perf(math): classify finite high-low components by binary64 bits

tests/unit/math/high_low_arithmetic_test.cpp

@@ -144,6 +144,23 @@ double FromBits(const std::uint64_t bits) {
   return result;
 }
 
+TEST(HighLowArithmetic, FiniteClassificationMatchesBinary64Boundaries) {
+  const auto check = [](const double value) {
+    const bool expected = std::isfinite(value);
+    EXPECT_EQ(IsFinite(HighLow{value, 0.0}), expected);
+    EXPECT_EQ(IsFinite(HighLow{1.0, value}), expected);
+  };
+  for (std::uint64_t exponent = 0; exponent < 2048U; ++exponent) {
+    for (const auto fraction : {0ULL, 1ULL, 1ULL << 51U,
+                                (1ULL << 52U) - 1ULL}) {
+      for (const auto sign : {0ULL, 1ULL << 63U})
+        check(FromBits(sign | (exponent << 52U) | fraction));
+    }
+  }
+  std::mt19937_64 random{0x5800f17U};
+  for (int sample = 0; sample < 10000; ++sample) check(FromBits(random()));
+}
+
 void ExpectSamePair(const HighLow actual,
                     const fesa::high_low_original::HighLow expected) {
   EXPECT_EQ(Bits(actual.high), Bits(expected.high));