HP 35s Gnome Sort



#2

Well, I decided to try my hand at something a bit more ambitious than my last little project (linear interpolation, released here to stunning, and yet oddly silent fanfair. I'm sure everyone was just over-awed and unable to comment. Yeah, that's the ticket).

I thought maybe a simple sort routine would be a good project. I did a search, and found a nice page on Wiki with all sorts of algorimthms, with a nice summary of speed, complexity, storage requirements, etc.

I selected the Gnome Sort, since it seemed to be the smallest, simplest. Pseudo-code follows:

void gnomesort(int n, int ar[])
{
int i = 0;

while (i < n)
{
if (i == 0 || ar[i-1] <= ar[i])
i++;
else
{
int tmp = ar[i];
ar[i] = ar[i-1];
ar[--i] = tmp;
}
}
}

Couldn't be much simpler, right?

Well, as I set about transforming this simple, benign bit of C code into HP-calc-ese, with all it's GTO and lack of labelling capability glory, I quickly re-learned the lesson of why I haven't used a "goto" command in over two decades. Goto sucks.

I REALLY struggled to transform the if-then-else logic into goto-ese. It was made more complex because the operand of the if() statement is a compound statement with OR logic. I'm quite confident someone could turn that into something better than I came up with, I ended up kludging it together with several GTO statements and Flag 0.

For better or worse, here is the program. It is called assuming

bbb.eee

is in the X-stack, and will then gnome-Sort the contents of memory registers 'bbb' to 'eee', in ascending order. Note that it will not sort complex or vector contents.

Memory registers used: I, J, Y, Z
Flags used: 0

S001	LBL S	
S002 INTG
S003 STO I
S004 STO Y first register to be sorted
S005 LASTX
S006 FP
S007 1000
S008 *
S009 STO Z last register to be sorted
S010 CF 0 start of while (I < n) loop
S011 RCL Y first register
S012 RCL I current register
S013 x == y? if(i==0)
S014 SF 0
S015 1
S016 -
S017 STO J
S018 RCL (I) ar[i]
S019 RCL (J) ar[i-1]
S020 x <= y? if(ar[i-1] <= ar[i])
S021 SF 0
S022 FS? 0 if ( (i==0) || (ar[i-1] <= ar[i]) )
S023 GTO S030
S024 STO (I) ar[i] = ar[i-1]
S025 RDN
S026 STO (J) ar[i-1] = ar[i]
S027 1
S028 STO- I i--;
S029 GTO S032
S030 1
S031 STO+ I i++;
S032 RCL Z
S033 RCL I
S034 X <= Y? while(i<n)
S035 GTO S010
S036 CF 0
S037 RTN

LN=118 CK=B393

A useful little program to load a bbb.eee range of memory registers with random numbers is as shown:

A001 LBL A
A002 STO I
A003 RANDOM
A004 STO(I)
A005 ISG I
A006 GTO A003
A007 RTN

Some timings:

21 registers, 10.030:  33 seconds
21 registers, 10.030: 37 seconds
101 registers, 10.110: ~15 minutes

Clearly the advantage of this program is simplicity at the cost of run time, but given we are talking about a calculator without the ability to move software on/off electronically, simplicity becomes pretty important.

I may try a bubble sort, and if I get crazy, a heap sort.

Edited: 14 Feb 2009, 12:06 a.m.


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