Summation on HP 42S

[Didier Lachieze]

(09-23-2018 06:51 PM)lrdheat Wrote:  100 in Y.

No, I 'm using the stack registers X & Y, not variables "X" or "Y". So before calling the program you enter 100 (it's in the stack register X), at step 02 in the program 0 is enter in the stack register X and 100 is pushed to stack register Y which is then used by the two other instructions: RCL+ ST Y and DSE ST Y.

(09-23-2018 09:25 PM)lrdheat Wrote:  Neat stuff. For something a little more complex such as summation 1 through 100 of x^2 - 3*x,

I used the idea from post 2
[...]
Store 100 in "T", 0 in "X", Produces 323,200 in ~25 seconds

Here is a shorter way to do it. 100 XEQ SUM returns 323200 in ~11 seconds.

Code:

01 LBL "SUM"
02 0
03 LBL 00
04 RCL ST Y
05 3
06 -
07 RCL* ST Z
08 +
09 DSE ST Y
10 GTO 00
11 END

At step 04 we have the current sum in X and the current value of x in Y, so we recall Y to calculate x-3.
At step 07 we have x-3 in X, the current sum in Y and the current value of x in Z, so we recall and multiply Z to X to get x*(x-3) which is x^2 - 3*x. Then with + we get the updated sum in X and x moves down from Z to Y.

For more complex functions it may not be possible to use only the stack so variables may be needed to store x and the sum but with the stack it's generally shorter and faster.

Note: in your program you can remove the RCL "T" before the DSE, it's useless.