TI-60: Triangle Numbers

[Eddie W. Shore]

Here I exploit TI-60's RST function's ability to continue program execution and using the square root function as a "tester" to calculate triangle numbers.

Instructions:

1. In RUN mode (outside of LRN), store the following values:

R0 = 0
R1 = n

2. Execute the program by pressing [RST], [R/S]. The program is done when you see "Error".

3. Clear the error by pressing [CE/C].

4. Recall R0. This is your triangle number. (R1 will have -1).

TI-60 Program: Triangle Numbers

Code:


PC00  OP71:  RCL 
PC01  OP01:  1
PC02  OP61:  STO 
PC03  OP85:  +
PC04  OP00:  0     // sum R1 in R0
PC05  OP75:  -
PC06  OP01:  1
PC07  OP95:  =
PC08  OP61:  STO
PC09  OP01:  1    // store R1 -1 in R1
PC10  OP86:  √  // take the square root of R1, if R1<0, the error occurs, ending the "loop"
PC11  OP22:  RST  // reset back to step 00

Link to blog post: https://edspi31415.blogspot.com/2018/12/...mbers.html

[Dieter]

(12-16-2018 03:35 AM)Eddie W. Shore Wrote:  Here I exploit TI-60's RST function's ability to continue program execution and using the square root function as a "tester" to calculate triangle numbers.

This is essentially a "proof of concept" on how to do loops on a calculator with an extremely limited function set without tests and goto – rskey.org calls the TI-60 "almost programmable". ;-)

In real life, if you want the sum of all integers from 1 to n you'd of course use the direct formula ½n(n+1) or ½(n²+n). Less steps, direct result.

Dieter

[grsbanks]

(12-16-2018 03:35 AM)Eddie W. Shore Wrote:  Here I exploit TI-60's RST function's ability to continue program execution

Such a pain in the rear end that the TI-56 (and presumably the TI-55III) halt execution before resetting the program counter making it impossible to program loops of any kind! Even the prehistoric TI-53 does it "right"

[Thomas Klemm]

(12-16-2018 05:33 PM)Dieter Wrote:  In real life, if you want the sum of all integers from 1 to n you'd of course use the direct formula ½n(n+1) or ½(n²+n). Less steps, direct result.

The TI-60 provides an nCr key with a bit weird usage:

Quote:The values of n and r are entered as n.rrr.

Thus we could use:

Code:

+
1.002
=
nCr

Cheers
Thomas

[ijabbott]

(12-16-2018 09:56 PM)Thomas Klemm Wrote:  

(12-16-2018 05:33 PM)Dieter Wrote:  In real life, if you want the sum of all integers from 1 to n you'd of course use the direct formula ½n(n+1) or ½(n²+n). Less steps, direct result.

The TI-60 provides an nCr key with a bit weird usage:

Quote:The values of n and r are entered as n.rrr.

Thus we could use:

Code:

+
1.002
=
nCr

Cheers
Thomas

Using the formula saves a couple of program steps (assuming there are no pending operations before running the program):

Code:

+
x²
=
÷
2
=

[Thomas Klemm]

(12-16-2018 05:33 PM)Dieter Wrote:  This is essentially a "proof of concept" on how to do loops on a calculator with an extremely limited function set without tests and goto

We could exploit the integration key and do some calculations in a loop as a side effect.
This allows to implement a solver using fixed point iteration or Newton's method.
However you could specify only up to 99 loops.

To solve Kepler's equation:

\( M = E - e \sin E \)

We would rewrite it as a fixed point equation:

\( E = M + e \sin E \)

Using the following mapping to the data memories:

E: 3
M: 4
e: 5

We could then use this program:

Code:

RCL 4
+
RCL 5
×
RCL 3
sin
=
STO 3

We don't really care about the lower and upper limits of the interval so we could just use:

0 STO 1
1 STO 2

The integration would be started with:

∫dx nn R/S

The result could then be found in register 3.

Using realistic values (e.g. e = 0.0167 for the Earth) this needs only a few iterations.
Don't forget to put the calculator into the radian mode.

Cheers
Thomas