CPU overhead is minimized through tracking speculative exceptions (202) for later processing during exception resolution (204) including pointing to the addresses of these speculative instructions, and resolving (204) these exceptions by correcting (206) what caused the exception and re-executing (208) the instructions which are known to be in a taken path. Tracking speculative exceptions has two components which use an exception bit which is set in response to an exception condition (213). The invention tracks an original speculative exception which occurs when a speculative instruction whose operand(s) do not have any exception bits set encounters an exception condition. Speculative exception resolution is triggered when a non-speculative instruction-which is in the taken path of a conditional branch-uses an operand from a register having its exception bit set. The presence of an exception condition and a non-speculative instruction yields an exception signal (220) to exception resolution (204). Speculative exception resolution (204) includes responding to output signals from the extra register and extra exception bit for correcting (204) the exception condition which caused the exception and re-executing (208) the instructions which depended on the results of the instructions causing the speculative exception. This invention also handles the case where a speculative instruction attempts to use a register having its exception bit set as above.
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