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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