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t/data/zx81_version_2_rom_source.asm  view on Meta::CPAN

; required for these are allocated. ZX81 programmers who wish to
; use the floating point routines from assembly language may wish to
; alter the system variable MEM to point to 160 bytes of RAM to have
; use the full range available.
; A holds derived offset $00-$1F.
; Unary so on entry HL points to last value, DE to STKEND.

;; st-mem-xx
L1A63:  PUSH    HL              ; save the result pointer.
        EX      DE,HL           ; transfer to DE.
        LD      HL,($401F)      ; fetch MEM the base of memory area.
        CALL    L1A3C           ; routine LOC-MEM sets HL to the destination.
        EX      DE,HL           ; swap - HL is start, DE is destination.
        CALL    L19F6           ; routine MOVE-FP.
                                ; note. a short ld bc,5; ldir
                                ; the embedded memory check is not required
                                ; so these instructions would be faster!
        EX      DE,HL           ; DE = STKEND
        POP     HL              ; restore original result pointer
        RET                     ; return.

; -------------------------
; THE 'EXCHANGE' SUBROUTINE
; -------------------------
; offset $01: 'exchange'
; This routine exchanges the last two values on the calculator stack
; On entry, as always with binary operations,
; HL=first number, DE=second number
; On exit, HL=result, DE=stkend.

;; exchange
L1A72:  LD      B,$05           ; there are five bytes to be swapped

; start of loop.

;; SWAP-BYTE
L1A74:  LD      A,(DE)          ; each byte of second
        LD      C,(HL)          ; each byte of first
        EX      DE,HL           ; swap pointers
        LD      (DE),A          ; store each byte of first
        LD      (HL),C          ; store each byte of second
        INC     HL              ; advance both
        INC     DE              ; pointers.
        DJNZ    L1A74           ; loop back to SWAP-BYTE until all 5 done.

        EX      DE,HL           ; even up the exchanges
                                ; so that DE addresses STKEND.
        RET                     ; return.

; ---------------------------------
; THE 'SERIES GENERATOR' SUBROUTINE
; ---------------------------------
; offset $86: 'series-06'
; offset $88: 'series-08'
; offset $8C: 'series-0C'
; The ZX81 uses Chebyshev polynomials to generate approximations for
; SIN, ATN, LN and EXP. These are named after the Russian mathematician
; Pafnuty Chebyshev, born in 1821, who did much pioneering work on numerical
; series. As far as calculators are concerned, Chebyshev polynomials have an
; advantage over other series, for example the Taylor series, as they can
; reach an approximation in just six iterations for SIN, eight for EXP and
; twelve for LN and ATN. The mechanics of the routine are interesting but
; for full treatment of how these are generated with demonstrations in
; Sinclair BASIC see "The Complete Spectrum ROM Disassembly" by Dr Ian Logan
; and Dr Frank O'Hara, published 1983 by Melbourne House.

;; series-xx
L1A7F:  LD      B,A             ; parameter $00 - $1F to B counter
        CALL    L19A0           ; routine GEN-ENT-1 is called.
                                ; A recursive call to a special entry point
                                ; in the calculator that puts the B register
                                ; in the system variable BREG. The return
                                ; address is the next location and where
                                ; the calculator will expect its first
                                ; instruction - now pointed to by HL'.
                                ; The previous pointer to the series of
                                ; five-byte numbers goes on the machine stack.

; The initialization phase.

        DEFB    $2D             ;;duplicate       x,x
        DEFB    $0F             ;;addition        x+x
        DEFB    $C0             ;;st-mem-0        x+x
        DEFB    $02             ;;delete          .
        DEFB    $A0             ;;stk-zero        0
        DEFB    $C2             ;;st-mem-2        0

; a loop is now entered to perform the algebraic calculation for each of
; the numbers in the series

;; G-LOOP
L1A89:  DEFB    $2D             ;;duplicate       v,v.
        DEFB    $E0             ;;get-mem-0       v,v,x+2
        DEFB    $04             ;;multiply        v,v*x+2
        DEFB    $E2             ;;get-mem-2       v,v*x+2,v
        DEFB    $C1             ;;st-mem-1
        DEFB    $03             ;;subtract
        DEFB    $34             ;;end-calc

; the previous pointer is fetched from the machine stack to H'L' where it
; addresses one of the numbers of the series following the series literal.

        CALL    L19FC           ; routine STK-DATA is called directly to
                                ; push a value and advance H'L'.
        CALL    L19A4           ; routine GEN-ENT-2 recursively re-enters
                                ; the calculator without disturbing
                                ; system variable BREG
                                ; H'L' value goes on the machine stack and is
                                ; then loaded as usual with the next address.

        DEFB    $0F             ;;addition
        DEFB    $01             ;;exchange
        DEFB    $C2             ;;st-mem-2
        DEFB    $02             ;;delete

        DEFB    $31             ;;dec-jr-nz
        DEFB    $EE             ;;back to L1A89, G-LOOP

; when the counted loop is complete the final subtraction yields the result
; for example SIN X.