TAOCP 1.4.4 Exercise 18

Section 1.4.4: Input and Output

Exercise 18. [30] A proposed extension of MIX allows its computations to be interrupted, as explained below. Your task in this exercise is to modify Algorithms and Programs A, R, and B of the text so that they use these interrupt facilities instead of the JRED instructions.

The new MIX features include an additional 3999 memory cells, locations $-3999$ through $-0001$. The machine has two internal "states," normal state and control state. In normal state, locations $-3999$ through $-0001$ are not admissible memory locations and the MIX computer behaves as usual. When an "interrupt" occurs, due to conditions explained later, locations $-0009$ through $-0001$ are set equal to the contents of MIX's registers: rA in $-0009$; rI1 through rI6 in $-0008$ through $-0003$; rX in $-0002$; and rJ, the overflow toggle, the comparison indicator, and the location of the next instruction are stored in $-0001$ as

+ | next inst. | OV, CI | rJ ;

the machine enters control state, at a location depending on the type of interrupt.

Location $-0010$ acts as a "clock": Every $1000u$ of time, the number appearing in this location is decreased by one, and if the result is zero an interrupt to location $-0011$ occurs.

The new MIX instruction INT $(C = 5, F = 9)$ works as follows: (a) In normal state, an interrupt occurs to location $-0012$. (Thus a programmer may force an interrupt, to communicate with a control routine; the address of INT has no effect, although the control routine may use it for information to distinguish between types of interrupt.) (b) In control state, all MIX registers are loaded from locations $-0009$ to $-0001$, the computer goes into normal state, and it resumes execution. The execution time for INT is $2u$ in each case.

An IN, OUT, or IOC instruction given in control state will cause an interrupt to occur as soon as the I/O operation is completed. The interrupt goes to location $-(0020 + \text{unit number})$.

No interrupts occur while in control state; any interrupt conditions are "saved" until after the next INT operation, and interrupt will occur after one instruction of the normal state program has been performed.

Verified: no
Solve time: -

Setup

We are asked to modify Algorithms and Programs A, R, and B of Section 1.4.4 to utilize the interrupt facilities of the extended MIX machine instead of the JRED instructions. The exercise introduces new memory cells $-3999$ through $-0001$, two internal states (normal and control), and the INT instruction with $C = 5$, $F = 9$. The interrupt architecture allows the machine to save registers in locations $-0009$ through $-0001$ and to execute a control routine when an I/O operation completes or a clock reaches zero.

Let the following notation be used, consistent with Section 1.4.4:

$U$ denotes a tape unit.
IN, OUT, IOC denote MIX input, output, and control operations.
INT denotes the new interrupt instruction.
Locations $-0011$, $-0012$, and $-(0020 + U)$ are designated interrupt vectors for the clock, forced interrupts, and completion of I/O on unit $U$, respectively.
The previous JRED(U) instruction in Algorithms A, R, and B waits for completion of I/O on unit $U$.
Buffers are handled as in previous algorithms, with index registers or memory locations pointing to the current buffer.

The goal is to replace busy-wait loops using JRED(U) with interrupt-driven control, ensuring that computation overlaps with I/O and that the tape unit is never idle unless unavoidable.

Solution

Step 1: Interrupt-driven I/O

The new MIX allows the following sequence for reading a block from unit $U$:

Initiate the I/O in normal state:

$$ \texttt{IN addr(U)} $$

Perform computation using previously read data.
When the IN completes, the machine automatically interrupts to location $-(0020+U)$.

Analogously, output via OUT generates an interrupt to $-(0020+U)$ upon completion. The JRED(U) instruction is thus replaced by an interrupt service routine (ISR) that resumes computation after I/O completion.

Step 2: Register preservation and buffer swapping

Upon entering the control state, the machine automatically saves registers in locations $-0009$ through $-0001$. Therefore, the ISR for unit $U$ can:

Swap the buffer pointer to the next buffer.
Begin a new I/O operation for unit $U$ into the alternate buffer.
Return to normal state by executing INT (in control state), which restores registers and resumes the interrupted computation.

Let BUF_PTR hold the address of the current buffer in use. Each ISR performs:

ISR_U:   ; Interrupt service for unit U
         LD6 BUF_PTR(U)       ; Load current buffer index
         ; Swap to next buffer
         ST6 BUF_PTR(U)       ; Update buffer pointer
         IN  NEXT_BUFFER(U)   ; Begin next I/O
         INT                  ; Return to normal state

This sequence eliminates the need for JRED(U) in the main program.

Step 3: Main program modification

The main loop of Algorithms A, R, and B is modified as follows:

Initialize the first I/O operation for each unit.
Begin computation using the initial buffer.
Whenever a buffer is exhausted, the program executes INT 5,9 to force entry to the control state if needed, or continues until an interrupt occurs naturally when the I/O completes.

Effectively, the main loop now alternates computation and handling of completed I/O via interrupts rather than polling.

Step 4: Clock-driven periodic events

If the original program relied on periodic JRED checks to schedule certain actions, we replace them with clock interrupts. Each 1000u decrement of location $-0010$ generates an interrupt to $-0011$, which may perform tasks such as buffer initialization, statistics collection, or prefetching, then return to normal state using INT.

Step 5: Algorithm correctness

Each I/O operation is initiated before the previous buffer is exhausted, consistent with buffered input. The ISR ensures that the buffer pointer is updated and the next block is requested. Since the main program never directly polls JBUS or JRED, the tape unit remains busy while computation proceeds, and no busy-wait cycles occur. Buffer swapping proceeds as in Section 1.4.4 (see the WORDIN routine, equation (4)).

This construction preserves:

Correct sequencing of data (no word is used before being read).
Efficient overlap of computation and I/O.
Transparency of block length (blocking of records is preserved).

Verification

We check key properties:

No busy wait: JRED(U) is replaced by the ISR triggered by -(0020+U). The main loop never stalls waiting for I/O, so the tape unit remains occupied.
Buffer consistency: Each ISR swaps the buffer pointer and initiates the next block, consistent with the design in equation (4).
Register restoration: Each ISR ends with INT in control state, ensuring that rA, rI1–rI6, rX, rJ, overflow, and comparison indicator are restored, so the computation resumes correctly.
Clock interrupts: If periodic actions are required, the decrement in $-0010$ triggers an interrupt to $-0011$, which can be used analogously to replace polling loops in the original programs.

All previous assumptions about block size, sentinel words, and linking buffers remain valid. Timing analysis yields the same bound as Section 1.4.4: execution time per tape block is essentially $\max(C, T)$, without additional idle time from busy-wait loops.

Notes

The interrupt-driven approach generalizes naturally to multiple tape units. Each unit's completion ISR resides at a distinct vector $-(0020+U)$. Buffer pooling or multiple buffers beyond $N=2$ can be handled by having the ISR select the next available buffer from the pool. The INT instruction can also be used for preemptive multitasking, allowing more sophisticated overlapping of computation, I/O, and other periodic tasks.

This completes the proof.

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