10-15-2021, 01:56 PM

Yesterday there was some question as to whether or not the INV DSZ (decrement and skip if not zero) instruction present on some TIs was at all useful. I maintain that it's useful in any situation where you decrement a counter and break out of the middle of a loop, rather than at the end of the loop body.

I put together a little example by way of a cumulative binomial distribution program. First, a BASIC version for the 71B that makes the algorithm a little easier to read:

To use it, run the program, enter the number of trials N, the probability of success in a single trial P, and the number of successful trials X. The program will show the cumulative lower tail binomial probability, i.e. probability of the number of successes being between 0 and X.

Note line 90, where the program decrements a counter, and breaks out of the middle of the loop (lines 80 to 110) when the counter reaches zero.

Now, here are printouts of both an HP 97 version, and a TI-59 version. On the HP version, you have to do something like using an extra LBL and GTO to invert the DSZ test behavior. On the TI-59, you can simply use INV DSZ directly.

To run either of these, store N in R01, P in R02, X in R03, and press A.

https://i.imgur.com/rxENjWN.jpg

Ignoring the fact that the TI program is about twice the size of the HP one it's clear that this is a case where INV DSZ can be used to save a couple of steps, and make the program flow easier to read.

I put together a little example by way of a cumulative binomial distribution program. First, a BASIC version for the 71B that makes the algorithm a little easier to read:

Code:

`0001 DESTROY ALL `

0010 INPUT "N?";N

0020 INPUT "P?";P

0030 INPUT "X?";X

0040 T=0 @ R=0

0050 F=P/(1-P)

0060 K=X+1

0070 B=(1-P)^N

0080 T=T+B

0090 K=K-1 @ IF K=0 THEN GOTO 120 @ REM INV DSZ!

0100 B=B*(N-R)/(R+1)*F @ R=R+1

0110 GOTO 80

0120 PRINT T

To use it, run the program, enter the number of trials N, the probability of success in a single trial P, and the number of successful trials X. The program will show the cumulative lower tail binomial probability, i.e. probability of the number of successes being between 0 and X.

Note line 90, where the program decrements a counter, and breaks out of the middle of the loop (lines 80 to 110) when the counter reaches zero.

Now, here are printouts of both an HP 97 version, and a TI-59 version. On the HP version, you have to do something like using an extra LBL and GTO to invert the DSZ test behavior. On the TI-59, you can simply use INV DSZ directly.

To run either of these, store N in R01, P in R02, X in R03, and press A.

https://i.imgur.com/rxENjWN.jpg

Ignoring the fact that the TI program is about twice the size of the HP one it's clear that this is a case where INV DSZ can be used to save a couple of steps, and make the program flow easier to read.