TAOCP 1.4.3.1 Exercise 7

We are asked to modify the input-output subroutines of the MIX simulator so that the execution of the `IN` and `OUT` operators does not trigger immediate transmission.

taocpmathematicsalgorithmsvolume-1hard

Section 1.4.3.1: A MIX Simulator

Exercise 7. [32] Modify the solutions of the previous exercise in such a way that execution of IN or OUT does not cause I/O transmission immediately; the transmission should take place after approximately half of the time required by the simulated devices has elapsed. (This will prevent a frequent student error, in which IN and OUT are used improperly.)

Verified: no
Solve time: -

Setup

We are asked to modify the input-output subroutines of the MIX simulator so that the execution of the IN and OUT operators does not trigger immediate transmission. Instead, the transmission should occur after approximately half of the nominal device time, as indicated in the previous exercise (1.4.3.1-6). The goal is to simulate a delay in device operations in order to prevent premature or repeated I/O actions when student programs execute.

Let $T_{\text{device}}$ denote the standard simulated execution time for a given I/O device: $T = 10000u$ for "read-card" or "skip-to-new-page" operations, and $T = 7500u$ for "print-line". Previously, the simulator incremented the CLOCK variable immediately after executing IN or OUT. We must defer the actual update of simulated time by roughly half of $T_{\text{device}}$.

The required modifications apply to the I/O subroutines called by lines 073 (IN) and 074 (OUT) in Program M. The entry conditions remain rI5 = memory address for storage (if relevant), and rI3 = field specification (if relevant). Exit conditions must be consistent with the delayed timing semantics.

We define a new variable IODELAY in simulated memory to track the pending fractional execution time for I/O devices.

Solution

  1. Introduce a new word in the simulator memory:
125 IODELAY CON 0    Tracks half-device time remaining for delayed I/O
  1. Modify the IN subroutine (device 16 or 18 only) so that the read request is registered, but the actual transmission is delayed:
073 IN    STJ  9F         Save return address
        LDA  TIME(0:2)    Get nominal time for IN operation
        SLA  0,1           Shift into IODELAY units
        DIV  =2=           Divide by 2 to get half-time
        STA  IODELAY       Store half-device time
        JMP  CYCLE         Return to main simulator loop without performing I/O
  1. Modify the OUT subroutine analogously:
074 OUT   STJ  9F         Save return address
        LDA  TIME(0:2)    Get nominal time for OUT operation
        SLA  0,1
        DIV  =2=
        STA  IODELAY
        JMP  CYCLE
  1. Adjust the main CYCLE routine to check IODELAY at the start of each instruction cycle. If IODELAY > 0, decrement it by 1 unit (or by the simulation granularity) and defer the actual I/O transmission:
007 CYCLE LDA  IODELAY
        JZ   1F            No pending I/O delay
        DEC  IODELAY
        JMP  CYCLE         Return without executing instruction
1H      LDA  CLOCK        Proceed with normal instruction fetch and execution
  1. In the actual IN or OUT subroutine, after IODELAY reaches zero, perform the device operation and increment CLOCK by the remaining half of the device time.
073 IN    ...
        JZ   PERFORM_IO
        JMP  CYCLE
PERFORM_IO
        ...               Perform the read or print operation
        INCA  CLOCK       Increment CLOCK by remaining half-time
        JMP  CYCLE

This procedure ensures that the first half of the device time is simulated as "pending," so that student programs do not immediately observe the effect of the I/O instruction.

Verification

  1. The IODELAY variable is initialized to zero. Any IN or OUT instruction sets it to half the nominal device time in MIX units. This matches the requirement of delaying the transmission by approximately half of $T_{\text{device}}$.
  2. The main cycle routine (CYCLE) checks IODELAY before fetching the next instruction. If IODELAY > 0, the simulator defers the instruction fetch, decrementing IODELAY each cycle. Therefore, execution of non-I/O instructions proceeds only after the simulated delay has elapsed.
  3. After IODELAY reaches zero, the corresponding IN or OUT operation is performed, and CLOCK is incremented by the remaining half of the device time. This ensures the total simulated time equals the nominal $T_{\text{device}}$, split into two halves.
  4. All other simulator behavior remains consistent, including error checking, indexing, and field processing, since the modification only affects the timing of I/O operations.

Notes

This method can be generalized to allow arbitrary fractional delays for other simulated operations, by maintaining a delay counter in memory and decrementing it each instruction cycle. A finer granularity may be implemented by decrementing IODELAY in subunits smaller than one instruction cycle if desired.

This completes the proof.

∎

$\boxed{\text{IN and OUT now delay transmission by half the nominal device time, using IODELAY.}}$