Add partial vectorization for matrices and tensors of bool. This speeds up boolean operations on Tensors by up to 25x.

Benchmark numbers for the logical and of two NxN tensors:

name                                               old time/op             new time/op             delta
BM_booleanAnd_1T/3   [using 1 threads]             14.6ns ± 0%             14.4ns ± 0%   -0.96%
BM_booleanAnd_1T/4   [using 1 threads]             20.5ns ±12%              9.0ns ± 0%  -56.07%
BM_booleanAnd_1T/7   [using 1 threads]             41.7ns ± 0%             10.5ns ± 0%  -74.87%
BM_booleanAnd_1T/8   [using 1 threads]             52.1ns ± 0%             10.1ns ± 0%  -80.59%
BM_booleanAnd_1T/10  [using 1 threads]             76.3ns ± 0%             13.8ns ± 0%  -81.87%
BM_booleanAnd_1T/15  [using 1 threads]              167ns ± 0%               16ns ± 0%  -90.45%
BM_booleanAnd_1T/16  [using 1 threads]              188ns ± 0%               16ns ± 0%  -91.57%
BM_booleanAnd_1T/31  [using 1 threads]              667ns ± 0%               34ns ± 0%  -94.83%
BM_booleanAnd_1T/32  [using 1 threads]              710ns ± 0%               35ns ± 0%  -95.01%
BM_booleanAnd_1T/64  [using 1 threads]             2.80µs ± 0%             0.11µs ± 0%  -95.93%
BM_booleanAnd_1T/128 [using 1 threads]             11.2µs ± 0%              0.4µs ± 0%  -96.11%
BM_booleanAnd_1T/256 [using 1 threads]             44.6µs ± 0%              2.5µs ± 0%  -94.31%
BM_booleanAnd_1T/512 [using 1 threads]              178µs ± 0%               10µs ± 0%  -94.35%
BM_booleanAnd_1T/1k  [using 1 threads]              717µs ± 0%               78µs ± 1%  -89.07%
BM_booleanAnd_1T/2k  [using 1 threads]             2.87ms ± 0%             0.31ms ± 1%  -89.08%
BM_booleanAnd_1T/4k  [using 1 threads]             11.7ms ± 0%              1.9ms ± 4%  -83.55%
BM_booleanAnd_1T/10k [using 1 threads]             70.3ms ± 0%             17.2ms ± 4%  -75.48%

5 files changed, 147 insertions, 63 deletions

diff --git a/Eigen/src/Core/GenericPacketMath.h b/Eigen/src/Core/GenericPacketMath.h
index 637aac9f9..ec61ac697 100644
--- a/Eigen/src/Core/GenericPacketMath.h
+++ b/Eigen/src/Core/GenericPacketMath.h
@@ -224,36 +224,6 @@ pabs(const unsigned long long& a) { return a; }
 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
 parg(const Packet& a) { using numext::arg; return arg(a); }
 
-/** \internal \returns the bitwise and of \a a and \a b */
-template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
-pand(const Packet& a, const Packet& b) { return a & b; }
-
-/** \internal \returns the bitwise or of \a a and \a b */
-template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
-por(const Packet& a, const Packet& b) { return a | b; }
-
-/** \internal \returns the bitwise xor of \a a and \a b */
-template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
-pxor(const Packet& a, const Packet& b) { return a ^ b; }
-
-/** \internal \returns the bitwise andnot of \a a and \a b */
-template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
-pandnot(const Packet& a, const Packet& b) { return a & (~b); }
-
-/** \internal \returns ones */
-template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
-ptrue(const Packet& /*a*/) { Packet b; memset((void*)&b, 0xff, sizeof(b)); return b;}
-
-template <typename RealScalar>
-EIGEN_DEVICE_FUNC inline std::complex<RealScalar> ptrue(const std::complex<RealScalar>& /*a*/) {
-  RealScalar b;
-  b = ptrue(b);
-  return std::complex<RealScalar>(b, b);
-}
-
-/** \internal \returns the bitwise not of \a a */
-template <typename Packet> EIGEN_DEVICE_FUNC inline Packet
-pnot(const Packet& a) { return pxor(ptrue(a), a);}
 
 /** \internal \returns \a a logically shifted by N bits to the right */
 template<int N> EIGEN_DEVICE_FUNC inline int
@@ -294,6 +264,35 @@ pldexp(const Packet &a, const Packet &exponent) {
   return ldexp(a, static_cast<int>(exponent));
 }
 
+// Notice: The following ops accept and operator on bitwise masks.
+// The value of each field in a masks is Scalar(0) or ~Scalar(0).
+// For boolean packet like Packet16b, this is different from the
+// representation of true and false, which are 1 and 0.
+// As an example
+//    ptrue<Packet16b>()     = 0xffffffffffffffffffffffffffffffff
+// while
+//    pset1<Packet16b>(true) = 0x01010101010101010101010101010101
+
+/** \internal \returns the bitwise and of \a a and \a b */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+pand(const Packet& a, const Packet& b) { return a & b; }
+
+/** \internal \returns the bitwise or of \a a and \a b */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+por(const Packet& a, const Packet& b) { return a | b; }
+
+/** \internal \returns the bitwise xor of \a a and \a b */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+pxor(const Packet& a, const Packet& b) { return a ^ b; }
+
+/** \internal \returns the bitwise and of \a a and not \a b */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+pandnot(const Packet& a, const Packet& b) { return a & (~b); }
+
+/** \internal \returns ones */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+ptrue(const Packet& /*a*/) { Packet b; memset((void*)&b, 0xff, sizeof(b)); return b;}
+
 /** \internal \returns zeros */
 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
 pzero(const Packet& a) { return pxor(a,a); }
@@ -308,21 +307,16 @@ template<> EIGEN_DEVICE_FUNC inline double pzero<double>(const double& a) {
   return 0.;
 }
 
-/** \internal \returns bits of \a or \b according to the input bit mask \a mask */
-template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
-pselect(const Packet& mask, const Packet& a, const Packet& b) {
-  return por(pand(a,mask),pandnot(b,mask));
-}
-
-template<> EIGEN_DEVICE_FUNC inline float pselect<float>(
-    const float& mask, const float& a, const float&b) {
-  return numext::equal_strict(mask,0.f) ? b : a;
+template <typename RealScalar>
+EIGEN_DEVICE_FUNC inline std::complex<RealScalar> ptrue(const std::complex<RealScalar>& /*a*/) {
+  RealScalar b;
+  b = ptrue(b);
+  return std::complex<RealScalar>(b, b);
 }
 
-template<> EIGEN_DEVICE_FUNC inline double pselect<double>(
-    const double& mask, const double& a, const double& b) {
-  return numext::equal_strict(mask,0.) ? b : a;
-}
+/** \internal \returns the bitwise not of \a a */
+template <typename Packet> EIGEN_DEVICE_FUNC inline Packet
+pnot(const Packet& a) { return pxor(ptrue(a), a);}
 
 /** \internal \returns a <= b as a bit mask */
 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
@@ -340,6 +334,24 @@ pcmp_eq(const Packet& a, const Packet& b) { return a==b ? ptrue(a) : pzero(a); }
 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
 pcmp_lt_or_nan(const Packet& a, const Packet& b) { return pnot(pcmp_le(b,a)); } 
 
+/** \internal \returns \a or \b for each field in packet according to \mask */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+pselect(const Packet& mask, const Packet& a, const Packet& b) {
+  return por(pand(a,mask),pandnot(b,mask));
+}
+
+template<> EIGEN_DEVICE_FUNC inline float pselect<float>(
+    const float& cond, const float& a, const float&b) {
+  return numext::equal_strict(cond,0.f) ? b : a;
+}
+
+template<> EIGEN_DEVICE_FUNC inline double pselect<double>(
+    const double& cond, const double& a, const double& b) {
+  return numext::equal_strict(cond,0.) ? b : a;
+}
+
+
+
 /** \internal \returns the min of \a a and \a b  (coeff-wise) */
 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
 pabsdiff(const Packet& a, const Packet& b) { return pselect(pcmp_lt(a, b), psub(b, a), psub(a, b)); }
diff --git a/Eigen/src/Core/arch/SSE/PacketMath.h b/Eigen/src/Core/arch/SSE/PacketMath.h
index 6a4dd5253..a56ae9dde 100755
--- a/Eigen/src/Core/arch/SSE/PacketMath.h
+++ b/Eigen/src/Core/arch/SSE/PacketMath.h
@@ -44,10 +44,12 @@ typedef __m128d Packet2d;
 #endif
 
 typedef eigen_packet_wrapper<__m128i, 0> Packet4i;
+typedef eigen_packet_wrapper<__m128i, 1> Packet16b;
 
 template<> struct is_arithmetic<__m128>  { enum { value = true }; };
 template<> struct is_arithmetic<__m128i> { enum { value = true }; };
 template<> struct is_arithmetic<__m128d> { enum { value = true }; };
+template<> struct is_arithmetic<Packet16b>  { enum { value = true }; };
 
 #define EIGEN_SSE_SHUFFLE_MASK(p,q,r,s) ((s)<<6|(r)<<4|(q)<<2|(p))
 
@@ -158,6 +160,30 @@ template<> struct packet_traits<int>    : default_packet_traits
   };
 };
 
+template<> struct packet_traits<bool> : default_packet_traits
+{
+  typedef Packet16b type;
+  typedef Packet16b half;
+  enum {
+    Vectorizable = 1,
+    AlignedOnScalar = 1,
+    HasHalfPacket = 0,
+    size=16,
+
+    HasAdd       = 0,
+    HasSub       = 0,
+    HasShift     = 0,
+    HasMul       = 0,
+    HasNegate    = 0,
+    HasAbs       = 0,
+    HasAbs2      = 0,
+    HasMin       = 0,
+    HasMax       = 0,
+    HasConj      = 0,
+    HasReduxp    = 0
+  };
+};
+
 template<> struct unpacket_traits<Packet4f> {
   typedef float     type;
   typedef Packet4f  half;
@@ -174,6 +200,11 @@ template<> struct unpacket_traits<Packet4i> {
   typedef Packet4i  half;
   enum {size=4, alignment=Aligned16, vectorizable=false, masked_load_available=false, masked_store_available=false};
 };
+template<> struct unpacket_traits<Packet16b> {
+  typedef bool       type;
+  typedef Packet16b  half;
+  enum {size=16, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false};
+};
 
 #ifndef EIGEN_VECTORIZE_AVX
 template<> struct scalar_div_cost<float,true> { enum { value = 7 }; };
@@ -192,6 +223,7 @@ template<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float&  from) { re
 template<> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double& from) { return _mm_set1_pd(from); }
 template<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int&    from) { return _mm_set1_epi32(from); }
 #endif
+template<> EIGEN_STRONG_INLINE Packet16b pset1<Packet16b>(const bool&    from) { return _mm_set1_epi8(static_cast<char>(from)); }
 
 template<> EIGEN_STRONG_INLINE Packet4f pset1frombits<Packet4f>(unsigned int from) { return _mm_castsi128_ps(pset1<Packet4i>(from)); }
 
@@ -385,8 +417,11 @@ template<> EIGEN_STRONG_INLINE Packet2d pcmp_eq(const Packet2d& a, const Packet2
 
 template<> EIGEN_STRONG_INLINE Packet4i pcmp_lt(const Packet4i& a, const Packet4i& b) { return _mm_cmplt_epi32(a,b); }
 template<> EIGEN_STRONG_INLINE Packet4i pcmp_eq(const Packet4i& a, const Packet4i& b) { return _mm_cmpeq_epi32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16b pcmp_eq(const Packet16b& a, const Packet16b& b) { return _mm_cmpeq_epi8(a,b); }
+
 
 template<> EIGEN_STRONG_INLINE Packet4i ptrue<Packet4i>(const Packet4i& a) { return _mm_cmpeq_epi32(a, a); }
+template<> EIGEN_STRONG_INLINE Packet16b ptrue<Packet16b>(const Packet16b& a) { return _mm_cmpeq_epi32(a, a); }
 template<> EIGEN_STRONG_INLINE Packet4f
 ptrue<Packet4f>(const Packet4f& a) {
   Packet4i b = _mm_castps_si128(a);
@@ -398,17 +433,21 @@ ptrue<Packet2d>(const Packet2d& a) {
   return _mm_castsi128_pd(_mm_cmpeq_epi32(b, b));
 }
 
+
 template<> EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_and_ps(a,b); }
 template<> EIGEN_STRONG_INLINE Packet2d pand<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_and_pd(a,b); }
 template<> EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_and_si128(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16b pand<Packet16b>(const Packet16b& a, const Packet16b& b) { return _mm_and_si128(a,b); }
 
 template<> EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_or_ps(a,b); }
 template<> EIGEN_STRONG_INLINE Packet2d por<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_or_pd(a,b); }
 template<> EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_or_si128(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16b por<Packet16b>(const Packet16b& a, const Packet16b& b) { return _mm_or_si128(a,b); }
 
 template<> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_xor_ps(a,b); }
 template<> EIGEN_STRONG_INLINE Packet2d pxor<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_xor_pd(a,b); }
 template<> EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_xor_si128(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16b pxor<Packet16b>(const Packet16b& a, const Packet16b& b) { return _mm_xor_si128(a,b); }
 
 template<> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_andnot_ps(b,a); }
 template<> EIGEN_STRONG_INLINE Packet2d pandnot<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_andnot_pd(b,a); }
@@ -471,6 +510,7 @@ template<> EIGEN_STRONG_INLINE Packet2d pfloor<Packet2d>(const Packet2d& a)
 template<> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float*   from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm_load_ps(from); }
 template<> EIGEN_STRONG_INLINE Packet2d pload<Packet2d>(const double*  from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm_load_pd(from); }
 template<> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int*     from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm_load_si128(reinterpret_cast<const __m128i*>(from)); }
+template<> EIGEN_STRONG_INLINE Packet16b pload<Packet16b>(const bool*     from) { EIGEN_DEBUG_ALIGNED_LOAD return  _mm_load_si128(reinterpret_cast<const __m128i*>(from)); }
 
 #if EIGEN_COMP_MSVC
   template<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float*  from) {
@@ -505,6 +545,11 @@ template<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from)
   EIGEN_DEBUG_UNALIGNED_LOAD
   return _mm_loadu_si128(reinterpret_cast<const __m128i*>(from));
 }
+template<> EIGEN_STRONG_INLINE Packet16b ploadu<Packet16b>(const bool*     from) {
+  EIGEN_DEBUG_UNALIGNED_LOAD
+  return _mm_loadu_si128(reinterpret_cast<const __m128i*>(from));
+}
+
 
 template<> EIGEN_STRONG_INLINE Packet4f ploaddup<Packet4f>(const float*   from)
 {
@@ -522,10 +567,12 @@ template<> EIGEN_STRONG_INLINE Packet4i ploaddup<Packet4i>(const int*     from)
 template<> EIGEN_STRONG_INLINE void pstore<float>(float*   to, const Packet4f& from) { EIGEN_DEBUG_ALIGNED_STORE _mm_store_ps(to, from); }
 template<> EIGEN_STRONG_INLINE void pstore<double>(double* to, const Packet2d& from) { EIGEN_DEBUG_ALIGNED_STORE _mm_store_pd(to, from); }
 template<> EIGEN_STRONG_INLINE void pstore<int>(int*       to, const Packet4i& from) { EIGEN_DEBUG_ALIGNED_STORE _mm_store_si128(reinterpret_cast<__m128i*>(to), from); }
+template<> EIGEN_STRONG_INLINE void pstore<bool>(bool*     to, const Packet16b& from) { EIGEN_DEBUG_ALIGNED_STORE _mm_store_si128(reinterpret_cast<__m128i*>(to), from); }
 
 template<> EIGEN_STRONG_INLINE void pstoreu<double>(double* to, const Packet2d& from) { EIGEN_DEBUG_UNALIGNED_STORE _mm_storeu_pd(to, from); }
 template<> EIGEN_STRONG_INLINE void pstoreu<float>(float*   to, const Packet4f& from) { EIGEN_DEBUG_UNALIGNED_STORE _mm_storeu_ps(to, from); }
 template<> EIGEN_STRONG_INLINE void pstoreu<int>(int*       to, const Packet4i& from) { EIGEN_DEBUG_UNALIGNED_STORE _mm_storeu_si128(reinterpret_cast<__m128i*>(to), from); }
+template<> EIGEN_STRONG_INLINE void pstoreu<bool>(bool*     to, const Packet16b& from) { EIGEN_DEBUG_ALIGNED_STORE _mm_storeu_si128(reinterpret_cast<__m128i*>(to), from); }
 
 template<> EIGEN_DEVICE_FUNC inline Packet4f pgather<float, Packet4f>(const float* from, Index stride)
 {
diff --git a/Eigen/src/Core/functors/BinaryFunctors.h b/Eigen/src/Core/functors/BinaryFunctors.h
index 0ea40bab0..a2bc58c76 100644
--- a/Eigen/src/Core/functors/BinaryFunctors.h
+++ b/Eigen/src/Core/functors/BinaryFunctors.h
@@ -382,11 +382,14 @@ struct functor_traits<scalar_quotient_op<LhsScalar,RhsScalar> > {
 struct scalar_boolean_and_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_boolean_and_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator() (const bool& a, const bool& b) const { return a && b; }
+  template<typename Packet>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
+  { return internal::pand(a,b); }
 };
 template<> struct functor_traits<scalar_boolean_and_op> {
   enum {
     Cost = NumTraits<bool>::AddCost,
-    PacketAccess = false
+    PacketAccess = true
   };
 };
 
@@ -398,11 +401,14 @@ template<> struct functor_traits<scalar_boolean_and_op> {
 struct scalar_boolean_or_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_boolean_or_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator() (const bool& a, const bool& b) const { return a || b; }
+  template<typename Packet>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
+  { return internal::por(a,b); }
 };
 template<> struct functor_traits<scalar_boolean_or_op> {
   enum {
     Cost = NumTraits<bool>::AddCost,
-    PacketAccess = false
+    PacketAccess = true
   };
 };
 
@@ -414,11 +420,14 @@ template<> struct functor_traits<scalar_boolean_or_op> {
 struct scalar_boolean_xor_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_boolean_xor_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator() (const bool& a, const bool& b) const { return a ^ b; }
+  template<typename Packet>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
+  { return internal::pxor(a,b); }
 };
 template<> struct functor_traits<scalar_boolean_xor_op> {
   enum {
     Cost = NumTraits<bool>::AddCost,
-    PacketAccess = false
+    PacketAccess = true
   };
 };
 
diff --git a/test/packetmath.cpp b/test/packetmath.cpp
index 5d38ce6b4..761273b86 100644
--- a/test/packetmath.cpp
+++ b/test/packetmath.cpp
@@ -70,6 +70,23 @@ void test_cast() {
   test_cast_helper<FromScalar, FromPacket, ToScalar, ToPacket, CanCast>::run();
 }
 
+template<typename Scalar,typename Packet> void packetmath_boolean()
+{
+  const int PacketSize = internal::unpacket_traits<Packet>::size;
+  const int size = 2*PacketSize;
+  EIGEN_ALIGN_MAX Scalar data1[size];
+  EIGEN_ALIGN_MAX Scalar data2[size];
+  EIGEN_ALIGN_MAX Scalar ref[size];
+
+  for (int i=0; i<size; ++i)
+  {
+    data1[i] = internal::random<Scalar>();
+  }
+  CHECK_CWISE2_IF(true, internal::por, internal::por);
+  CHECK_CWISE2_IF(true, internal::pxor, internal::pxor);
+  CHECK_CWISE2_IF(true, internal::pand, internal::pand);
+}
+
 template<typename Scalar,typename Packet> void packetmath()
 {
   typedef internal::packet_traits<Scalar> PacketTraits;
@@ -338,21 +355,6 @@ template<typename Scalar,typename Packet> void packetmath()
   }
 
   {
-    for (int i=0; i<PacketSize; ++i)
-    {
-      data1[i] = internal::random<Scalar>();
-      unsigned char v = internal::random<bool>() ? 0xff : 0;
-      char* bytes = (char*)(data1+PacketSize+i);
-      for(int k=0; k<int(sizeof(Scalar)); ++k) {
-        bytes[k] = v;
-      }
-    }
-    CHECK_CWISE2_IF(true, internal::por, internal::por);
-    CHECK_CWISE2_IF(true, internal::pxor, internal::pxor);
-    CHECK_CWISE2_IF(true, internal::pand, internal::pand);
-    CHECK_CWISE2_IF(true, internal::pandnot, internal::pandnot);
-  }
-  {
     for (int i = 0; i < PacketSize; ++i) {
       // "if" mask
       unsigned char v = internal::random<bool>() ? 0xff : 0;
@@ -377,8 +379,17 @@ template<typename Scalar,typename Packet> void packetmath()
   }
 
   CHECK_CWISE1_IF(PacketTraits::HasSqrt, numext::sqrt, internal::psqrt);
+
+  for (int i=0; i<size; ++i)
+  {
+    data1[i] = internal::random<Scalar>();
+  }
+  CHECK_CWISE2_IF(true, internal::pandnot, internal::pandnot);
+
+  packetmath_boolean<Scalar, Packet>();
 }
 
+
 template<typename Scalar,typename Packet> void packetmath_real()
 {
   typedef internal::packet_traits<Scalar> PacketTraits;
@@ -807,6 +818,9 @@ EIGEN_DECLARE_TEST(packetmath)
     CALL_SUBTEST_11( test::runner<std::complex<float> >::run() );
     CALL_SUBTEST_12( test::runner<std::complex<double> >::run() );
     CALL_SUBTEST_13(( packetmath<half,internal::packet_traits<half>::type>() ));
+#ifdef EIGEN_PACKET_MATH_SSE_H
+    CALL_SUBTEST_14(( packetmath_boolean<bool,internal::packet_traits<bool>::type>() ));
+#endif
     g_first_pass = false;
   }
 }
diff --git a/unsupported/test/cxx11_tensor_expr.cpp b/unsupported/test/cxx11_tensor_expr.cpp
index 30924b6b6..d56da28d8 100644
--- a/unsupported/test/cxx11_tensor_expr.cpp
+++ b/unsupported/test/cxx11_tensor_expr.cpp
@@ -7,6 +7,8 @@
 // Public License v. 2.0. If a copy of the MPL was not distributed
 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
 
+#include <numeric>
+
 #include "main.h"
 
 #include <Eigen/CXX11/Tensor>
@@ -193,8 +195,8 @@ static void test_constants()
 
 static void test_boolean()
 {
-  Tensor<int, 1> vec(6);
-  std::copy_n(std::begin({0, 1, 2, 3, 4, 5}), 6, vec.data());
+  Tensor<int, 1> vec(31);
+  std::iota(vec.data(), vec.data() + 31, 0);
 
   // Test ||.
   Tensor<bool, 1> bool1 = vec < vec.constant(1) || vec > vec.constant(4);