为什么用parantesses分隔和用语句分隔时,C中的浮点精度不同?

我知道在常规情况下浮点精度是如何工作的,但我在C代码中偶然发现了一个奇怪的情况。

为什么result1和result2在这里不是完全相同的浮点值?

const float A;   // Arbitrary value
const float B;   // Arbitrary value

float result1 = (A*B)*dt;

float result2 = (A*B); 
result2 *= dt;

从 this page 我认为float算术是左关联的,这意味着值是以从左到右的方式计算和计算的。

完整的源代码涉及xna的四元数。我认为这与我的常量和vectorhelper.addPitchRollYaw()的作用无关。如果我以同样的方式计算三角俯仰/侧倾/偏航角,则测试通过得很好,但由于代码如下所示,测试不通过:

X
  Expected: 0.275153548f
  But was:  0.275153786f

[TestFixture]
    internal class QuaternionPrecisionTest
    {
        [Test]
        public void Test()
        {
            JoystickInput input;
            input.Pitch = 0.312312432f;
            input.Roll = 0.512312432f;
            input.Yaw = 0.912312432f;
            const float dt = 0.017001f;

            float pitchRate = input.Pitch * PhysicsConstants.MaxPitchRate;
            float rollRate = input.Roll * PhysicsConstants.MaxRollRate;
            float yawRate = input.Yaw * PhysicsConstants.MaxYawRate;

            Quaternion orient1 = Quaternion.Identity;
            Quaternion orient2 = Quaternion.Identity;

            for (int i = 0; i < 10000; i++)
            {
                float deltaPitch = 
                      (input.Pitch * PhysicsConstants.MaxPitchRate) * dt;
                float deltaRoll = 
                      (input.Roll * PhysicsConstants.MaxRollRate) * dt;
                float deltaYaw = 
                      (input.Yaw * PhysicsConstants.MaxYawRate) * dt;

                // Add deltas of pitch, roll and yaw to the rotation matrix
                orient1 = VectorHelper.AddPitchRollYaw(
                                orient1, deltaPitch, deltaRoll, deltaYaw);

                deltaPitch = pitchRate * dt;
                deltaRoll = rollRate * dt;
                deltaYaw = yawRate * dt;
                orient2 = VectorHelper.AddPitchRollYaw(
                                orient2, deltaPitch, deltaRoll, deltaYaw);
            }

            Assert.AreEqual(orient1.X, orient2.X, "X");
            Assert.AreEqual(orient1.Y, orient2.Y, "Y");
            Assert.AreEqual(orient1.Z, orient2.Z, "Z");
            Assert.AreEqual(orient1.W, orient2.W, "W");
        }
    }

当然,错误很小,只在大量迭代之后才会出现,但它给我带来了一些巨大的麻烦。