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|
;--------------------------------------
; Lychrel numbers.
;
; :author: Marc 'BlackJack' Rintsch
; :date: 2008-03-07
; :version: 0.1
;
; Prints all `Lychrel numbers`_ between 1 and 100000.
;
; The numbers are stored as array of "digits" in little endian
; order. Each digit is a byte with a value between 0 and 9.
;
; Runtime on C64: 00:21:01
;
; .. _Lychrel numbers: http://en.wikipedia.org/wiki/Lychrel_number
;
; .. cl65 -l -tnone -C simple.cfg lychrel.s -o lychrel.prg
;--------------------------------------
;--------------------------------------
; External addresses.
;--------------------------------------
chrout = $ffd2
;--------------------------------------
; Constants.
;--------------------------------------
TO = 100000
TO_DIGITS = 10
ITERATIONS = 100
MAX_DIGITS = TO_DIGITS + ITERATIONS
;--------------------------------------
; Global variables.
;--------------------------------------
.zeropage
;
; Length of the currently tested `n` in digits.
;
n_length:
.res 1
;
; Length of the number(s) `xa` and `xb` while testing.
;
length:
.res 1
.bss
;
; Number to be tested as digits i.e. bytes with values between
; 0 and 9. The length is stored in `n_length`.
;
n:
.res TO_DIGITS
;
; Space for calculating the reversed and added values.
; In the `main` code the current number is copied into `xa`
; and then repeatedly `reverse_add`\ed to itself with the
; result of that adding stored in `xb`.
;
xa:
.res MAX_DIGITS
xb:
.res MAX_DIGITS
;--------------------------------------
; BASIC header.
;--------------------------------------
.code
.word 0800h ; Load address.
.byte 0
.word @line_end
.word 2008 ; Line number.
.byte $9e ; SYS token.
.byte "2080 " ; SYS argument.
.byte "LYCHREL NUMBERS/BJ"
@line_end:
.byte 0, 0, 0 ; Line and program end marker.
;--------------------------------------
; Main program.
;--------------------------------------
.proc main
.zeropage
;
; Three byte counter for `TO` iterations (100000 = $0186a0).
;
i:
.res 3
.code
;
; Clear and set `n` and `i` to 1.
;
lda #0 ; n := 0; n := 1; i := 1
sta i+1
sta i+2
ldx #TO_DIGITS
clear_n:
sta n-1,x
dex
bne clear_n
inx
stx i
stx n
stx n_length
mainloop:
jsr is_lychrel
bcc no_lychrel
jsr print_n
no_lychrel:
jsr increase_n
inc i ; INC(i)
bne skip
inc i+1
bne skip
inc i+2
skip:
lda i
cmp #<TO
bne mainloop
lda i+1
cmp #>TO
bne mainloop
lda i+2
cmp #^TO
bne mainloop
rts
.endproc
;--------------------------------------
; Print `n` and a trailing newline.
;
; :in: `n_length`, `n`
;--------------------------------------
.proc print_n
ldy n_length
L1:
lda n-1,y
ora #%110000 ; = '0'
jsr chrout
dey
bne L1
lda #13
jmp chrout
.endproc
;--------------------------------------
; Increase `n` by one.
;
; This procedure expects n[n_length] == 0 in case the number gets
; one digit longer.
;
; :in: `n`, `n_length`
; :out: `n`, `n_length`
;--------------------------------------
.proc increase_n
ldx #0
L1:
inc n,x ; Increase digit.
lda n,x
cmp #10 ; If "carry", store 0 and go to next digit.
bne return
lda #0
sta n,x
inx
bne L1
return:
cpx n_length ; If "carry" after last digit, increase length.
bcc skip
inc n_length
skip:
rts
.endproc
;--------------------------------------
; Tests if `n` is a Lychrel number.
;
; :in: `n`, `n_length`
; :out: C is set if yes, cleared otherwise.
; :uses: `length`, `xa`, `xb`
;--------------------------------------
.proc is_lychrel
.zeropage
i:
.res 1
.code
ldx n_length ; xa := n; length := n_length
stx length
L1:
lda n-1,x
sta xa-1,x
dex
bne L1
lda #ITERATIONS ; i := ITERATIONS
sta i
L2:
jsr reverse_add
jsr is_palindrome
bne no_palindrome
clc
rts
no_palindrome:
ldx length ; a := b
L3:
lda xb-1,x
sta xa-1,x
dex
bne L3
dec i ; Loop body end.
bne L2
sec
rts
.endproc
;--------------------------------------
; Add the reverse to `xa` to itself and store the result in `xb`.
;
; :in: `length`, `xa`
; :out: `length`, `xb`
;--------------------------------------
.proc reverse_add
.code
ldx #0
ldy length
clc
L1:
lda xa,x
adc xa-1,y
cmp #10
bcc no_adjust
sbc #10
no_adjust:
sta xb,x
dey
inx
txa ; ``eor`` instead of ``cpx`` to keep the carry flag
eor length ; of the addition above.
bne L1
bcc no_carry
lda #1
sta xb,x
inc length
no_carry:
rts
.endproc
;--------------------------------------
; Checks if `xb` is a palindrome.
;
; :in: `length`, `xb`
; :out: Z flag set if `xb` is a palindrome, cleared otherwise.
;--------------------------------------
.proc is_palindrome
.code
ldx #0
lda length
tay
lsr
sta L1+1 ; Self modifying code!
L1:
cpx #0 ; <<< 0 replaced by (`length` / 2).
beq return
lda xb,x
cmp xb-1,y
bne return
dey
inx
bne L1
return:
rts
.endproc
|
