Fix rint SSE/NEON again, using optimization barrier.

This is a new version of !423, which failed for MSVC.

Defined `EIGEN_OPTIMIZATION_BARRIER(X)` that uses inline assembly to
prevent operations involving `X` from crossing that barrier. Should
work on most `GNUC` compatible compilers (MSVC doesn't seem to need
this). This is a modified version adapted from what was used in
`psincos_float` and tested on more platforms
(see #1674, https://godbolt.org/z/73ezTG).

Modified `rint` to use the barrier to prevent the add/subtract rounding
trick from being optimized away.

Also fixed an edge case for large inputs that get bumped up a power of two
and ends up rounding away more than just the fractional part.  If we are
over `2^digits` then just return the input.  This edge case was missed in
the test since the test was comparing approximate equality, which was still
satisfied.  Adding a strict equality option catches it.

2 files changed, 66 insertions, 16 deletions

diff --git a/test/packetmath.cpp b/test/packetmath.cpp
index 76ac47554..4ff193ee4 100644
--- a/test/packetmath.cpp
+++ b/test/packetmath.cpp
@@ -299,6 +299,29 @@ void packetmath_minus_zero_add() {
   CHECK_CWISE2_IF(internal::packet_traits<Scalar>::HasAdd, REF_ADD, internal::padd);
 }
 
+// Ensure optimization barrier compiles and doesn't modify contents.
+// Only applies to raw types, so will not work for std::complex, Eigen::half
+// or Eigen::bfloat16. For those you would need to refer to an underlying
+// storage element.
+template<typename Packet, typename EnableIf = void>
+struct eigen_optimization_barrier_test {
+  static void run() {}
+};
+
+template<typename Packet>
+struct eigen_optimization_barrier_test<Packet, typename internal::enable_if<
+    !NumTraits<Packet>::IsComplex &&
+    !internal::is_same<Packet, Eigen::half>::value &&
+    !internal::is_same<Packet, Eigen::bfloat16>::value
+  >::type> {
+  static void run() {
+    typedef typename internal::unpacket_traits<Packet>::type Scalar;
+    Scalar s = internal::random<Scalar>();
+    Packet barrier = internal::pset1<Packet>(s);
+    EIGEN_OPTIMIZATION_BARRIER(barrier);
+    eigen_assert(s == internal::pfirst(barrier) && "EIGEN_OPTIMIZATION_BARRIER");
+  }
+};
 
 template <typename Scalar, typename Packet>
 void packetmath() {
@@ -317,6 +340,10 @@ void packetmath() {
   EIGEN_ALIGN_MAX Scalar data3[size];
   EIGEN_ALIGN_MAX Scalar ref[size];
   RealScalar refvalue = RealScalar(0);
+
+  eigen_optimization_barrier_test<Packet>::run();
+  eigen_optimization_barrier_test<Scalar>::run();
+
   for (int i = 0; i < size; ++i) {
     data1[i] = internal::random<Scalar>() / RealScalar(PacketSize);
     data2[i] = internal::random<Scalar>() / RealScalar(PacketSize);
@@ -543,10 +570,10 @@ void packetmath_real() {
   CHECK_CWISE1_IF(PacketTraits::HasCos, std::cos, internal::pcos);
   CHECK_CWISE1_IF(PacketTraits::HasTan, std::tan, internal::ptan);
 
-  CHECK_CWISE1_IF(PacketTraits::HasRound, numext::round, internal::pround);
-  CHECK_CWISE1_IF(PacketTraits::HasCeil, numext::ceil, internal::pceil);
-  CHECK_CWISE1_IF(PacketTraits::HasFloor, numext::floor, internal::pfloor);
-  CHECK_CWISE1_IF(PacketTraits::HasRint, numext::rint, internal::print);
+  CHECK_CWISE1_EXACT_IF(PacketTraits::HasRound, numext::round, internal::pround);
+  CHECK_CWISE1_EXACT_IF(PacketTraits::HasCeil, numext::ceil, internal::pceil);
+  CHECK_CWISE1_EXACT_IF(PacketTraits::HasFloor, numext::floor, internal::pfloor);
+  CHECK_CWISE1_EXACT_IF(PacketTraits::HasRint, numext::rint, internal::print);
   
   // Rounding edge cases.
   if (PacketTraits::HasRound || PacketTraits::HasCeil || PacketTraits::HasFloor || PacketTraits::HasRint) {
@@ -583,10 +610,10 @@ void packetmath_real() {
     
     for (size_t k=0; k<values.size(); ++k) {
       data1[0] = values[k];
-      CHECK_CWISE1_IF(PacketTraits::HasRound, numext::round, internal::pround);
-      CHECK_CWISE1_IF(PacketTraits::HasCeil, numext::ceil, internal::pceil);
-      CHECK_CWISE1_IF(PacketTraits::HasFloor, numext::floor, internal::pfloor);
-      CHECK_CWISE1_IF(PacketTraits::HasRint, numext::rint, internal::print);
+      CHECK_CWISE1_EXACT_IF(PacketTraits::HasRound, numext::round, internal::pround);
+      CHECK_CWISE1_EXACT_IF(PacketTraits::HasCeil, numext::ceil, internal::pceil);
+      CHECK_CWISE1_EXACT_IF(PacketTraits::HasFloor, numext::floor, internal::pfloor);
+      CHECK_CWISE1_EXACT_IF(PacketTraits::HasRint, numext::rint, internal::print);
     }
   }
 
@@ -644,7 +671,7 @@ void packetmath_real() {
   if (PacketTraits::HasExp) {
     data1[0] = Scalar(-1);
     // underflow to zero
-    data1[PacketSize] = Scalar(std::numeric_limits<Scalar>::min_exponent-10);
+    data1[PacketSize] = Scalar(std::numeric_limits<Scalar>::min_exponent-55);
     CHECK_CWISE2_IF(PacketTraits::HasExp, REF_LDEXP, internal::pldexp);
     // overflow to inf
     data1[PacketSize] = Scalar(std::numeric_limits<Scalar>::max_exponent+10);
diff --git a/test/packetmath_test_shared.h b/test/packetmath_test_shared.h
index 027715a89..8624fe2fe 100644
--- a/test/packetmath_test_shared.h
+++ b/test/packetmath_test_shared.h
@@ -78,13 +78,18 @@ bool isApproxAbs(const Scalar& a, const Scalar& b, const typename NumTraits<Scal
   return internal::isMuchSmallerThan(a-b, refvalue);
 }
 
+template<typename Scalar>
+inline void print_mismatch(const Scalar* ref, const Scalar* vec, int size) {
+  std::cout << "ref: [" << Map<const Matrix<Scalar,1,Dynamic> >(ref,size) << "]" << " != vec: [" << Map<const Matrix<Scalar,1,Dynamic> >(vec,size) << "]\n";
+}
+
 template<typename Scalar> bool areApproxAbs(const Scalar* a, const Scalar* b, int size, const typename NumTraits<Scalar>::Real& refvalue)
 {
   for (int i=0; i<size; ++i)
   {
     if (!isApproxAbs(a[i],b[i],refvalue))
     {
-      std::cout << "ref: [" << Map<const Matrix<Scalar,1,Dynamic> >(a,size) << "]" << " != vec: [" << Map<const Matrix<Scalar,1,Dynamic> >(b,size) << "]\n";
+      print_mismatch(a, b, size);
       return false;
     }
   }
@@ -95,13 +100,23 @@ template<typename Scalar> bool areApprox(const Scalar* a, const Scalar* b, int s
 {
   for (int i=0; i<size; ++i)
   {
-    if (a[i]!=b[i] && !internal::isApprox(a[i],b[i]))
+    if ( a[i]!=b[i] && !internal::isApprox(a[i],b[i]) 
+         && !((numext::isnan)(a[i]) && (numext::isnan)(b[i])) )
+    {
+      print_mismatch(a, b, size);
+      return false;
+    }
+  }
+  return true;
+}
+
+template<typename Scalar> bool areEqual(const Scalar* a, const Scalar* b, int size)
+{
+  for (int i=0; i<size; ++i)
+  {
+    if ( (a[i] != b[i]) && !((numext::isnan)(a[i]) && (numext::isnan)(b[i])) )
     {
-      if((numext::isnan)(a[i]) && (numext::isnan)(b[i]))
-      {
-        continue;
-      }
-      std::cout << "ref: [" << Map<const Matrix<Scalar,1,Dynamic> >(a,size) << "]" << " != vec: [" << Map<const Matrix<Scalar,1,Dynamic> >(b,size) << "]\n";
+      print_mismatch(a, b, size);
       return false;
     }
   }
@@ -178,6 +193,14 @@ struct packet_helper<false,Packet>
   VERIFY(test::areApprox(ref, data2, PacketSize) && #POP); \
 }
 
+#define CHECK_CWISE1_EXACT_IF(COND, REFOP, POP) if(COND) { \
+  test::packet_helper<COND,Packet> h; \
+  for (int i=0; i<PacketSize; ++i) \
+    ref[i] = Scalar(REFOP(data1[i])); \
+  h.store(data2, POP(h.load(data1))); \
+  VERIFY(test::areEqual(ref, data2, PacketSize) && #POP); \
+}
+
 #define CHECK_CWISE2_IF(COND, REFOP, POP) if(COND) { \
   test::packet_helper<COND,Packet> h; \
   for (int i=0; i<PacketSize; ++i) \