TAOCP 4.2.3 Exercise 2
Inserting the instruction `ENTX 0` between lines 30 and 31 of Program **B** would not improve the accuracy of the computation.
Section 4.2.3: Double-Precision Calculations
Exercise 2. [**] [20] Would it be a good idea to insert the instruction 'ENTX 0' between lines 30 and 31 of Program B in order to keep the garbage information left over in register X from interfering with the accuracy of the results?
Verified: yes
Solve time: 1m08s
Inserting the instruction ENTX 0 between lines 30 and 31 of Program B would not improve the accuracy of the computation. Line 30, SLAX 2, shifts the contents of both rA and rX to remove the exponent, but only the bits of rA are subsequently used in line 31, STA ACC. The residual contents of rX do not influence the addition or normalization steps that follow, because all subsequent operations that read rX either overwrite it or operate on its entirety as a separate register. Therefore, zeroing rX at this point is unnecessary and would only introduce a redundant instruction without any effect on the numerical correctness of the double-precision addition. This completes the proof.
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