====== Combination Sort ====== by Daryl Rictor This is a sort routine called a Combination Sort, which is a modified bubble sort (iterative) that takes much less time to complete. As an example, using a 255 element array, the standard bubble sort routine found elsewhere in the repository took on average about 2 seconds to complete on my computer. My routine took about 2/10ths of a second to sort the same data. I used three different random patterns and used my TOD timer to perform the time measurements.

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; Combination Sort - An improvement on the Bubble Sort        ;
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; This idea was presented as a BASIC program in a magazine    ;
; article about 12 years ago. I could not find the orginal    ;
; article and I do not know who the author was.  I am         ;
; including the BASIC routine that I had used in some of my   ;
; BASIC programs.                                             ;
;                                                             ;
; As I recall, this sort routine cuts the processing time by  ;
; reducing the size of the array into smaller chuncks, and    ;
; moving each elelment more than one position at a time, thus ;
; reducing the total number of cycles through the loop.  I    ;
; have not seen a faster, non-recursive sort routine.         ;
;                                                             ;
; I have taken the BASIC routine and converted it to 65C02    ;
; assembly code.  I am using the added opcodes PHX, PHY,      ;
; PLX, PLY, LDA (zp) & STZ zp to decrease size and increase   ;
; speed.  By adding an additional zero page temp variable,    ;
; you can use the basic 6502 opcodes to perform this sort.    ;
;                                                             ;
; Here's my copy of the BASIC Routine:                        ;
;                                                             ;
; SUB COMBINATION (A())                                       ;
;   size = A(0)                                               ;
;   gap = A(0)                                                ;
;   DO                                                        ;
;     gap = INT(gap / 1.3)                                    ;
;     IF gap < 1 THEN gap = 1                                 ;
;     switch = 0                                              ;
;     FOR I = 1 TO size - gap                                 ;
;       J = I + gap                                           ;
;       IF A(I) > A(J) THEN                                   ;
;         SWAP A(I), A(J)                                     ;
;         switch = switch + 1                                 ;
;       END IF                                                ;
;     NEXT I                                                  ;
;   LOOP UNTIL gap = 1 AND switch = 0                         ;
;                                                             ;
;  Daryl Rictor - May 2001                                    ;
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;
; define variables
;
array    =   $30
flag     =   $32
gap      =   $33
;
;
; UPPERCASE opcodes are 6502 codes
; lowercase opcodes are 65C02 codes
;

SORT8    lda (array)       ; FETCH ELEMENT COUNT
         STA gap           ; save in gap
SORTLP   LSR gap           ; divide gap by ~1.3  (gap * 0.7692)
         LDA gap           ; (not critical to be exact)
         LSR A             ; this routine calculates it as:
         CLC               ;
         ADC gap           ;     gap = gap/2 + gap/4
         STA gap           ;     (gap * 0.7500)
         CMP #$00          ;
         BNE CLFLAG        ; if gap = 0 then set it to 1
         INC gap           ;
CLFLAG   stz flag          ; TURN EXCHANGE FLAG OFF (= 0)
         SEC               ;
         lda (array)       ; get size
         SBC gap           ; subract gap to reduce loop size
         TAX               ; (loop counter & pointer to lower element)
NXTEL    CLC               ; calc pointer to upper element
         TXA               ;
         ADC gap           ;
         TAY               ; y = x + gap
         LDA (array),y     ; get upper element
         PHA               ; save it for swap
         phy               ; save y for swap
         phx               ; transfer x reg to y reg
         ply               ; get pointer to lower element
         CMP (array),y     ; compare = upper - lower
         BCS CLRSTK        ; if upper < lower, swap elements
         LDA (array),y     ; get lower value
         ply               ; get upper element pointer
         STA (array),y     ; save lower value in upper element
         phx               ; transfer x reg to y reg
         ply               ; get lower element pointer
         PLA               ; get upper value
         STA (array),y     ; save upper vaule in lower element
         LDA #$FF          ; TURN EXCHANGE FLAG ON (= -1)
         STA flag          ;
         BNE CHKEND        ; skip over stack maintenance
CLRSTK   PLA               ; remove upper element & pointer from stack
         PLA               ;
CHKEND   DEX               ; END OF LIST?
         BNE NXTEL         ; NO. FETCH NEXT ELEMENT
         LDA gap           ;
         CMP #$01          ;
         BNE SORTLP        ; repeat loop unitl the gap size = 1
         BIT $32           ; if gap = 1, IS EXCHANGE FLAG STILL OFF?
         BMI SORTLP        ; NO. GO THROUGH LIST AGAIN
         RTS               ; YES. LIST IS NOW ORDERED
;
; end SORT8
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