I have also adapted S. Judd's division routine (just copied it, really... little modifications needed).

It can divide two 16-bit numbers and generate a result of 8-bit integer division and the remainder as a fraction of 256 (so .5 is 128).

He is using a predictor/corrector method, first estimating the integer result with a table of logs, then adjusting it with two tables, one of exp and another of negative exp.

He also employs the fast multiplication routine I also posted before.

Some figures now. Running a loop like:

Code: Select all

```
for (i=10;i<1000;i+=10)
for (j=10;j<1000;j+=10)
k=(int)(i/j);
```

Here is the code:

Code: Select all

```
.zero
DIVXLO .byt 00 ;Division: DIVX/DIVY
DIVXHI .byt 00
DIVY .byt 00
DIVTEMP .byt 00 ;High byte of DY
TEMP1 .byt 00
TEMP2 .byt 00
.text
DIVSHIFT
.(
LSR DIVTEMP
ROR DIVY
LSR DIVXHI
ROR DIVXLO
.)
DIVXY
.(
LDA DIVTEMP ;Div by 2 if dy>255
BNE DIVSHIFT
LDA DIVXHI
CMP #2
BCS DIVSHIFT ;Or if dx>511
LSR ;Compute dx/2
LDA DIVXLO
ROR
TAX
LDA DIVY
LSR ;dy/2
BEQ TWOSTEP ;If Y=1 then handle special
TAY
LDA tab_log,X ;This is the division part
SEC
SBC tab_log,Y
BCC NEG
TAX
LDA tab_exp,X
TAX ;Now we have int estimate
STA MultLo1
STA MultHi1
EOR #$FF
ADC #00 ;Carry is guaranteed set
STA MultLo2
STA MultHi2
LDY DIVY
LDA (MultLo1),Y
SEC
SBC (MultLo2),Y ;a=N*dy
STA TEMP1
LDA (MultHi1),Y
SBC (MultHi2),Y
STA TEMP2
LDA DIVXLO ;R=dx-a
SBC TEMP1 ;C set
STA TEMP1
LDA DIVXHI
SBC TEMP2
LDA TEMP1 ;A=remainder
BCC RNEG
;If R>0 then assume R<255
;(true unless dx>500 or so)
RPOS CMP DIVY ;If R>=dy then
BCC DONE
L1 INX ;a=a+1
SBC DIVY ;R=R-dy
CMP DIVY
BCS L1
DONE ;Now X contains integer, A rem
;y=dy
;
; Compute remainder as a fraction of 256, i.e.
; 256*r/dy
;
; Currently, a small error may occur for large r
; (cumulative error of 1-2 pixels, up to 4 in rare cases)
;
FRACREM
STX TEMP1
TAX
BEQ ZERO
LDA tab_log,X
SEC
SBC tab_log,Y
TAX
LDA tab_negexp,X
ZERO LDX TEMP1
RTS
;And, if R<0 then assume
;R>-255
RNEG DEX
ADC DIVY
BCC RNEG
JMP FRACREM
NEG LDX #00 ;Since log is monotonic, and
LDA DIVXLO ;we /2, there is no chance
LDY DIVY
JMP FRACREM ;of undershooting.
TWOSTEP LDA DIVXHI ;If Y=1
LSR
LDA DIVXLO ;then just two steps of size
ROR ;dx/2
TAX
LDA #255
RTS
.)
```

Code: Select all

```
tab_log
.byt $00,$00,$1f,$32,$3f,$4a,$52,$59,$5f,$65,$69,$6e,$72,$76,$79,$7c
.byt $7f,$82,$85,$87,$89,$8c,$8e,$90,$92,$94,$95,$97,$99,$9a,$9c,$9e
.byt $9f,$a0,$a2,$a3,$a4,$a6,$a7,$a8,$a9,$aa,$ac,$ad,$ae,$af,$b0,$b1
.byt $b2,$b3,$b4,$b4,$b5,$b6,$b7,$b8,$b9,$ba,$ba,$bb,$bc,$bd,$bd,$be
.byt $bf,$c0,$c0,$c1,$c2,$c2,$c3,$c4,$c4,$c5,$c6,$c6,$c7,$c7,$c8,$c9
.byt $c9,$ca,$ca,$cb,$cb,$cc,$cc,$cd,$ce,$ce,$cf,$cf,$d0,$d0,$d1,$d1
.byt $d2,$d2,$d2,$d3,$d3,$d4,$d4,$d5,$d5,$d6,$d6,$d7,$d7,$d7,$d8,$d8
.byt $d9,$d9,$d9,$da,$da,$db,$db,$db,$dc,$dc,$dd,$dd,$dd,$de,$de,$de
.byt $df,$df,$df,$e0,$e0,$e1,$e1,$e1,$e2,$e2,$e2,$e3,$e3,$e3,$e4,$e4
.byt $e4,$e5,$e5,$e5,$e5,$e6,$e6,$e6,$e7,$e7,$e7,$e8,$e8,$e8,$e8,$e9
.byt $e9,$e9,$ea,$ea,$ea,$ea,$eb,$eb,$eb,$ec,$ec,$ec,$ec,$ed,$ed,$ed
.byt $ed,$ee,$ee,$ee,$ee,$ef,$ef,$ef,$ef,$f0,$f0,$f0,$f0,$f1,$f1,$f1
.byt $f1,$f2,$f2,$f2,$f2,$f3,$f3,$f3,$f3,$f4,$f4,$f4,$f4,$f4,$f5,$f5
.byt $f5,$f5,$f6,$f6,$f6,$f6,$f6,$f7,$f7,$f7,$f7,$f7,$f8,$f8,$f8,$f8
.byt $f9,$f9,$f9,$f9,$f9,$fa,$fa,$fa,$fa,$fa,$fb,$fb,$fb,$fb,$fb,$fc
.byt $fc,$fc,$fc,$fc,$fc,$fd,$fd,$fd,$fd,$fd,$fe,$fe,$fe,$fe,$fe,$ff
tab_exp
.byt $01,$01,$01,$01,$01,$01,$01,$01,$01,$01,$01,$01,$01,$01,$01,$01
.byt $01,$01,$01,$01,$01,$01,$01,$01,$01,$01,$01,$01,$01,$01,$01,$01
.byt $02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02
.byt $02,$02,$02,$03,$03,$03,$03,$03,$03,$03,$03,$03,$03,$03,$03,$03
.byt $04,$04,$04,$04,$04,$04,$04,$04,$04,$04,$04,$05,$05,$05,$05,$05
.byt $05,$05,$05,$06,$06,$06,$06,$06,$06,$06,$07,$07,$07,$07,$07,$07
.byt $08,$08,$08,$08,$08,$08,$09,$09,$09,$09,$0a,$0a,$0a,$0a,$0a,$0b
.byt $0b,$0b,$0b,$0c,$0c,$0c,$0c,$0d,$0d,$0d,$0e,$0e,$0e,$0f,$0f,$0f
.byt $10,$10,$10,$11,$11,$11,$12,$12,$13,$13,$14,$14,$14,$15,$15,$16
.byt $16,$17,$17,$18,$18,$19,$1a,$1a,$1b,$1b,$1c,$1d,$1d,$1e,$1e,$1f
.byt $20,$21,$21,$22,$23,$24,$24,$25,$26,$27,$28,$29,$29,$2a,$2b,$2c
.byt $2d,$2e,$2f,$30,$31,$33,$34,$35,$36,$37,$38,$3a,$3b,$3c,$3e,$3f
.byt $40,$42,$43,$45,$46,$48,$49,$4b,$4d,$4e,$50,$52,$54,$56,$57,$59
.byt $5b,$5d,$5f,$62,$64,$66,$68,$6a,$6d,$6f,$72,$74,$77,$79,$7c,$7f
.byt $82,$84,$87,$8a,$8d,$90,$94,$97,$9a,$9e,$a1,$a5,$a8,$ac,$b0,$b4
.byt $b8,$bc,$c0,$c4,$c8,$cd,$d1,$d6,$db,$df,$e4,$e9,$ee,$f4,$f9,$fe
tab_negexp
.byt $fe,$01,$01,$01,$01,$01,$01,$01,$01,$01,$01,$01,$01,$01,$01,$01
.byt $01,$01,$01,$01,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02
.byt $02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$03,$03,$03,$03,$03
.byt $03,$03,$03,$03,$03,$03,$03,$03,$03,$03,$03,$04,$04,$04,$04,$04
.byt $04,$04,$04,$04,$04,$04,$04,$05,$05,$05,$05,$05,$05,$05,$05,$05
.byt $06,$06,$06,$06,$06,$06,$06,$07,$07,$07,$07,$07,$07,$07,$08,$08
.byt $08,$08,$08,$08,$09,$09,$09,$09,$09,$0a,$0a,$0a,$0a,$0a,$0b,$0b
.byt $0b,$0b,$0c,$0c,$0c,$0c,$0d,$0d,$0d,$0e,$0e,$0e,$0f,$0f,$0f,$10
.byt $10,$10,$11,$11,$11,$12,$12,$12,$13,$13,$14,$14,$15,$15,$15,$16
.byt $16,$17,$17,$18,$18,$19,$1a,$1a,$1b,$1b,$1c,$1d,$1d,$1e,$1e,$1f
.byt $20,$20,$21,$22,$23,$23,$24,$25,$26,$27,$28,$28,$29,$2a,$2b,$2c
.byt $2d,$2e,$2f,$30,$31,$32,$33,$34,$36,$37,$38,$39,$3a,$3c,$3d,$3e
.byt $40,$41,$43,$44,$46,$47,$49,$4a,$4c,$4d,$4f,$51,$53,$55,$56,$58
.byt $5a,$5c,$5e,$60,$62,$65,$67,$69,$6b,$6e,$70,$73,$75,$78,$7a,$7d
.byt $80,$83,$85,$88,$8b,$8e,$92,$95,$98,$9b,$9f,$a2,$a6,$a9,$ad,$b1
.byt $b5,$b9,$bd,$c1,$c5,$ca,$ce,$d3,$d7,$dc,$e1,$e6,$eb,$f0,$f5,$fa
```