245 };
    246 
    247 template <typename Scalar, typename Packet>
    248 void packetmath_boolean_mask_ops() {
    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];
    253   EIGEN_ALIGN_MAX Scalar ref[size];
    254 
    255   for (int i = 0; i < size; ++i) {
    256     data1[i] = internal::random<Scalar>();
    257   }
    258   CHECK_CWISE1(internal::ptrue, internal::ptrue);
    259   CHECK_CWISE2_IF(true, internal::pandnot, internal::pandnot);
    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 
    265   CHECK_CWISE2_IF(true, internal::pcmp_eq, internal::pcmp_eq);
    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   }
    272   CHECK_CWISE2_IF(true, internal::pcmp_eq, internal::pcmp_eq);
    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   }
    279   CHECK_CWISE2_IF(true, internal::pcmp_eq, internal::pcmp_eq);
    280 }
    281 
    282 template <typename Scalar, typename Packet>
    283 void packetmath_boolean_mask_ops_real() {
    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];
    288   EIGEN_ALIGN_MAX Scalar ref[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 
    295   CHECK_CWISE2_IF(true, internal::pcmp_lt_or_nan, internal::pcmp_lt_or_nan);
    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   }
    302   CHECK_CWISE2_IF(true, internal::pcmp_lt_or_nan, internal::pcmp_lt_or_nan);
    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   }
    309   CHECK_CWISE2_IF(true, internal::pcmp_lt_or_nan, internal::pcmp_lt_or_nan);
    310 }
    311 
    312 template <typename Scalar, typename Packet>
    313 void packetmath_boolean_mask_ops_notcomplex() {
    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];
    318   EIGEN_ALIGN_MAX Scalar ref[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 
    325   CHECK_CWISE2_IF(true, internal::pcmp_le, internal::pcmp_le);
    326   CHECK_CWISE2_IF(true, internal::pcmp_lt, internal::pcmp_lt);
    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   }
    333   CHECK_CWISE2_IF(true, internal::pcmp_le, internal::pcmp_le);
    334   CHECK_CWISE2_IF(true, internal::pcmp_lt, internal::pcmp_lt);
    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   }
    341   CHECK_CWISE2_IF(true, internal::pcmp_le, internal::pcmp_le);
    342   CHECK_CWISE2_IF(true, internal::pcmp_lt, internal::pcmp_lt);
    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<>
    348 void packetmath_boolean_mask_ops<bool, internal::packet_traits<bool>::type>() {}
    349 template<>
    350 void packetmath_boolean_mask_ops_notcomplex<bool, internal::packet_traits<bool>::type>() {}
    351 
    352 template <typename Scalar, typename Packet>
    353 void packetmath_minus_zero_add() {
    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];
    358   EIGEN_ALIGN_MAX Scalar ref[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>
    372 struct eigen_optimization_barrier_test {
    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() {
    383     typedef typename internal::unpacket_traits<Packet>::type Scalar;
    384     Scalar s = internal::random<Scalar>();
    385     Packet barrier = internal::pset1<Packet>(s);
    386     EIGEN_OPTIMIZATION_BARRIER(barrier);
    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];
    406   EIGEN_ALIGN_MAX Scalar ref[size];
    407   RealScalar refvalue = RealScalar(0);
    408 
    409   eigen_optimization_barrier_test<Packet>::run();
    410   eigen_optimization_barrier_test<Scalar>::run();
    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);
    468   CHECK_CWISE1(numext::conj, internal::pconj);
    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);
    579     EIGEN_ALIGN_MAX Scalar result[size];
    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     }
    599     CHECK_CWISE3_IF(true, internal::pselect, internal::pselect);
    600   }
    601 
    602   for (int i = 0; i < size; ++i) {
    603     data1[i] = internal::random<Scalar>();
    604   }
    605   CHECK_CWISE1(internal::pzero, internal::pzero);
    606   CHECK_CWISE2_IF(true, internal::por, internal::por);
    607   CHECK_CWISE2_IF(true, internal::pxor, internal::pxor);
    608   CHECK_CWISE2_IF(true, internal::pand, internal::pand);
    609 
    610   packetmath_boolean_mask_ops<Scalar, Packet>();
    611   packetmath_pcast_ops_runner<Scalar, Packet>::run();
    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>
    624 Scalar log2(Scalar x) {
    625   return Scalar(EIGEN_LOG2E) * std::log(x);
    626 }
    627 
    628 template <typename Scalar, typename Packet>
    629 void packetmath_real() {
    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()),
    670         NumTraits<Scalar>::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());
    695     values.push_back(NumTraits<Scalar>::quiet_NaN());
    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(), 
    738                         -NumTraits<Scalar>::infinity(),
    739                          NumTraits<Scalar>::quiet_NaN()};
    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()
    780                                +NumTraits<Scalar>::max_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()
    785                                -NumTraits<Scalar>::max_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.
    803     if (!internal::is_same<Scalar, bfloat16>::value) {
    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.
    811     if (!internal::is_same<Scalar, bfloat16>::value) {
    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)));
    819     VERIFY_IS_APPROX(std::exp((std::numeric_limits<Scalar>::min)()), data2[0]);
    820     VERIFY_IS_APPROX(std::exp(-(std::numeric_limits<Scalar>::min)()), data2[1]);
    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.
    867       if (!internal::is_same<Scalar, bfloat16>::value) {
    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.
    881       if (!internal::is_same<Scalar, bfloat16>::value) {
    882         VERIFY_IS_APPROX(std::log((std::numeric_limits<Scalar>::min)()), data2[0]);
    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
    928         && !internal::is_same<Scalar, half>::value
    929         && !internal::is_same<Scalar, bfloat16>::value) {
    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>
    986 Scalar propagate_nan_max(const Scalar& a, const Scalar& b) {
    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>
    993 Scalar propagate_nan_min(const Scalar& a, const Scalar& b) {
    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>
   1000 Scalar propagate_number_max(const Scalar& a, const Scalar& b) {
   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>
   1007 Scalar propagate_number_min(const Scalar& a, const Scalar& b) {
   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>
   1014 void packetmath_notcomplex() {
   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>);
   1032   CHECK_CWISE1(numext::abs, internal::pabs);
   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.
   1070   if (!NumTraits<Scalar>::IsInteger) {
   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   }
   1134   internal::pstore(
   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>
   1140 void packetmath_complex() {
   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     }
   1172     CHECK_CWISE1_N(numext::sqrt, internal::psqrt, size);
   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);
   1183     CHECK_CWISE1_N(numext::sqrt, internal::psqrt, 4);
   1184     data1[0] = Scalar(-one, zero);
   1185     data1[1] = Scalar(zero, -one);
   1186     data1[2] = Scalar(one, one);
   1187     data1[3] = Scalar(-one, -one);
   1188     CHECK_CWISE1_N(numext::sqrt, internal::psqrt, 4);
   1189     data1[0] = Scalar(inf, zero);
   1190     data1[1] = Scalar(zero, inf);
   1191     data1[2] = Scalar(-inf, zero);
   1192     data1[3] = Scalar(zero, -inf);
   1193     CHECK_CWISE1_N(numext::sqrt, internal::psqrt, 4);
   1194     data1[0] = Scalar(inf, inf);
   1195     data1[1] = Scalar(-inf, inf);
   1196     data1[2] = Scalar(inf, -inf);
   1197     data1[3] = Scalar(-inf, -inf);
   1198     CHECK_CWISE1_N(numext::sqrt, internal::psqrt, 4);
   1199     data1[0] = Scalar(nan, zero);
   1200     data1[1] = Scalar(zero, nan);
   1201     data1[2] = Scalar(nan, one);
   1202     data1[3] = Scalar(one, nan);
   1203     CHECK_CWISE1_N(numext::sqrt, internal::psqrt, 4);
   1204     data1[0] = Scalar(nan, nan);
   1205     data1[1] = Scalar(inf, nan);
   1206     data1[2] = Scalar(nan, inf);
   1207     data1[3] = Scalar(-inf, nan);
   1208     CHECK_CWISE1_N(numext::sqrt, internal::psqrt, 4);
   1209   }
   1210 }
   1211 
   1212 template <typename Scalar, typename Packet>
   1213 void packetmath_scatter_gather() {
   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 
   1282 EIGEN_DECLARE_TEST(packetmath) {
   1283   g_first_pass = true;
   1284   for (int i = 0; i < g_repeat; i++) {
   1285     CALL_SUBTEST_1(test::runner<float>::run());
   1286     CALL_SUBTEST_2(test::runner<double>::run());
   1287     CALL_SUBTEST_3(test::runner<int8_t>::run());
   1288     CALL_SUBTEST_4(test::runner<uint8_t>::run());
   1289     CALL_SUBTEST_5(test::runner<int16_t>::run());
   1290     CALL_SUBTEST_6(test::runner<uint16_t>::run());
   1291     CALL_SUBTEST_7(test::runner<int32_t>::run());
   1292     CALL_SUBTEST_8(test::runner<uint32_t>::run());
   1293     CALL_SUBTEST_9(test::runner<int64_t>::run());
   1294     CALL_SUBTEST_10(test::runner<uint64_t>::run());
   1295     CALL_SUBTEST_11(test::runner<std::complex<float> >::run());
   1296     CALL_SUBTEST_12(test::runner<std::complex<double> >::run());
   1297     CALL_SUBTEST_13(test::runner<half>::run());
   1298     CALL_SUBTEST_14((packetmath<bool, internal::packet_traits<bool>::type>()));
   1299     CALL_SUBTEST_15(test::runner<bfloat16>::run());
   1300     g_first_pass = false;
   1301   }
   1302 }