Short Note on Costs of Floating Point Operations on current x86-64 Architectures: Denormals, Overflow, Underflow, and Division by Zero

Simple floating point operations like addition or multiplication on normalized floating point values can nowadays be computed by current AMD and Intel processors in three to five cycles. This is different for denormalized numbers, which appear when an underflow occurs and the value can no longer be represented as a normalized floating-point value. Here the costs are about two magnitudes larger. Often this is not noticed as this gradual underflow is normally avoided, by configuring the floating point units to tread underflowed values as zero, as described in section 2. The object of this short report is to quantify the performance impact on floating point operations when denormalized/NaN values, overflows, or divisions by zero occur. Hereby the focus is only on