Some cleanup.

functions/sin_cos_test.cpp

@@ -37,7 +37,7 @@ TEST_F(SinCosTest, Random) {
 #if _DEBUG
   static constexpr std::int64_t iterations = 100;
 #else
-  static constexpr std::int64_t iterations = 4'000'000;
+  static constexpr std::int64_t iterations = 1'000'000;
 #endif
 
   for (std::int64_t i = 0; i < iterations; ++i) {
@@ -80,10 +80,10 @@ TEST_F(SinCosTest, Random) {
   }
 
   // This implementation is not quite correctly rounded, but not far from it.
-  EXPECT_LE(max_sin_ulps_error, 0.500002);
-  EXPECT_LE(max_cos_ulps_error, 0.500002);
-  EXPECT_LE(incorrectly_rounded_sin, 1);
-  EXPECT_LE(incorrectly_rounded_cos, 1);
+  EXPECT_LE(max_sin_ulps_error, 0.5);
+  EXPECT_LE(max_cos_ulps_error, 0.5);
+  EXPECT_EQ(incorrectly_rounded_sin, 0);
+  EXPECT_EQ(incorrectly_rounded_cos, 0);
 
   LOG(ERROR) << "Sin error: " << max_sin_ulps_error << std::setprecision(25)
              << " ulps for argument: " << worst_sin_argument

numerics/sin_cos.cpp

@@ -63,10 +63,13 @@ double FusedMultiplyAdd(double const a, double const b, double const c) {
   }
 }
 
-//TODO(phl) comment
-double DetectDangerousRounding(double const x, double const dx) {
-  double const value = x + dx;
-  double const error = (value - x) - dx;
+// Evaluates the sum `x + Δx`.  If that sum has a dangerous rounding
+// configuration (that is, the bits after the last mantissa bit of the sum are
+// either 1000... or 0111..., then return `NaN`.  Otherwise returns the sum.
+double DetectDangerousRounding(double const x, double const Δx) {
+  DoublePrecision<double> const sum = QuickTwoSum(x, Δx);
+  double const& value = sum.value;
+  double const& error = sum.error;
   __m128i const value_exponent_128i =
       _mm_castpd_si128(_mm_and_pd(masks::exponent_bits, _mm_set_sd(value)));
   double const value_exponent =