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Routines |
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The address of this routine is found in the table of addresses. It is called via the calculator literal +25 by the routine at to_power. It is also called indirectly via fp_calc_2.
This subroutine handles the function LN X and is the second of the four routines that use the series generator to produce Chebyshev polynomials.
The approximation to LN X is found as follows:
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ln | 3713 | RST $28 | X | |||||
Perform step i.
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3714 | DEFB $3D | re_stack: X (in full floating-point form) | ||||||
3715 | DEFB $31 | duplicate: X, X | ||||||
3716 | DEFB $37 | greater_0: X, (1/0) | ||||||
3717 | DEFB $00 | jump_true to VALID: X | ||||||
3718 | DEFB $04 | multiply: X | ||||||
3719 | DEFB $38 | end_calc: X | ||||||
Report A - Invalid argument.
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371A | RST $08 | Call the error handling routine. | ||||||
371B | DEFB $09 | |||||||
Perform step ii.
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VALID | 371C | DEFB $A0 | stk_zero: X, 0 (the deleted 1 is overwritten with zero) | |||||
371D | DEFB $02 | delete: X | ||||||
371E | DEFB $38 | end_calc: X | ||||||
371F | LD A,(HL) | The exponent, e, goes into A. | ||||||
3720 | LD (HL),$80 | X is reduced to X'. | ||||||
3722 | CALL STACK_A | The stack holds: X', e. | ||||||
3725 | RST $28 | X', e | ||||||
3726 | DEFB $34 | stk_data: X', e, 128 | ||||||
3727 | DEFB $38,$00 | |||||||
3729 | DEFB $03 | subtract: X', e' | ||||||
Perform step iii.
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372A | DEFB $01 | exchange: e', X' | ||||||
372B | DEFB $31 | duplicate: e', X', X' | ||||||
372C | DEFB $34 | stk_data: e', X', X', 0.8 | ||||||
372D | DEFB $F0,$4C,$CC,$CC,$CD | |||||||
3732 | DEFB $03 | subtract: e', X', X'-0.8 | ||||||
3733 | DEFB $37 | greater_0: e', X', (1/0) | ||||||
3734 | DEFB $00 | jump_true to GRE_8: e', X' | ||||||
3735 | DEFB $08 | |||||||
3736 | DEFB $01 | exchange: X', e' | ||||||
3737 | DEFB $A1 | stk_one: X', e', 1 | ||||||
3738 | DEFB $03 | subtract: X', e'-1 | ||||||
3739 | DEFB $01 | exchange: e'-1, X' | ||||||
373A | DEFB $38 | end_calc | ||||||
373B | INC (HL) | Double X' to give 2*X'. | ||||||
373C | RST $28 | e'-1, 2*X' | ||||||
GRE_8 | 373D | DEFB $01 | exchange: X', e' (X'>0.8) or 2*X', e'-1 (X'<=0.8) | |||||
373E | DEFB $34 | stk_data: X', e', LN 2 or 2*X', e'-1, LN 2 | ||||||
373F | DEFB $F0,$31,$72,$17,$F8 | |||||||
3744 | DEFB $04 | multiply: X', e'*LN 2=Y1 or 2*X', (e'-1)*LN 2=Y2 | ||||||
Perform step iv.
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3745 | DEFB $01 | exchange: Y1, X' (X'>0.8) or Y2, 2*X' (X'<=0.8) | ||||||
3746 | DEFB $A2 | stk_half: Y1, X', .5 or Y2, 2*X', .5 | ||||||
3747 | DEFB $03 | subtract: Y1, X'-.5 or Y2, 2*X'-.5 | ||||||
3748 | DEFB $A2 | stk_half: Y1, X'-.5, .5 or Y2, 2*X'-.5, .5 | ||||||
3749 | DEFB $03 | subtract: Y1, X'-1 or Y2, 2*X'-1 | ||||||
Perform step v.
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374A | DEFB $31 | duplicate: Y, X'-1, X'-1 or Y2, 2*X'-1, 2*X'-1 | ||||||
374B | DEFB $34 | stk_data: Y1, X'-1, X'-1, 2.5 or Y2, 2*X'-1, 2*X'-1, 2.5 | ||||||
374C | DEFB $32,$20 | |||||||
374E | DEFB $04 | multiply: Y1, X'-1, 2.5*X'-2.5 or Y2, 2*X'-1, 5*X'-2.5 | ||||||
374F | DEFB $A2 | stk_half: Y1, X'-1, 2.5*X'-2.5, .5 or Y2, 2*X'-1, 5*X'-2.5, .5 | ||||||
3750 | DEFB $03 | subtract: Y1, X'-1, 2.5*X'-3=Z or Y2, 2*X'-1, 5*X'-3=Z | ||||||
Perform step vi, passing to the series generator the parameter '12', and the twelve constants required.
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3751 | DEFB $8C | series_0C: Y1, X'-1, Z or Y2, 2*X'-1, Z | ||||||
3752 | DEFB $11,$AC | |||||||
3754 | DEFB $14,$09 | |||||||
3756 | DEFB $56,$DA,$A5 | |||||||
3759 | DEFB $59,$30,$C5 | |||||||
375C | DEFB $5C,$90,$AA | |||||||
375F | DEFB $9E,$70,$6F,$61 | |||||||
3763 | DEFB $A1,$CB,$DA,$96 | |||||||
3767 | DEFB $A4,$31,$9F,$B4 | |||||||
376B | DEFB $E7,$A0,$FE,$5C,$FC | |||||||
3770 | DEFB $EA,$1B,$43,$CA,$36 | |||||||
3775 | DEFB $ED,$A7,$9C,$7E,$5E | |||||||
377A | DEFB $F0,$6E,$23,$80,$93 | |||||||
At the end of the last loop the 'last value' is:
Perform step vii.
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377F | DEFB $04 | multiply: Y1=LN (2**e'), LN X' or Y2=LN (2**(e'-1)), LN (2*X') | ||||||
3780 | DEFB $0F | addition: LN (2**e')*X')=LN X or LN (2**(e'-1)*2*X')=LN X | ||||||
3781 | DEFB $38 | end_calc: LN X | ||||||
3782 | RET | Finished: 'last value' is LN X. |
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