Identity table

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	tyx
ldy identity_table,x	txy
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.)

Constant offsets with two identity tables

By defining another identity table immediately after the first one, the values of X and Y can be offset by a constant, at the cost of 255 more ROM bytes:

identity_table1:
    .byte $00, $01, ..., $ff  ; as above
identity_table2:
    .byte $00, $01, ..., $fe  ; $ff not needed

For example:

• adc identity_table1+constant,x is equivalent to adc x+constant where constant = 0-255
• adc identity_table2-constant,x is equivalent to adc x-constant where constant = 1-255

See also

• 6502 assembly optimisations
• Synthetic instructions

References

• NESDev forum – “6502 ASM trick”