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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 37 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 | 14099 | RST 40 | X | |||||
Perform step i.
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14100 | DEFB 61 | re_stack: X (in full floating-point form) | ||||||
14101 | DEFB 49 | duplicate: X, X | ||||||
14102 | DEFB 55 | greater_0: X, (1/0) | ||||||
14103 | DEFB 0 | jump_true to VALID: X | ||||||
14104 | DEFB 4 | multiply: X | ||||||
14105 | DEFB 56 | end_calc: X | ||||||
Report A - Invalid argument.
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14106 | RST 8 | Call the error handling routine. | ||||||
14107 | DEFB 9 | |||||||
Perform step ii.
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VALID | 14108 | DEFB 160 | stk_zero: X, 0 (the deleted 1 is overwritten with zero) | |||||
14109 | DEFB 2 | delete: X | ||||||
14110 | DEFB 56 | end_calc: X | ||||||
14111 | LD A,(HL) | The exponent, e, goes into A. | ||||||
14112 | LD (HL),128 | X is reduced to X'. | ||||||
14114 | CALL STACK_A | The stack holds: X', e. | ||||||
14117 | RST 40 | X', e | ||||||
14118 | DEFB 52 | stk_data: X', e, 128 | ||||||
14119 | DEFB 56,0 | |||||||
14121 | DEFB 3 | subtract: X', e' | ||||||
Perform step iii.
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14122 | DEFB 1 | exchange: e', X' | ||||||
14123 | DEFB 49 | duplicate: e', X', X' | ||||||
14124 | DEFB 52 | stk_data: e', X', X', 0.8 | ||||||
14125 | DEFB 240,76,204,204,205 | |||||||
14130 | DEFB 3 | subtract: e', X', X'-0.8 | ||||||
14131 | DEFB 55 | greater_0: e', X', (1/0) | ||||||
14132 | DEFB 0 | jump_true to GRE_8: e', X' | ||||||
14133 | DEFB 8 | |||||||
14134 | DEFB 1 | exchange: X', e' | ||||||
14135 | DEFB 161 | stk_one: X', e', 1 | ||||||
14136 | DEFB 3 | subtract: X', e'-1 | ||||||
14137 | DEFB 1 | exchange: e'-1, X' | ||||||
14138 | DEFB 56 | end_calc | ||||||
14139 | INC (HL) | Double X' to give 2*X'. | ||||||
14140 | RST 40 | e'-1, 2*X' | ||||||
GRE_8 | 14141 | DEFB 1 | exchange: X', e' (X'>0.8) or 2*X', e'-1 (X'<=0.8) | |||||
14142 | DEFB 52 | stk_data: X', e', LN 2 or 2*X', e'-1, LN 2 | ||||||
14143 | DEFB 240,49,114,23,248 | |||||||
14148 | DEFB 4 | multiply: X', e'*LN 2=Y1 or 2*X', (e'-1)*LN 2=Y2 | ||||||
Perform step iv.
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14149 | DEFB 1 | exchange: Y1, X' (X'>0.8) or Y2, 2*X' (X'<=0.8) | ||||||
14150 | DEFB 162 | stk_half: Y1, X', .5 or Y2, 2*X', .5 | ||||||
14151 | DEFB 3 | subtract: Y1, X'-.5 or Y2, 2*X'-.5 | ||||||
14152 | DEFB 162 | stk_half: Y1, X'-.5, .5 or Y2, 2*X'-.5, .5 | ||||||
14153 | DEFB 3 | subtract: Y1, X'-1 or Y2, 2*X'-1 | ||||||
Perform step v.
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14154 | DEFB 49 | duplicate: Y, X'-1, X'-1 or Y2, 2*X'-1, 2*X'-1 | ||||||
14155 | DEFB 52 | stk_data: Y1, X'-1, X'-1, 2.5 or Y2, 2*X'-1, 2*X'-1, 2.5 | ||||||
14156 | DEFB 50,32 | |||||||
14158 | DEFB 4 | multiply: Y1, X'-1, 2.5*X'-2.5 or Y2, 2*X'-1, 5*X'-2.5 | ||||||
14159 | DEFB 162 | stk_half: Y1, X'-1, 2.5*X'-2.5, .5 or Y2, 2*X'-1, 5*X'-2.5, .5 | ||||||
14160 | DEFB 3 | 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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14161 | DEFB 140 | series_0C: Y1, X'-1, Z or Y2, 2*X'-1, Z | ||||||
14162 | DEFB 17,172 | |||||||
14164 | DEFB 20,9 | |||||||
14166 | DEFB 86,218,165 | |||||||
14169 | DEFB 89,48,197 | |||||||
14172 | DEFB 92,144,170 | |||||||
14175 | DEFB 158,112,111,97 | |||||||
14179 | DEFB 161,203,218,150 | |||||||
14183 | DEFB 164,49,159,180 | |||||||
14187 | DEFB 231,160,254,92,252 | |||||||
14192 | DEFB 234,27,67,202,54 | |||||||
14197 | DEFB 237,167,156,126,94 | |||||||
14202 | DEFB 240,110,35,128,147 | |||||||
At the end of the last loop the 'last value' is:
Perform step vii.
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14207 | DEFB 4 | multiply: Y1=LN (2**e'), LN X' or Y2=LN (2**(e'-1)), LN (2*X') | ||||||
14208 | DEFB 15 | addition: LN (2**e')*X')=LN X or LN (2**(e'-1)*2*X')=LN X | ||||||
14209 | DEFB 56 | end_calc: LN X | ||||||
14210 | RET | Finished: 'last value' is LN X. |
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