TAOCP 1.4.1 Exercise 2
The semantics of `JSJ X` in MIX are: 1.
Exercise 2. [10] Suggest code to substitute for (6) without using the JSJ instruction.
Verified: yes
Solve time: 1m49s
The semantics of JSJ X in MIX are:
- Store the current contents of register $J$ into memory location $X$.
- Transfer control to location $X+1$.
A correct replacement must therefore satisfy both requirements exactly, using only primitive instructions.
Correct replacement of JSJ MAX50
The operand must be used directly as the storage address, and the jump must go to the next sequential location of that same address.
Assume the subroutine body begins at label 2F, which corresponds to location MAX50 + 1.
The correct replacement is:
MAX50 STJ MAX50
JMP 2F
Correctness argument
1. Correct preservation of the jump register
STJ MAX50 stores the current value of register $J$ into memory location MAX50, exactly matching the first semantic requirement of JSJ MAX50.
This directly fixes the critical error in the proposed solution, where the value of $J$ was incorrectly stored into EXIT instead of the operand location.
2. Correct transfer of control
JMP 2F transfers execution to the first instruction of the subroutine body.
Since 2F is defined as the location immediately following MAX50 in the original program layout, this implements the required semantics $X+1$.
This removes the earlier unjustified jump target and correctly ties control flow to the operand-relative entry point.
3. Removal of irrelevant instructions
The instruction ENT3 50 is not part of the transformation of JSJ and plays no role in preserving linkage. It is eliminated entirely.
Conclusion
The sequence
STJ MAX50
JMP 2F
correctly reproduces the behavior of JSJ MAX50 without using the JSJ instruction, preserving both the stored return address and the required transfer of control.