Identity table: Difference between revisions

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The identity table is an assembly optimization trick. It is simply a table consisting of bytes 0 to 255 in ascending order. The table should be page-aligned (start at <tt>$xx00</tt>) to avoid slowdown with indexed addressing modes.
An identity table is simply a table with bytes 0 to 255 in ascending order. The value at any index is equal to the index:


The identity table can be used with the absolute, absolute,x and absolute,y addressing modes as follows:
identity_table:
    .byte $00,$01,$02,$03,$04,$05,$06,$07,$08,$09,$0a,$0b,$0c,$0d,$0e,$0f
    .byte $10,$11,$12,$13,$14,$15,$16,$17,$18,$19,$1a,$1b,$1c,$1d,$1e,$1f
    .byte $20,$21,$22,$23,$24,$25,$26,$27,$28,$29,$2a,$2b,$2c,$2d,$2e,$2f
    .byte $30,$31,$32,$33,$34,$35,$36,$37,$38,$39,$3a,$3b,$3c,$3d,$3e,$3f
    .byte $40,$41,$42,$43,$44,$45,$46,$47,$48,$49,$4a,$4b,$4c,$4d,$4e,$4f
    .byte $50,$51,$52,$53,$54,$55,$56,$57,$58,$59,$5a,$5b,$5c,$5d,$5e,$5f
    .byte $60,$61,$62,$63,$64,$65,$66,$67,$68,$69,$6a,$6b,$6c,$6d,$6e,$6f
    .byte $70,$71,$72,$73,$74,$75,$76,$77,$78,$79,$7a,$7b,$7c,$7d,$7e,$7f
    .byte $80,$81,$82,$83,$84,$85,$86,$87,$88,$89,$8a,$8b,$8c,$8d,$8e,$8f
    .byte $90,$91,$92,$93,$94,$95,$96,$97,$98,$99,$9a,$9b,$9c,$9d,$9e,$9f
    .byte $a0,$a1,$a2,$a3,$a4,$a5,$a6,$a7,$a8,$a9,$aa,$ab,$ac,$ad,$ae,$af
    .byte $b0,$b1,$b2,$b3,$b4,$b5,$b6,$b7,$b8,$b9,$ba,$bb,$bc,$bd,$be,$bf
    .byte $c0,$c1,$c2,$c3,$c4,$c5,$c6,$c7,$c8,$c9,$ca,$cb,$cc,$cd,$ce,$cf
    .byte $d0,$d1,$d2,$d3,$d4,$d5,$d6,$d7,$d8,$d9,$da,$db,$dc,$dd,$de,$df
    .byte $e0,$e1,$e2,$e3,$e4,$e5,$e6,$e7,$e8,$e9,$ea,$eb,$ec,$ed,$ee,$ef
    .byte $f0,$f1,$f2,$f3,$f4,$f5,$f6,$f7,$f8,$f9,$fa,$fb,$fc,$fd,$fe,$ff
 
Using the identity table, new assembly instructions can be synthesized as follows:


{|
{|
|-
!instruction
!description
|-
|-
|<tt>ldx identity_table,y</tt>
|<tt>ldx identity_table,y</tt>
|X = Y
|<tt>ldx Y</tt>
|-
|-
|<tt>ldy identity_table,x</tt>
|<tt>ldy identity_table,x</tt>
|Y = X
|<tt>ldy X</tt>
|-
|-
|<tt>and identity_table,x</tt>
|<tt>and identity_table,x</tt>
|A = A AND X
|<tt>and X</tt>
|-
|-
|<tt>and identity_table,y</tt>
|<tt>and identity_table,y</tt>
|A = A AND Y
|<tt>and Y</tt>
|-
|-
|<tt>ora identity_table,x</tt>
|<tt>ora identity_table,x</tt>
|A = A OR X
|<tt>ora X</tt>
|-
|-
|<tt>ora identity_table,y</tt>
|<tt>ora identity_table,y</tt>
|A = A OR Y
|<tt>ora Y</tt>
|-
|-
|<tt>eor identity_table,x</tt>
|<tt>eor identity_table,x</tt>
|A = A XOR X
|<tt>eor X</tt>
|-
|-
|<tt>eor identity_table,y</tt>
|<tt>eor identity_table,y</tt>
|A = A XOR Y
|<tt>eor Y</tt>
|-
|-
|<tt>adc identity_table,x</tt>
|<tt>adc identity_table,x</tt>
|A = A + X + C
|<tt>adc X</tt>
|-
|-
|<tt>adc identity_table,y</tt>
|<tt>adc identity_table,y</tt>
|A = A + Y + C
|<tt>adc Y</tt>
|-
|-
|<tt>sbc identity_table,x</tt>
|<tt>sbc identity_table,x</tt>
|A = A − X − 1 + C
|<tt>sbc X</tt>
|-
|-
|<tt>sbc identity_table,y</tt>
|<tt>sbc identity_table,y</tt>
|A = A − Y − 1 + C
|<tt>sbc Y</tt>
|-
|-
|<tt>cmp identity_table,x</tt>
|<tt>cmp identity_table,x</tt>
|compare A with X
|<tt>cmp X</tt>
|-
|-
|<tt>cmp identity_table,y</tt>
|<tt>cmp identity_table,y</tt>
|compare A with Y
|<tt>cmp Y</tt>
|-
|-
|<tt>bit identity_table+''constant''</tt>
|<tt>bit identity_table+''constant''</tt>
|test bits of ''constant''
|<tt>bit #''constant''</tt>
|}
|}


All the instructions above take 3 bytes and 4 CPU cycles (if the table is page-aligned and not on zero page).
All the instructions above take 3 bytes and 4 CPU cycles, assuming the table is page-aligned (starts at <tt>$xx00</tt>) and not on zero page. (Crossing a page boundary causes slowdown with indexed addressing modes.)


== References ==
== References ==


* [http://forums.nesdev.org/viewtopic.php?f=2&t=3682 NESDev forum – “6502 ASM trick”]
* [http://forums.nesdev.org/viewtopic.php?f=2&t=3682 NESDev forum – “6502 ASM trick”]

Revision as of 11:21, 16 August 2017

An identity table is simply a table with bytes 0 to 255 in ascending order. The value at any index is equal to the index: 

identity_table:
    .byte $00,$01,$02,$03,$04,$05,$06,$07,$08,$09,$0a,$0b,$0c,$0d,$0e,$0f
    .byte $10,$11,$12,$13,$14,$15,$16,$17,$18,$19,$1a,$1b,$1c,$1d,$1e,$1f
    .byte $20,$21,$22,$23,$24,$25,$26,$27,$28,$29,$2a,$2b,$2c,$2d,$2e,$2f
    .byte $30,$31,$32,$33,$34,$35,$36,$37,$38,$39,$3a,$3b,$3c,$3d,$3e,$3f
    .byte $40,$41,$42,$43,$44,$45,$46,$47,$48,$49,$4a,$4b,$4c,$4d,$4e,$4f
    .byte $50,$51,$52,$53,$54,$55,$56,$57,$58,$59,$5a,$5b,$5c,$5d,$5e,$5f
    .byte $60,$61,$62,$63,$64,$65,$66,$67,$68,$69,$6a,$6b,$6c,$6d,$6e,$6f
    .byte $70,$71,$72,$73,$74,$75,$76,$77,$78,$79,$7a,$7b,$7c,$7d,$7e,$7f
    .byte $80,$81,$82,$83,$84,$85,$86,$87,$88,$89,$8a,$8b,$8c,$8d,$8e,$8f
    .byte $90,$91,$92,$93,$94,$95,$96,$97,$98,$99,$9a,$9b,$9c,$9d,$9e,$9f
    .byte $a0,$a1,$a2,$a3,$a4,$a5,$a6,$a7,$a8,$a9,$aa,$ab,$ac,$ad,$ae,$af
    .byte $b0,$b1,$b2,$b3,$b4,$b5,$b6,$b7,$b8,$b9,$ba,$bb,$bc,$bd,$be,$bf
    .byte $c0,$c1,$c2,$c3,$c4,$c5,$c6,$c7,$c8,$c9,$ca,$cb,$cc,$cd,$ce,$cf
    .byte $d0,$d1,$d2,$d3,$d4,$d5,$d6,$d7,$d8,$d9,$da,$db,$dc,$dd,$de,$df
    .byte $e0,$e1,$e2,$e3,$e4,$e5,$e6,$e7,$e8,$e9,$ea,$eb,$ec,$ed,$ee,$ef
    .byte $f0,$f1,$f2,$f3,$f4,$f5,$f6,$f7,$f8,$f9,$fa,$fb,$fc,$fd,$fe,$ff

Using the identity table, new assembly instructions can be synthesized as follows:

ldx identity_table,y ldx Y
ldy identity_table,x ldy X
and identity_table,x and X
and identity_table,y and Y
ora identity_table,x ora X
ora identity_table,y ora Y
eor identity_table,x eor X
eor identity_table,y eor Y
adc identity_table,x adc X
adc identity_table,y adc Y
sbc identity_table,x sbc X
sbc identity_table,y sbc Y
cmp identity_table,x cmp X
cmp identity_table,y cmp Y
bit identity_table+constant bit #constant

All the instructions above take 3 bytes and 4 CPU cycles, assuming the table is page-aligned (starts at $xx00) and not on zero page. (Crossing a page boundary causes slowdown with indexed addressing modes.)

References

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