The comprehensive technical report provides an in-depth analysis of subnormal floating-point numbers, which are tiny values in the IEEE-754 standard designed to facilitate gradual underflow between the smallest normal number and zero. The source details the mathematical representation of subnormals, explaining how they ensure numerical robustness by preventing the abrupt loss of significance that occurs in a flush-to-zero regime. A major focus is the significant performance penalties subnormals introduce on many CPU architectures (particularly older Intel designs), due to the need for slow microcode assists in processing these non-normalized values. Finally, the report outlines various mitigation strategies, such as enabling hardware Flush-to-Zero (FTZ) and Denormals-Are-Zero (DAZ) modes through compilers or explicit code, which sacrifices strict IEEE compliance for substantial speed gains in applications like digital signal processing.