perf(hex8): elide exact zero paired cross products

src/fesa/elements/hex8_high_low.cpp

@@ -6,6 +6,7 @@
 
 #include "../math/high_low_arithmetic.h"
 #include "hex8_geometry.h"
+#include "hex8_pair_arithmetic.h"
 
 namespace fesa {
 namespace {
@@ -18,7 +19,7 @@ HighLow operator-(HighLow a, HighLow b) {
   return math_internal::Subtract(a, b);
 }
 HighLow operator*(HighLow a, HighLow b) {
-  return math_internal::Multiply(a, b);
+  return hex8_internal::MultiplyPair(a, b);
 }
 HighLow operator/(HighLow a, HighLow b) {
   return math_internal::Divide(a, b);

src/fesa/elements/hex8_pair_arithmetic.h

@@ -0,0 +1,28 @@
+#ifndef FESA_ELEMENTS_HEX8_PAIR_ARITHMETIC_H_
+#define FESA_ELEMENTS_HEX8_PAIR_ARITHMETIC_H_
+
+#include "../math/high_low_arithmetic.h"
+
+namespace fesa::hex8_internal {
+/// @brief Omits exact-zero cross products without changing nonzero association.
+/// @note A retained zero addition performs the original canonicalization and
+/// invalid-result check; its repeated application is idempotent.
+inline math_internal::HighLow MultiplyPair(math_internal::HighLow left,
+                                          math_internal::HighLow right) {
+  using namespace math_internal;
+  if (!IsNormalized(left) || !IsNormalized(right)) return InvalidHighLow();
+  if (left.low != 0 && right.low != 0) return Multiply(left, right);
+  auto product = TwoProduct(left.high, right.high);
+  if (right.low != 0) {
+    product = Add(product, TwoProduct(left.high, right.low));
+  } else if (left.low != 0) {
+    // The original zero addition precedes the nonzero low-high term.
+    product = Add(product, HighLow{});
+  }
+  if (left.low != 0)
+    product = Add(product, TwoProduct(left.low, right.high));
+  return Add(product, HighLow{});
+}
+}  // namespace fesa::hex8_internal
+
+#endif  // FESA_ELEMENTS_HEX8_PAIR_ARITHMETIC_H_