PCG PoC for the SNES using XSH-RR with 16-bit state and 8-bit output.

pcg.asm

!state_const = $5621
!state = $0123 ; some freeram
!multiplier = $12 ; keep this 1 byte only
!increment = $02AB

lorom
org $008000
baseaddr:
lda #$80
sta $2100
clc : xce
rep #$38
lda #$0000
tcd
lda #$01ff
tcs
sep #$30
jsr init_state		; call init_state once at startup
jsr gen_random
jml baseaddr

rotr8:
;  A = $00 >> $01; 
{
	lda $00
	ldx $01
	dex
	.shloop
	lsr
	dex 
	bpl .shloop
}
sta $02

;  A = $00 << (-$01 & 7)
{
	lda $01
	eor #$ff : inc
	and #$07 : dec
	tax
	lda $00
	.shloop2
	asl
	dex
	bpl .shloop2
}

ora $02
rts

inc_state:
{
	; x * multiplier
	lda !state
	sta $211b
	lda !state+1
	sta $211b
	lda #!multiplier
	sta $211c
	lda $2135
	xba
	lda $2134
}
rep #$20
clc : adc #!increment	; + increment
; leave in 16-bit mode, the code after this wants it anyway
rts

init_state:
rep #$20
lda #!state_const
sta !state
sep #$20
rts

gen_random:
rep #$20
lda !state
sta $02		;  x in $02-$03
lsr #11
sep #$20
sta $04	; count in $04
jsr inc_state
lda $02
lsr #6
eor $02
lsr #3 
sta $02
sep #$20
lda $04
sta $01
lda $02
sta $00
jsr rotr8
rts