TAOCP 1.4.3.2 Exercise 1

We are asked to modify the trace routine so that it restores register J upon leaving, assuming $rJ \neq 0$.

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Section 1.4.3.2: Trace Routines

Exercise 1. [22] Modify the trace routine of the text so that it restores register J when leaving. (You may assume that register J is not zero.)

Verified: no
Solve time: -

Solution

We are asked to modify the trace routine so that it restores register J upon leaving, assuming $rJ \neq 0$. By examining the routine in Section 1.4.3.2, we see that JREG holds the simulated contents of the J-register. When the traced program executes a jump, the current value of rJ is stored in JREG(0:2) (line 45). Upon normal execution, rJ is never explicitly restored before leaving (line 49 LEAVEX JMP *), which violates the requirement of the exercise.

We introduce a restoration step immediately before leaving the trace routine. We need to move the value stored in JREG back into the actual J-register rJ. MIX provides the ENTA instruction to load a value into rA and the STA instruction to store rA into memory. To restore rJ, we can exploit ENTA with indirect addressing for rJ. A minimal solution is to add a line before LEAVEX:

LEAVEX  LDA  JREG(0:2)   rA <- saved J
        ENTA *           rJ <- rA
        JMP  *           leave

We now integrate this into the trace routine. The modified leaving sequence becomes:

48 LEAVE   LDA  AREG        Restore register A.
49 LEAVEX  LDA  JREG(0:2)   Restore register J.
50          ENTA *          
51          JMP  *
50 AREG    CON  0           Simulated rA contents

Step justification:

  1. LDA JREG(0:2) loads the saved contents of rJ into rA. This is necessary because ENTA transfers the value of rA into rJ.
  2. ENTA * sets rJ to the saved value. This restores rJ to the value it had before tracing began.
  3. JMP * leaves the trace routine and resumes the original program.

This modification preserves all invariants of the original routine: rA is restored, no other registers are affected, and the trace routine remains minimal in space. Every register, including rJ, now has its proper contents when tracing ends.

This completes the proof.

∎

Final modified sequence for leaving the trace routine:

48 LEAVE   LDA  AREG
49 LEAVEX  LDA  JREG(0:2)
50          ENTA *
51          JMP  *
50 AREG    CON  0