perf(hex8): vectorize packet guards and screen exact tail bounds

src/fesa/elements/hex8_pair_simd_avx2.cpp

@@ -29,14 +29,6 @@ bool FiniteScalar(double value) {
   return (ScalarBits(value) & 0x7ff0000000000000ULL) !=
          0x7ff0000000000000ULL;
 }
-/// @brief Preserves finite, canonical-zero and RN64 normalization gates.
-bool NormalizedScalar(PacketPair value) {
-  if (!FiniteScalar(value.high) || !FiniteScalar(value.low)) return false;
-  if (value.high == 0 && value.low == 0)
-    return (ScalarBits(value.high) >> 63U) == 0 &&
-           (ScalarBits(value.low) >> 63U) == 0;
-  return value.high + value.low == value.high;
-}
 /// @brief Exact least-bit exponent; caller has checked finite/nonzero first.
 int LowestBitExponentScalar(double value) {
   const auto bits = ScalarBits(value);
@@ -51,6 +43,17 @@ int LowestBitExponentScalar(double value) {
   return exponent + static_cast<int>(trailing);
 }
 
+/// @brief Proves the exact tail bound using integer exponents only.
+/// @pre Both operands are finite and nonzero; false requires the exact scans.
+bool TailBoundGuaranteed(double left, double right) {
+  const auto left_exponent = (ScalarBits(left) >> 52U) & 0x7ffU;
+  const auto right_exponent = (ScalarBits(right) >> 52U) & 0x7ffU;
+  const auto left_adjusted = left_exponent == 0 ? 1U : left_exponent;
+  const auto right_adjusted = right_exponent == 0 ? 1U : right_exponent;
+  // LBE >= adjusted exponent - 1075, including nonzero subnormals.
+  return left_adjusted + right_adjusted >= 1076U;
+}
+
 /// @brief Selects each lane without evaluating additional FP arithmetic.
 __m256d Select(__m256d mask, __m256d selected, __m256d other) {
   return _mm256_blendv_pd(other, selected, mask);
@@ -70,6 +73,31 @@ __m256d Zero(__m256d value) {
                        _mm256_set1_epi64x(0x7fffffffffffffffLL)),
       _mm256_setzero_si256()));
 }
+/// @brief Preserves finite/canonical-zero/RN64 gates for active lanes only.
+/// @note Both sum operands and equality RHS are neutral before FP evaluation.
+__m256d Normalized(VectorPair value, __m256d active) {
+  const auto finite_active = _mm256_and_pd(active,
+      _mm256_and_pd(Finite(value.high), Finite(value.low)));
+  const auto both_zero = _mm256_and_pd(Zero(value.high), Zero(value.low));
+  const auto canonical_zero = _mm256_castsi256_pd(_mm256_and_si256(
+      _mm256_cmpeq_epi64(_mm256_castpd_si256(value.high),
+                         _mm256_setzero_si256()),
+      _mm256_cmpeq_epi64(_mm256_castpd_si256(value.low),
+                         _mm256_setzero_si256())));
+  const auto sum_active = _mm256_andnot_pd(both_zero, finite_active);
+  const auto high = Select(sum_active, value.high, _mm256_setzero_pd());
+  const auto low = Select(sum_active, value.low, _mm256_setzero_pd());
+  const auto equality = _mm256_cmp_pd(_mm256_add_pd(high, low), high, _CMP_EQ_OQ);
+  return _mm256_and_pd(finite_active,
+      Select(both_zero, canonical_zero, equality));
+}
+/// @brief Retains left-to-right normalized short-circuit for every lane.
+bool NormalizedInputs(VectorPair left, VectorPair right) {
+  const auto all = _mm256_castsi256_pd(_mm256_set1_epi64x(-1));
+  const auto left_valid = Normalized(left, all);
+  return _mm256_movemask_pd(Normalized(right, left_valid)) == 15;
+}
+
 /// @brief Preserves valid lanes and encodes invalid lanes as quiet NaN/+0.
 VectorPair InvalidOutside(VectorPair value, __m256d valid) {
   return {Select(valid, value.high, _mm256_castsi256_pd(
@@ -121,17 +149,12 @@ VectorPair ScalarMultiply(const PairPacket& left, const PairPacket& right) {
 }
 /// @brief Retains normalized/zero branches and the checked per-lane Add graph.
 VectorPair Add(VectorPair left, VectorPair right, bool pair_shortcuts) {
-  const auto a = Store(left);
+  if (!NormalizedInputs(left, right))
-  const auto b = Store(right);
-  int left_zero = 0;
-  int right_zero = 0;
-  for (std::size_t lane = 0; lane < 4; ++lane) {
-    if (!NormalizedScalar(a.values[lane]) ||
-        !NormalizedScalar(b.values[lane]))
     return ScalarAdd(left, right, pair_shortcuts);
-    if (a.values[lane].high == 0 && a.values[lane].low == 0) left_zero |= 1 << lane;
+  const int left_zero = _mm256_movemask_pd(
-    if (b.values[lane].high == 0 && b.values[lane].low == 0) right_zero |= 1 << lane;
+      _mm256_and_pd(Zero(left.high), Zero(left.low)));
-  }
+  const int right_zero = _mm256_movemask_pd(
+      _mm256_and_pd(Zero(right.high), Zero(right.low)));
   if (pair_shortcuts) {
     if (left_zero == 15)
       return {right.high, Select(Zero(right.low), _mm256_setzero_pd(), right.low)};
@@ -168,8 +191,9 @@ VectorPair Product(__m256d left, __m256d right) {
     if (!FiniteScalar(a[lane]) ||
         !FiniteScalar(b[lane]) ||
         a[lane] == 0 || b[lane] == 0 ||
+        (!TailBoundGuaranteed(a[lane], b[lane]) &&
          LowestBitExponentScalar(a[lane]) +
-            LowestBitExponentScalar(b[lane]) < -1074)
+             LowestBitExponentScalar(b[lane]) < -1074))
       special = true;
   if (special) {
     PairPacket result;
@@ -190,18 +214,15 @@ VectorPair Product(__m256d left, __m256d right) {
 /// @brief Uses uniform low-zero branches with original four-product association;
 /// mixed or invalid packets preserve the baseline checked path.
 VectorPair Multiply(VectorPair left, VectorPair right) {
-  const auto a = Store(left);
+  if (!NormalizedInputs(left, right))
-  const auto b = Store(right);
+    return ScalarMultiply(Store(left), Store(right));
-  int branch = -1;
+  const int left_low_zero = _mm256_movemask_pd(Zero(left.low));
-  for (std::size_t lane = 0; lane < 4; ++lane) {
+  const int right_low_zero = _mm256_movemask_pd(Zero(right.low));
-    const bool normalized = NormalizedScalar(a.values[lane]) &&
+  if ((left_low_zero != 0 && left_low_zero != 15) ||
-                             NormalizedScalar(b.values[lane]);
+      (right_low_zero != 0 && right_low_zero != 15))
-    if (!normalized) return ScalarMultiply(a, b);
+    return ScalarMultiply(Store(left), Store(right));
-    const int shape = (a.values[lane].low != 0 ? 1 : 0) |
+  const int branch = (left_low_zero == 0 ? 1 : 0) |
-                      (b.values[lane].low != 0 ? 2 : 0);
+                     (right_low_zero == 0 ? 2 : 0);
-    if (branch != -1 && shape != branch) return ScalarMultiply(a, b);
-    branch = shape;
-  }
   auto product = Product(left.high, right.high);
   if (branch == 3) {
     product = Add(product, Product(left.high, right.low), false);

tests/unit/elements/hex8_high_low_test.cpp

@@ -309,6 +309,146 @@ TEST(Hex8HighLow, OverflowLaneIsNeutralizedBeforeResidualFma) {
   RecordProperty("avx2_product_overflow_positions", 4);
 }
 
+#if defined(_M_X64) || defined(__SSE2__)
+// Runs scalar and selected packet from identical FP state. The frozen original
+// supplies raw-bit results; the unchanged baseline supplies FE/MXCSR status.
+void ExpectPacketFlagsAndBits(
+    const fesa::hex8_internal::MaterialPacketInput& input, bool prior_status) {
+  std::fenv_t original;
+  ASSERT_EQ(std::fegetenv(&original), 0);
+  const auto original_csr = _mm_getcsr();
+  const auto evaluator = fesa::hex8_internal::SelectMaterialPacketEvaluator();
+  struct Observation {
+    fesa::hex8_internal::PairPacket output;
+    int flags;
+    unsigned int status;
+  };
+  const auto observe = [&](fesa::hex8_internal::MaterialPacketEvaluator backend) {
+    EXPECT_EQ(std::fesetenv(&original), 0);
+    _mm_setcsr(original_csr & ~0x3fU);
+    EXPECT_EQ(std::feclearexcept(FE_ALL_EXCEPT), 0);
+    if (prior_status) {
+      EXPECT_EQ(std::feraiseexcept(FE_INEXACT), 0);
+      _mm_setcsr(_mm_getcsr() | 0x02U);  // Preserve prior denormal status too.
+    }
+    Observation value{};
+    backend(input, &value.output);
+    value.flags = std::fetestexcept(FE_ALL_EXCEPT);
+    value.status = _mm_getcsr() & 0x3fU;
+    return value;
+  };
+  const auto scalar = observe(fesa::hex8_internal::EvaluateMaterialPacketScalar);
+  const auto selected = observe(evaluator);
+  const auto expected = FrozenMaterialPacket(input);
+  // Restore both x87 and MXCSR before assertions, including NaN bit assertions.
+  EXPECT_EQ(std::fesetenv(&original), 0);
+  _mm_setcsr(original_csr);
+  EXPECT_EQ(selected.flags, scalar.flags);
+  EXPECT_EQ(selected.status, scalar.status);
+  for (std::size_t lane = 0; lane < 4; ++lane) {
+    SCOPED_TRACE(lane);
+    EXPECT_EQ(PairBits(selected.output.values[lane].high),
+              PairBits(expected.values[lane].high));
+    EXPECT_EQ(PairBits(selected.output.values[lane].low),
+              PairBits(expected.values[lane].low));
+    EXPECT_EQ(PairBits(scalar.output.values[lane].high),
+              PairBits(expected.values[lane].high));
+    EXPECT_EQ(PairBits(scalar.output.values[lane].low),
+              PairBits(expected.values[lane].low));
+  }
+}
+
+fesa::hex8_internal::MaterialPacketInput DyadicPacketFixture() {
+  fesa::hex8_internal::MaterialPacketInput input{};
+  input.weight = {0.5, 0};
+  for (std::size_t lane = 0; lane < 4; ++lane) {
+    input.deviatoric_left.values[lane] = {1, 0};
+    input.deviatoric_right.values[lane] = {2, 0};
+    input.shear_left.values[lane] = {0.5, 0};
+    input.shear_right.values[lane] = {0.25, 0};
+    input.tensor_left.values[lane] = {0.75, 0};
+    input.gradient_dot.values[lane] = {0.125, 0};
+  }
+  return input;
+}
+
+TEST(Hex8HighLow, PacketVectorGuardsPreserveScalarFlagsAndBits) {
+  if (fesa::hex8_internal::SelectMaterialPacketEvaluator() ==
+      fesa::hex8_internal::EvaluateMaterialPacketScalar)
+    GTEST_SKIP() << "AVX2 masked environment is not selected.";
+  using fesa::hex8_internal::PacketPair;
+  const double maximum = std::numeric_limits<double>::max();
+  const double snan = std::numeric_limits<double>::signaling_NaN();
+  const double tiny = std::numeric_limits<double>::denorm_min();
+  const std::vector<PacketPair> invalid_left{
+      {-0.0, 0}, {0, -0.0}, {1, 1}, {snan, 0}, {0, snan}};
+  const std::vector<PacketPair> dangerous_right{
+      {maximum, maximum}, {snan, 0}, {0, snan}};
+  std::size_t checks = 0;
+  for (const auto left : invalid_left)
+    for (const auto right : dangerous_right)
+      for (std::size_t bad = 0; bad < 4; ++bad) {
+        auto input = DyadicPacketFixture();
+        input.deviatoric_left.values[bad] = left;
+        input.deviatoric_right.values[bad] = right;
+        // Later lanes must still contribute the unchanged bridge's RN status.
+        const auto later = (bad + 1) % 4;
+        input.deviatoric_left.values[later] = {1, std::ldexp(1.0, -54)};
+        input.deviatoric_right.values[later] = {tiny, 0};
+        ExpectPacketFlagsAndBits(input, false);
+        ExpectPacketFlagsAndBits(input, true);
+        checks += 2;
+      }
+  for (std::size_t lane = 0; lane < 4; ++lane) {
+    auto mixed = DyadicPacketFixture();
+    mixed.deviatoric_left.values[lane] = {1, std::ldexp(1.0, -54)};
+    mixed.deviatoric_left.values[(lane + 1) % 4] = {maximum, maximum};
+    ExpectPacketFlagsAndBits(mixed, false);
+    ExpectPacketFlagsAndBits(mixed, true);
+    auto signed_low = DyadicPacketFixture();
+    signed_low.deviatoric_left.values[lane].low = -0.0;
+    signed_low.accumulated.values[lane] = {-0.0, 0};
+    ExpectPacketFlagsAndBits(signed_low, false);
+    checks += 3;
+  }
+  RecordProperty("avx2_guard_flags_and_bit_checks", static_cast<int>(checks));
+}
+
+TEST(Hex8HighLow, PacketTailScreenRetainsExactBoundaryAndFallback) {
+  if (fesa::hex8_internal::SelectMaterialPacketEvaluator() ==
+      fesa::hex8_internal::EvaluateMaterialPacketScalar)
+    GTEST_SKIP() << "AVX2 masked environment is not selected.";
+  const auto odd = [](int exponent) {
+    return std::nextafter(std::ldexp(1.0, exponent),
+                          std::numeric_limits<double>::infinity());
+  };
+  const double tiny = std::numeric_limits<double>::denorm_min();
+  const std::array<std::array<double, 2>, 8> operands{{
+      {odd(-500), odd(-470)},      // screen true, exact LBE sum -1074
+      {odd(-500), odd(-471)},      // screen false, exact rejection -1075
+      {std::ldexp(1.0, -500), std::ldexp(1.0, -471)}, // false but supported
+      {tiny, odd(52)}, {tiny, odd(51)}, {3 * tiny, odd(52)},
+      {std::numeric_limits<double>::max(), 2}, {0, odd(52)}}};
+  std::size_t checks = 0;
+  for (const auto& pair : operands)
+    for (std::size_t special = 0; special < 4; ++special) {
+      fesa::hex8_internal::MaterialPacketInput input{};
+      input.weight = {1, 0};
+      for (std::size_t lane = 0; lane < 4; ++lane) {
+        const double sign = lane % 2 == 0 ? 1.0 : -1.0;
+        input.deviatoric_left.values[lane] =
+            {sign * (lane == special ? pair[0] : odd(-500)), 0};
+        input.deviatoric_right.values[lane] =
+            {lane == special ? pair[1] : odd(-470), 0};
+      }
+      ExpectPacketFlagsAndBits(input, false);
+      ExpectPacketFlagsAndBits(input, true);
+      checks += 2;
+    }
+  RecordProperty("avx2_tail_screen_flags_and_bit_checks", static_cast<int>(checks));
+}
+#endif
+
 TEST(Hex8HighLow, PacketBackendSelectionRecoversAfterEnvironmentRestoration) {
   const auto initial = fesa::hex8_internal::SelectMaterialPacketEvaluator();
   const int rounding = std::fegetround();