An apparatus and method for performing a check on inputs to a mathematical instruction and selecting a default sequence efficiently managing the architectural state of a processor. For example, one embodiment of a processor comprises: an arithmetic logic unit (ALU) to perform a plurality of mathematical operations using one or more source operands; instruction check logic to evaluate the source operands for a current mathematical instruction and to determine, based on the evaluation, whether to execute a default sequence of operations including executing the current mathematical instruction by the ALU or to jump to an alternate sequence of operations adapted to provide a result for the mathematical instruction having particular types of source operands more efficiently than the default sequence of operations.