TI59 Diagnostic forensics

[Paul Berger (Canada)]

(07-28-2020 06:55 PM)rprosperi Wrote:  

(07-28-2020 04:47 PM)Paul Berger (Canada) Wrote:  How did you get that result on a 67? I have tried a few times now and always end up with 0

Paul.

Keystrokes:

30
[ENTER]
5
[g]
[->R]
[g]
[->P]
896
[ENTER]
4
+
[f][SqRoot]
- <========= display shows 1.269600000-04
[h]
[Pi]
[g]
[X^2]
[h]
[Pi]
[g]
[X^2]
[g]
[FRAC]
-
3
[g]
[X^2]
[/]
[+]
1
[-]

Ok one thing to keep in mind that on the TI59 for the polar to rectangular and rectangular to polar conversions when entering in polar you enter the magnitude first and move that to the t register and then enter the angle and do the conversion and when you covert back to polar the angle 30 is in the x register. This is what a trace on the program on the TI59 looks like note the order of execution is not obvious looking at the formula posted.

Code:


X                Operation
------         ----------
896                 +
4                       =
900
900                   SQ Root
30                     RTN  ( the above was a sub routine)
30                     STO 
                         2
30
3.141592654           Pi
3.141592654           X2 (SQ)
9.869604401
9.869604401          STO
                         1
9.869604401
9.869604401          IINT (inverse INT or FRAC)
.8696044011
.8696044011          STO
                        30
.8696044011
.8696044011          (
.8696044011          RCL
                         1
9.869604401
9.869604401          -
9.869604401          RCL
                        30
.8696044011
.8696044011          )
  9
  9                   divide
  3                     Yx
  2                     -
  1                    =
  0
  0                   RTN
  0                   SUM
                            2
  0
  5                    x<->t
  0
  30                 P/R
  2.5
  2.5               IP/R  (Rec -> polar)
  30
  30                -
  30                RCL
                           2
 30                 =
-.0000000001
                       CP  (clear t reg)
-.0000000001          *
       10                ILOG (inverse LOG)
     1.    10
     1.    10          =
-0.7
-0.7                  INT
  0
  0                    EQ
                        C
  9                   1/x
.1111111111
1.1111111  -01        *
 -8.                =
-.8888888888

[Pjwum]

(07-28-2020 07:01 PM)rprosperi Wrote:  [Actually of course after POL(REC(30,5)), X contains 30.00012692.

I believe the 67 uses 15 internal digits, as do all Woodstocks.

Actually the TI diagnostic programme multiplies the result of your keystroke listing by 1E10 before testing it. See my first post, 2nd inequality. Thus the 67 would output 1.2692E6 versus 0.7 with the 59.

Wow! I just checked again, result is -0.7 after multiplication with 1E10. The programme precisely tests if integer(error x 1E10)=0, thus taking the absolute error value.

[Paul Berger (Canada)]

(07-28-2020 06:55 PM)rprosperi Wrote:  

(07-28-2020 04:47 PM)Paul Berger (Canada) Wrote:  How did you get that result on a 67? I have tried a few times now and always end up with 0

Paul.

Keystrokes:

Code:

30
[ENTER]
5
[g]
[->R]
[g]
[->P]
896
[ENTER]
4
+
[f][SqRoot]
-                  <========= display shows 1.269600000-04
[h]
[Pi]
[g]
[X^2]
[h]              \
[Pi]             |
[g]              | Could all be replaced by [ENTER], depending on your desired purity
[X^2]            /
[g]
[FRAC]
-
3
[g]
[X^2]
[/]
[+]
1
[-]

Edit: Noted possible substitution to simplify

As previously mentioned on the TI59 the terms for the polar format number is the reverse of the 67, on a TI59 after the P->R and R->P conversions you end up with 30 in the x register, so to work like the t159 after you do the R->P conversion press x<->y to get 30 into x. The other thing is in your list above the P->R conversion should be f-1 not g-2, g-2 is conversion to radians.

Paul.

[rprosperi]

(07-28-2020 08:49 PM)Pjwum Wrote:  

(07-28-2020 07:01 PM)rprosperi Wrote:  [Actually of course after POL(REC(30,5)), X contains 30.00012692.

I believe the 67 uses 15 internal digits, as do all Woodstocks.

Actually the TI diagnostic programme multiplies the result of your keystroke listing by 1E10 before testing it. See my first post, 2nd inequality. Thus the 67 would output 1.2692E6 versus 0.7 with the 59.

Wow! I just checked again, result is -0.7 after multiplication with 1E10. The programme precisely tests if integer(error x 1E10)=0, thus taking the absolute error value.

So, all that makes sense as I've thought the 59 had better accuracy than the 67.

I don't have the 59 listing handy, so was not sure what that was about, and missed the initial comments about multiplying the result. So, actually less impressive than I initially thought; I presumed they were manipulating numbers to actually come up with the -.888888888 result.

[rprosperi]

(07-28-2020 09:52 PM)Paul Berger (Canada) Wrote:  

(07-28-2020 06:55 PM)rprosperi Wrote:  Keystrokes:

Code:

30
[ENTER]
5
[g]
[->R]
[g]
[->P]
896
[ENTER]
4
+
[f][SqRoot]
-                  <========= display shows 1.269600000-04
[h]
[Pi]
[g]
[X^2]
[h]              \
[Pi]             |
[g]              | Could all be replaced by [ENTER], depending on your desired purity
[X^2]            /
[g]
[FRAC]
-
3
[g]
[X^2]
[/]
[+]
1
[-]

Edit: Noted possible substitution to simplify

As previously mentioned on the TI59 the terms for the polar format number is the reverse of the 67, on a TI59 after the P->R and R->P conversions you end up with 30 in the x register, so to work like the t159 after you do the R->P conversion press x<->y to get 30 into x. The other thing is in your list above the P->R conversion should be f-1 not g-2, g-2 is conversion to radians.

Paul.

Thanks Paul! I ran this probably 10 times, and got alternately the 0 and the above, and could not find why. They should never have put R<>P and D<>R so close together on the keyboard, this is not the first time this got me.

So, yes, on the 67 it is indeed 0.

I suppose I should go correct the listing [Now done] since the original has been quoted and for all time will show this error . How humbling...

[johanw]

(07-27-2020 03:51 PM)Pjwum Wrote:  - 5<30 stands for the polar notation of length 5 and 30 degrees (didn't find the suitable TeX-command).

I know of 3: \angle, \measuredangle and \sphericalangle:
\begin{equation}
error = pol(rec(5 \measuredangle 30))
\end{equation}

(07-28-2020 10:09 AM)Werner Wrote:  RCL59 on iOS, which, as far as I know, is an emulator, not a simulator, returns 0 for (in Deg mode):

I once tried to recreate a known error of the TI59 on the Android version and could not, when I mailed the author he said that he uses floating point math and did not try to recreate numerical errors of the original.

[Pjwum]

(07-29-2020 07:46 PM)johanw Wrote:  I know of 3: \angle, \measuredangle and \sphericalangle:
\begin{equation}
error = pol(rec(5 \measuredangle 30))
\end{equation}

Perfect, thanks! You never stop learning. Honestly, I haven't used TeX since many, many years.

[Werner]

(07-29-2020 07:46 PM)johanw Wrote:  

(07-28-2020 10:09 AM)Werner Wrote:  RCL59 on iOS, which, as far as I know, is an emulator, not a simulator, returns 0 for (in Deg mode):

I once tried to recreate a known error of the TI59 on the Android version and could not, when I mailed the author he said that he uses floating point math and did not try to recreate numerical errors of the original.

I was thrown off scent because SIN(45°)-COS(45°) is not zero, as in the orginal, I think. (lost my '58 somewhere)
Werner