CLEAR STORAGE 1 ,008015,022026,030037,044,049,053053N000000N00001026 1
CLEAR STORAGE 2 L068116,105106,110117B101/I9I#071029C029056B026/B001/0991,001/001117I0? 2
BOOTSTRAP ,008015,022029,036040,047054,061068,072/061039 ,0010011040 3
0 SUBROUTINE PI PAGE 1
0 SEQ PG LIN LABEL OP OPERANDS SFX CT LOCN INSTRUCTION TYPE CARD
101 JOB SUBROUTINE PI
102 * SO - WE HAVE 5,000 VALID PI CHARACTERS :-))
103 * NOW LETS PRETTY IT UP A BIT, ORGANIZE SUBROUTINES
104 * CALL A SUBROUTINE DEPENDS UPON
105 * IF THE INDEX REGISTER OPTION IS INSTALLED,
106 * ANY BRANCH LEAVES THE ADDRESS OF THE NEXT SEQUENTIAL
107 * INSTRUCTION IF THE BRANCH NOT TAKEN IN THE
108 * B ADDRESS REGISTER :-))
109 * THE ARCTAN ROUTINE IS WRITTEN AS A SUBROUTINE.
110 * NOW LETS TRY TO CHAIN SOMETHING :-))
111 *
112 CTL 6611 *6=16,000C;6=16,000T;1=OBJDECK;,1=MODADD
113 * 1 2 3 4 5 6 7 8
114 *78901234567890123456789012345678901234567890123456789012345678901234567890
115 * LABEL | OP | OPERATION |XXXXXXX
116 ORG 87 0087
117 X1 DSA 0 INDEX REGISTER 1 3 0089 000 4
118 ORG 92 0092
119 * X2 DSA 0 INDEX REGISTER 2 3 0094 000 5
120 * ORG 97 0097
121 * X3 DSA 0 INDEX REGISTER 3 3 0099 000 6
122 *
123 * START STORAGE AREAS
124 * SMALL AREAS
125 * ORG 100 * PUT SMALL STUFF IN PUNCH AREA 0100
126 ITCNT DCW 000000 * ITERATION COUNTER, STARTS AT ZERO 6 0105 6
127 DIVBAS DCW 000000 * DIVISOR FOR BASET 6 0111 6
128 IX2P1 DCW 000000 * ITCNT TIMES 2 PLUS 1, DIVISOR FOR INTER 6 0117 6
129 C0 DCW 000000 6 0123 6
130 C1 DCW 000001 6 0129 6
131 C2 DCW 000002 6 0135 6
132 C25 DCW 000025 * 5^2 6 0141 7
133 C239P2 DCW 057121 * 239^2 6 0147 7
134 CNTZRO DCW 000000 * COUNT LEADING ZEROS, DONE YET? 6 0153 7
135 CF DCW 1 * "1"=ADD, "0" OR OTHER = SUBTRACT 1 0154 7
136 LC0L9 DCW 000000000 9 0163 7
137 *
138 * COMPUTE 16*ARCTAN(1/5)
139 START B PRINTD * MCW @+@,ACCUM&5049 * ZERO ACCUMULATOR, F 4 0164 B 634 7
140 MCW @0@,ACCUM&5048 7 0168 M H7E H7C 7
141 B START1 * SKIP PRINT AREA 4 0175 B 335 8
142 ORG 335 0335
143 START1 MCW ACCUM&5048,ACCUM&5047 7 0335 M H7C H7B 9
144 MCW @0@,BASET&5048 * ZERO BASE 7 0342 M H7E X7T 9
145 MCW BASET&5048,BASET&5047 7 0349 M X7T X7S 9
146 * BIG REGISTERS SET
147 MCW @80@,BASET&8 * SET A HIGH ORDER TO 1*5*16 7 0356 M H7G 733 9
1 SUBROUTINE PI PAGE 2
0 SEQ PG LIN LABEL OP OPERANDS SFX CT LOCN INSTRUCTION TYPE CARD
148 MCW @1@,CF * SET NEXT TO ADD 7 0363 M H7H 154 9
149 MCW C25,DIVBAS * SET NEXT TO ADD 7 0370 M 141 111 10
150 B ATAN *** CALL ATAN SUBROUTINE 4 0377 B 428 10
151 *
152 * NOW, ADD MINUS 4*ARCTAN(1/239) TO ABOVE 16*ARCTAN(1/5)
153 * DO NOT ZERO ACCUMULATOR
154 START2 MCW @0@,BASET&5048 * ZERO BASE 7 0381 M H7E X7T 10
155 MCW BASET&5048,BASET&5047 7 0388 M X7T X7S 10
156 MCW @956@,BASET&8 * SET A HIGH ORDER TO 1*4*239 7 0395 M H8A 733 10
157 MCW @0@,CF * SET NEXT SUBTRACT 7 0402 M H7E 154 10
158 MCW C239P2,DIVBAS * SET SET BASE DIVISOR 7 0409 M 147 111 11
159 B ATAN *** CALL ATAN SUBROUTINE 4 0416 B 428 11
160 * WE NOW HAVE PI IN MEMORY, PRINT IT OUT
161 B PRINT * CALL PRINT ROUTINE 4 0420 B 626 11
162 HALT H START *** HALT HERE - 4 0424 . 164 11
163 *
164 ATAN SBR ATANX&3 * SET RETURN 4 0428 H 625 11
165 MCW C0,CNTZRO * CLEAR LEADING ZERO COUNTER 7 0432 M 123 153 11
166 MCW C0,ITCNT * ZERO ITERATION CNTR 7 0439 M 123 105 11
167 MCW C1,IX2P1 * INIT INTER DIVISOR 7 0446 M 129 117 12
168 MCW @000@,X1 * CLEAR ASSOCIATED INDEX REGISTER 7 0453 M H8D 089 12
169 ATANL MCW @+@,BASET&5049 * SET POSITIVE SIGN 7 0460 M H8E X7U 12
170 D DIVBAS,BASET&6 * TRIAL ARITH 7 0467 % 111 731 12
171 MCW BASET&5042,BASET&5049 * SHIFT QUOTIENT 7 0474 M X6X X7U 12
172 MCW LC0L9,BASET&6 * REMOVE UNSHIFTED 7 0481 M 163 731 13
173 MCW BASET&5049,INTER&5049 * MOVE QUOTIENT TO NEXT 7 0488 M X7U Q2M 13
174 MCW @+@,INTER&5049 * SET POSITIVE SIGN 7 0495 M H8E Q2M 13
175 D IX2P1,INTER&6 DIVIDE INTERMEDIATE 7 0502 % 117 X8/ 13
176 MCW INTER&5042,INTER&5049 * SHIFT INTERMEDIATE 7 0509 M Q1P Q2M 13
177 MCW LC0L9,INTER&6 * REMOVE UNSHIFTED 7 0516 M 163 X8/ 14
178 MCW @+@,INTER&5049 * SET UP BASE 7 0523 M H8E Q2M 14
179 BCE ATANA,CF,1 * COMPARE FOR ADD 8 0530 B 556 154 1 14
180 ATANS MCW @1@,CF * SET NEXT ADD 7 0538 M H7H 154 14
181 S INTER&5049,ACCUM&5049 * DO THE SUBTRACTION 7 0545 S Q2M H7D 14
182 B ATANW * GO TO WRAP-UP 4 0552 B 570 15
183 ATANA A INTER&5049,ACCUM&5049 * ADD TO ACCUMULATOR 7 0556 A Q2M H7D 15
184 MCW @0@,CF * SET NEXT SUBTRACT 7 0563 M H7E 154 15
185 ATANW A C1,ITCNT * INC ITERATION COUNT 7 0570 A 129 105 15
186 A C2,IX2P1 * FORM NEXT DIVISOR 7 0577 A 135 117 15
187 ATANB BCE ATANI,BASET&X1,0 * CHAR = 0, DONE? 8 0584 B 596 7S5 0 16
188 B ATANL * GO DO ANOTHER LOOP PASS 4 0592 B 460 16
189 ATANI A C1,CNTZRO * INCREMENT # LEADING ZEROS 7 0596 A 129 153 16
190 SBR X1,1&X1 * INCREMENT X1 7 0603 H 089 0'1 16
191 C CNTZRO,@5049@ * CHECK END 7 0610 C 153 H8I 16
192 BU ATANB * NO, CHECK MORE ZEROS 5 0617 B 584 / 16
193 ATANX B 0 *** RETURN TO CALL 4 0622 B 000 17
194 *
195 *
196 * -------------------------------------------------------------
197 *
1 SUBROUTINE PI PAGE 3
0 SEQ PG LIN LABEL OP OPERANDS SFX CT LOCN INSTRUCTION TYPE CARD
198 * NOW WE PRINT THAT BABY OUT :-))
199 * PROPOSED FORMAT
200 * 2
201 * 0 1 2 3 4 5 6 7
202 * 1234567890123456789012345678901234567890123456789012345678901234567890123
203 * 3. * 10E-00000
204 * + NNNNNNNNNN NNNNNNNNNN NNNNNNNNNN NNNNNNNNNN NNNNNNNNNN * 10E-00050
205 * + NNNNNNNNNN NNNNNNNNNN NNNNNNNNNN NNNNNNNNNN NNNNNNNNNN * 10E-00100
206 PRINT SBR PRINTX&3 4 0626 H 724 17
207 SBR PRINTX&3 * PUSH THINGS UP A LITTLE 4 0630 H 724 17
208 PRINTD CS 633 * START CLEARING DOWN TO 200, PRINT AREA 4 0634 / 633 17
209 CS * 500S 1 0638 / 17
210 CS * 400S 1 0639 / 17
211 CS * 300S 1 0640 / 17
212 CS * 200S 1 0641 / 18
213 SW 500,350 7 0642 , 500 350 18
214 SW 200 4 0649 , 200 18
215 MCW @1@,632 7 0653 M H7H 632 18
216 MCW @123456789@,204 7 0660 M H9H 204 18
217 W *WRITE THE PRINT AREA TO THE PRINTER 1 0667 2 18
218 *
219 PR1LOP ZA @1@,334 7 0668 ? H7H 334 18
220 MCE 632,332 7 0675 E 632 332 19
221 W *WRITE THE PRINT AREA TO THE PRINTER 1 0682 2 19
222 MCW 632,482 * COPY 7 0683 M 632 482 19
223 SW 200 * RESTORE WORD MARK OBLITERATED BY MCW 4 0690 , 200 19
224 A 482,632 * 7 0694 A 482 632 19
225 C @ @,201 7 0701 C I0? 201 19
226 BE PR1LOP 5 0708 B 668 S 19
227 H PRINTD 4 0713 . 634 20
228 B PRINTD 4 0717 B 634 20
229 PRINTX B 0 *** RETURN TO CALL 4 0721 B 000 20
230 *
231 *
232 * LARGE AREAS RON MAK SAYS THAT BLANKS PROCESS AS ZEROS
233 * ORG 780
234 *FLDLEN EQU 5050 * LENGTH OF THE 3 BIG FIELDS
235 BASET DA 1X5050,C * BASE, 1ST DIVISION HERE 0725 5774
236 INTER DA 1X5050,C * INTERMEDIATE BUFFER, 2ND DIVISION HERE 5775 10824
237 ACCUM DA 1X5050,C * ACCUMULATOR, ANSWER IS FORMED HERE 10825 15874
238 * 1 2 3 4 5 6 7 8
239 *78901234567890123456789012345678901234567890123456789012345678901234567890
240 * LABEL | OP | OPERATION |XXXXXXX
241 *
242 *** NOV 15
243 * MACHIN'S METHOD -
244 * PI = 16ARCTAN(1/5) - 4ARCTAN(1/239)
245 * AN ARCTAN SERIES IS 1/N - 1/(3XN^3) + 1/(5XN^5) - ...
246 *
247 *** NOV 16
1 SUBROUTINE PI PAGE 4
0 SEQ PG LIN LABEL OP OPERANDS SFX CT LOCN INSTRUCTION TYPE CARD
248 * IN ANY CASE,
249 *LETS DO ARCTAN(X), X = 1/5
250 * 0.19739555984988075837004976519479
251 *THEN 16ARCTAN(1/5)
252 * 3.1583289575980921339207962431166
253 * THEN AECTAN(1/239)
254 * 0.0041840760020747238645382149592855
255 * TIMES 4
256 * 0.016736304008298895458152859837142
257 * PI =
258 * 3.1415926535897932384626433832795
259 * :-))
260 *
261 * SET N TO 1/X = 5 (THIS IS THE FANCY FOOTWORK :-))
262 *
263 * 1) A) FORM THREE LARGE AS PRACTICAL EQUAL SIZED AREAS IN MEMORY.
264 * LETS CALL THEM "ACCUMULATOR", ACCUM
265 * "INTERMEDIATE", INTER
266 * "BASE OF NEXT TERM" BASET
267 * B) FORM SMALLER WORKING AREAS
268 * ITERATION COUNTER ITCNT USED FOR OBSERVATION
269 * STARTS AT ZERO, COUNTS UP AFTER A PASS
270 * DIVISOR OF BASET, DIVBAS, USUALLY 5^2 OR 239^2
271 * 5^2 = 25, 239^2 = 57121
272 * ADD/SUBTRACT CONTROL FLAG, CF , TOGGLED AFTER A PASS
273 * 0 MEANS ADD, OTHER IS SUBTRACT
274 * DIVISOR OF INTER IS IX2P1 , ITCNT TIMES 2 PLUS 1
275 *
276 * 2) FIGURE WHERE THE DECIMAL POINT WILL BE
277 * (SAME RELATIVE PLACE IN EACH AREA)
278 * ( SEVERAL CHARACTERS OR WORDS TO THE "RIGHT" OF
279 * THE TOP SIGNIFICANCE.)
280 *
281 * 3) A) ZERO THE ACCUM
282 * B) ( INTER DOES NOT NEED INITIALIZATION)
283 * C) SET X (5.0 IN OUR EXAMPLE) INTO BASET
284 * D) SET COUNTER N TO 1
285 *
286 * 4) WHILE BASET IS NON-ZERO
287 * A) DIVIDE BASET BY X^2 ( 25 IN OUR EXAMPLE ) GIVING BASET
288 * B) DIVIDE BASET BY (2XN - 1) GIVING INTER
289 * C) IF N IS ODD, ADD INTERMEDIATE TO ACCUMULATOR
290 * ELSE, SUBTRACT INTERMEDIATE FROM ACCUMULATOR
291 * D) ADD 1 TO N (ASSURE THAT MACHINE CAN DIVIDE BY 2N)
292 *
293 * 5) ACCUMULATOR IS A FINE APPROXIMATION OF ARCTAN(X) ;-))
DCW @0@ 1 15875 LIT 410
DCW @80@ 2 15877 LIT 410
DCW @1@ 1 15878 LIT 410
DCW @956@ 3 15881 LIT 411
1 SUBROUTINE PI PAGE 5
0 SEQ PG LIN LABEL OP OPERANDS SFX CT LOCN INSTRUCTION TYPE CARD
DCW @000@ 3 15884 LIT 411
DCW @+@ 1 15885 LIT 411
DCW @5049@ 4 15889 LIT 411
DCW @123456789@ 9 15898 LIT 411
DCW @ @ 2 15900 LIT 411
294 END START * LAST CARD IN DECK, TRANSFER ADDRESS / 164 080
1 SUBROUTINE PI PAGE 6
0SYMBOL ADDRESS SYMBOL ADDRESS SYMBOL ADDRESS SYMBOL ADDRESS SYMBOL ADDRESS SYMBOL ADDRESS SYMBOL ADDRESS
ACCUM 10825 ATAN 428 ATANA 556 ATANB 584 ATANI 596 ATANL 460 ATANS 538
ATANW 570 ATANX 622 BASET 725 C0 123 C1 129 C2 135 C239P2 147
C25 141 CF 154 CNTZRO 153 DIVBAS 111 HALT 424 INTER 5775 ITCNT 105
IX2P1 117 LC0L9 163 PR1LOP 668 PRINT 626 PRINTD 634 PRINTX 721 START 164
START1 335 START2 381 X1 89 X2 94 X3 99