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

        DEFB    $18             ;;negate
        DEFB    $2F             ;;jump
        DEFB    $03             ;;to L1D8B, CASES

; ---

;; SMALL
L1D89:  RST     28H             ;; FP-CALC
        DEFB    $A0             ;;stk-zero

;; CASES
L1D8B:  DEFB    $01             ;;exchange
        DEFB    $2D             ;;duplicate
        DEFB    $2D             ;;duplicate
        DEFB    $04             ;;multiply
        DEFB    $2D             ;;duplicate
        DEFB    $0F             ;;addition
        DEFB    $A1             ;;stk-one
        DEFB    $03             ;;subtract

        DEFB    $8C             ;;series-0C
        DEFB    $10             ;;Exponent: $60, Bytes: 1
        DEFB    $B2             ;;(+00,+00,+00)
        DEFB    $13             ;;Exponent: $63, Bytes: 1
        DEFB    $0E             ;;(+00,+00,+00)
        DEFB    $55             ;;Exponent: $65, Bytes: 2
        DEFB    $E4,$8D         ;;(+00,+00)
        DEFB    $58             ;;Exponent: $68, Bytes: 2
        DEFB    $39,$BC         ;;(+00,+00)
        DEFB    $5B             ;;Exponent: $6B, Bytes: 2
        DEFB    $98,$FD         ;;(+00,+00)
        DEFB    $9E             ;;Exponent: $6E, Bytes: 3
        DEFB    $00,$36,$75     ;;(+00)
        DEFB    $A0             ;;Exponent: $70, Bytes: 3
        DEFB    $DB,$E8,$B4     ;;(+00)
        DEFB    $63             ;;Exponent: $73, Bytes: 2
        DEFB    $42,$C4         ;;(+00,+00)
        DEFB    $E6             ;;Exponent: $76, Bytes: 4
        DEFB    $B5,$09,$36,$BE ;;
        DEFB    $E9             ;;Exponent: $79, Bytes: 4
        DEFB    $36,$73,$1B,$5D ;;
        DEFB    $EC             ;;Exponent: $7C, Bytes: 4
        DEFB    $D8,$DE,$63,$BE ;;
        DEFB    $F0             ;;Exponent: $80, Bytes: 4
        DEFB    $61,$A1,$B3,$0C ;;

        DEFB    $04             ;;multiply
        DEFB    $0F             ;;addition
        DEFB    $34             ;;end-calc

        RET                     ; return.


; ---------------------
; THE 'ARCSIN' FUNCTION
; ---------------------
; (Offset $1F: 'asn')
;   The inverse sine function with result in radians.
;   Derived from arctan function above.
;   Error A unless the argument is between -1 and +1 inclusive.
;   Uses an adaptation of the formula asn(x) = atn(x/sqr(1-x*x))
;
;
;                 /|
;                / |
;              1/  |x
;              /a  |
;             /----|    
;               y
;
;   e.g. We know the opposite side (x) and hypotenuse (1) 
;   and we wish to find angle a in radians.
;   We can derive length y by Pythagoras and then use ATN instead. 
;   Since y*y + x*x = 1*1 (Pythagoras Theorem) then
;   y=sqr(1-x*x)                         - no need to multiply 1 by itself.
;   So, asn(a) = atn(x/y)
;   or more fully,
;   asn(a) = atn(x/sqr(1-x*x))

;   Close but no cigar.

;   While PRINT ATN (x/SQR (1-x*x)) gives the same results as PRINT ASN x,
;   it leads to division by zero when x is 1 or -1.
;   To overcome this, 1 is added to y giving half the required angle and the 
;   result is then doubled. 
;   That is, PRINT ATN (x/(SQR (1-x*x) +1)) *2
;
;
;               . /|
;            .  c/ |
;         .     /1 |x
;      . c   b /a  |
;    ---------/----|    
;      1      y
;
;   By creating an isosceles triangle with two equal sides of 1, angles c and 
;   c are also equal. If b+c+d = 180 degrees and b+a = 180 degrees then c=a/2.
;
;   A value higher than 1 gives the required error as attempting to find  the
;   square root of a negative number generates an error in Sinclair BASIC.

;; asn
L1DC4:  RST     28H             ;; FP-CALC      x.
        DEFB    $2D             ;;duplicate     x, x.
        DEFB    $2D             ;;duplicate     x, x, x.
        DEFB    $04             ;;multiply      x, x*x.
        DEFB    $A1             ;;stk-one       x, x*x, 1.
        DEFB    $03             ;;subtract      x, x*x-1.
        DEFB    $18             ;;negate        x, 1-x*x.
        DEFB    $25             ;;sqr           x, sqr(1-x*x) = y.
        DEFB    $A1             ;;stk-one       x, y, 1.
        DEFB    $0F             ;;addition      x, y+1.
        DEFB    $05             ;;division      x/y+1.
        DEFB    $21             ;;atn           a/2     (half the angle)
        DEFB    $2D             ;;duplicate     a/2, a/2.
        DEFB    $0F             ;;addition      a.
        DEFB    $34             ;;end-calc      a.

        RET                     ; return.