Multiply Function [x]

[Dieter]

(08-03-2018 09:27 AM)Gamo Wrote:  I'm wondering what algorithm is use in calculator for the multiply function.

There was a series of HP Journal articles that described how calculators do their calculations. I remember something about log, exponential and trig functions, and maybe there also was something about multiplication and division.

(08-03-2018 09:27 AM)Gamo Wrote:  Example: 6903 x 103

6903 [ENTER] 103 [R/S] ---> 711009

When I ran this it returned 711012,14.

Why is that? Register 2 happened to have pi stored in it (from a previous calculation – the 12C has continuous memory). And your program does not clear this register before it starts adding! I have mentioned this point several times: always clear a sum before you start adding data! Clearing the sum afterwards, as your program does it, is not a solution.

(08-03-2018 09:27 AM)Gamo Wrote:  Step can be reverse: 103 [ENTER] 6903 [R/S] ---> 711009

But the program takes much longer to finish. You should start with the smaller number in X. Why not have the program care for this? Simply start with

X<=Y?
X<>Y
X<>Y

You can also speed up (and shorten) the program by using storage arithmetics.

Edit: here's my attempt of such a program. Only one data register is required.

Code:

01 X<=Y?
02 X<>Y    // this way the larger factor is in X
03 X<>Y    // and now it's the smaller factor
04 INTG    // this must be an integer
05 STO 0   // store smaller factor as counter
06 X<>Y    // the larger factor (may be fractional)
07 INTG    // is moved into LastX (INTG used only for this purpose)
08 0       // initialize sum to zero
09 RCL 0   // check counter
10 X=0?    // has it become zero?
11 GTO 19  // then exit
12 1
13 STO-0   // else decrement counter
14 R↓
15 R↓      // pop back sum (was in Z)
16 LstX
17 +       // add larger factor
18 GTO 09
19 +       // sum was in Y while X=0, so this returns the result in X

Note: the smaller (!) of the two factors must be an integer ≥0. If there is a fractional part it is discarded.
The larger factor may be fractional.

123,4 [ENTER] 17 [R/S] => 2097,80
17 [ENTER] 123,4 [R/S] => 2097,80

Dieter