In a first aspect, a first method of reciprocal estimate computation using floating point pipeline logic is provided. The first method includes the steps of (1) receiving an input value having an exponent and a mantissa when represented as a floating point number on which a reciprocal estimate computation is to be performed; (2) determining whether the exponent is one of a plurality of predetermined numbers; and (3) if the exponent is one of the plurality of predetermined numbers, adjusting at least one of a plurality of modified mantissa bits (e.g., mantissa bits internal to leading zero anticipator (LZA) logic) and the exponent so as to prevent an underflow result of the reciprocal estimate computation. Numerous other aspects are provided.