Source Code

These source-code files were transcribed from a printout in Don Eyles's personal collection, scanned by archive.org, and financially sponsored by Linden Sims. A team of volunteers performed the transcription and proof-reading. The scanned page images are available at the Virtual AGC Project website, as well as higher-quality (but much larger) images at the Virtual AGC Project's collection in the Internet Archive. Report any problems by creating "issues" at the Virtual AGC Project's GitHub Repository.

Notations on the program listing read, in part:

	GAP:  ASSEMBLE REVISION 56 OF AGC PROGRAM ZERLINA BY ZOROASTER
	9:12 OCT. 21,1970
Note that the date is the date of the printout, not the date of the program revision.

044370,000002:                                                                                                  ## Copyright:   Public domain.
044371,000003:                                                                                                  ## Filename:    INTERPRETER.agc
044372,000004:                                                                                                  ## Purpose:     A log section of Zerlina 56, the final revision of
044373,000005:                                                                                                  ##              Don Eyles's offline development program for the variable 
044374,000006:                                                                                                  ##              guidance period servicer. It also includes a new P66 with LPD 
044375,000007:                                                                                                  ##              (Landing Point Designator) capability, based on an idea of John 
044376,000008:                                                                                                  ##              Young's. Neither of these advanced features were actually flown,
044377,000009:                                                                                                  ##              but Zerlina was also the birthplace of other big improvements to
044378,000010:                                                                                                  ##              Luminary including the terrain model and new (Luminary 1E)
044379,000011:                                                                                                  ##              analog display programs. Zerlina was branched off of Luminary 145,
044380,000012:                                                                                                  ##              and revision 56 includes all changes up to and including Luminary
044381,000013:                                                                                                  ##              183. It is therefore quite close to the Apollo 14 program,
044382,000014:                                                                                                  ##              Luminary 178, where not modified with new features.
044383,000015:                                                                                                  ## Reference:   pp. 993-1085
044384,000016:                                                                                                  ## Assembler:   yaYUL
044385,000017:                                                                                                  ## Contact:     Ron Burkey <info@sandroid.org>.
044386,000018:                                                                                                  ## Website:     www.ibiblio.org/apollo/index.html
044387,000019:                                                                                                  ## Mod history: 2017-07-28 MAS  Created from Luminary 210.
044388,000020:                                                                                                  ##              2017-08-28 RSB  Completed transcribing through page 1032.  Pages
044389,000021:                                                                                                  ##                              1033-1085 remain.
044390,000022:                                                                                                  ##              2017-08-29 RSB  Completed remainder of transcription.
044391,000023: 

Page 993

044393,000025:                                                                                                  #  SECTION 1  DISPATCHER
044394,000026: 
044395,000027:                                                                                                  #           ENTRY TO THE INTERPRETER. INTPRET SETS LOC TO THE FIRST  INSTRUCTION, BANKSET TO THE BBANK OF THE
044396,000028:                                                                                                  #  OBJECT INTERPRETIVE PROGRAM, AND INTBIT15 TO THE BIT15 CONTENTS OF FBANK. INTERPRETIVE PROGRAMS MAY BE IN
044397,000029:                                                                                                  #  VIRTUALLY ALL BANKS PRESENT UNDER ANY SUPER-BANK SETTING, WITH THE RESTRICTION THAT PROGRAMS IN HIGH BANKS
044398,000030:                                                                                                  #  (BIT15 OF FBANK = 1) DO NOT REFER TO LOWBANKS, AND VICE-VERSA. THE INTERPRETER DOES NOT SWITCH SUPERBANKS.
044399,000031:                                                                                                  #  E-BANK SWITCHING OCCURS WHENEVER GENERAL ERASABLE (100 - 3777) IS ADDRESSED.
044400,000032: 
044401,000033:    6051                                           BLOCK    03                                    
044402,000034: 
044403,000035:    6051                                           COUNT*   $$/INTER                              
044404,000036:    6051           00003        INTPRET            RELINT                                         
044405,000037:    6052           00006                           EXTEND                                         #  SET LOC TO THE WORD FOLLOWING THE TC.
044406,000038:    6053           22164                           QXCH     LOC                                   
044407,000039: 
044408,000040:    6054           30006                 +2        CA       BBANK                                 #  INTERPRETIVE BRANCHES FINISH HERE.
044409,000041:    6055           54165                           TS       BANKSET                               
044410,000042:    6056           74735                           MASK     BIT15                                 #  GET 15TH BIT FOR INDEXABLE ADDRESSES.
044411,000043:    6057           54115                           TS       INTBIT15                              
044412,000044: 
044413,000045:    6060           54023                           TS       EDOP                                  #  MAKE SURE NO INSTRUCTIONS LEFT OVER
044414,000046: 
044415,000047:    6061           16102                           TCF      NEWOPS                                #  PICK UP OP CODE PAIR AND BEGIN.
044416,000048: 
044417,000049: 
044418,000050:    6062           22006        INTRSM             LXCH     BBANK                                 #  RESUME SUSPENDED INTERPRETIVE JOB
044419,000051:    6063           16054                           TCF      INTPRET    +3                         
044420,000052:                                                                                                  #           DLOAD LOADS MPAC, MPAC +1, LEAVING ZERO IN MPAC +2.
044421,000053: 
044422,000054:    6064           00006        DLOAD              EXTEND                                         
044423,000055:    6065           50116                           INDEX    ADDRWD                                
044424,000056:    6066           30001                           DCA      0                                     #  LOAD DP C(C(ADDRWD)) INTO MPAC,MPAX +1
044425,000057:    6067           52155        SLOAD2             DXCH     MPAC                                  
044426,000058:    6070           34755                           CAF      ZERO                                  #  ZERO MPAC +2
044427,000059: 

Page 994

044429,000061:                                                                                                  #           AT THE END OF MOST INSTRUCTIONS, CONTROL IS GIVEN TO DANZIG TO DISPATCH THE NEXT OPERATION.
044430,000062: 
044431,000063:    6071           54156                           TS       MPAC       +2                         #  AND DECLARE DP MODE
044432,000064: 
044433,000065:    6072           54163        NEWMODE            TS       MODE                                  #  PROLOGUE FOR MODE-CHANGING INSTRUCTIONS.
044434,000066: 
044435,000067:    6073           30165        DANZIG             CA       BANKSET                               #  SET BBANK BEFORE TESTING NEWJOB SO THAT
044436,000068:    6074           54006                           TS       BBANK                                 #  IT MAY BE SAVED DIRECTLY BY CHANJOB.
044437,000069: 
044438,000070:    6075           10023        NOIBNKSW           CCS      EDOP                                  #  SEE IF AN ORDER CODE IS LEFT OVER FROM
044439,000071:    6076           16111                           TCF      OPJUMP                                #  THE LAST PAIR RETRIEVED. IF SO, EXECUTE.
044440,000072:                                                                                                  #  EDOP IS SET TO ZERO ON ITS RE-EDITING.
044441,000073: 
044442,000074:    6077           10067                           CCS      NEWJOB                                #  SEE IF A JOB OF HIGHER PRIORITY IS
044443,000075:    6100           15126                           TCF      CHANG2                                #  PRESENT, AND IF SO, CHANGE JOBS.
044444,000076: 
044445,000077:    6101           24164                           INCR     LOC                                   #  ADVANCE THE LOCATION COUNTER.
044446,000078:                                                                                                  #           ITRACE (1) REFERS TO "NEWOPS".
044447,000079:    6102           50164        NEWOPS             INDEX    LOC                                   #  ENTRY TO BEGIN BY PICKING OP CODE PAIR.
044448,000080:    6103           30000                           CA       0                                     #  MAY BE AN OPCODE PAIR OR A STORE CODE.
044449,000081:    6104           10000                           CCS      A                                     #  TEST SIGN AND GET DABS(A).
044450,000082:    6105           16374                           TCF      DOSTORE                               #  PROCESS STORE CODE.
044451,000083: 
044452,000084:    6106           00177        LOW7               OCT      177                                   
044453,000085: 
044454,000086:    6107           54023                           TS       EDOP                                  #  OP CODE PAIR. LEAVE THE OTHER IN EDOP
044455,000087:    6110           76106                           MASK     LOW7                                  #  WHERE  CCS EDOP  WILL HONOR IT NEXT.
044456,000088: 
044457,000089:    6111           54020        OPJUMP             TS       CYR                                   #  LOWWD ENTERS HERE IF A RIGHT-HAND OP
044458,000090:    6112           10020                           CCS      CYR                                   #  CODE IS TO BE PROCESSED. TEST PREFICES.
044459,000091:    6113           16261                           TCF      OPJUMP2                               #  TEST SECOND PREFIX BIT.
044460,000092: 
044461,000093:    6114           16755                           TCF      EXIT                                  #  +0 OP CODE IS EXIT.
044462,000094: 

Page 995

044464,000096:                                                                                                  #           PROCESS ADDRESSES WHICH MAY BE DIRECT, INDEXED, OR REFERENCE THE PUSHDOWN LIST.
044465,000097: 
044466,000098:    6115           74753        ADDRESS            MASK     BIT1                                  #  SEE IF ADDRESS IS INDEXED. CYR CONTAINED
044467,000099:    6116           10000                           CCS      A                                     #  400XX, SO BIT 1 IS NOW AS IT WAS IN CYR.
044468,000100:    6117           16160                           TCF      INDEX                                 #  FORM INDEXED ADDRESS.
044469,000101: 
044470,000102:    6120           50164        DIRADRES           INDEX    LOC                                   #  LOOK AHEAD TO NEXT WORD TO SEE IF
044471,000103:    6121           40001        OCT40001           CS       1                                     #  ADDRESS IS GIVEN.
044472,000104:    6122           10000                           CCS      A                                     
044473,000105:    6123           16227                           TCF      PUSHUP                                #  IF NOT.
044474,000106: 
044475,000107:    6124           77773        NEG4               DEC      -4         B-14                       
044476,000108: 
044477,000109:    6125           24164                           INCR     LOC                                   #  IF SO, TO SHOW WE PICKED UP A WORD.
044478,000110:    6126           54116                           TS       ADDRWD                                
044479,000111: 

Page 996

044481,000113:                                                                                                  #           FINAL DIGESTION OF DIRECT ADDRESSES OF OP CODES WITH 01 PREFIX IS DONE HERE. IN EACH CASE, THE
044482,000114:                                                                                                  #  REQUIRED 12-BIT SUB-ADDRESS IS LEFT IN ADDRWD, WITH ANY REQUIRED E OR F BANK SWITCHING DONE. ADDRESSES LESS
044483,000115:                                                                                                  #  THAN 45D ARE TAKEN TO BE RELATIVE TO THE WORK AREA. THE OP CODE IS NOW IN BITS 1-5 OF CYR WITH BIT 14 = 1.
044484,000116: 
044485,000117:    6127           66263                           AD       -ENDVAC                               #  SEE IF ADDRESS RELATIVE TO WORK AREA.
044486,000118:    6130           10000                           CCS      A                                     
044487,000119:    6131           67755                           AD       -ENDERAS                              #  IF NOT, SEE IF IN GENERAL ERASABLE.
044488,000120:    6132           16137                           TCF      IERASTST                              
044489,000121: 
044490,000122:    6133           30120        NETZERO            CA       FIXLOC                                #  IF SO, LEAVE THE MODIFIED ADDRESS IN
044491,000123:    6134           26116                           ADS      ADDRWD                                #  ADDRWD AND DISPATCH.
044492,000124:    6135           50020        ITR15              INDEX    CYR                                   #  THIS INDEX MAKES THE NEXT INSTRUCTION
044493,000125:    6136           76305                           7        INDJUMP    -1                         #  TCF INDJUMP + OP, EDITING CYR.
044494,000126: 
044495,000127:    6137           00006        IERASTST           EXTEND                                         
044496,000128:    6140           66150                           BZMF     GEADDR                                #  GO PROCESS GENERAL-ERASABLE ADDRESS.
044497,000129: 
044498,000130:    6141           75012                           MASK     LOW10                                 #  FIXED BANK ADDRESS. RESTORE AND ADD B15.
044499,000131:    6142           65012                           AD       LOW10                                 #  SWITCH BANKS AND LEAVE SUBADDRESS IN
044500,000132:    6143           56116                           XCH      ADDRWD                                #  ADDRWD FOR OPERAND RETRIEVAL. (THIS
044501,000133:    6144           60115                           AD       INTBIT15                              #  METHOD PRECLUDES USE OF THE LAST
044502,000134:    6145           54004                           TS       FBANK                                 #  LOCATION IN EACH FBANK.)
044503,000135:    6146           50020        ITR12              INDEX    CYR                                   
044504,000136:    6147           76305                           7        INDJUMP    -1                         
044505,000137: 
044506,000138:    6150           74357        GEADDR             MASK     LOW8                                  
044507,000139:    6151           65007                           AD       OCT1400                               
044508,000140:    6152           56116                           XCH      ADDRWD                                
044509,000141:    6153           54003                           TS       EBANK                                 
044510,000142:    6154           50020        ITR10              INDEX    CYR                                   
044511,000143:    6155           76305                           7        INDJUMP    -1                         
044512,000144: 

Page 997

044514,000146:                                                                                                  #           THE FOLLOWING ROUTINE PROCESSES INTERPRETIVE INDEXED ADDRESSES. AN INTERPRETER INDEX REGISTER MAY
044515,000147:                                                                                                  #  CONTAIN THE ADDRESS OF ANY ERASABLE REGISTER (0-42 BEING RELATIVE TO THE VAC AREA) OR ANY INTERPRETIVE PROGRAM
044516,000148:                                                                                                  #  BANK, OR ANY INTEGER IN THAT RANGE.
044517,000149: 
044518,000150:    6156           37745        DODLOAD*           CAF      DLOAD*                                #  STODL* COMES HERE TO PROCESS LOAD ADR.
044519,000151:    6157           54020                           TS       CYR                                   #  (STOVL* ENTERS HERE).
044520,000152: 
044521,000153:    6160           30120        INDEX              CA       FIXLOC                                #  SET UP INDEX LOCATION.
044522,000154:    6161           54130                           TS       INDEXLOC                              
044523,000155:    6162           24164                           INCR     LOC                                   #  (ADDRESS ALWAYS GIVEN).
044524,000156:    6163           50164                           INDEX    LOC                                   
044525,000157:    6164           40000                           CS       0                                     
044526,000158:    6165           10000                           CCS      A                                     #  INDEX 2 IF ADDRESS STORED COMPLEMENTED.
044527,000159:    6166           24130                           INCR     INDEXLOC                              
044528,000160:    6167           16170                           NOOP                                           
044529,000161: 
044530,000162:    6170           54116                           TS       ADDRWD                                #  14 BIT ADDRESS TO ADDRWD.
044531,000163:    6171           77754                           MASK     HIGH4                                 #  IF ADDRESS GREATER THAN 2K, ADD INTBIT15
044532,000164:    6172           00006                           EXTEND                                         
044533,000165:    6173           16176                           BZF      INDEX2                                
044534,000166:    6174           30115                           CA       INTBIT15                              
044535,000167:    6175           26116                           ADS      ADDRWD                                
044536,000168: 
044537,000169:    6176           50130        INDEX2             INDEX    INDEXLOC                              
044538,000170:    6177           40046                           CS       X1                                    
044539,000171:    6200           26116                           ADS      ADDRWD                                #  DO AUGMENT, IGNORING AND CORRECTING OVF.
044540,000172: 
044541,000173:    6201           77756                           MASK     HIGH9                                 #  SEE IF ADDRESS IS IN WORK AREA.
044542,000174:    6202           00006                           EXTEND                                         
044543,000175:    6203           16216                           BZF      INDWORK                               
044544,000176:    6204           77754                           MASK     HIGH4                                 #  SEE IF IN FIXED BANK.
044545,000177:    6205           00006                           EXTEND                                         
044546,000178:    6206           16220                           BZF      INDERASE                              
044547,000179: 
044548,000180:    6207           30116                           CA       ADDRWD                                #  IN FIXED - SWITCH BANKS AND CREATE
044549,000181:    6210           54004                           TS       FBANK                                 #  SUB-ADDRESS.
044550,000182:    6211           75012                           MASK     LOW10                                 
044551,000183:    6212           64741                           AD       2K                                    
044552,000184:    6213           54116                           TS       ADDRWD                                
044553,000185:    6214           50020        ITR11              INDEX    CYR                                   
044554,000186:    6215           36305                           3        INDJUMP    -1                         
044555,000187: 
044556,000188:    6216           30120        INDWORK            CA       FIXLOC                                #  MAKE ADDRWD RELATIVE TO WORK AREA.
044557,000189:    6217           16224                           TCF      ITR13      -1                         
044558,000190: 
044559,000191:    6220           35007        INDERASE           CA       OCT1400                               
044560,000192:    6221           56116                           XCH      ADDRWD                                
044561,000193:    6222           54003                           TS       EBANK                                 
044562,000194:    6223           74357                           MASK     LOW8                                  
044563,000195:    6224           26116                 -1        ADS      ADDRWD                                

Page 998

044565,000197:    6225           50020        ITR13              INDEX    CYR                                   
044566,000198:    6226           36305                           3        INDJUMP    -1                         
044567,000199: 

Page 999

044569,000201:                                                                                                  #           PUSH-UP ROUTINES. WHEN NO OPERAND ADDRESS IS GIVEN, THE APPROPRIATE OPERAND IS TAKEN FROM THE PUSH-DOWN
044570,000202:                                                                                                  #  LIST. IN MOST CASES THE MODE OF THE RESULT (VECTOR OR SCALAR) OF THE LAST ARITHMETIC OPERATION PERFORMED
044571,000203:                                                                                                  #  IS THE SAME AS THE TYPE OF OPERAND DESIRED (ALL ADD/SUBTRACT ETC.). EXCEPTIONS TO THIS GENERAL RULE ARE LISTED
044572,000204:                                                                                                  #  BELOW (NOTE THAT IN EVERY CASE THE MODE REGISTER IS LEFT INTACT):
044573,000205: 
044574,000206:                                                                                                  #           1.  VXSC AND V/SC WANT THE OPPOSITE TYPE OF OPERAND, E.G., IF THE LAST OPERATION YIELDED A VECTOR
044575,000207:                                                                                                  #  RESULT, VXSC WANTS A SCALAR.
044576,000208: 
044577,000209:                                                                                                  #           2.  THE LOAD CODES SHOULD LOAD THE ACCUMULATOR INDEPENDENT OF THE RESULT OF THE LAST OPERATION. THIS
044578,000210:                                                                                                  #  INCLUDES VLOAD, DLOAD, TLOAD, PDDL, AND PDVL (NO PUSHUP WITH SLOAD).
044579,000211: 
044580,000212:                                                                                                  #           3.  SOME ARITHMETIC OPERATIONS REQUIRE A STANDARD TYPE OF OPERAND REGARDLESS OF THE PREVIOUS OPERATION.
044581,000213:                                                                                                  #  THIS INCLUDES SIGN WANTING DP AND TAD REQUIRING TP.
044582,000214: 
044583,000215:    6227           34360        PUSHUP             CAF      OCT23                                 #  IF THE LOW 5 BITS OF CYR ARE LESS THAN
044584,000216:    6230           70020                           MASK     CYR                                   #  20, THIS OP REQUIRES SPECIAL ATTENTION.
044585,000217:    6231           66234                           AD       -OCT10                                #  (NO -0).
044586,000218:    6232           10000                           CCS      A                                     
044587,000219:    6233           16245                           TCF      REGUP                                 #  FOR ALL CODES GREATER THAN OCT 7.
044588,000220: 
044589,000221:    6234           77767        -OCT10             OCT      -10                                   
044590,000222: 
044591,000223:    6235           66124                           AD       NEG4                                  #  WE NOW HAVE 7 - OP CODE(MOD4). SEE IF
044592,000224:    6236           10000                           CCS      A                                     #  THE OP CODE (MOD4) IS THREE (REVERSE).
044593,000225:    6237           50000                           INDEX    A                                     #  NO - THE MODE IS DEFINITE. PICK UP THE
044594,000226:    6240           46256                           CS       NO.WDS                                
044595,000227:    6241           16247                           TCF      REGUP      +2                         
044596,000228: 
044597,000229:    6242           50163                           INDEX    MODE                                  #  FOR VXSC AND V/SC WE WANT THE REQUIRED
044598,000230:    6243           46254                           CS       REVCNT                                #  PUSHLOC DECREMENT WITHOUT CHANGING THE
044599,000231:    6244           16247                           TCF      REGUP      +2                         #  MODE AT THIS TIME.
044600,000232: 
044601,000233:    6245           50163        REGUP              INDEX    MODE                                  #  MOST ALL OP CODES PUSHUP HERE.
044602,000234:    6246           46256                           CS       NO.WDS                                
044603,000235:    6247           26166                 +2        ADS      PUSHLOC                               
044604,000236:    6250           54116                           TS       ADDRWD                                
044605,000237:    6251           50020        ITR14              INDEX    CYR                                   
044606,000238:    6252           76305                           7        INDJUMP    -1                         #  (THE INDEX MAKES THIS A TCF.)
044607,000239: 
044608,000240:    6253           00002                           OCT      2                                     #  REVERSE PUSHUP DECREMENT. VECTOR TAKES 2
044609,000241:    6254           00006        REVCNT             OCT      6                                     #  WORDS, SCALAR TAKES 6.
044610,000242:    6255           00006                           OCT      6                                     
044611,000243:    6256           00002        NO.WDS             OCT      2                                     #  CONVENTIONAL DECREMENT IS 6 WORDS VECTOR
044612,000244:    6257           00003        OCTAL3             OCT      3                                     #  2 IN DP, AND 3 IN TP.
044613,000245:    6260           00006                           OCT      6                                     
044614,000246: 

Page 1000

044616,000248:                                                                                                  #           TEST THE SECOND PREFIX BIT TO SEE IF THIS IS A MISCELLANEOUS OR A UNARY/SHORT SHIFT OPERATION.
044617,000249: 
044618,000250:    6261           10020        OPJUMP2            CCS      CYR                                   #  TEST SECOND PREFIX BIT.
044619,000251:    6262           16275                           TCF      OPJUMP3                               #  TEST THIRD BIT TO SEE IF UNARY OR SHIFT.
044620,000252: 
044621,000253:    6263           77722        -ENDVAC            DEC      -45        B-14                       
044622,000254: 
044623,000255:                                                                                                  #           THE FOLLOWING ROUTINE PROCESSES ADDRESSES OF SUFFIX CLASS 10. THEY ARE BASICALLY WORK AREA ADDRESSES
044624,000256:                                                                                                  #  IN THE RANGE 0 - 52, ERASABLE ECADR CONSTANTS FROM 100 - 3777, AND FCADRS ABOVE THAT. ALL 15 BITS ARE AVAILABLE
044625,000257:                                                                                                  #  IN CONTRAST TO SUFFIX 1, IN WHICH ONLY THE LOW ORDER 14 ARE AVAILABLE.
044626,000258: 
044627,000259:    6264           24164        15BITADR           INCR     LOC                                   #  (ENTRY HERE FROM STCALL).
044628,000260:    6265           50164                           INDEX    LOC                                   #  PICK UP ADDRESS WORD.
044629,000261:    6266           30000                           CA       0                                     
044630,000262:    6267           54117                           TS       POLISH                                #  WE MAY NEED A SUBADDRESS LATER.
044631,000263: 
044632,000264:    6270           35013                           CAF      LOW7+2K                               #  THESE INSTRUCTIONS ARE IN BANK 1.
044633,000265:    6271           54004                           TS       FBANK                                 
044634,000266:    6272           70020                           MASK     CYR                                   
044635,000267:    6273           50000        ITR7               INDEX    A                                     
044636,000268:    6274           16346                           TCF      MISCJUMP                              
044637,000269: 

Page 1001

044639,000271:                                                                                                  #           COMPLETE THE DISPATCHING OF UNARY AND SHORT SHIFT OPERATIONS.
044640,000272: 
044641,000273:    6275           54004        OPJUMP3            TS       FBANK                                 #  CALL IN BANK 0 (BITS 11-15 OF A ARE 0.)
044642,000274:                                                                                                  #           ITRACE (6) REFERS TO "OPJUMP3".
044643,000275:    6276           10020                           CCS      CYR                                   #  TEST THIRD PREFIX BIT.
044644,000276:    6277           50000                           INDEX    A                                     #  THE DECREMENTED UNARY CODE IS IN BITS
044645,000277:    6300           12000                           TCF      UNAJUMP                               #  1-4 OF A (ZERO, EXIT, HAS BEEN DETECTED)
044646,000278: 
044647,000279:    6301           10163                           CCS      MODE                                  #  ITS A SHORT SHIFT CODE. SEE IF PRESENT
044648,000280:    6302           12017                           TCF      SHORTT                                #  SCALAR OR VECTOR.
044649,000281:    6303           12017                           TCF      SHORTT                                
044650,000282:    6304           12121                           TCF      SHORTV                                #  CALLS THE APPROPRIATE ROUTINE.
044651,000283: 
044652,000284:    6305     4350               FBANKMSK           EQUALS   BANKMASK                              
044653,000285:    6305           00122        LVBUF              ADRES    VBUF                                  
044654,000286: 

Page 1002

044656,000288:                                                                                                  #           THE FOLLOWING IS THE JUMP TABLE FOR OP CODES WHICH MAY HAVE INDEXABLE ADDRESSES OR MAY PUSH UP.
044657,000289: 
044658,000290:    6306           16517        INDJUMP            TCF      VLOAD                                 #  00 - LOAD MPAC WITH A VECTOR.
044659,000291:    6307           17103                           TCF      TAD                                   #  01 - TRIPLE PRECISION ADD TO MPAC.
044660,000292:    6310           17667                           TCF      SIGN                                  #  02 - COMPLEMENT MPAC (V OR SC) IF X NEG.
044661,000293:    6311           17413                           TCF      VXSC                                  #  03 - VECTOR TIMES SCALAR.
044662,000294:    6312           16715                           TCF      CGOTO                                 #  04 - COMPUTED GO TO.
044663,000295:    6313           16502                           TCF      TLOAD                                 #  05 - LOAD MPAC WITH TRIPLE PRECISION.
044664,000296:    6314           16064                           TCF      DLOAD                                 #  06 - LOAD MPAC WITH A DP SCALAR.
044665,000297:    6315           17636                           TCF      V/SC                                  #  07 - VECTOR DIVIDED BY SCALAR.
044666,000298: 
044667,000299:    6316           16513                           TCF      SLOAD                                 #  10 - LOAD MPAC IN SINGLE PRECISION.
044668,000300:    6317           16632                           TCF      SSP                                   #  11 - SET SINGLE PRECISION INTO X.
044669,000301:    6320           16535                           TCF      PDDL                                  #  12 - PUSH DOWN MPAC AND RE-LOAD IN DP.
044670,000302:    6321           17346                           TCF      MXV                                   #  13 - MATRIX POST-MULTIPLIED BY VECTOR.
044671,000303:    6322           16571                           TCF      PDVL                                  #  14 - PUSH DOWN AND VECTOR LOAD.
044672,000304:    6323           16640                           TCF      CCALL                                 #  15 - COMPUTED CALL.
044673,000305:    6324           17351                           TCF      VXM                                   #  16 - MATRIX PRE-MULTIPLIED BY VECTOR.
044674,000306:    6325           17630                           TCF      TSLC                                  #  17 - NORMALIZE MPAC (SCALAR ONLY).
044675,000307: 
044676,000308:    6326           17606                           TCF      DMPR                                  #  20 - DP MULTIPLY AND ROUND.
044677,000309:    6327           17611                           TCF      DDV                                   #  21 - DP DIVIDE BY.
044678,000310:    6330           17615                           TCF      BDDV                                  #  22 - DP DIVIDE INTO.
044679,000311:    6331           17633                           TCF      GSHIFT                                #  23 - GENERAL SHIFT INSTRUCTION.
044680,000312:    6332           16763                           TCF      VAD                                   #  24 - VECTOR ADD.
044681,000313:    6333           16761                           TCF      VSU                                   #  25 - VECTOR SUBTRACT.
044682,000314:    6334           17050                           TCF      BVSU                                  #  26 - VECTOR SUBTRACT FROM.
044683,000315:    6335           17343                           TCF      DOT                                   #  27 - VECTOR DOT PRODUCT.
044684,000316: 
044685,000317:    6336           17472                           TCF      VXV                                   #  30 - VECTOR CROSS PRODUCT.
044686,000318:    6337           17437                           TCF      VPROJ                                 #  31 - VECTOR PROJECTION.
044687,000319:    6340           17017                           TCF      DSU                                   #  32 - DP SUBTRACT.
044688,000320:    6341           17074                           TCF      BDSU                                  #  33 - DP SUBTRACT FROM.
044689,000321:    6342           17007                           TCF      DAD                                   #  34 - DP ADD.
044690,000322:    6343           16343                           TCF      +0                                    #  35 - AVAILABLE
044691,000323:    6344           17604                           TCF      DMP1                                  #  36 - DP MULTIPLY.
044692,000324:    6345           17625                           TCF      SETPD                                 #  37 - SET PUSH DOWN POINTER (DIRECT ONLY)
044693,000325: 
044694,000326:                                                                                                  #  CODES 10 AND 14 MUST NOT PUSH UP. CODE 04 MAY BE USED FOR VECTOR DECLARE BEFORE PUSHUP IF DESIRED.
044695,000327: 

Page 1003

044697,000329:                                                                                                  #           THE FOLLOWING JUMP TABLE APPLIES TO INDEX, BRANCH, AND MISCELLANEOUS INSTRUCTIONS.
044698,000330: 
044699,000331:    6346           12350        MISCJUMP           TCF      AXT                                   #  00 - ADDRESS TO INDEX TRUE.
044700,000332:    6347           12355                           TCF      AXC                                   #  01 - ADDRESS TO INDEX COMPLEMENTED.
044701,000333:    6350           12360                           TCF      LXA                                   #  02 - LOAD INDEX FROM ERASABLE.
044702,000334:    6351           12364                           TCF      LXC                                   #  03 - LOAD INDEX FROM COMPLEMENT OF ERAS.
044703,000335:    6352           12370                           TCF      SXA                                   #  04 - STORE INDEX IN ERASABLE.
044704,000336:    6353           12376                           TCF      XCHX                                  #  05 - EXCHANGE INDEX WITH ERASABLE.
044705,000337:    6354           12412                           TCF      INCR                                  #  06 - INCREMENT INDEX REGISTER.
044706,000338:    6355           12421                           TCF      TIX                                   #  07 - TRANSFER ON INDEX.
044707,000339: 
044708,000340:    6356           12404                           TCF      XAD                                   #  10 - INDEX REGISTER ADD FROM ERASABLE.
044709,000341:    6357           12415                           TCF      XSU                                   #  11 - INDEX SUBTRACT FROM ERASABLE.
044710,000342:    6360           12473                           TCF      BZE/GOTO                              #  12 - BRANCH ZERO AND GOTO.
044711,000343:    6361           12500                           TCF      BPL/BMN                               #  13 - BRANCH PLUS AND BRANCH MINUS.
044712,000344:    6362           12453                           TCF      RTB/BHIZ                              #  14 - RETURN TO BASIC AND BRANCH HI ZERO.
044713,000345:    6363           12513                           TCF      CALL/ITA                              #  15 - CALL AND STORE QPRET.
044714,000346:    6364           12522                           TCF      SW/                                   #  16 - SWITCH INSTRUCTIONS AND AVAILABLE.
044715,000347:    6365           12463                           TCF      BOV(B)                                #  17 - BRANCH ON OVERFLOW TO BASIC OR INT.
044716,000348: 

Page 1004

044718,000350:                                                                                                  #           THE FOLLOWING JUMP TABLE APPIES TO UNARY INSTRUCTIONS.
044719,000351: 
044720,000352:    6366                                           COUNT*   $$/INTER                              
044721,000353: 00,2000                                           BANK     0                                     #  00 - EXIT - DETECTED EARLIER.
044722,000354: 00,2000           13207        UNAJUMP            TCF      SQRT                                  #  01 - SQUARE ROOT.
044723,000355: 00,2001           13530                           TCF      SINE                                  #  02 - SIN.
044724,000356: 00,2002           13517                           TCF      COSINE                                #  03 - COS.
044725,000357: 00,2003           13610                           TCF      ARCSIN                                #  04 - ARC SIN.
044726,000358: 00,2004           13612                           TCF      ARCCOS                                #  05 - ARC COS.
044727,000359: 00,2005           13174                           TCF      DSQ                                   #  06 - DP SQUARE.
044728,000360: 00,2006           12116                           TCF      ROUND                                 #  07 - ROUND TO DP.
044729,000361: 
044730,000362: 00,2007           17702                           TCF      COMP                                  #  10 - COMPLEMENT VECTOR OR SCALAR.
044731,000363: 00,2010           13232                           TCF      VDEF                                  #  11 - VECTOR DEFINE.
044732,000364: 00,2011           13023                           TCF      UNIT                                  #  12 - UNIT VECTOR.
044733,000365: 00,2012           13176                           TCF      ABVALABS                              #  13 - LENGTH OF VECTOR OR MAG OF SCALAR.
044734,000366: 00,2013           13245                           TCF      VSQ                                   #  14 - SQUARE OF LENGTH OF VECTOR.
044735,000367: 00,2014           16366                           TCF      STADR                                 #  15 - PUSH UP ON STORE CODE.
044736,000368: 00,2015           13274                           TCF      RVQ                                   #  16 - RETURN VIA QPRET.
044737,000369: 00,2016           13247                           TCF      PUSH                                  #  17 - PUSH MPAC DOWN.
044738,000370: 

Page 1005

044740,000372:                                                                                                  #  SECTION 2  LOAD AND STORE PACKAGE.
044741,000373: 
044742,000374:                                                                                                  #           A SET OF EIGHT STORE CODES IS PROVIDED AS THE PRIMARY METHOD OF STORING THE MULTI-PURPOSE
044743,000375:                                                                                                  #  ACCUMULATOR (MPAC). IF IN THE DANZIG SECTION LOC REFERS TO AN ALGEBRAICALLY POSITIVE WORD, IT IS TAKEN AS A 
044744,000376:                                                                                                  #  STORE CODE WITH A CORRESPONDING ERASABLE ADDRESS. MOST OF THESE CODES ARE TWO ADDRESS, SPECIFYING THAT THE WORD
044745,000377:                                                                                                  #  FOLLOWING THE STORE CODE IS TO BE USED AS AN ADDRESS FROM WHICH TO RE-LOAD MPAC. FOUR OPTIONS ARE AVAILABLE:
044746,000378: 
044747,000379:                                                                                                  #           1. STORE               STORE MPAC. THE E ADDRESS MAY BE INDEXED.
044748,000380:                                                                                                  #           2. STODL               STORE MPAC AND RE-LOAD IT IN DP WITH THE NEXT ADDRESS (THE LOAD MAY BE INDEXED).
044749,000381:                                                                                                  #           3. STOVL               STORE MPAC AND RE-LOAD A VECTOR (AS ABOVE).
044750,000382:                                                                                                  #           4. STCALL              STORE AND DO A CALL (BOTH ADDRESSES MUST BE DIRECT HERE).
044751,000383: 
044752,000384:                                                                                                  #           STODL AND STOVL WILL TAKE FROM THE PUSH-DOWN LIST IF NO LOAD ADDRESS IS GIVEN.
044753,000385: 
044754,000386:    6366                                           BLOCK    3                                     
044755,000387: 
044756,000388:    6366                                           COUNT*   $$/INTER                              
044757,000389:    6366           30165        STADR              CA       BANKSET                               #  THE STADR CODE (PUSHUP UP ON STORE
044758,000390:    6367           54004                           TS       FBANK                                 #  ADDRESS) ENTERS HERE.
044759,000391:    6370           24164                           INCR     LOC                                   
044760,000392:    6371           50164        ITR1               INDEX    LOC                                   #  THE STORECODE WAS STORED COMPLEMENTED TO
044761,000393:    6372           40000                           CS       0                                     #  MAKE IT LOOK LIKE AN OPCODE PAIR.
044762,000394:    6373           67761                           AD       NEGONE                                #  (YUL CANT REMOVE 1 BECAUSE OF EARLY CCS)
044763,000395: 
044764,000396:    6374           54116        DOSTORE            TS       ADDRWD                                
044765,000397:    6375           74356                           MASK     LOW11                                 #  ENTRY FROM DISPATCHER. SAVE THE ERASABLE
044766,000398:    6376           56116                           XCH      ADDRWD                                #  ADDRESS AND JUMP ON THE STORE CODE NO.
044767,000399:    6377           77734                           MASK     B12T14                                
044768,000400:    6400           00006                           EXTEND                                         
044769,000401:    6401           74747                           MP       BIT5                                  #  EACH TRANSFER VECTOR ENTRY IS TWO WORDS.
044770,000402:    6402           50000        ITR0               INDEX    A                                     
044771,000403:    6403           16404                           TCF      STORJUMP                              
044772,000404: 

Page 1006

044774,000406:                                                                                                  #           STORE CODE JUMP TABLE. CALLS THE APPROPRIATE STORING ROUTINE AND EXITS TO DANZIG OR TO ADDRESS WITH
044775,000407:                                                                                                  #  A SUPPLIED OPERATION CODE.
044776,000408: 
044777,000409:                                                                                                  #           STORE STORE,1 AND STORE,2 RETURN TO DANZIG, THUS RESETTING THE EBANK TO ITS STATE AT INTPRET.
044778,000410: 
044779,000411:    6404           06434        STORJUMP           TC       STORE                                 #  STORE.
044780,000412:    6405           16073                           TCF      DANZIG                                #  PICK UP NEW OP CODE(S).
044781,000413:    6406           06426                           TC       STORE,1                               
044782,000414:    6407           16073                           TCF      DANZIG                                
044783,000415:    6410           06431                           TC       STORE,2                               
044784,000416:    6411           16073                           TCF      DANZIG                                
044785,000417: 
044786,000418:    6412           06434                           TC       STORE                                 #  STODL.
044787,000419:    6413           16472                           TCF      DODLOAD                               
044788,000420: 
044789,000421:    6414           06434                           TC       STORE                                 #  STODL WITH INDEXED LOAD ADDRESS.
044790,000422:    6415           16156                           TCF      DODLOAD*                              
044791,000423: 
044792,000424:    6416           06434                           TC       STORE                                 #  STOVL.
044793,000425:    6417           16475                           TCF      DOVLOAD                               
044794,000426: 
044795,000427:    6420           06434                           TC       STORE                                 #  STOVL WITH INDEXED LOAD ADDRESS.
044796,000428:    6421           16500                           TCF      DOVLOAD*                              
044797,000429:    6422           06434                           TC       STORE                                 #  STOTC.
044798,000430:    6423           34766                           CAF      CALLCODE                              
044799,000431:    6424           54020                           TS       CYR                                   
044800,000432:    6425           16264                           TCF      15BITADR                              #  GET A 15 BIT ADDRESS.
044801,000433: 

Page 1007

044803,000435:                                                                                                  #           STORE CODE ADDRESS PROCESSOR.
044804,000436: 
044805,000437:    6426           50120        STORE,1            INDEX    FIXLOC                                
044806,000438:    6427           40046                           CS       X1                                    
044807,000439:    6430           16433                           TCF      PRESTORE                              
044808,000440: 
044809,000441:    6431           50120        STORE,2            INDEX    FIXLOC                                
044810,000442:    6432           40047                           CS       X2                                    
044811,000443:    6433           26116        PRESTORE           ADS      ADDRWD                                #  RESULTANT ADDRESS IS IN ERASABLE.
044812,000444: 
044813,000445:    6434           40116        STORE              CS       ADDRWD                                
044814,000446:    6435           64772                           AD       DEC45                                 
044815,000447:    6436           10000                           CCS      A                                     #  DOES THE ADDRESS POINT TO THE WORK AREA?
044816,000448:    6437           30120                           CA       FIXLOC                                #  YES.
044817,000449:    6440           16445                           TCF      AHEAD5                                
044818,000450:    6441           35007                           CA       OCT1400                               #  NO.  SET EBANK & MAKE UP SUBADDRESS.
044819,000451:    6442           56116                           XCH      ADDRWD                                
044820,000452:    6443           54003                           TS       EBANK                                 
044821,000453:    6444           74357                           MASK     LOW8                                  
044822,000454:    6445           26116        AHEAD5             ADS      ADDRWD                                
044823,000455: 

Page 1008

044825,000457:                                                                                                  #           STORING ROUTINES. STORE DP, TP, OR VECTOR AS INDICATED BY MODE.
044826,000458: 
044827,000459:    6446           00006        STARTSTO           EXTEND                                         #  MPAC,+1 MUST BE STORED IN ANY EVENT.
044828,000460:                                                                                                  #           ITRACE (5) REFERS TO "STARTSTO".
044829,000461:    6447           30155                           DCA      MPAC                                  
044830,000462:    6450           50116                           INDEX    ADDRWD                                
044831,000463:    6451           52001                           DXCH     0                                     
044832,000464: 
044833,000465:    6452           10163                           CCS      MODE                                  
044834,000466:    6453           16466                           TCF      TSTORE                                
044835,000467:    6454           00002                           TC       Q                                     
044836,000468: 
044837,000469:    6455           00006        VSTORE             EXTEND                                         
044838,000470:    6456           30160                           DCA      MPAC       +3                         
044839,000471:    6457           50116                           INDEX    ADDRWD                                
044840,000472:    6460           52003                           DXCH     2                                     
044841,000473: 
044842,000474:    6461           00006                           EXTEND                                         
044843,000475:    6462           30162                           DCA      MPAC       +5                         
044844,000476:    6463           50116                           INDEX    ADDRWD                                
044845,000477:    6464           52005                           DXCH     4                                     
044846,000478:    6465           00002                           TC       Q                                     
044847,000479: 
044848,000480:    6466           30156        TSTORE             CA       MPAC       +2                         
044849,000481:    6467           50116                           INDEX    ADDRWD                                
044850,000482:    6470           54002                           TS       2                                     
044851,000483:    6471           00002                           TC       Q                                     
044852,000484: 

Page 1009

044854,000486:                                                                                                  #           ROUTINES TO BEGIN PROCESSING OF THE SECOND ADDRESS ASSOCIATED WITH ALL STORE-TYPE CODES EXCEPT STORE
044855,000487:                                                                                                  #  ITSELF.
044856,000488: 
044857,000489:    6472           37744        DODLOAD            CAF      DLOADCOD                              
044858,000490:    6473           54020                           TS       CYR                                   
044859,000491:    6474           16120                           TCF      DIRADRES                              #  GO GET A DIRECT ADDRESS.
044860,000492: 
044861,000493:    6475           34735        DOVLOAD            CAF      VLOADCOD                              
044862,000494:    6476           54020                           TS       CYR                                   
044863,000495:    6477           16120                           TCF      DIRADRES                              
044864,000496: 
044865,000497:    6500           36121        DOVLOAD*           CAF      VLOAD*                                
044866,000498:    6501           16157                           TCF      DODLOAD*   +1                         #  PROLOGUE TO INDEX ROUTINE.
044867,000499: 

Page 1010

044869,000501:                                                                                                  #           THE FOLLOWING LOAD INSTRUCTIONS ARE PROVIDED FOR LOADING THE MULTI-PURPOSE ACCUMULATOR MPAC.
044870,000502: 
044871,000503:    6502           50116        TLOAD              INDEX    ADDRWD                                
044872,000504:    6503           30002                           CA       2                                     #  LOAD A TRIPLE PRECISION ARGUMENT INTO
044873,000505:    6504           54156                           TS       MPAC       +2                         #  THE FIRST THREE MPAC REGISTERS, WITH THE
044874,000506:    6505           00006                           EXTEND                                         #  CONTENTS OF THE OTHER FOUR IRRELEVANT.
044875,000507:    6506           50116                           INDEX    ADDRWD                                
044876,000508:    6507           30001                           DCA      0                                     
044877,000509:    6510           52155                           DXCH     MPAC                                  
044878,000510:    6511           34753        TMODE              CAF      ONE                                   
044879,000511:    6512           16072                           TCF      NEWMODE                               #  DECLARE TRIPLE PRECISION MODE.
044880,000512: 
044881,000513:    6513           22007        SLOAD              ZL                                             #  LOAD A SINGLE PRECISION NUMBER INTO
044882,000514:    6514           50116                           INDEX    ADDRWD                                #  MPAC, SETTING MPAC+1,2 TO ZERO. THE
044883,000515:    6515           30000                           CA       0                                     #  CONTENTS OF THE REMAINING MPAC REGISTERS
044884,000516:    6516           16067                           TCF      SLOAD2                                #  ARE IRRELEVANT.
044885,000517: 
044886,000518:    6517           00006        VLOAD              EXTEND                                         #  LOAD A DOUBLE PRECISION VECTOR INTO
044887,000519:    6520           50116                           INDEX    ADDRWD                                #  MPAC,+1, MPAC+3,4, AND MPAC+5,6. THE
044888,000520:    6521           30001                           DCA      0                                     #  CONTENTS OF MPAC +2 ARE IRRELEVANT.
044889,000521:    6522           52155                           DXCH     MPAC                                  
044890,000522: 
044891,000523:    6523           00006        ENDVLOAD           EXTEND                                         #  PDVL COMES HERE TO FINISH UP FOR DP, TP.
044892,000524:    6524           50116                           INDEX    ADDRWD                                
044893,000525:    6525           30003                           DCA      2                                     
044894,000526:    6526           52160                           DXCH     MPAC       +3                         
044895,000527: 
044896,000528:    6527           00006                 +4        EXTEND                                         #  TPDVL FINISHES HERE.
044897,000529:    6530           50116                           INDEX    ADDRWD                                
044898,000530:    6531           30005                           DCA      4                                     
044899,000531:    6532           52162                           DXCH     MPAC       +5                         
044900,000532: 
044901,000533:    6533           44753        VMODE              CS       ONE                                   #  DECLARE VECTOR MODE.
044902,000534:    6534           16072                           TCF      NEWMODE                               
044903,000535: 

Page 1011

044905,000537:                                                                                                  #           THE FOLLOWING INSTRUCTIONS ARE PROVIDED FOR STORING OPERANDS IN THE PUSHDOWN LIST:
044906,000538: 
044907,000539:                                                                                                  #           1.  PUSH               PUSHDOWN AND NO LOAD.
044908,000540:                                                                                                  #           2.  PDDL               PUSHDOWN AND DOUBLE PRECISION LOAD.
044909,000541:                                                                                                  #           3.  PDVL               PUSHDOWN AND VECTOR LOAD.
044910,000542: 
044911,000543:    6535           00006        PDDL               EXTEND                                         
044912,000544:    6536           50116                           INDEX    ADDRWD                                #  LOAD MPAC,+1, PUSHING THE FORMER
044913,000545:    6537           30001                           DCA      0                                     #  CONTENTS DOWN.
044914,000546:    6540           52155                           DXCH     MPAC                                  
044915,000547:    6541           50166                           INDEX    PUSHLOC                               
044916,000548:    6542           52001                           DXCH     0                                     
044917,000549: 
044918,000550:    6543           50163                           INDEX    MODE                                  #  ADVANCE THE PUSHDOWN POINTER APPRO-
044919,000551:    6544           36256                           CAF      NO.WDS                                #  PRIATELY.
044920,000552:    6545           26166                           ADS      PUSHLOC                               
044921,000553: 
044922,000554:    6546           10163                           CCS      MODE                                  
044923,000555:    6547           16564                           TCF      ENDTPUSH                              
044924,000556:    6550           16562                           TCF      ENDDPUSH                              
044925,000557: 
044926,000558:    6551           54163                           TS       MODE                                  #  NOW DP.
044927,000559:    6552           54156        ENDVPUSH           TS       MPAC       +2                         
044928,000560:    6553           52160                           DXCH     MPAC       +3                         #  PUSH DOWN THE REST OF THE VECTOR HERE.
044929,000561:    6554           50166                           INDEX    PUSHLOC                               
044930,000562:    6555           51775                           DXCH     0          -4                         
044931,000563: 
044932,000564:    6556           52162                           DXCH     MPAC       +5                         
044933,000565:    6557           50166                           INDEX    PUSHLOC                               
044934,000566:    6560           51777                           DXCH     0          -2                         
044935,000567: 
044936,000568:    6561           16073                           TCF      DANZIG                                
044937,000569: 
044938,000570:    6562           54156        ENDDPUSH           TS       MPAC       +2                         #  SET MPAC +2 TO ZERO AND EXIT ON DP.
044939,000571:    6563           16073                           TCF      DANZIG                                
044940,000572: 
044941,000573:    6564           54163        ENDTPUSH           TS       MODE                                  
044942,000574:    6565           56156                           XCH      MPAC       +2                         #  ON TRIPLE, SET MPAC +2 TO ZERO, PUSHING
044943,000575:    6566           50166                 +2        INDEX    PUSHLOC                               #  DOWN THE OLD CONTENTS
044944,000576:    6567           53777                           TS       0          -1                         
044945,000577:    6570           16073                           TCF      DANZIG                                
044946,000578: 

Page 1012

044948,000580:                                                                                                  #           PDVL - PUSHDOWN AND VECTOR LOAD.
044949,000581: 
044950,000582:    6571           00006        PDVL               EXTEND                                         #  RELOAD MPAC AND PUSH DOWN ITS CONTENTS.
044951,000583:    6572           50116                           INDEX    ADDRWD                                
044952,000584:    6573           30001                           DCA      0                                     
044953,000585:    6574           52155                           DXCH     MPAC                                  
044954,000586:    6575           50166                           INDEX    PUSHLOC                               
044955,000587:    6576           52001                           DXCH     0                                     
044956,000588: 
044957,000589:    6577           50163                           INDEX    MODE                                  #  ADVANCE THE PUSHDOWN POINTER.
044958,000590:    6600           36256                           CAF      NO.WDS                                
044959,000591:    6601           26166                           ADS      PUSHLOC                               
044960,000592: 
044961,000593:    6602           10163                           CCS      MODE                                  #  TEST PAST MODE.
044962,000594:    6603           16622                           TCF      TPDVL                                 
044963,000595:    6604           16523                           TCF      ENDVLOAD                              #  JUST LOAD LAST FOUR REGISTERS ON DP.
044964,000596: 
044965,000597:    6605           00006        VPDVL              EXTEND                                         #  PUSHDOWN AND RE-LOAD LAST TWO COMPONENTS
044966,000598:    6606           50116                           INDEX    ADDRWD                                
044967,000599:    6607           30003                           DCA      2                                     
044968,000600:    6610           52160                           DXCH     MPAC       +3                         
044969,000601:    6611           50166                           INDEX    PUSHLOC                               
044970,000602:    6612           51775                           DXCH     0          -4                         
044971,000603: 
044972,000604:    6613           00006                           EXTEND                                         
044973,000605:    6614           50116                           INDEX    ADDRWD                                
044974,000606:    6615           30005                           DCA      4                                     
044975,000607:    6616           52162                           DXCH     MPAC       +5                         
044976,000608:    6617           50166                           INDEX    PUSHLOC                               
044977,000609:    6620           51777                           DXCH     0          -2                         
044978,000610: 
044979,000611:    6621           16073                           TCF      DANZIG                                
044980,000612: 
044981,000613:    6622           00006        TPDVL              EXTEND                                         #  ON TP, WE MUST LOAD THE Y COMPONENT
044982,000614:    6623           50116                           INDEX    ADDRWD                                #  BEFORE STORING MPAC +2 INCASE THIS IS A
044983,000615:    6624           30003                           DCA      2                                     #  PUSHUP.
044984,000616:    6625           52160                           DXCH     MPAC       +3                         
044985,000617: 
044986,000618:    6626           30156                           CA       MPAC       +2                         
044987,000619:    6627           50166                           INDEX    PUSHLOC                               #  IN DP.
044988,000620:    6630           53777                           TS       0          -1                         
044989,000621:    6631           16527                           TCF      ENDVLOAD   +4                         
044990,000622: 
044991,000623:                                                                                                  #           SSP (STORE SINGLE PRECISION) IS EXECUTED HERE.
044992,000624: 
044993,000625:    6632           24164        SSP                INCR     LOC                                   #  PICK UP THE WORD FOLLOWING THE GIVEN
044994,000626:    6633           50164                           INDEX    LOC                                   #  ADDRESS AND STORE IT AT X.
044995,000627:    6634           30000                           CA       0                                     
044996,000628:    6635           50116        STORE1             INDEX    ADDRWD                                #  SOME INDEX AND MISCELLANEOUS OPS END
044997,000629:    6636           54000                           TS       0                                     #  HERE.

Page 1013

044999,000631:    6637           16073                           TCF      DANZIG                                
045000,000632: 

Page 1014

045002,000634:                                                                                                  #  SEQUENCE CHANGING AND SUBROUTINE CALLING OPTIONS.
045003,000635: 
045004,000636:                                                                                                  #           THE FOLLOWING OPERATIONS ARE AVAILABLE FOR SEQUENCING CHANGING, BRANCHING, AND CALLING SUBROUTINES:
045005,000637: 
045006,000638:                                                                                                  #           1.  GOTO               GO TO.
045007,000639:                                                                                                  #           2.  CALL               CALL SUBROUTINE SETTING QPRET.
045008,000640:                                                                                                  #           3.  CGOTO              COMPUTED GO TO.
045009,000641:                                                                                                  #           4.  CCALL              COMPUTED CALL.
045010,000642:                                                                                                  #           7.  BPL                BRANCH IF MPAC POSITIVE OR ZERO.
045011,000643:                                                                                                  #           8.  BZE                BRANCH IF MPAC ZERO.
045012,000644:                                                                                                  #           9.  BMN                BRANCH IF MPAC NEGATIVE NON-ZERO.
045013,000645: 
045014,000646:    6640           24164        CCALL              INCR     LOC                                   #  MAINTAIN LOC FOR QPRET COMPUTATION.
045015,000647:    6641           50164                           INDEX    LOC                                   
045016,000648:    6642           30000                           CAF      0                                     #  GET BASE ADDRESS OF CADR LIST.
045017,000649:    6643           50116                           INDEX    ADDRWD                                
045018,000650:    6644           60000                           AD       0                                     #  ADD INCREMENT.
045019,000651:    6645           54004                           TS       FBANK                                 #  SELECT DESIRED CADR.
045020,000652:    6646           75012                           MASK     LOW10                                 
045021,000653:    6647           50000                           INDEX    A                                     
045022,000654:    6650           32000                           CAF      10000                                 
045023,000655:    6651           54117                           TS       POLISH                                
045024,000656: 
045025,000657:    6652           30165        CALL               CA       BANKSET                               #  FOR ANY OF THE CALL OPTIONS, MAKE UP THE
045026,000658:    6653           74350                           MASK     BANKMASK                              #  ADDRESS OF THE NEXT OP-CODE PAIR/STORE
045027,000659:    6654           64350                           AD       BANKMASK                              #  CODE AND LEAVE IT IN QPRET.  NOTE THAT
045028,000660:    6655           60164                           AD       LOC                                   #  BANKMASK = -(2000 - 1).
045029,000661:    6656           50120                           INDEX    FIXLOC                                
045030,000662:    6657           54052                           TS       QPRET                                 
045031,000663: 
045032,000664:    6660           30117        GOTO               CA       POLISH                                #  BASIC BRANCHING SEQUENCE.
045033,000665:    6661           77754                 +1        MASK     HIGH4                                 
045034,000666:    6662           00006                           EXTEND                                         
045035,000667:    6663           16674                           BZF      GOTOERS                               #  SEE IF ADDRESS POINTS TO FIXED OR ERAS.
045036,000668:    6664           30165                 +4        CA       BANKSET                               #  SET EBANK PART OF BBANK. NEXT, SET UP
045037,000669:    6665           54006                           TS       BBANK                                 #  FBANK. THE COMBINATION IS PICKED UP &
045038,000670:    6666           30117                           CA       POLISH                                #  PUT INTO BANKSET AT INTPRET +2.
045039,000671:    6667           54004                           TS       FBANK                                 
045040,000672:    6670           75012                           MASK     LOW10                                 
045041,000673:    6671           64741                           AD       2K                                    
045042,000674:    6672           54164                           TS       LOC                                   
045043,000675:    6673           16054                           TCF      INTPRET    +3                         
045044,000676: 
045045,000677:    6674  E3,1400                                  EBANK=   1400                                  #  SO YUL DOESN'T CUSS THE "CA 1400" BELOW.
045046,000678: 
045047,000679:    6674           30117        GOTOERS            CA       POLISH                                #  THE GIVEN ADDRESS IS IN ERASABLE - SEE
045048,000680:    6675           66263                           AD       -ENDVAC                               #  IF RELATIVE TO THE WORK AREA.
045049,000681:    6676           10000                           CCS      A                                     
045050,000682:    6677           30117                           CA       POLISH                                #  GENERAL ERASABLE.
045051,000683:    6700           16707                           TCF      GOTOGE                                
045052,000684: 

Page 1015

045054,000686:    6701           30120                           CA       FIXLOC                                #  WORK AREA.
045055,000687:    6702           60117                           AD       POLISH                                
045056,000688:    6703           50000                           INDEX    A                                     #  USE THE GIVEN ADDRESS AS THE ADDRESS OF
045057,000689:    6704           30000                           CA       0                                     #  THE BRANCH ADDRESS.
045058,000690:    6705           54117                           TS       POLISH                                
045059,000691:    6706           16661                           TCF      GOTO       +1                         #  ALLOWS ARBITRARY INDIRECTNESS LEVELS.
045060,000692: 
045061,000693:    6707           54003        GOTOGE             TS       EBANK                                 
045062,000694:    6710           74357                           MASK     LOW8                                  
045063,000695:    6711           50000                           INDEX    A                                     #  USE THE GIVEN ADDRESS AS THE ADDRESS OF
045064,000696:    6712           31400                           CA       1400                                  #  THE BRANCH ADDRESS.
045065,000697:    6713           54117                           TS       POLISH                                
045066,000698:    6714           16661                           TCF      GOTO       +1                         
045067,000699: 
045068,000700:    6715           50164        CGOTO              INDEX    LOC                                   #  COMPUTED GO TO. PICK UP ADDRESS OF CADR
045069,000701:    6716           30001                           CA       1                                     #  LIST.
045070,000702:    6717           50116                           INDEX    ADDRWD                                #  ADD MODIFIER.
045071,000703:    6720           60000                           AD       0                                     
045072,000704:    6721           54004                           TS       FBANK                                 #  SELECT GOTO ADDRESS.
045073,000705:    6722           75012                           MASK     LOW10                                 
045074,000706:    6723           50000                           INDEX    A                                     
045075,000707:    6724           32000                           CA       10000                                 
045076,000708:    6725           54117                           TS       POLISH                                
045077,000709:    6726           16661                           TCF      GOTO       +1                         #  WITH ADDRESS IN A.
045078,000710: 
045079,000711:    6727           30165        SWBRANCH           CA       BANKSET                               #  SWITCH INSTRUCTIONS WHICH ELECT TO
045080,000712:    6730           54004                           TS       FBANK                                 #  BRANCH COME HERE TO DO SO.
045081,000713:    6731           50164                           INDEX    LOC                                   
045082,000714:    6732           30001                           CA       1                                     
045083,000715:    6733           54117                           TS       POLISH                                
045084,000716:    6734           16661                           TCF      GOTO       +1                         
045085,000717: 

Page 1016

045087,000719:                                                                                                  #           TRIPLE PRECISION BRANCHING ROUTINE. IF CALLING TC IS AT L, RETURN IS AS FOLLOWS:
045088,000720: 
045089,000721:                                                                                                  #           L+1  IF MPAC IS GREATER THAN ZERO.
045090,000722:                                                                                                  #           L+2  IF MPAC IS EQUAL TO +0 OR -0.
045091,000723:                                                                                                  #           L+3  IF MPAC IS LESS THAN ZERO.
045092,000724: 
045093,000725:    6735           10154        BRANCH             CCS      MPAC                                  
045094,000726:    6736           00002                           TC       Q                                     
045095,000727:    6737           16741                           TCF      +2                                    #  ON ZERO.
045096,000728:    6740           16753                           TCF      NEG                                   
045097,000729: 
045098,000730:    6741           10155                           CCS      MPAC       +1                         
045099,000731:    6742           00002                           TC       Q                                     
045100,000732:    6743           16745                           TCF      +2                                    
045101,000733:    6744           16753                           TCF      NEG                                   
045102,000734: 
045103,000735:    6745           10156                           CCS      MPAC       +2                         
045104,000736:    6746           00002                           TC       Q                                     
045105,000737:    6747           16751                           TCF      +2                                    
045106,000738:    6750           16753                           TCF      NEG                                   
045107,000739: 
045108,000740:    6751           50002        Q+1                INDEX    Q                                     
045109,000741:    6752           00001                           TC       1                                     
045110,000742: 
045111,000743:    6753           50002        NEG                INDEX    Q                                     #  IF FIRST NON-ZERO REGISTER WAS NEGATIVE.
045112,000744:    6754           00002                           TC       2                                     
045113,000745: 
045114,000746: 
045115,000747:    6755     6753               Q+2                =        NEG                                   
045116,000748: 
045117,000749:                                                                                                  #           ITRACE (3) REFERS TO "EXIT".
045118,000750:    6755           30165        EXIT               CA       BANKSET                               #  RESTORE USER'S BANK SETTING, AND LEAVE
045119,000751:    6756           54006                           TS       BBANK                                 #  INTERPRETIVE MODE.
045120,000752:    6757           50164                           INDEX    LOC                                   
045121,000753:    6760           00001                           TC       1                                     
045122,000754: 

Page 1017

045124,000756:                                                                                                  #  SECTION 3 - ADD/SUBTRACT PACKAGE.
045125,000757: 
045126,000758:                                                                                                  #           THE FOLLOWING OPERATIONS ARE PROVIDED FOR ADDING TO AND SUBTRACTING FROM THE MULTI-PURPOSE ACCUMULATOR
045127,000759:                                                                                                  #  MPAC:
045128,000760: 
045129,000761:                                                                                                  #           1.  DAD                DOUBLE PRECISION ADD.
045130,000762:                                                                                                  #           2.  DSU                DOUBLE PRECISION SUBTRACT.
045131,000763:                                                                                                  #           3.  BDSU               DOUBLE PRECISION SUBTRACT FROM.
045132,000764: 
045133,000765:                                                                                                  #           4.  TAD                TRIPLE PRECISION ADD.
045134,000766: 
045135,000767:                                                                                                  #           5.  VAD                VECTOR ADD.
045136,000768:                                                                                                  #           6.  VSU                VECTOR SUBTRACT.
045137,000769:                                                                                                  #           7.  BVSU               VECTOR SUBTRACT FROM.
045138,000770: 
045139,000771:                                                                                                  #  THE INTERPRETIVE OVERFLOW INDICATOR OVFIND IS SET NON-ZERO IF OVERFLOW OCCURS IN ANY OF THE ABOVE.
045140,000772: 
045141,000773:    6761           34735        VSU                CAF      BIT15                                 #  CHANGES 0 TO DCS.
045142,000774:    6762           16764                           TCF      +2                                    
045143,000775: 
045144,000776:    6763           34355        VAD                CAF      PRIO30                                #  CHANGES 0 TO DCA.
045145,000777:    6764           26116                           ADS      ADDRWD                                
045146,000778:    6765           00006                           EXTEND                                         
045147,000779:    6766           50116                           INDEX    ADDRWD                                
045148,000780:    6767           00003                           READ     HISCALAR                              #  DCA  2   OR   DCS  2
045149,000781:    6770           20160                           DAS      MPAC       +3                         
045150,000782:    6771           00006                           EXTEND                                         #  CHECK OVERFLOW.
045151,000783:    6772           16774                           BZF      +2                                    
045152,000784:    6773           07026                           TC       OVERFLWY                              
045153,000785: 
045154,000786:    6774           00006                           EXTEND                                         
045155,000787:    6775           50116                           INDEX    ADDRWD                                
045156,000788:    6776           00005                           READ     CHAN5                                 #  DCA  4  OR  DCS  4
045157,000789:    6777           20162                           DAS      MPAC       +5                         
045158,000790:    7000           00006                           EXTEND                                         
045159,000791:    7001           17003                           BZF      +2                                    
045160,000792:    7002           07023                           TC       OVERFLWZ                              
045161,000793: 
045162,000794:    7003           00006                           EXTEND                                         
045163,000795:    7004           50116                           INDEX    ADDRWD                                
045164,000796:    7005           00001                           READ     LCHAN                                 #  DCA  0  OR  DCS  0
045165,000797:    7006           17012                           TCF      ENDVXV                                
045166,000798: 
045167,000799:    7007           00006        DAD                EXTEND                                         
045168,000800:    7010           50116                           INDEX    ADDRWD                                
045169,000801:    7011           30001                           DCA      0                                     
045170,000802:    7012           20155        ENDVXV             DAS      MPAC                                  #  VXV FINISHES HERE.
045171,000803:    7013           00006                           EXTEND                                         
045172,000804:    7014           16073                           BZF      DANZIG                                
045173,000805: 

Page 1018

045175,000807:    7015           07031        SETOVF             TC       OVERFLOW                              
045176,000808:    7016           16073                           TCF      DANZIG                                
045177,000809: 

Page 1019

045179,000811:    7017           00006        DSU                EXTEND                                         
045180,000812:    7020           50116                           INDEX    ADDRWD                                
045181,000813:    7021           40001                           DCS      0                                     
045182,000814:    7022           17012                           TCF      ENDVXV                                
045183,000815: 
045184,000816:    7023           54001        OVERFLWZ           TS       L                                     #  ENTRY FOR THIRD COMPONENT.
045185,000817:    7024           34756                           CAF      FIVE                                  
045186,000818:    7025           17030                           TCF      +3                                    
045187,000819: 
045188,000820:    7026           54001        OVERFLWY           TS       L                                     #  ENTRY FOR SECOND COMPONENT.
045189,000821:    7027           36257                           CAF      THREE                                 
045190,000822:    7030           56001                           XCH      L                                     
045191,000823: 
045192,000824:    7031           50000        OVERFLOW           INDEX    A                                     #  ENTRY FOR 1ST COMP OR DP (L=0).
045193,000825:    7032           44734                           CS       LIMITS                                #  PICK UP POSMAX OR NEGMAX.
045194,000826:    7033           54130                           TS       BUF                                   
045195,000827:    7034           00006                           EXTEND                                         
045196,000828:    7035           24000                           AUG      A                                     #  FORCE OVERFLOW.
045197,000829:    7036           50001                           INDEX    L                                     
045198,000830:    7037           26155                           ADS      MPAC       +1                         
045199,000831:    7040           54007                           TS       7                                     
045200,000832:    7041           34755                           CAF      ZERO                                  
045201,000833:    7042           60130                           AD       BUF                                   
045202,000834:    7043           50001                           INDEX    L                                     
045203,000835:    7044           26154                           ADS      MPAC                                  
045204,000836:    7045           54007                           TS       7                                     
045205,000837:    7046           00002                           TC       Q                                     #  NO OVERFLOW EXIT.
045206,000838:    7047           17164                           TCF      SETOVF2                               #  SET OVFIND AND EXIT.
045207,000839: 
045208,000840:    7050           00006        BVSU               EXTEND                                         
045209,000841:    7051           50116                           INDEX    ADDRWD                                
045210,000842:    7052           30003                           DCA      2                                     
045211,000843:    7053           52160                           DXCH     MPAC       +3                         
045212,000844:    7054           00006                           EXTEND                                         
045213,000845:    7055           40001                           DCOM                                           
045214,000846:    7056           20160                           DAS      MPAC       +3                         
045215,000847:    7057           00006                           EXTEND                                         
045216,000848:    7060           17062                           BZF      +2                                    
045217,000849:    7061           07026                           TC       OVERFLWY                              
045218,000850: 
045219,000851:    7062           00006                           EXTEND                                         
045220,000852:    7063           50116                           INDEX    ADDRWD                                
045221,000853:    7064           30005                           DCA      4                                     
045222,000854:    7065           52162                           DXCH     MPAC       +5                         
045223,000855:    7066           00006                           EXTEND                                         
045224,000856:    7067           40001                           DCOM                                           
045225,000857:    7070           20162                           DAS      MPAC       +5                         
045226,000858:    7071           00006                           EXTEND                                         
045227,000859:    7072           17074                           BZF      +2                                    
045228,000860:    7073           07023                           TC       OVERFLWZ                              
045229,000861: 

Page 1020

045231,000863:    7074           00006        BDSU               EXTEND                                         
045232,000864:    7075           50116                           INDEX    ADDRWD                                
045233,000865:    7076           30001                           DCA      0                                     
045234,000866:    7077           52155                           DXCH     MPAC                                  
045235,000867:    7100           00006                           EXTEND                                         
045236,000868:    7101           40001                           DCOM                                           
045237,000869:    7102           17012                           TCF      ENDVXV                                
045238,000870: 

Page 1021

045240,000872:                                                                                                  #           TRIPLE PRECISION ADD ROUTINE.
045241,000873: 
045242,000874:    7103           00006        TAD                EXTEND                                         
045243,000875:    7104           50116                           INDEX    ADDRWD                                
045244,000876:    7105           30002                           DCA      1                                     #  ADD MINOR PARTS FIRST.
045245,000877:    7106           20156                           DAS      MPAC       +1                         
045246,000878:    7107           50116                           INDEX    ADDRWD                                
045247,000879:    7110           60000                           AD       0                                     
045248,000880:    7111           60154                           AD       MPAC                                  
045249,000881:    7112           54154                           TS       MPAC                                  
045250,000882:    7113           16073                           TCF      DANZIG                                
045251,000883: 
045252,000884:    7114           17015                           TCF      SETOVF                                #  SET OVFIND IF SUCH OCCURS.
045253,000885: 

Page 1022

045255,000887:                                                                                                  #  ARITHMETIC SUBROUTINES REQUIRED IN FIXED-FIXED.
045256,000888: 
045257,000889:                                                                                                  #           1.  DMPSUB     DOUBLE PRECISION MULTIPLY. MULTIPLY THE CONTENTS OF MPAC,+1 BY THE DP WORD WHOSE ADDRESS
045258,000890:                                                                                                  #                          IS IN ADDRWD AND LEAVE A TRIPLE PRECISION RESULT IN MPAC.
045259,000891:                                                                                                  #           2.  ROUNDSUB   ROUND THE TRIPLE PRECISON CONTENTS OF MPAC TO DOUBLE PRECISION.
045260,000892:                                                                                                  #           3.  DOTSUB     TAKE THE DOT PRODUCT OF THE VECTOR IN MPAC AND THE VECTOR WHOSE ADDRESS IS IN ADDRWD
045261,000893:                                                                                                  #                          AND LEAVE THE TRIPLE PRECISION RESULT IN MPAC.
045262,000894:                                                                                                  #           4.  POLY       USING THE CONTENTS OF MPAC AS A DP ARGUMENT, EVALUATE THE POLYNOMIAL WHOSE DEGREE AND
045263,000895:                                                                                                  #                          COEFFICIENTS IMMEDIATELY FOLLOW THE TC POLY INSTRUCTION (SEE ROUTINE FOR DETAILS.)
045264,000896: 
045265,000897: 
045266,000898:    7115           50002        DMP                INDEX    Q                                     #  BASIC SUBROUTINE FOR USE BY PINBALL, ETC
045267,000899:    7116           30000                           CAF      0                                     #  ADRES OF ARGUMENT FOLLOWS  TC DMP  .
045268,000900:    7117           24002                           INCR     Q                                     
045269,000901:    7120           54116                 -1        TS       ADDRWD                                #  (PROLOGUE FOR SETTING ADDRWD.)
045270,000902: 
045271,000903:    7121           50116        DMPSUB             INDEX    ADDRWD                                #  GET MINOR PART OF OPERAND AT C(ADDRWD).
045272,000904:    7122           30001                           CA       1                                     
045273,000905:    7123           54156                           TS       MPAC       +2                         #  THIS WORKS FOR SQUARING MPAC AS WELL.
045274,000906:    7124           34755                           CAF      ZERO                                  #  SET MPAC +1 TO ZERO SO WE CAN ACCUMULATE
045275,000907:    7125           56155                           XCH      MPAC       +1                         #  THE PARTIAL PRODUCTS WITH DAS
045276,000908:    7126           54135                           TS       MPTEMP                                #  INSTRUCTIONS.
045277,000909:    7127           00006                           EXTEND                                         
045278,000910:    7130           70156                           MP       MPAC       +2                         #  MINOR OF MPAC X MINOR OF C(ADDRWD).
045279,000911: 
045280,000912:    7131           56156                           XCH      MPAC       +2                         #  DISCARD MINOR PART OF ABOVE RESULT AND
045281,000913:    7132           00006                           EXTEND                                         #  FORM MAJOR OF MPAC X MINOR OF C(ADDRWD).
045282,000914:    7133           70154                           MP       MPAC                                  
045283,000915:    7134           20156                           DAS      MPAC       +1                         #  GUARANTEED NO OVERFLOW.
045284,000916: 
045285,000917:    7135           50116                           INDEX    ADDRWD                                #  GET MAJOR PART OF ARGUMENT AT C(ADDRWD).
045286,000918:    7136           30000                           CA       0                                     
045287,000919:    7137           56135                           XCH      MPTEMP                                #  SAVE AND BRING OUT MINOR OF MPAC.
045288,000920:    7140           00006        DMPSUB2            EXTEND                                         
045289,000921:    7141           70135                           MP       MPTEMP                                #  MAJOR OF C(ADDRWD) X MINOR OF MPAC.
045290,000922:    7142           20156                           DAS      MPAC       +1                         #  ACCUMULATE, SETTING A TO NET OVERFLOW.
045291,000923: 
045292,000924:    7143           56154                           XCH      MPAC                                  #  SETTING MPAC TO 0 OR +-1.
045293,000925:    7144           00006                           EXTEND                                         
045294,000926:    7145           70135                           MP       MPTEMP                                #  MAJOR OF MPAC X MAJOR OF C(ADDRWD).
045295,000927:    7146           20155                           DAS      MPAC                                  #  GUARANTEED NO OVERFLOW.
045296,000928:    7147           00002                           TC       Q                                     #  49 MCT = .573 MS. INCLUDING RETURN.
045297,000929: 

Page 1023

045299,000931:                                                                                                  #           ROUND MPAC TO DOUBLE PRECISION, SETTING OVFIND ON THE RARE EVENT OF OVERFLOW.
045300,000932: 
045301,000933:    7150           34755        ROUNDSUB           CAF      ZERO                                  #  SET MPAC +2 = 0 FOR SCALARS AND CHANGE
045302,000934:    7151           54163                 +1        TS       MODE                                  #  MODE TO DP.
045303,000935: 
045304,000936:    7152           56156        VROUND             XCH      MPAC       +2                         #  BUT WE NEEDNT TAKE THE TIME FOR VECTORS.
045305,000937:    7153           60000                           DOUBLE                                         
045306,000938:    7154           54001                           TS       L                                     
045307,000939:    7155           00002                           TC       Q                                     
045308,000940: 
045309,000941:    7156           60155                           AD       MPAC       +1                         #  ADD ROUNDING BIT IF MPAC +2 WAS GREATER
045310,000942:    7157           54155                           TS       MPAC       +1                         #  THAN .5 IN MAGNITUDE.
045311,000943:    7160           00002                           TC       Q                                     
045312,000944: 
045313,000945:    7161           60154                           AD       MPAC                                  #  PROPAGATE INTERFLOW.
045314,000946:    7162           54154                           TS       MPAC                                  
045315,000947:    7163           00002                           TC       Q                                     
045316,000948: 
045317,000949:    7164           54121        SETOVF2            TS       OVFIND                                #  (RARE).
045318,000950:    7165           00002                           TC       Q                                     
045319,000951: 

Page 1024

045321,000953:                                                                                                  #           THE DOT PRODUCT SUBROUTINE USUALLY FORMS THE DOT PRODUCT OF THE VECTOR IN MPAC WITH A STANDARD SIX
045322,000954:                                                                                                  #  REGISTER VECTOR WHOSE ADDRESS IS IN ADDRWD. IN THIS CASE C(DOTINC) ARE SET TO 2. VXM, HOWEVER, SETS C(DOTINC) TO
045323,000955:                                                                                                  #  6 SO THAT DOTSUB DOTS MPAC WITH A COLUMN VECTOR OF THE MATRIX IN QUESTION IN THIS CASE.
045324,000956: 
045325,000957:    7166           34752        PREDOT             CAF      TWO                                   #  PROLOGUE TO SET DOTINC TO 2.
045326,000958:    7167           54136                           TS       DOTINC                                
045327,000959: 
045328,000960:    7170           00006        DOTSUB             EXTEND                                         
045329,000961:    7171           22137                           QXCH     DOTRET                                #  SAVE RETURN.
045330,000962:    7172           07121                           TC       DMPSUB                                #  DOT X COMPONENTS.
045331,000963:    7173           52160                           DXCH     MPAC       +3                         #  POSITION Y COMPONENT OF MPAC FOR
045332,000964:    7174           52155                           DXCH     MPAC                                  #  MULTIPLICATION WHILE SAVING RESULT IN
045333,000965:    7175           52131                           DXCH     BUF                                   #  THREE WORD BUFFER, BUF.
045334,000966:    7176           30156                           CA       MPAC       +2                         
045335,000967:    7177           54132                           TS       BUF        +2                         
045336,000968: 
045337,000969:    7200           30136                           CA       DOTINC                                #  ADVANCE ADDRWD TO Y COMPONENT OF
045338,000970:    7201           26116                           ADS      ADDRWD                                #  OTHER ARGUMENT.
045339,000971:    7202           07121                           TC       DMPSUB                                
045340,000972:    7203           52156                           DXCH     MPAC       +1                         #  ACCUMULATE PARTIAL PRODUCTS.
045341,000973:    7204           20132                           DAS      BUF        +1                         
045342,000974:    7205           60154                           AD       MPAC                                  
045343,000975:    7206           60130                           AD       BUF                                   
045344,000976:    7207           54130                           TS       BUF                                   
045345,000977:    7210           17212                           TCF      +2                                    
045346,000978:    7211           54121                           TS       OVFIND                                #  IF OVERFLOW OCCURS.
045347,000979: 
045348,000980:    7212           52162                           DXCH     MPAC       +5                         #  MULTIPLY Z COMPONENTS.
045349,000981:    7213           52155                           DXCH     MPAC                                  
045350,000982:    7214           30136                           CA       DOTINC                                
045351,000983:    7215           26116                           ADS      ADDRWD                                
045352,000984:    7216           07121                           TC       DMPSUB                                
045353,000985:    7217           52132        ENDDOT             DXCH     BUF        +1                         #  LEAVE FINAL ACCUMULATION IN MPAC.
045354,000986:    7220           20156                           DAS      MPAC       +1                         
045355,000987:    7221           60154                           AD       MPAC                                  
045356,000988:    7222           60130                           AD       BUF                                   
045357,000989:    7223           54154                           TS       MPAC                                  
045358,000990:    7224           00137                           TC       DOTRET                                
045359,000991: 
045360,000992:    7225           07031                           TC       OVERFLOW                              #  ON OVERFLOW HERE.
045361,000993:    7226           00137                           TC       DOTRET                                
045362,000994: 

Page 1025

045364,000996:                                                                                                  #  DOUBLE PRECISION POLYNOMIAL EVALUATOR
045365,000997: 
045366,000998:                                                                                                  #                                     N        N-1
045367,000999:                                                                                                  #           THIS ROUTINE EVALUATES A X  + A   X    + ... + A X + A  LEAVING THE DP RESULT IN MPAC ON EXIT.
045368,001000:                                                                                                  #                                   N      N-1              1     0
045369,001001: 
045370,001002:                                                                                                  #  THE ROUTINE HAS TWO ENTRIES
045371,001003: 
045372,001004:                                                                                                  #           1. ENTRY THRU POWRSERS. THE COEFFICIENTS MAY BE EITHER IN FIXED OR ERASABLE, THE CALL IS BY
045373,001005:                                                                                                  #              TC POWRSERS, AND THE RETURN IS TO LOC(TC POWRSERS)+1. THE ENTERING DATA MUST BE AS FOLLOWS
045374,001006: 
045375,001007:                                                                                                  #                                          A        SP     LOC-3           ADDRESS FOR REFERENCING COEF TABLE
045376,001008:                                                                                                  #                                          L        SP     N-1             N IS THE DEGREE OF THE POWER SERIES
045377,001009:                                                                                                  #                                          MPAC     DP     X               ARGUMENT
045378,001010: 
045379,001011:                                                                                                  #                                          LOC-2N   DP     A(0)
045380,001012:                                                                                                  #                                                   ...
045381,001013:                                                                                                  #                                          LOC      DP     A(N)
045382,001014: 
045383,001015:                                                                                                  #           2. ENTRY THRU POLY. THE CALL TO POLY AND THE ENTERING DATA MUST BE AS FOLLOWS
045384,001016: 
045385,001017:                                                                                                  #                                          MPAC     DP     X               ARGUMENT
045386,001018: 
045387,001019:                                                                                                  #                                          LOC      TC     POLY
045388,001020:                                                                                                  #                                          LOC+1    SP     N-1
045389,001021:                                                                                                  #                                          LOC+2    DP     A(0)
045390,001022:                                                                                                  #                                                   ...
045391,001023:                                                                                                  #                                          LOC+2N+2 DP     A(N)            RETURN IS TO LOC+2N+4
045392,001024: 
045393,001025:    7227           00006        POWRSERS           EXTEND                                         
045394,001026:    7230           22141                           QXCH     POLYRET                               #  RETURN ADDRESS
045395,001027:    7231           54117                           TS       POLISH                                #  POWER SERIES ADDRESS
045396,001028:    7232           22140                           LXCH     POLYCNT                               #  N-1 TO COUNTER
045397,001029:    7233           17244                           TCF      POLYCOM                               #  SKIP SET UP BY POLY
045398,001030: 
045399,001031:    7234           50002        POLY               INDEX    Q                                     
045400,001032:    7235           30000                           CAF      0                                     
045401,001033:    7236           54140                           TS       POLYCNT                               #  N-1 TO COUNTER
045402,001034:    7237           60000                           DOUBLE                                         
045403,001035:    7240           60002                           AD       Q                                     
045404,001036:    7241           54117                           TS       POLISH                                #  L(A(N))-3 TO POLISH
045405,001037:    7242           64756                           AD       FIVE                                  
045406,001038:    7243           54141                           TS       POLYRET                               #  STORE RETURN ADDRESS
045407,001039: 
045408,001040:    7244           36305        POLYCOM            CAF      LVBUF                                 #  INCOMING X WILL BE MOVED TO VBUF, SO
045409,001041:    7245           54116                           TS       ADDRWD                                #  SET ADDRWD SO DMPSUB WILL MPY BY VBUF.
045410,001042: 
045411,001043:    7246           00006                           EXTEND                                         
045412,001044:    7247           50117                           INDEX    POLISH                                
045413,001045:    7250           30004                           DCA      3                                     
045414,001046: 

Page 1026

045416,001048:    7251           52155                           DXCH     MPAC                                  #  LOAD A(N) INTO MPAC,
045417,001049:    7252           52123                           DXCH     VBUF                                  #  SAVING X IN VBUF
045418,001050:    7253           17257                           TCF      POLY2                                 
045419,001051: 
045420,001052:    7254           54140        POLYLOOP           TS       POLYCNT                               #  SAVE DECREMENTED LOOP COUNTER
045421,001053:    7255           44752                           CS       TWO                                   
045422,001054:    7256           26117                           ADS      POLISH                                #  REGRESS COEFFICIENT POINTER
045423,001055: 
045424,001056:    7257           07121        POLY2              TC       DMPSUB                                #  MULTIPLY BY X
045425,001057:    7260           00006                           EXTEND                                         
045426,001058:    7261           50117                           INDEX    POLISH                                
045427,001059:    7262           30002                           DCA      1                                     #  ADD IN NEXT COEFFICIENT
045428,001060:    7263           20155                           DAS      MPAC                                  #  USERS RESPONSIBILITY TO ASSURE NO OVFLOW
045429,001061: 
045430,001062:    7264           10140                           CCS      POLYCNT                               
045431,001063:    7265           17254                           TCF      POLYLOOP                              
045432,001064:    7266           00141                           TC       POLYRET                               #  RETURN CALLER
045433,001065: 

Page 1027

045435,001067:                                                                                                  #           MISCELLANEOUS MULTI-PRECISION ROUTINES REQUIRED IN FIXED-FIXED BUT NOT USED BY THE INTERPRETER.
045436,001068: 
045437,001069:    7267           34755        DPAGREE            CAF      ZERO                                  #  DOUBLE PRECISION ENTRY -
045438,001070:    7270           54156                           TS       MPAC       +2                         #  ZERO LOW-ORDER WORD
045439,001071: 
045440,001072:    7271           22002        TPAGREE            LXCH     Q                                     #  FORCE SIGN AGREEMENT AMONG THE TRIPLE
045441,001073:    7272           06735                           TC       BRANCH                                #  PRECISION CONTENTS OF MPAC.  RETURNING
045442,001074:    7273           17277                           TCF      ARG+                                  #  WITH SIGNUM OF THE INPUT IN A.
045443,001075:    7274           17317                           TCF      ARGZERO                               
045444,001076: 
045445,001077:    7275           44733                           CS       POSMAX                                #  IF NEGATIVE.
045446,001078:    7276           17300                           TCF      +2                                    
045447,001079: 
045448,001080:    7277           34733        ARG+               CAF      POSMAX                                
045449,001081:    7300           54002                           TS       Q                                     
045450,001082:    7301           00006                           EXTEND                                         
045451,001083:    7302           24000                           AUG      A                                     #  FORMS +-1.0.
045452,001084:    7303           60156                           AD       MPAC       +2                         
045453,001085:    7304           54156                           TS       MPAC       +2                         
045454,001086:    7305           34755                           CAF      ZERO                                  
045455,001087:    7306           60002                           AD       Q                                     
045456,001088:    7307           60155                           AD       MPAC       +1                         
045457,001089:    7310           54155                           TS       MPAC       +1                         
045458,001090:    7311           34755                           CAF      ZERO                                  
045459,001091:    7312           60002                           AD       Q                                     #  Q STILL HAS POSMAX OR NEGMAX IN IT.
045460,001092:    7313           60154                           AD       MPAC                                  
045461,001093:    7314           54154        ARGZERO2           TS       MPAC                                  #  ALWAYS SKIPPING UNLESS ARGZERO.
045462,001094:    7315           54155                           TS       MPAC       +1                         
045463,001095:    7316           00001                           TC       L                                     #  RETURN VIA L.
045464,001096: 
045465,001097:    7317           54156        ARGZERO            TS       MPAC       +2                         #  SET ALL THREE MPAC REGISTERS TO ZERO.
045466,001098:    7320           17314                           TCF      ARGZERO2                              
045467,001099: 
045468,001100:                                                                                                  #           SHORTMP MULTIPLIES THE TP CONTENTS OF MPAC BY THE SINGLE PRECISION NUMBER ARRIVING IN A.
045469,001101: 
045470,001102:    7321           54135        SHORTMP            TS       MPTEMP                                
045471,001103:    7322           00006                           EXTEND                                         
045472,001104:    7323           70156                           MP       MPAC       +2                         
045473,001105:    7324           54156                           TS       MPAC       +2                         
045474,001106:    7325           34755        SHORTMP2           CAF      ZERO                                  #  SO SUBSEQUENT DAS WILL WORK.
045475,001107:    7326           56155                           XCH      MPAC       +1                         
045476,001108:    7327           17140                           TCF      DMPSUB2                               
045477,001109: 

Page 1028

045479,001111:                                                                                                  #         DMPNSUB MULTIPLIES THE DP FRACTION ARRIVING IN MPAC BY THE SP
045480,001112:                                                                                                  #  INTEGER ARRIVING IN A.  THE DP PRODUCT DEPARTS BOTH IN MPAC AND IN
045481,001113:                                                                                                  #  A AND L.  NOTE THAT DMPNSUB NORMALLY INCREASES THE MAGNITUDE OF THE
045482,001114:                                                                                                  #  CONTENTS OF MPAC.  THE CUSTOMER MUST INSURE THAT B(A) X B(MPAC,MPAC+1)
045483,001115:                                                                                                  #  AND B(A) X B(MPAC) ARE LESS THAN 1 IN MAGNITUDE, WHERE B, AS IS OBVIOUS,
045484,001116:                                                                                                  #  INDICATES THE ARRIVING CONTENTS.
045485,001117: 
045486,001118:    7330           54135        DMPNSUB            TS       DMPNTEMP                              
045487,001119:    7331           00006                           EXTEND                                         
045488,001120:    7332           70155                           MP       MPAC       +1                         
045489,001121:    7333           52155                           DXCH     MPAC                                  #  LOW PRODUCT TO MPAC, HIGH FACTOR TO A
045490,001122:    7334           00006                           EXTEND                                         
045491,001123:    7335           70135                           MP       DMPNTEMP                              
045492,001124:    7336           30001                           CA       L                                     
045493,001125:    7337           26154                           ADS      MPAC                                  #  COMPLETING THE PRODUCT IN MPAC
045494,001126:    7340           00006                           EXTEND                                         
045495,001127:    7341           30155                           DCA      MPAC                                  #  BRINGING THE PRODUCT INTO A AND L
045496,001128:    7342           00002                           TC       Q                                     
045497,001129: 

Page 1029

045499,001131:                                                                                                  #  MISCELLANEOUS VECTOR OPERATIONS. INCLUDED HERE ARE THE FOLLOWING:
045500,001132: 
045501,001133:                                                                                                  #           1.  DOT                DP VECTOR DOT PRODUCT.
045502,001134:                                                                                                  #           2.  VXV                DP VECTOR CROSS PRODUCT.
045503,001135:                                                                                                  #           3.  VXSC               DP VECTOR TIMES SCALAR.
045504,001136:                                                                                                  #           4.  V/SC               DP VECTOR DIVIDED BY SCALAR.
045505,001137:                                                                                                  #           5.  VPROJ              DP VECTOR PROJECTION. ( (MPAC.X)MPAC ).
045506,001138:                                                                                                  #           6.  VXM                DP VECTOR POST-MULTIPLIED BY MATRIX.
045507,001139:                                                                                                  #           7.  MXV                DP VECTOR PRE-MULTIPLIED BY MATRIX.
045508,001140: 
045509,001141:    7343           07166        DOT                TC       PREDOT                                #  DO THE DOT PRODUCT AND EXIT, CHANGING
045510,001142:    7344           34755        DMODE              CAF      ZERO                                  #  THE MODE TO DP SCALAR.
045511,001143:    7345           16072                           TCF      NEWMODE                               
045512,001144: 
045513,001145: 
045514,001146:    7346           34752        MXV                CAF      TWO                                   #  SET UP MATINC AND DOTINC FOR ROW
045515,001147:    7347           54140                           TS       MATINC                                #  VECTORS.
045516,001148:    7350           17354                           TCF      VXM/MXV                               #  GO TO COMMON PORTION.
045517,001149: 
045518,001150:    7351           44363        VXM                CS       TEN                                   #  SET MATINC AND DOTINC TO REFER TO MATRIX
045519,001151:    7352           54140                           TS       MATINC                                #  AS THREE COLUMN VECTORS.
045520,001152:    7353           36254                           CAF      SIX                                   
045521,001153: 

Page 1030

045523,001155:                                                                                                  #           COMMON PORTION OF MXV AND VXM.
045524,001156: 
045525,001157:    7354           54136        VXM/MXV            TS       DOTINC                                
045526,001158:                                                                                                  #           ITRACE (2) REFERS TO "VXM/MXV".
045527,001159:    7355           07544                           TC       MPACVBUF                              #  SAVE VECTOR IN MPAC FOR FURTHER USE.
045528,001160: 
045529,001161:    7356           07170                           TC       DOTSUB                                #  GO DOT TO GET X COMPONENT OF ANSWER.
045530,001162:    7357           00006                           EXTEND                                         
045531,001163:    7360           30123                           DCA      VBUF                                  #  MOVE MPAC VECTOR BACK INTO MPAC, SAVING
045532,001164:    7361           52155                           DXCH     MPAC                                  #  NEW X COMPONENT IN BUF2.
045533,001165:    7362           52134                           DXCH     BUF2                                  
045534,001166:    7363           00006                           EXTEND                                         
045535,001167:    7364           30125                           DCA      VBUF       +2                         
045536,001168:    7365           52160                           DXCH     MPAC       +3                         
045537,001169:    7366           00006                           EXTEND                                         
045538,001170:    7367           30127                           DCA      VBUF       +4                         
045539,001171:    7370           52162                           DXCH     MPAC       +5                         
045540,001172:    7371           30140                           CA       MATINC                                #  INITIALIZE ADDRWD FOR NEXT DOT PRODUCT.
045541,001173:    7372           26116                           ADS      ADDRWD                                #  FORMS BASE ADDRESS OF NEXT COLUMN(ROW).
045542,001174: 
045543,001175:    7373           07170                           TC       DOTSUB                                
045544,001176:    7374           52123                           DXCH     VBUF                                  #  MOVE GIVEN VECTOR BACK TO MPAC, SAVING Y
045545,001177:    7375           52155                           DXCH     MPAC                                  #  COMPONENT OF ANSWER IN VBUF +2.
045546,001178:    7376           52125                           DXCH     VBUF       +2                         
045547,001179:    7377           52160                           DXCH     MPAC       +3                         
045548,001180:    7400           52127                           DXCH     VBUF       +4                         
045549,001181:    7401           52162                           DXCH     MPAC       +5                         
045550,001182:    7402           30140                           CA       MATINC                                #  FORM ADDRESS OF LAST COLUMN OR ROW.
045551,001183:    7403           26116                           ADS      ADDRWD                                
045552,001184: 
045553,001185:    7404           07170                           TC       DOTSUB                                
045554,001186:    7405           52134                           DXCH     BUF2                                  #  ANSWER NOW COMPLETE. PUT COMPONENTS INTO
045555,001187:    7406           52155                           DXCH     MPAC                                  #  PROPER MPAC REGISTERS.
045556,001188:    7407           52162                           DXCH     MPAC       +5                         
045557,001189:    7410           52125                           DXCH     VBUF       +2                         
045558,001190:    7411           52160                           DXCH     MPAC       +3                         
045559,001191:    7412           16073                           TCF      DANZIG                                #  EXIT.
045560,001192: 

Page 1031

045562,001194:                                                                                                  #           VXSC - VECTOR TIMES SCALAR.
045563,001195: 
045564,001196:    7413           10163        VXSC               CCS      MODE                                  #  TEST PRESENT MODE.
045565,001197:    7414           17442                           TCF      DVXSC                                 #  SEPARATE ROUTINE WHEN SCALAR IS IN MPAC.
045566,001198:    7415           17442                           TCF      DVXSC                                 
045567,001199: 
045568,001200:    7416           07121        VVXSC              TC       DMPSUB                                #  COMPUTE X COMPONENT
045569,001201:    7417           07152                           TC       VROUND                                #  AND ROUND IT.
045570,001202:    7420           52160                           DXCH     MPAC       +3                         #  PUT Y COMPONENT INTO MPAC SAVING MPAC IN
045571,001203:    7421           52155                           DXCH     MPAC                                  #  MPAC +3.
045572,001204:    7422           52160                           DXCH     MPAC       +3                         
045573,001205: 
045574,001206:    7423           07121                           TC       DMPSUB                                #  DO SAME FOR Y AND Z COMPONENTS.
045575,001207:    7424           07152                           TC       VROUND                                
045576,001208:    7425           52162                           DXCH     MPAC       +5                         
045577,001209:    7426           52155                           DXCH     MPAC                                  
045578,001210:    7427           52162                           DXCH     MPAC       +5                         
045579,001211: 
045580,001212:    7430           07121                           TC       DMPSUB                                
045581,001213:    7431           07152                           TC       VROUND                                
045582,001214:    7432           52155        VROTATEX           DXCH     MPAC                                  #  EXIT USED TO RESTORE MPAC AFTER THIS
045583,001215:    7433           52162                           DXCH     MPAC       +5                         #  TYPE OF ROTATION. CALLED BY VECTOR SHIFT
045584,001216:    7434           52160                           DXCH     MPAC       +3                         #  RIGHT, V/SC, ETC.
045585,001217:    7435           52155                           DXCH     MPAC                                  
045586,001218:    7436           16073                           TCF      DANZIG                                
045587,001219: 

Page 1032

045589,001221:                                                                                                  #           DP VECTOR PROJECTION ROUTINE.
045590,001222: 
045591,001223:    7437           07166        VPROJ              TC       PREDOT                                #  (MPAC.X)MPAC IS COMPUTED AND LEFT IN
045592,001224:    7440           44751                           CS       FOUR                                  #  MPAC. DO DOT AND FALL INTO DVXSC.
045593,001225:    7441           26116                           ADS      ADDRWD                                
045594,001226: 
045595,001227:                                                                                                  #           VXSC WHEN SCALAR ARRIVES IN MPAC AND VECTOR IS AT X.
045596,001228: 
045597,001229:    7442           00006        DVXSC              EXTEND                                         #  SAVE SCALAR IN MPAC +3 AND GET X
045598,001230:    7443           30155                           DCA      MPAC                                  #  COMPONENT OF ANSWER.
045599,001231:    7444           52160                           DXCH     MPAC       +3                         
045600,001232:    7445           07121                           TC       DMPSUB                                
045601,001233:    7446           07152                           TC       VROUND                                
045602,001234: 
045603,001235:    7447           34752                           CAF      TWO                                   #  ADVANCE ADDRWD TO Y COMPONENT OF X.
045604,001236:    7450           26116                           ADS      ADDRWD                                
045605,001237:    7451           00006                           EXTEND                                         
045606,001238:    7452           30160                           DCA      MPAC       +3                         #  PUT SCALAR BACK INTO MPAC AND SAVE
045607,001239:    7453           52155                           DXCH     MPAC                                  #  X RESULT IN MPAC +5.
045608,001240:    7454           52162                           DXCH     MPAC       +5                         
045609,001241:    7455           07121                           TC       DMPSUB                                
045610,001242:    7456           07152                           TC       VROUND                                
045611,001243: 
045612,001244:    7457           34752                           CAF      TWO                                   
045613,001245:    7460           26116                           ADS      ADDRWD                                #  TO Z COMPONENT.
045614,001246:    7461           52160                           DXCH     MPAC       +3                         #  BRING SCALAR BACK, PUTTING Y RESULT IN
045615,001247:    7462           52155                           DXCH     MPAC                                  #  THE PROPER PLACE.
045616,001248:    7463           52160                           DXCH     MPAC       +3                         
045617,001249:    7464           07121                           TC       DMPSUB                                
045618,001250:    7465           07152                           TC       VROUND                                
045619,001251: 
045620,001252:    7466           52155                           DXCH     MPAC                                  #  PUT Z COMPONENT IN PROPER PLACE, ALSO
045621,001253:    7467           52162                           DXCH     MPAC       +5                         #  POSITIONING X.
045622,001254:    7470           52155                           DXCH     MPAC                                  
045623,001255: 
045624,001256:    7471           16533                           TCF      VMODE                                 #  MODE HAS CHANGED TO VECTOR.
045625,001257: 

Page 1033

045627,001259:                                                                                                  #           THE VECTOR CROSS PRODUCT ROUTINE CALCULATES (X M -X M ,X M -X M ,X M -X M ) WHERE M IS THE VECTOR IN
045628,001260:                                                                                                  #                                                         3 2  2 3  1 3  3 1  2 1  1 2
045629,001261:                                                                                                  #  MPAC AND X THE VECTOR AT THE GIVEN ADDRESS.
045630,001262: 
045631,001263:    7472           00006        VXV                EXTEND                                         
045632,001264:    7473           30162                           DCA      MPAC       +5                         #  FORM UP M3X1, LEAVING M1 IN VBUF.
045633,001265:    7474           52155                           DXCH     MPAC                                  
045634,001266:    7475           52123                           DXCH     VBUF                                  
045635,001267:    7476           07121                           TC       DMPSUB                                #  BY X1.
045636,001268: 
045637,001269:    7477           00006                           EXTEND                                         
045638,001270:    7500           40160                           DCS      MPAC       +3                         #  CALCULATE -X1M2, SAVING X1M3 IN VBUF +2.
045639,001271:    7501           52155                           DXCH     MPAC                                  
045640,001272:    7502           52125                           DXCH     VBUF       +2                         
045641,001273:    7503           07121                           TC       DMPSUB                                
045642,001274: 
045643,001275:    7504           34752                           CAF      TWO                                   #  ADVANCE ADDRWD TO X2.
045644,001276:    7505           26116                           ADS      ADDRWD                                
045645,001277:    7506           00006                           EXTEND                                         
045646,001278:    7507           40162                           DCS      MPAC       +5                         #  PREPARE TO GET -X2M3, SAVING -X1M2 IN
045647,001279:    7510           52155                           DXCH     MPAC                                  #  MPAC +5.
045648,001280:    7511           52162                           DXCH     MPAC       +5                         
045649,001281:    7512           07121                           TC       DMPSUB                                
045650,001282: 
045651,001283:    7513           00006                           EXTEND                                         
045652,001284:    7514           30123                           DCA      VBUF                                  #  GET X2M1, SAVING -X2M3 IN VBUF +4.
045653,001285:    7515           52155                           DXCH     MPAC                                  
045654,001286:    7516           52127                           DXCH     VBUF       +4                         
045655,001287:    7517           07121                           TC       DMPSUB                                
045656,001288: 
045657,001289:    7520           34752                           CAF      TWO                                   #  ADVANCE ADDRWD TO X3.
045658,001290:    7521           26116                           ADS      ADDRWD                                
045659,001291:    7522           00006                           EXTEND                                         
045660,001292:    7523           40123                           DCS      VBUF                                  #  GET -X3M1, ADDING X2M1 TO MPAC +5 TO
045661,001293:    7524           52155                           DXCH     MPAC                                  #  COMPLETE THE Z COMPONENT OF THE ANSWER.
045662,001294:    7525           20162                           DAS      MPAC       +5                         
045663,001295: 
045664,001296:    7526           00006                           EXTEND                                         
045665,001297:    7527           17531                           BZF      +2                                    
045666,001298:    7530           07023                           TC       OVERFLWZ                              
045667,001299: 
045668,001300:    7531           07121                           TC       DMPSUB                                
045669,001301:    7532           52125                           DXCH     VBUF       +2                         #  MOVE X1M3 TO MPAC +3 SETTING UP FOR X3M2
045670,001302:    7533           52160                           DXCH     MPAC       +3                         #  AND ADD -X3M1 TO MPAC +3 TO COMPLETE THE
045671,001303:    7534           52155                           DXCH     MPAC                                  #  Y COMPONENT OF THE RESULT.
045672,001304:    7535           20160                           DAS      MPAC       +3                         
045673,001305: 
045674,001306:    7536           00006                           EXTEND                                         
045675,001307:    7537           17541                           BZF      +2                                    

Page 1034

045677,001309:    7540           07026                           TC       OVERFLWY                              
045678,001310: 
045679,001311:    7541           07121                           TC       DMPSUB                                
045680,001312:    7542           52127                           DXCH     VBUF       +4                         #  GO ADD -X2M3 TO X3M2 TO COMPLETE THE X
045681,001313:    7543           17012                           TCF      ENDVXV                                #  COMPONENT (TAIL END OF DAD).
045682,001314: 
045683,001315:                                                                                                  #           THE MPACVBUF SUBROUTINE SAVES THE VECTOR IN MPAC IN VBUF WITHOUT CLOBBERING MPAC.
045684,001316: 
045685,001317:    7544           00006        MPACVBUF           EXTEND                                         #  CALLED BY MXV, VXM, AND UNIT.
045686,001318:    7545           30155                           DCA      MPAC                                  
045687,001319:    7546           52123                           DXCH     VBUF                                  
045688,001320:    7547           00006                           EXTEND                                         
045689,001321:    7550           30160                           DCA      MPAC       +3                         
045690,001322:    7551           52125                           DXCH     VBUF       +2                         
045691,001323:    7552           00006                           EXTEND                                         
045692,001324:    7553           30162                           DCA      MPAC       +5                         
045693,001325:    7554           52127                           DXCH     VBUF       +4                         
045694,001326:    7555           00002                           TC       Q                                     #  RETURN TO CALLER.
045695,001327: 
045696,001328: 
045697,001329:                                                                                                  #           DOUBLE PRECISION SIGN AGREE ROUTINE. ARRIVE WITH INPUT IN A+L. OUTPUT IS IN A + L.
045698,001330: 
045699,001331:    7556           10000        ALSIGNAG           CCS      A                                     #  TEST UPPER PART.
045700,001332:    7557           17563                           TCF      UPPOS                                 #  IT IS POSITIVE
045701,001333:    7560           00002                           TC       Q                                     #  ZERO
045702,001334:    7561           17573                           TCF      UPNEG                                 #  NEGATIVE
045703,001335:    7562           00002                           TC       Q                                     #  ZERO
045704,001336: 
045705,001337:    7563           56001        UPPOS              XCH      L                                     #  SAVE DECREMENTED UPPER PART.
045706,001338:    7564           64736                           AD       HALF                                  
045707,001339:    7565           64736                           AD       HALF                                  
045708,001340:    7566           54000                           TS       A                                     #  SKIPS ON OVERFLOW
045709,001341:    7567           17571                           TCF      +2                                    
045710,001342:    7570           24001                           INCR     L                                     #  RESTORE UPPER TO ROIGINAL VALUE
045711,001343:    7571           56001                           XCH      L                                     #  SWAP A + L BACK.
045712,001344:    7572           00002                           TC       Q                                     
045713,001345: 
045714,001346:    7573           56001        UPNEG              XCH      L                                     #  SAVE COMPLEMENTED + DECREMENTED UPPER PT
045715,001347:    7574           64735                           AD       NEGMAX                                
045716,001348:    7575           67761                           AD       NEGONE                                
045717,001349:    7576           54000                           TS       A                                     
045718,001350:    7577           17601                           TCF      +2                                    #  DONT INCREMENT IF NO OVERFLOW.
045719,001351:    7600           24001                           INCR     L                                     
045720,001352:    7601           56001                           XCH      L                                     
045721,001353:    7602           40000                           COM                                            #  MAKE NEGATIVE AGAIN.
045722,001354:    7603           00002                           TC       Q                                     
045723,001355: 

Page 1035

045725,001357:                                                                                                  #           INTERPRETIVE INSTRUCTIONS WHOSE EXECUTION CONSISTS OF PRINCIPALLY CALLING SUBROUTINES.
045726,001358: 
045727,001359:    7604           07121        DMP1               TC       DMPSUB                                #  DMP INSTRUCTION.
045728,001360:    7605           16073                           TCF      DANZIG                                
045729,001361: 
045730,001362:    7606           07121        DMPR               TC       DMPSUB                                
045731,001363:    7607           07151                           TC       ROUNDSUB   +1                         #  (C(A) = +0).
045732,001364:    7610           16073                           TCF      DANZIG                                
045733,001365: 
045734,001366:    7611           00006        DDV                EXTEND                                         
045735,001367:    7612           50116                           INDEX    ADDRWD                                #  MOVE DIVIDEND INTO BUF.
045736,001368:    7613           30001                           DCA      0                                     
045737,001369:    7614           17621                           TCF      BDDV       +4                         
045738,001370: 
045739,001371:    7615           00006        BDDV               EXTEND                                         #  MOVE DIVISOR INTO MPAC SAVING MPAC, THE
045740,001372:    7616           50116                           INDEX    ADDRWD                                #  DIVIDEND, IN BUF.
045741,001373:    7617           30001                           DCA      0                                     
045742,001374:    7620           52155                           DXCH     MPAC                                  
045743,001375:    7621           52131                 +4        DXCH     BUF                                   
045744,001376:    7622           34755                           CAF      ZERO                                  #  DIVIDE ROUTINES IN BANK 0.
045745,001377:    7623           54004                           TS       FBANK                                 
045746,001378:    7624           12353                           TCF      DDV/BDDV                              
045747,001379: 
045748,001380:    7625           30116        SETPD              CA       ADDRWD                                #  MUST SET TO WORK AREA, OR EBANK TROUBLE.
045749,001381:    7626           54166                           TS       PUSHLOC                               
045750,001382:    7627           16075                           TCF      NOIBNKSW                              #  NO FBANK SWITCH REQUIRED.
045751,001383: 
045752,001384:    7630           34755        TSLC               CAF      ZERO                                  #  SHIFTING ROUTINES LOCATED IN BANK 00.
045753,001385:    7631           54004                           TS       FBANK                                 
045754,001386:    7632           12172                           TCF      TSLC2                                 
045755,001387: 
045756,001388:    7633           36106        GSHIFT             CAF      LOW7                                  #  USED AS MASK AT GENSHIFT. THIS PROCESSES
045757,001389:    7634           54004                           TS       FBANK                                 #  ANY SHIFT INSTRUCTION (EXCEPT TSLC) WITH
045758,001390:    7635           12214                           TCF      GENSHIFT                              #  AN ADDRESS (ROUTINES IN BANK 0).
045759,001391: 

Page 1036

045761,001393:                                                                                                  #           THE FOLLOWING IS THE PROLOGUE TO V/SC. IF THE PRESENT MODE IS VECTOR, IT SAVES THE SCALAR AT X IN BUF
045762,001394:                                                                                                  #  AND CALLS THE V/SC ROUTINE IN BANK 0. IF THE PRESENT MODE IS SCALAR, IT MOVES THE VECTOR AT X INTO MPAC, SAVING
045763,001395:                                                                                                  #  THE SCALAR IN MPAC IN BUF BEFORE CALLING THE V/SC ROUTINE IN BANK 0.
045764,001396: 
045765,001397:    7636           10163        V/SC               CCS      MODE                                  
045766,001398:    7637           17650                           TCF      DV/SC                                 #  MOVE VECTOR INTO MPAC.
045767,001399:    7640           17650                           TCF      DV/SC                                 
045768,001400: 
045769,001401:    7641           00006        VV/SC              EXTEND                                         
045770,001402:    7642           50116                           INDEX    ADDRWD                                
045771,001403:    7643           30001                           DCA      0                                     
045772,001404:    7644           52131        V/SC1              DXCH     BUF                                   #  IN BOTH CASES, VECTOR IS NOW IN MPAC AND
045773,001405:    7645           34755                           CAF      ZERO                                  #  SCALAR IN BUF.
045774,001406:    7646           54004                           TS       FBANK                                 
045775,001407:    7647           12654                           TCF      V/SC2                                 
045776,001408: 
045777,001409:    7650           00006        DV/SC              EXTEND                                         
045778,001410:    7651           50116                           INDEX    ADDRWD                                
045779,001411:    7652           30003                           DCA      2                                     
045780,001412:    7653           52160                           DXCH     MPAC       +3                         
045781,001413:    7654           00006                           EXTEND                                         
045782,001414:    7655           50116                           INDEX    ADDRWD                                
045783,001415:    7656           30005                           DCA      4                                     
045784,001416:    7657           52162                           DXCH     MPAC       +5                         
045785,001417: 
045786,001418:    7660           44753                           CS       ONE                                   #  CHANGE MODE TO VECTOR.
045787,001419:    7661           54163                           TS       MODE                                  
045788,001420: 
045789,001421:    7662           00006                           EXTEND                                         
045790,001422:    7663           50116                           INDEX    ADDRWD                                
045791,001423:    7664           30001                           DCA      0                                     
045792,001424:    7665           52155                           DXCH     MPAC                                  
045793,001425:    7666           17644                           TCF      V/SC1                                 #  FINISH PROLOGUE AT COMMON SECTION.
045794,001426: 

Page 1037

045796,001428:                                                                                                  #           SIGN AND COMPLEMENT INSTRUCTIONS.
045797,001429: 
045798,001430:    7667           50116        SIGN               INDEX    ADDRWD                                #  CALL COMP INSTRUCTION IF WORD AT X IS
045799,001431:    7670           10000                           CCS      0                                     #  NEGATIVE NON-ZERO.
045800,001432:    7671           16073                           TCF      DANZIG                                
045801,001433:    7672           17674                           TCF      +2                                    
045802,001434:    7673           17702                           TCF      COMP                                  #  DO THE COMPLEMENT.
045803,001435: 
045804,001436:    7674           50116                           INDEX    ADDRWD                                
045805,001437:    7675           10001        CCSL               CCS      1                                     
045806,001438:    7676           16073                           TCF      DANZIG                                
045807,001439:    7677           16073                           TCF      DANZIG                                
045808,001440:    7700           17702                           TCF      COMP                                  
045809,001441:    7701           16073                           TCF      DANZIG                                
045810,001442:    7702           00006        COMP               EXTEND                                         #  COMPLEMENT DP MPAC IN EVERY CASE.
045811,001443:    7703           40155                           DCS      MPAC                                  
045812,001444:    7704           52155                           DXCH     MPAC                                  
045813,001445: 
045814,001446:    7705           10163                           CCS      MODE                                  #  EITHER COMPLEMENT MPAC +3 OR THE REST OF
045815,001447:    7706           17717                           TCF      DCOMP                                 #  THE VECTOR ACCUMULATOR.
045816,001448:    7707           17717                           TCF      DCOMP                                 
045817,001449: 
045818,001450:    7710           00006                           EXTEND                                         #  VECTOR COMPLEMENT.
045819,001451:    7711           40160                           DCS      MPAC       +3                         
045820,001452:    7712           52160                           DXCH     MPAC       +3                         
045821,001453:    7713           00006                           EXTEND                                         
045822,001454:    7714           40162                           DCS      MPAC       +5                         
045823,001455:    7715           52162                           DXCH     MPAC       +5                         
045824,001456:    7716           16073                           TCF      DANZIG                                
045825,001457: 
045826,001458:    7717           40156        DCOMP              CS       MPAC       +2                         
045827,001459:    7720           54156                           TS       MPAC       +2                         
045828,001460:    7721           16073                           TCF      DANZIG                                
045829,001461: 

Page 1038

045831,001463:                                                                                                  #           THE FOLLOWING SHORT SHIFT CODES REQUIRE NO ADDRESS WORD:
045832,001464: 
045833,001465:                                                                                                  #           1.  SR1 TO SR4         SCALAR SHIFT RIGHT.
045834,001466:                                                                                                  #           2.  SR1R TO SR4R       SCALAR SHIFT RIGHT AND ROUND.
045835,001467:                                                                                                  #           3.  SL1 TO SL4         SCALAR SHIFT LEFT.
045836,001468:                                                                                                  #           4.  SL1R TO SL4R       SCALAR SHIFT LEFT AND ROUND.
045837,001469: 
045838,001470:                                                                                                  #           5.  VSR1 TO VSR8       VECTOR SHIFT RIGHT (ALWAYS ROUNDS).
045839,001471:                                                                                                  #           6.  VSL1 TO VSL8       VECTOR SHIFT LEFT (NEVER ROUNDS).
045840,001472: 
045841,001473:                                                                                                  #           THE FOLLOWING CODES REQUIRE AN ADDRESS WHICH MAY BE INDEXED:*
045842,001474: 
045843,001475:                                                                                                  #           1.  SR                 SCALAR SHIFT RIGHT.
045844,001476:                                                                                                  #           2.  SRR                SCALAR SHIFT RIGHT AND ROUND.
045845,001477:                                                                                                  #           3.  SL                 SCALAR SHIFT LEFT.
045846,001478:                                                                                                  #           4.  SLR                SCALAR SHIFT LEFT AND ROUND.
045847,001479: 
045848,001480:                                                                                                  #           5.  VSR                VECTOR SHIFT RIGHT.
045849,001481:                                                                                                  #           6.  VSL                VECTOR SHIFT LEFT.
045850,001482: 
045851,001483:                                                                                                  #  *  IF THE ADDRESS IS INDEXED, AND THE INDEX MODIFICATION RESULTS IN A NEGATIVE SHIFT COUNT, A SHIFT OF THE
045852,001484:                                                                                                  #  ABSOLUTE VALUE OF THE COUNT IS DONE IN THE OPPOSITE DIRECTION.
045853,001485: 
045854,001486: 
045855,001487: 00,2017                                           BANK     00                                    
045856,001488: 
045857,001489: 00,2017                                           COUNT*   $$/INTER                              
045858,001490: 00,2017           36254        SHORTT             CAF      SIX                                   #  SCALAR SHORT SHIFTS COME HERE. THE SHIFT
045859,001491: 00,2020           70020                           MASK     CYR                                   #  COUNT-1 IS NOW IN BITS 2-3 OF CYR. THE
045860,001492: 00,2021           54021                           TS       SR                                    #  ROUNDING BIT IS IN BIT1 AT THIS POINT.
045861,001493: 
045862,001494: 00,2022           10020                           CCS      CYR                                   #  SEE IF RIGHT OR LEFT SHIFT DESIRED.
045863,001495: 00,2023           12101                           TCF      TSSL                                  #  SHIFT LEFT.
045864,001496: 
045865,001497: 00,2024           00024        SRDDV              DEC      20         B-14                       #  MPTEMP SETTING FOR SR BEFORE DDV.
045866,001498: 
045867,001499: 00,2025           50021        TSSR               INDEX    SR                                    #  GET SHIFTING BIT.
045868,001500: 00,2026           34736                           CAF      BIT14                                 
045869,001501: 00,2027           54135                           TS       MPTEMP                                
045870,001502: 
045871,001503: 00,2030           10020                           CCS      CYR                                   #  SEE IF A ROUND IS DESIRED.
045872,001504: 00,2031           02050        RIGHTR             TC       MPACSRND                              #  YES - SHIFT RIGHT AND ROUND.
045873,001505: 00,2032           16072                           TCF      NEWMODE                               #  SET MODE TO DP (C(A) = 0).
045874,001506: 00,2033           30135        MPACSHR            CA       MPTEMP                                #  DO A TRIPLE PRECISION SHIFT RIGHT.
045875,001507: 00,2034           00006                           EXTEND                                         
045876,001508: 00,2035           70156                           MP       MPAC       +2                         
045877,001509: 00,2036           54156                 +3        TS       MPAC       +2                         #  (EXIT FROM SQRT AND ABVAL).
045878,001510: 00,2037           30135                           CA       MPTEMP                                
045879,001511: 00,2040           00006                           EXTEND                                         
045880,001512: 00,2041           70154                           MP       MPAC                                  #  SHIFT MAJOR PART INTO A,L AND PLACE IN

Page 1039

045882,001514: 00,2042           52155                           DXCH     MPAC                                  #  MPAC,+1.
045883,001515: 00,2043           30135                           CA       MPTEMP                                
045884,001516: 00,2044           00006                           EXTEND                                         
045885,001517: 00,2045           70001                           MP       L                                     #  ORIGINAL C(MPAC +1).
045886,001518: 00,2046           20156                           DAS      MPAC       +1                         #  GUARANTEED NO OVERFLOW.
045887,001519: 00,2047           16073                           TCF      DANZIG                                
045888,001520: 
045889,001521:                                                                                                  #           MPAC SHIFT RIGHT AND ROUND SUBROUTINES.
045890,001522: 
045891,001523: 00,2050           30156        MPACSRND           CA       MPAC       +2                         #  WE HAVE TO DO ALL THREE MULTIPLIES SINCE
045892,001524: 00,2051           00006                           EXTEND                                         #  MPAC +1 AND MPAC +2 MIGHT HAVE SIGN
045893,001525: 00,2052           70135                           MP       MPTEMP                                #  DISAGREEMENT WITH A SHIFT RIGHT OF 1.
045894,001526: 00,2053           56155                           XCH      MPAC       +1                         
045895,001527: 00,2054           00006                           EXTEND                                         
045896,001528: 00,2055           70135                           MP       MPTEMP                                
045897,001529: 00,2056           56155                           XCH      MPAC       +1                         #  TRIAL MINOR PART.
045898,001530: 00,2057           60001                           AD       L                                     
045899,001531: 
045900,001532: 00,2060           60000        VSHR2              DOUBLE                                         #  (FINISH VECTOR COMPONENT SHIFT RIGHT
045901,001533: 00,2061           54156                           TS       MPAC       +2                         #  AND ROUND.
045902,001534: 00,2062           12064                           TCF      +2                                    
045903,001535: 00,2063           26155                           ADS      MPAC       +1                         #  GUARANTEED NO OVERFLOW.
045904,001536: 
045905,001537: 00,2064           34755                           CAF      ZERO                                  
045906,001538: 00,2065           54156                           TS       MPAC       +2                         
045907,001539: 00,2066           56154                           XCH      MPAC                                  #  SETTING TO ZERO SO FOLLOWING DAS WORKS.
045908,001540: 00,2067           00006                           EXTEND                                         
045909,001541: 00,2070           70135                           MP       MPTEMP                                
045910,001542: 00,2071           20155                           DAS      MPAC                                  #  AGAIN NO OVERFLOW.
045911,001543: 00,2072           00002                           TC       Q                                     
045912,001544: 
045913,001545: 00,2073           30135        VSHRRND            CA       MPTEMP                                #  ENTRY TO SHIFT RIGHT AND ROUND MPAC WHEN
045914,001546: 00,2074           00006                           EXTEND                                         #  MPAC CONTAINS A VECTOR COMPONENT.
045915,001547: 00,2075           70155                           MP       MPAC       +1                         
045916,001548: 00,2076           54155                           TS       MPAC       +1                         
045917,001549: 00,2077           56001                           XCH      L                                     
045918,001550: 00,2100           12060                           TCF      VSHR2                                 #  GO ADD ONE IF NECESSARY AND FINISH.
045919,001551: 

Page 1040

045921,001553:                                                                                                  #           ROUTINE FOR SHORT SCALAR SHIFT LEFT (AND MAYBE ROUND).
045922,001554: 
045923,001555: 00,2101           30021        TSSL               CA       SR                                    #  GET SHIFT COUNT FOR SR.
045924,001556: 00,2102           54135                 +1        TS       MPTEMP                                
045925,001557: 
045926,001558: 00,2103           00006                 +2        EXTEND                                         #  ENTRY HERE FROM SL FOR SCALARS.
045927,001559: 00,2104           30156                           DCA      MPAC       +1                         #  SHIFTING LEFT ONE PLACE AT A TIME IS
045928,001560: 00,2105           20156                           DAS      MPAC       +1                         #  FASTER THAN DOING THE WHOLE SHIFT WITH
045929,001561: 00,2106           60154                           AD       MPAC                                  #  MULTIPLIES ASSUMING THAT FREQUENCY OF
045930,001562: 00,2107           60154                           AD       MPAC                                  #  SHIFT COUNTS GOES DOWN RAPIDLY AS A
045931,001563: 00,2110           54154                           TS       MPAC                                  #  FUNCTION OF THEIR MAGNITUDE.
045932,001564: 00,2111           12113                           TCF      +2                                    
045933,001565: 00,2112           54121                           TS       OVFIND                                #  OVERFLOW. (LEAVES OVERFLOW-CORRECTED
045934,001566:                                                                                                  #  RESULT ANYWAY).
045935,001567: 00,2113           10135                           CCS      MPTEMP                                #  LOOP ON DECREMENTED SHIFT COUNT.
045936,001568: 00,2114           12102                           TCF      TSSL       +1                         
045937,001569: 
045938,001570: 00,2115           10020                           CCS      CYR                                   #  SEE IF ROUND WANTED.
045939,001571: 00,2116           07150        ROUND              TC       ROUNDSUB                              #  YES - ROUND AND EXIT.
045940,001572: 00,2117           16073                           TCF      DANZIG                                #  SL LEAVES A ZERO IN CYR FOR NO ROUND.
045941,001573: 00,2120           16073                           TCF      DANZIG                                #  NO - EXIT IMMEDIATL
045942,001574: 

Page 1041

045944,001576:                                                                                                  #  VECTOR SHIFTING ROUTINES.
045945,001577: 
045946,001578: 00,2121           34757        SHORTV             CAF      LOW3                                  #  SAVE 3 BIT SHIFT COUNT - 1 WITHOUT
045947,001579: 00,2122           70020                           MASK     CYR                                   #  EDITING CYR.
045948,001580: 00,2123           54135                           TS       MPTEMP                                
045949,001581: 00,2124           10020                           CCS      CYR                                   #  SEE IF LEFT OR RIGHT SHIFT.
045950,001582: 00,2125           12145                           TCF      VSSL                                  #  VECTOR SHIFT LEFT.
045951,001583: 00,2126           00176        OCT176             OCT      176                                   #  USED IN PROCESSED SHIFTS WITH - COUNT.
045952,001584: 
045953,001585: 00,2127           50135        VSSR               INDEX    MPTEMP                                #  (ENTRY FROM SR). PICK UP SHIFTING BIT.
045954,001586: 00,2130           34736                           CAF      BIT14                                 #  MPTEMP CONTAINS THE SHIFT COUNT - 1.
045955,001587: 00,2131           54135                           TS       MPTEMP                                
045956,001588: 00,2132           02073                           TC       VSHRRND                               #  SHIFT X COMPONENT.
045957,001589: 
045958,001590: 00,2133           52155                           DXCH     MPAC                                  #  SWAP X AND Y COMPONENTS.
045959,001591: 00,2134           52160                           DXCH     MPAC       +3                         
045960,001592: 00,2135           52155                           DXCH     MPAC                                  
045961,001593: 00,2136           02073                           TC       VSHRRND                               #  SHIFT Y COMPONENT.
045962,001594: 
045963,001595: 00,2137           52155                           DXCH     MPAC                                  #  SWAP Y AND Z COMPONENTS.
045964,001596: 00,2140           52162                           DXCH     MPAC       +5                         
045965,001597: 00,2141           52155                           DXCH     MPAC                                  
045966,001598: 00,2142           02073                           TC       VSHRRND                               #  SHIFT Z COMPONENT.
045967,001599: 
045968,001600: 00,2143           17432                           TCF      VROTATEX                              #  RESTORE COMPONENTS TO PROPER PLACES.
045969,001601: 

Page 1042

045971,001603:                                                                                                  #  VECTOR SHIFT LEFT - DONE ONE PLACE AT A TIME.
045972,001604: 
045973,001605: 00,2144           54135                 -1        TS       MPTEMP                                #  SHIFTING LOOP.
045974,001606: 
045975,001607: 00,2145           00006        VSSL               EXTEND                                         
045976,001608: 00,2146           30155                           DCA      MPAC                                  
045977,001609: 00,2147           20155                           DAS      MPAC                                  
045978,001610: 00,2150           00006                           EXTEND                                         
045979,001611: 00,2151           12153                           BZF      +2                                    
045980,001612: 00,2152           07031                           TC       OVERFLOW                              
045981,001613: 
045982,001614: 00,2153           00006                           EXTEND                                         
045983,001615: 00,2154           30160                           DCA      MPAC       +3                         
045984,001616: 00,2155           20160                           DAS      MPAC       +3                         
045985,001617: 00,2156           00006                           EXTEND                                         
045986,001618: 00,2157           12161                           BZF      +2                                    
045987,001619: 00,2160           07026                           TC       OVERFLWY                              
045988,001620: 
045989,001621: 00,2161           00006                           EXTEND                                         
045990,001622: 00,2162           30162                           DCA      MPAC       +5                         
045991,001623: 00,2163           20162                           DAS      MPAC       +5                         
045992,001624: 00,2164           00006                           EXTEND                                         
045993,001625: 00,2165           12167                           BZF      +2                                    
045994,001626: 00,2166           07023                           TC       OVERFLWZ                              
045995,001627: 
045996,001628: 00,2167           10135                           CCS      MPTEMP                                #  LOOP ON DECREMENTED SHIFT COUNTER.
045997,001629: 00,2170           12144                           TCF      VSSL       -1                         
045998,001630: 00,2171           16073                           TCF      DANZIG                                #  EXIT.
045999,001631: 

Page 1043

046001,001633:                                                                                                  #           TSLC - TRIPLE SHIFT LEFT AND COUNT. SHIFTS MPAC LEFT UNTIL GREATER THAN .5 IN MAGNITUDE, LEAVING
046002,001634:                                                                                                  #  THE COMPLEMENT OF THE NUMBER OF SHIFTS REQUIRED IN X.
046003,001635: 
046004,001636: 00,2172           54135        TSLC2              TS       MPTEMP                                #  START BY ZEROING SHIFT COUNT (IN A NOW).
046005,001637: 00,2173           06735                           TC       BRANCH                                #  EXIT WITH NO SHIFTING IF ARGUMENT ZERO.
046006,001638: 00,2174           12176                           TCF      +2                                    
046007,001639: 00,2175           12212                           TCF      ENDTSLC                               #  STORES ZERO SHIFT COUNT IN THIS CASE.
046008,001640: 
046009,001641: 00,2176           07271                           TC       TPAGREE                               #  MAY CAUSE UPSHIFT OF ONE EXTRA PLACE.
046010,001642: 
046011,001643: 00,2177           30154                           CA       MPAC                                  #  BEGIN NORMALIZATION LOOP.
046012,001644: 00,2200           12207                           TCF      TSLCTEST                              
046013,001645: 
046014,001646: 00,2201           24135        TSLCLOOP           INCR     MPTEMP                                #  INCREMENT SHIFT COUNTER.
046015,001647: 00,2202           00006                           EXTEND                                         
046016,001648: 00,2203           30156                           DCA      MPAC       +1                         
046017,001649: 00,2204           20156                           DAS      MPAC       +1                         
046018,001650: 00,2205           60154                           AD       MPAC                                  
046019,001651: 00,2206           26154                           ADS      MPAC                                  
046020,001652: 00,2207           60000        TSLCTEST           DOUBLE                                         #  SEE IF (ANOTHER) SHIFT IS REQUIRED.
046021,001653: 00,2210           54000                           OVSK                                           
046022,001654: 00,2211           12201                           TCF      TSLCLOOP                              #  YES - INCREMENT COUNT AND SHIFT AGAIN.
046023,001655: 
046024,001656: 00,2212           40135        ENDTSLC            CS       MPTEMP                                
046025,001657: 00,2213           16635                           TCF      STORE1                                #  STORE SHIFT COUNT AND RETURN TO DANZIG.
046026,001658: 

Page 1044

046028,001660:                                                                                                  #           THE FOLLOWING ROUTINES PROCESSES THE GENERAL SHIFT INSTRUCTIONS SR, SRR, SL, AND SLR.
046029,001661:                                                                                                  #  THE GIVEN ADDRESS IS DECODED AS FOLLOWS:
046030,001662: 
046031,001663:                                                                                                  #           BITS 1-7    SHIFT COUNT (SUBADDRESS) LESS THAN 125 DECIMAL.
046032,001664:                                                                                                  #           BIT 8       PSEUDO SIGN BIT (DETECTS CHANGE IN SIGN IN INDEXED SHIFTS).
046033,001665:                                                                                                  #           BIT 9       0 FOR LEFT SHIFT, AND 1 FOR RIGHT SHIFT.
046034,001666:                                                                                                  #           BIT 10      1 FOR TERMINAL ROUND ON SCALAR SHIFTS, 0 OTHERWISE.
046035,001667:                                                                                                  #           BITS 11-13  0.
046036,001668:                                                                                                  #           BIT 14      1.
046037,001669:                                                                                                  #           BIT 15      0.
046038,001670: 
046039,001671:                                                                                                  #  THE ABOVE ENCODING IS DONE BY THE YUL SYSTEM.
046040,001672: 
046041,001673: 
046042,001674: 00,2214           70116        GENSHIFT           MASK     ADDRWD                                #  GET SHIFT COUNT, TESTING FOR ZERO.
046043,001675: 00,2215           10000                           CCS      A                                     #  (ARRIVES WITH C(A) = LOW7).
046044,001676: 00,2216           12224                           TCF      GENSHFT2                              #  IF NON-ZERO, PROCEED WITH DECREMENTED CT
046045,001677: 
046046,001678: 00,2217           34742                           CAF      BIT10                                 #  ZERO SHIFT COUNT. NO SHIFTS NEEDED BUT
046047,001679: 00,2220           70116                           MASK     ADDRWD                                #  WE MIGHT HAVE TO ROUND MPAC ON SLR AND
046048,001680: 00,2221           10000                           CCS      A                                     #  SRR (SCALAR ONLY).
046049,001681: 00,2222           07150                           TC       ROUNDSUB                              
046050,001682: 00,2223           16073                           TCF      DANZIG                                
046051,001683: 
046052,001684: 00,2224           54135        GENSHFT2           TS       MPTEMP                                #  DECREMENTED SHIFT COUNT TO MPTEMP.
046053,001685: 00,2225           34744                           CAF      BIT8                                  #  TEST MEANING OF LOW SEVEN BIT COUNT IN
046054,001686: 00,2226           00006                           EXTEND                                         #  MPTEMP NOW.
046055,001687: 00,2227           70116                           MP       ADDRWD                                
046056,001688: 00,2230           76257                           MASK     LOW2                                  #  JUMPS ON SHIFT DIRECTION (BIT8) AND
046057,001689: 00,2231           50000                           INDEX    A                                     
046058,001690: 00,2232           12233                           TCF      +1                                    #  ORIGINAL SHIFT DIRECTION (BIT 9).
046059,001691: 00,2233           12332                           TCF      RIGHT-                                #  NEGATIVE SHIFT COUNT FOR SL OR SLR.
046060,001692: 00,2234           12342                           TCF      LEFT                                  #  SL OR SLR.
046061,001693: 00,2235           12336                           TCF      LEFT-                                 #  NEGATIVE SHIFT COUNT WITH SR OR SRR.
046062,001694: 

Page 1045

046064,001696:                                                                                                  #           GENERAL SHIFT RIGHT.
046065,001697: 
046066,001698: 00,2236           10163        RIGHT              CCS      MODE                                  #  SEE IF VECTOR OR SCALAR.
046067,001699: 00,2237           12277                           TCF      GENSCR                                
046068,001700: 00,2240           12277                           TCF      GENSCR                                
046069,001701: 
046070,001702: 00,2241           30135                           CA       MPTEMP                                #  SEE IF SHIFT COUNT LESS THAN 14D.
046071,001703: 00,2242           63733        VRIGHT2            AD       NEG12                                 
046072,001704: 00,2243           00006                           EXTEND                                         
046073,001705: 00,2244           62127                           BZMF     VSSR                                  #  IF SO, BRANCH AND SHIFT IMMEDIATELY.
046074,001706: 
046075,001707: 00,2245           67761                           AD       NEGONE                                #  IF NOT, REDUCE MPTEMP BY A TOTAL OF 14,
046076,001708: 00,2246           54135                           TS       MPTEMP                                #  AND DO A SHIFT RIGHT AND ROUND BY 14.
046077,001709: 00,2247           34755                           CAF      ZERO                                  #  THE ROUND AT THIS STAGE MAY INTRODUCE A
046078,001710: 00,2250           54001                           TS       L                                     #  ONE BIT ERROR IN A SHIFT RIGHT 15D.
046079,001711: 00,2251           56154                           XCH      MPAC                                  
046080,001712: 00,2252           56155                           XCH      MPAC       +1                         
046081,001713: 00,2253           02272                           TC       SETROUND                              #  X COMPONENT NOW SHIFTED, SO MAKE UP THE
046082,001714: 00,2254           20155                           DAS      MPAC                                  #  ROUNDING QUANTITY (0 IN A AND 0 OR +-1
046083,001715:                                                                                                  #  IN L).
046084,001716: 00,2255           56157                           XCH      MPAC       +3                         #  REPEAT THE ABOVE PROCESS FOR Y AND Z.
046085,001717: 00,2256           56160                           XCH      MPAC       +4                         
046086,001718: 00,2257           02272                           TC       SETROUND                              
046087,001719: 00,2260           20160                           DAS      MPAC       +3                         #  NO OVERFLOW ON THESE ADDS.
046088,001720: 
046089,001721: 00,2261           56161                           XCH      MPAC       +5                         
046090,001722: 00,2262           56162                           XCH      MPAC       +6                         
046091,001723: 00,2263           02272                           TC       SETROUND                              
046092,001724: 00,2264           20162                           DAS      MPAC       +5                         
046093,001725: 
046094,001726: 00,2265           10135                           CCS      MPTEMP                                #  SEE IF DONE, DOING FINAL DECREMENT.
046095,001727: 00,2266           54135                           TS       MPTEMP                                
046096,001728: 00,2267           12242                           TCF      VRIGHT2                               
046097,001729: 00,2270           04604        BIASLO             DEC      .2974      B-1                        #  SQRT CONSTANT
046098,001730: 
046099,001731: 00,2271           16073                           TCF      DANZIG                                
046100,001732: 
046101,001733: 00,2272           60000        SETROUND           DOUBLE                                         #  MAKES UP ROUNDING QUANTITY FROM ARRIVING
046102,001734: 00,2273           54156                           TS       MPAC       +2                         #  C(A). L IS ZERO INITIALLY.
046103,001735: 00,2274           34755                           CAF      ZERO                                  
046104,001736: 00,2275           56001                           XCH      L                                     
046105,001737: 00,2276           00002                           TC       Q                                     #  RETURN AND DO THE DAS, RESETTING L TO 0.
046106,001738: 

Page 1046

046108,001740:                                                                                                  #           PROCESS SR AND SRR FOR SCALARS.
046109,001741: 
046110,001742: 00,2277           30135        GENSCR             CA       MPTEMP                                #  SEE IF THE ORIGINAL SHIFT COUNT WAS LESS
046111,001743: 00,2300           63733                 +1        AD       NEG12                                 #  THAN 14D.
046112,001744: 00,2301           00006                           EXTEND                                         
046113,001745: 00,2302           62322                           BZMF     DOSSHFT                               #  DO THE SHIFT IMMEDIATELY IF SO.
046114,001746: 
046115,001747: 00,2303           67761                 +4        AD       NEGONE                                #  IF NOT, DECREMENT SHIFT COUNT BY 14D AND
046116,001748: 00,2304           54135                           TS       MPTEMP                                #  SHIFT MPAC RIGHT 14 PLACES.
046117,001749: 00,2305           34755                           CAF      ZERO                                  
046118,001750: 00,2306           56154                           XCH      MPAC                                  
046119,001751: 00,2307           56155                           XCH      MPAC       +1                         
046120,001752: 00,2310           54156                           TS       MPAC       +2                         
046121,001753: 00,2311           10135                           CCS      MPTEMP                                #  SEE IF FINISHED, DO FINAL DECREMENT.
046122,001754: 00,2312           54135                           TS       MPTEMP                                
046123,001755: 00,2313           02300                           TC       GENSCR     +1                         
046124,001756: 00,2314           22650        SLOPEHI            DEC      .5884                                 #  SQRT CONSTANT.
046125,001757: 00,2315           34742                           CAF      BIT10                                 #  FINISHED WITH SHIFT. SEE IF ROUND
046126,001758: 00,2316           70116                           MASK     ADDRWD                                #  WANTED.
046127,001759: 00,2317           10000                           CCS      A                                     
046128,001760: 00,2320           07150                           TC       ROUNDSUB                              
046129,001761: 00,2321           16073                           TCF      DANZIG                                #  DO SO AND/OR EXIT.
046130,001762: 
046131,001763: 00,2322           50135        DOSSHFT            INDEX    MPTEMP                                #  PICK UP SHIFTING BIT.
046132,001764: 00,2323           34736                           CAF      BIT14                                 
046133,001765: 00,2324           54135                           TS       MPTEMP                                
046134,001766: 00,2325           34742                           CAF      BIT10                                 #  SEE IF TERMINAL ROUND DESIRED.
046135,001767: 00,2326           70116                           MASK     ADDRWD                                
046136,001768: 00,2327           10000                           CCS      A                                     
046137,001769: 00,2330           12031                           TCF      RIGHTR                                #  YES.
046138,001770: 00,2331           12033                           TCF      MPACSHR                               #  JUST SHIFT RIGHT.
046139,001771: 

Page 1047

046141,001773:                                                                                                  #           PROCESS THE RIGHT- (SL(R) WITH A NEGATIVE COUNT), LEFT-, AND LEFT OPTIONS.
046142,001774: 
046143,001775: 00,2332           40135        RIGHT-             CS       MPTEMP                                #  GET ABSOLUTE VALUE - 1 OF SHIFT COUNT
046144,001776: 00,2333           62126                           AD       OCT176                                #  UNDERSTANDING THAT BIT8 (PSEUDO-SIGN)
046145,001777: 00,2334           54135                           TS       MPTEMP                                #  WAS 1 INITIALLY.
046146,001778: 00,2335           12236                           TCF      RIGHT                                 #  DO NORMAL SHIFT RIGHT.
046147,001779: 
046148,001780: 00,2336           42126        LEFT-              CS       OCT176                                #  SAME PROLOGUE TO LEFT FOR INDEXED RIGHT
046149,001781: 00,2337           60135                           AD       MPTEMP                                #  SHIFTS WHOSE NET SHIFT COUNT IS NEGATIVE
046150,001782: 00,2340           40000                           COM                                            
046151,001783: 00,2341           54135                           TS       MPTEMP                                
046152,001784: 
046153,001785: 00,2342           10163        LEFT               CCS      MODE                                  #  SINCE LEFT SHIFTING IS SONE ONE PLACE AT
046154,001786: 00,2343           12346                           TCF      GENSCL                                #  A TIME, NO COMPARISON WITH 14 NEED BE
046155,001787: 00,2344           12346                           TCF      GENSCL                                #  DONE. FOR SCALARS, SEE IF TERMINAL ROUND
046156,001788: 00,2345           12145                           TCF      VSSL                                  #  DESIRED. FOR VECTORS, SHIFT IMMEDIATELY.
046157,001789: 
046158,001790: 00,2346           40116        GENSCL             CS       ADDRWD                                #  PUT ROUNDING BIT (BIT 10 OF ADDRWD)INTO
046159,001791: 00,2347           00006                           EXTEND                                         #  BIT 15 OF CYR WHERE THE ROUNDING BIT OF
046160,001792: 00,2350           74746                           MP       BIT6                                  #  A SHORT SHIFT LEFT WOULD BE
046161,001793: 00,2351           54020                           TS       CYR                                   
046162,001794: 00,2352           12103                           TCF      TSSL       +2                         #  DO THE SHIFT.
046163,001795: 

Page 1048

046165,001797:                                                                                                  #           SCALAR DIVISION INSTRUCTIONS, DDV AND BDDV, ARE EXECUTED HERE. AT THIS POINT, THE DIVIDEND IS IN MPAC
046166,001798:                                                                                                  #  AND THE DIVISOR IN BUF.
046167,001799: 
046168,001800: 00,2353           44753        DDV/BDDV           CS       ONE                                   #  INITIALIZATION.
046169,001801: 00,2354           54136                           TS       DVSIGN                                #  +-1 FOR POSITIVE QUOTIENT - -0 FOR NEG.
046170,001802: 00,2355           54137                           TS       DVNORMCT                              #  DIVIDEND NORMALIZATION COUNT.
046171,001803: 00,2356           54140                           TS       MAXDVSW                               #  NEAR-ONE DIVIDE FLAG.
046172,001804: 
046173,001805: 00,2357           10130                           CCS      BUF                                   #  FORCE BUF POSITIVE WITH THE MAJOR PART
046174,001806: 00,2360           12516                           TCF      BUFPOS                                #  NON-ZERO.
046175,001807: 00,2361           12363                           TCF      +2                                    
046176,001808: 00,2362           12531                           TCF      BUFNEG                                
046177,001809: 
046178,001810: 00,2363           54156        BUFZERO            TS       MPAC       +2                         #  ZERO THIS.
046179,001811: 00,2364           07271                           TC       TPAGREE                               #  FORCE SIGN AGREEMENT BEFORE OVERFLOW
046180,001812: 
046181,001813: 00,2365           10154                           CCS      MPAC                                  #  TEST TO SEE IF MPAC NON-ZERO.  (TOO BIG)
046182,001814: 00,2366           12414                           TCF      OVF+                                  #  MAJOR PART OF DIVIDEND IS POSITIVE NON-0
046183,001815: 00,2367           12371                           TCF      +2                                    
046184,001816: 00,2370           12413                           TCF      OVF+       -1                         #  MAJOR PART OF DIVIDEND IS NEG. NON-ZERO
046185,001817: 
046186,001818: 00,2371           56131                           XCH      BUF        +1                         #  SHIFT DIVIDEND AND DIVISOR LEFT 14.
046187,001819: 00,2372           56130                           XCH      BUF                                   
046188,001820: 00,2373           56155                           XCH      MPAC       +1                         
046189,001821: 00,2374           56154                           XCH      MPAC                                  
046190,001822: 00,2375           10130                           CCS      BUF                                   #  TRY AGAIN ON FORMER MINOR PART.
046191,001823: 00,2376           12422                           TCF      BUF+                                  
046192,001824: 00,2377           12401                           TCF      +2                                    #  OVERFLOW ON ZERO DIVISOR.
046193,001825: 00,2400           12416                           TCF      BUF-                                  
046194,001826: 
046195,001827: 00,2401           40154                           CS       MPAC                                  #  SIGN OF MPAC DETERMINES SIGN OF RESULT.
046196,001828: 00,2402           00006        SGNDVOVF           EXTEND                                         
046197,001829: 00,2403           62405                           BZMF     +2                                    
046198,001830: 00,2404           24136                           INCR     DVSIGN                                #  NEGMAX IN MPAC PERHAPS.
046199,001831: 00,2405           34733        DVOVF              CAF      POSMAX                                #  ON DIVISION OVERFLOW OF ANY SORT, SET
046200,001832: 00,2406           54154                           TS       MPAC                                  #  SET DP MPAC TO +-POSMAX.
046201,001833: 00,2407           02630                           TC       FINALDV    +3                         
046202,001834: 00,2410           34753                           CAF      ONE                                   #  SET OVERFLOW INDICATOR AND EXIT.
046203,001835: 00,2411           54121                           TS       OVFIND                                
046204,001836: 00,2412           06073                           TC       DANZIG                                
046205,001837: 
046206,001838: 00,2413           24136                 -1        INCR     DVSIGN                                
046207,001839: 00,2414           40131        OVF+               CS       BUF        +1                         #  LOAD LOWER ORDER PART OF DIVISOR.
046208,001840: 00,2415           12402                           TCF      SGNDVOVF                              #  GET SIGN OF RESULT.
046209,001841: 
046210,001842: 00,2416           00006        BUF-               EXTEND                                         #  IF BUF IS NEGATIVE, COMPLEMENT IT AND
046211,001843: 00,2417           40131                           DCS      BUF                                   #  MAINTAIN DVSIGN FOR FINAL QUOTIENT SIGN.
046212,001844: 00,2420           52131                           DXCH     BUF                                   
046213,001845: 00,2421           24136                           INCR     DVSIGN                                #  NOW -0.
046214,001846: 

Page 1049

046216,001848: 00,2422           10154        BUF+               CCS      MPAC                                  #  FORCE MPAC POSITIVE, CHECKING FOR ZERO
046217,001849: 00,2423           12437                           TCF      MPAC+                                 #  DIVIDEND IN THE PROCESS.
046218,001850: 00,2424           12426                           TCF      +2                                    
046219,001851: 00,2425           12433                           TCF      MPAC-                                 
046220,001852: 00,2426           10155                           CCS      MPAC       +1                         
046221,001853: 00,2427           12437                           TCF      MPAC+                                 
046222,001854: 00,2430           16073                           TCF      DANZIG                                #  EXIT IMMEDIATELY ON ZERO DIVIDEND.
046223,001855: 00,2431           12433                           TCF      MPAC-                                 
046224,001856: 00,2432           16073                           TCF      DANZIG                                
046225,001857: 
046226,001858: 00,2433           00006        MPAC-              EXTEND                                         #  FORCE MPAC POSITIVE AS BUF IN BUF-.
046227,001859: 00,2434           40155                           DCS      MPAC                                  
046228,001860: 00,2435           52155                           DXCH     MPAC                                  
046229,001861: 00,2436           24136                           INCR     DVSIGN                                #  NOW +1 OR -0.
046230,001862: 

Page 1050

046232,001864: 00,2437           40154        MPAC+              CS       MPAC                                  #  CHECK FOR DIVISION OVERFLOW. IF THE
046233,001865: 00,2440           67761                           AD       NEGONE                                #  MAJOR PART OF THE DIVIDEND IS LESS THAN
046234,001866: 00,2441           60130                           AD       BUF                                   #  THE MAJOR PART OF THE DIVISOR BY AT
046235,001867: 00,2442           10000                           CCS      A                                     #  LEAST TWO, WE CAN PROCEED IMMEDIATELY
046236,001868: 00,2443           12505                           TCF      DVNORM                                #  WITHOUT NORMALIZATION PRODUCING A DVMAX.
046237,001869: 00,2444           60001        -1/2+2             OCT      60001                                 #  USED IN SQRTSUB.
046238,001870: 
046239,001871: 00,2445           12446                           TCF      +1                                    #  IF THE ABOVE DOES NOT HOLD, FORCE SIGN
046240,001872: 00,2446           34736                           CAF      HALF                                  #  AGREEMENT IN NUMERATOR AND DENOMINATOR
046241,001873: 00,2447           60000                           DOUBLE                                         #  TO FACILITATE OVERFLOW AND NEAR-ONE
046242,001874: 00,2450           60155                           AD       MPAC       +1                         #  CHECKING.
046243,001875: 00,2451           54155                           TS       MPAC       +1                         
046244,001876: 00,2452           34755                           CAF      ZERO                                  
046245,001877: 00,2453           64733                           AD       POSMAX                                
046246,001878: 00,2454           26154                           ADS      MPAC                                  
046247,001879: 
046248,001880: 00,2455           34736                           CAF      HALF                                  #  SAME FOR BUF.
046249,001881: 00,2456           60000                           DOUBLE                                         
046250,001882: 00,2457           60131                           AD       BUF        +1                         
046251,001883: 00,2460           54131                           TS       BUF        +1                         
046252,001884: 00,2461           34755                           CAF      ZERO                                  
046253,001885: 00,2462           64733                           AD       POSMAX                                
046254,001886: 00,2463           26130                           ADS      BUF                                   
046255,001887: 
046256,001888: 00,2464           40154                           CS       MPAC                                  #  CHECK MAGNITUDE OF SIGN-CORRECTED
046257,001889: 00,2465           60130                           AD       BUF                                   #  OPERANDS.
046258,001890: 00,2466           10000                           CCS      A                                     
046259,001891: 00,2467           12505                           TCF      DVNORM                                #  DIVIDE OK - WILL NOT BECOME MAXDV CASE.
046260,001892: 00,2470           00133        LBUF2              ADRES    BUF2                                  
046261,001893: 00,2471           12405                           TCF      DVOVF                                 #  DIVISOR NOT LESS THAN DIVIDEND - OVF.
046262,001894: 
046263,001895: 00,2472           54140                           TS       MAXDVSW                               #  IF THE MAJOR PARTS OF THE DIVIDEND AND
046264,001896: 00,2473           40155                           CS       MPAC       +1                         #  DIVISOR ARE EQUAL, A SPECIAL APPROXIMA-
046265,001897: 00,2474           60131                           AD       BUF        +1                         #  TION IS USED (PROVIDED THE DIVISION IS
046266,001898: 00,2475           00006                           EXTEND                                         #  POSSIBLE, OF COURSE).
046267,001899: 00,2476           62405                           BZMF     DVOVF                                 
046268,001900: 00,2477           12505                           TCF      DVNORM                                #  IF NO OVERFLOW.
046269,001901: 

Page 1051

046271,001903: 00,2500           00006        BUFNORM            EXTEND                                         #  ADD -1 TO AUGMENT SHIFT COUNT AND SHIFT
046272,001904: 00,2501           24137                           AUG      DVNORMCT                              #  LEFT ONE PLACE.
046273,001905: 00,2502           00006                           EXTEND                                         
046274,001906: 00,2503           30131                           DCA      BUF                                   
046275,001907: 00,2504           20131                           DAS      BUF                                   
046276,001908: 
046277,001909: 00,2505           30130        DVNORM             CA       BUF                                   #  SEE IF DIVISOR NORMALIZED YET.
046278,001910: 00,2506           60000                           DOUBLE                                         
046279,001911: 00,2507           54000                           OVSK                                           
046280,001912: 00,2510           12500                           TCF      BUFNORM                               #  NO - SHIFT LEFT ONE AND TRY AGAIN.
046281,001913: 
046282,001914: 00,2511           52155                           DXCH     MPAC                                  #  CALL DIVIDEND NORMALIZATION SEQUENCE
046283,001915: 00,2512           50137                           INDEX    DVNORMCT                              #  PRIOR TO DOING THE DIVIDE.
046284,001916: 00,2513           02565                           TC       MAXTEST                               
046285,001917: 
046286,001918: 00,2514           54156                           TS       MPAC       +2                         #  RETURNS WITH DIVISION DONE AND C(A) = 0.
046287,001919: 00,2515           16073                           TCF      DANZIG                                
046288,001920: 
046289,001921: 00,2516           10000        BUFPOS             CCS      A                                     
046290,001922: 00,2517           12422                           TCF      BUF+                                  #  TO BUF+ IF BUF IS GREATER THAN +1.
046291,001923: 
046292,001924: 00,2520           40131                           CS       BUF        +1                         #  IF BUF IS +1, FORCING SIGN AGREEMENT
046293,001925: 00,2521           00006                           EXTEND                                         #  MAY CAUSE BUF TO BECOME ZERO.
046294,001926: 00,2522           62422                           BZMF     BUF+                                  #  BRANCH IF SIGNS AGREE.
046295,001927: 
046296,001928: 00,2523           34736                           CA       HALF                                  #  SIGNS DISAGREE.  FORCE AGREEMENT.
046297,001929: 00,2524           60000                 +6        DOUBLE                                         
046298,001930: 00,2525           26131                           ADS      BUF        +1                         
046299,001931: 00,2526           34755                           CA       ZERO                                  
046300,001932: 00,2527           54130                           TS       BUF                                   
046301,001933: 00,2530           12363                           TCF      BUFZERO                               
046302,001934: 
046303,001935: 00,2531           10000        BUFNEG             CCS      A                                     
046304,001936: 00,2532           12416                           TCF      BUF-                                  #  TO BUF- IF BUF IS LESS THAN -1.
046305,001937: 
046306,001938: 00,2533           30131                           CA       BUF        +1                         #  IF BUF IS -1, FORCING SIGN AGREEMENT
046307,001939: 00,2534           00006                           EXTEND                                         #  MAY CAUSE BUF TO BECOME ZERO.
046308,001940: 00,2535           62416                           BZMF     BUF-                                  #  BRANCH IF SIGNS AGREE.
046309,001941: 
046310,001942: 00,2536           44736                           CS       HALF                                  #  SIGNS DISAGREE.  FORCE AGREEMENT.
046311,001943: 00,2537           12524                           TCF      BUFPOS     +6                         
046312,001944: 

Page 1052

046314,001946:                                                                                                  #           THE FOLLOWING ARE PROLOGUES TO SHIFT THE DIVIDEND ARRIVING IN A AND L BEFORE THE DIVIDE.
046315,001947: 
046316,001948: 00,2540           22021                 -21D      LXCH     SR                                    #  SPECIAL PROLOGUE FOR UNIT WHEN THE
046317,001949: 00,2541           00006                           EXTEND                                         #  LENGTH OF THE ARGUMENT WAS NOT LESS THAN
046318,001950: 00,2542           74736                           MP       HALF                                  #  .5. IN THIS CASE, EACH COMPONENT MUST BE
046319,001951: 00,2543           56001                           XCH      L                                     #  SHIFTED RIGHT ONE TO PRODUCE A HALF-UNIT
046320,001952: 00,2544           60021                           AD       SR                                    #  VECTOR.
046321,001953: 00,2545           56001                           XCH      L                                     
046322,001954: 00,2546           12571                           TCF      GENDDV     +1                         #  WITH DP DIVIDEND IN A,L.
046323,001955: 
046324,001956: 00,2547           20001                           DDOUBL                                         #  PROLOGUE WHICH NORMALIZES THE DIVIDEND
046325,001957: 00,2550           20001                           DDOUBL                                         #  WHEN IT IS KNOWN THAT NO DIVISION
046326,001958: 00,2551           20001                           DDOUBL                                         #  OVERFLOW WILL OCCUR.
046327,001959: 00,2552           20001                           DDOUBL                                         
046328,001960: 00,2553           20001                           DDOUBL                                         
046329,001961: 00,2554           20001                           DDOUBL                                         
046330,001962: 00,2555           20001                           DDOUBL                                         
046331,001963: 00,2556           20001                           DDOUBL                                         
046332,001964: 00,2557           20001                           DDOUBL                                         
046333,001965: 00,2560           20001                           DDOUBL                                         
046334,001966: 00,2561           20001                           DDOUBL                                         
046335,001967: 00,2562           20001                           DDOUBL                                         
046336,001968: 00,2563           20001                           DDOUBL                                         
046337,001969: 00,2564           52155                           DXCH     MPAC                                  
046338,001970: 
046339,001971: 00,2565           10140        MAXTEST            CCS      MAXDVSW                               #  0 IF MAJORS MIGHT BE =, -1 OTHERWISE.
046340,001972: 00,2566           06552        BIASHI             DEC      .4192      B-1                        #  SQRT CONSTANTS
046341,001973: 
046342,001974: 00,2567           12642                           TCF      MAXDV                                 #  CHECK TO SEE IF THEY ARE NOW EQUAL.
046343,001975: 

Page 1053

046345,001977:                                                                                                  #           THE FOLLOWING IS A GENERAL PURPOSE DOUBLE PRECISION DIVISION ROUTINE. IT DIVIDES MPAC BY BUF AND LEAVES
046346,001978:                                                                                                  #  THE RESULT IN MPAC. THE FOLLOWING CONDITIONS MUST BE SATISFIED:
046347,001979: 
046348,001980:                                                                                                  #           1.  THE DIVISOR (BUF) MUST BE POSITIVE AND NOT LESS THAN .5.
046349,001981: 
046350,001982:                                                                                                  #           2.  THE DIVIDEND (MPAC) MUST BE POSITIVE WITH THE MAJOR PART OF MPAC STRICTLY LESS THAN THAT OF BUF
046351,001983:                                                                                                  #  (A SPECIAL APPROXIMATION, MAXDV, IS USED WHEN THE MAJOR PARTS ARE EQUAL).
046352,001984: 
046353,001985:                                                                                                  #           UNDERSTANDING THAT A/B = Q + S(R/B) WHERE S = 2(-14) AND Q AND R ARE QUOTIENT AND REMAINDER, RESPEC-
046354,001986:                                                                                                  #  TIVELY, THE FOLLOWING APPROXIMATION IS OBTAINED BY MULTIPLYING ABOVE AND BELOW BY C - SD AND NEGLECTING TERMS OF
046355,001987:                                                                                                  #  ORDER S-SQUARED (POSSIBLY INTRODUCING ERROR INTO THE LOW TWO BITS OF THE RESULT). SIGN AGREEMENT IS UNNECESSARY.
046356,001988: 
046357,001989:                                                                                                  #           A + SB .      (R - QD)                                             A + SB
046358,001990:                                                                                                  #           ------ = Q + S(------) WHERE Q AND R ARE QUOTIENT AND REMAINDER OF ------ RESPECTIVELY.
046359,001991:                                                                                                  #           C + SD        (  C   )                                               C
046360,001992: 
046361,001993: 
046362,001994: 00,2570           52155        GENDDV             DXCH     MPAC                                  #  WE NEED A AND B ONLY FOR FIRST DV.
046363,001995: 00,2571           00006                 +1        EXTEND                                         #  (SPECIAL UNIT PROLOGUE ENTERS HERE).
046364,001996: 00,2572           10130                           DV       BUF                                   #  A NOW CONTAINS Q AND L, R.
046365,001997: 00,2573           52155                           DXCH     MPAC                                  
046366,001998: 
046367,001999: 00,2574           40154                           CS       MPAC                                  #  FORM DIVIDEND FOR MINOR PART OF RESULT.
046368,002000: 00,2575           00006                           EXTEND                                         
046369,002001: 00,2576           70131                           MP       BUF        +1                         
046370,002002: 00,2577           60155                           AD       MPAC       +1                         #  OVERFLOW AT THIS POINT IS POSITIVE SINCE
046371,002003: 00,2600           54000                           OVSK                                           #  R IS POSITIVE IN EVERY CASE.
046372,002004: 00,2601           12606                           TCF      +5                                    
046373,002005: 
046374,002006: 00,2602           00006                           EXTEND                                         #  OVERFLOW CAN BE REMOVED BY SUBTRACTING C
046375,002007: 00,2603           60130                           SU       BUF                                   #  (BUF) ONCE SINCE R IS ALWAYS LESS THAN C
046376,002008: 00,2604           24154                           INCR     MPAC                                  #  IN THIS CASE. INCR COMPENSATES SUBTRACT.
046377,002009: 00,2605           12610                           TCF      +DOWN                                 #  (SINCE C(A) IS STILL POSITIVE).
046378,002010: 
046379,002011: 00,2606           00006                 +5        EXTEND                                         #  C(A) CAN BE MADE LESS THAN C IN MAGNI-
046380,002012: 00,2607           62620                           BZMF     -UP                                   #  TUDE BY DIMINISHING IT BY C (SINCE C IS
046381,002013:                                                                                                  #  NOT LESS THAN .5) UNLESS C(A) = 0.
046382,002014: 

Page 1054

046384,002016: 00,2610           00006        +DOWN              EXTEND                                         
046385,002017: 00,2611           60130                           SU       BUF                                   #  IF POSITIVE, REDUCE ONLY IF NECESSARY
046386,002018: 00,2612           00006                           EXTEND                                         #  SINCE THE COMPENSATING INCR MIGHT CAUSE
046387,002019: 00,2613           12616                           BZF      +3                                    #  OVERFLOW.
046388,002020: 00,2614           00006                           EXTEND                                         #  DONT SUBTRACT UNLESS RESULT IS POSITIVE
046389,002021: 00,2615           62624                           BZMF     ENDMAXDV                              #  OR ZERO.
046390,002022: 
046391,002023: 00,2616           24154                 +3        INCR     MPAC                                  #  KEEP SUBTRACT HERE AND COMPENSATE.
046392,002024: 00,2617           12625                           TCF      FINALDV                               
046393,002025: 
046394,002026: 00,2620           00006        -UP                EXTEND                                         #  IF ZERO, SET MINOR PART OF RESULT TO
046395,002027: 00,2621           12630                           BZF      FINALDV    +3                         #  ZERO.
046396,002028: 
046397,002029: 00,2622           00006                           EXTEND                                         #  IF NEGATIVE, ADD C TO A, SUBTRACTING ONE
046398,002030: 00,2623           26154                           DIM      MPAC                                  #  TO COMPENSATE. DIM IS OK HERE SINCE THE
046399,002031: 00,2624           60130        ENDMAXDV           AD       BUF                                   #  MAJOR PART NEVER GOES NEGATIVE.
046400,002032: 

Page 1055

046402,002034: 00,2625           22007        FINALDV            ZL                                             #  DO DV TO OBTAIN MINOR PART OF RESULT.
046403,002035: 00,2626           00006                           EXTEND                                         
046404,002036: 00,2627           10130                           DV       BUF                                   
046405,002037: 00,2630           54155                 +3        TS       MPAC       +1                         
046406,002038: 
046407,002039: 00,2631           10136                           CCS      DVSIGN                                #  LEAVE RESULT POSITIVE UNLESS C(DVSIGN)=
046408,002040: 00,2632           00002                           TC       Q                                     #  -0.
046409,002041: 00,2633           00002                           TC       Q                                     
046410,002042: 00,2634           00002                           TC       Q                                     
046411,002043: 
046412,002044: 00,2635           00006                           EXTEND                                         
046413,002045: 00,2636           40155                           DCS      MPAC                                  
046414,002046: 00,2637           52155                           DXCH     MPAC                                  
046415,002047: 00,2640           34755                           CAF      ZERO                                  #  SO WE ALWAYS RETURN WITH C(A) = 0.
046416,002048: 00,2641           00002                           TC       Q                                     
046417,002049: 

Page 1056

046419,002051:                                                                                                  #           IF THE MAJOR PARTS OF THE DIVISOR AND DIVIDEND ARE EQUAL, BUT THE MINOR PARTS ARE SUCH THAT THE
046420,002052:                                                                                                  #  DIVIDEND IS STRICTLY LESS THAN THE DIVISOR IN MAGNITUDE, THE FOLLOWING APPROXIMATION IS USED. THE ASSUMPTIONS
046421,002053:                                                                                                  #  ARE THE SAME AS THE GENERAL ROUTINE WITH THE ADDITION THAT SIGN AGREEMENT IS NECESSARY (B, C, & D POSITIVE).
046422,002054: 
046423,002055:                                                                                                  #                  C + SB .          (C + B - D)
046424,002056:                                                                                                  #                  ------ = 37777 + S(---------)
046425,002057:                                                                                                  #                  C + SD            (    C    )
046426,002058: 
046427,002059:                                                                                                  #           THE DIVISION MAY BE PERFORMED IMMEDIATELY SINCE B IS STRICTLY LESS THAN D AND C IS NOT LESS THAN .5.
046428,002060: 
046429,002061: 00,2642           40154        MAXDV              CS       MPAC                                  #  SEE IF MAXDV CASE STILL HOLDS AFTER
046430,002062: 00,2643           60130                           AD       BUF                                   #  NORMALIZATION.
046431,002063: 00,2644           00006                           EXTEND                                         
046432,002064: 00,2645           12647                           BZF      +2                                    
046433,002065: 00,2646           12570                           TCF      GENDDV                                #  MPAC NOW LESS THAN BUF - DIVIDE AS USUAL
046434,002066: 
046435,002067: 00,2647           34733                 +2        CAF      POSMAX                                #  SET MAJOR PART OF RESULT.
046436,002068: 00,2650           54154                           TS       MPAC                                  
046437,002069: 
046438,002070: 00,2651           40131                           CS       BUF        +1                         #  FORM DIVIDEND OF MINOR PART OF RESULT.
046439,002071: 00,2652           60155                           AD       MPAC       +1                         
046440,002072: 00,2653           12624                           TCF      ENDMAXDV                              #  GO ADD C AND DO DIVIDE, ATTACHING SIGN
046441,002073:                                                                                                  #  BEFORE EXITING.
046442,002074: 

Page 1057

046444,002076:                                                                                                  #           VECTOR DIVIDED BY SCALAR, V/SC, IS EXECUTED HERE. THE VECTOR IS NOW IN MPAC WITH SCALAR IN BUF.
046445,002077: 
046446,002078: 00,2654           44753        V/SC2              CS       ONE                                   #  INITIALIZE DIVIDEND NORMALIZATION COUNT
046447,002079: 00,2655           54137                           TS       DVNORMCT                              #  AND DIVISION SIGN REGISTER.
046448,002080: 00,2656           54127                           TS       VBUF       +5                         
046449,002081: 
046450,002082: 00,2657           03010                           TC       VECAGREE                              #  FORCE SIGN AGREEMENT IN VECTOR
046451,002083: 
046452,002084: 00,2660           52131                           DXCH     BUF                                   
046453,002085: 00,2661           07556                           TC       ALSIGNAG                              #  SIGN AGREE BUF
046454,002086: 00,2662           52131                           DXCH     BUF                                   
046455,002087: 00,2663           10130                           CCS      BUF                                   #  FORCE DIVISOR POSITIVE WITH MAJOR PART
046456,002088: 00,2664           12721                           TCF      /BUF+                                 #  NON-ZERO (IF POSSIBLE).
046457,002089: 00,2665           12667                           TCF      +2                                    
046458,002090: 00,2666           12715                           TCF      /BUF-                                 
046459,002091: 
046460,002092: 00,2667           56131                           XCH      BUF        +1                         #  SHIFT VECTOR AND SCALAR LEFT 14.
046461,002093: 00,2670           56130                           XCH      BUF                                   
046462,002094: 00,2671           56155                           XCH      MPAC       +1                         
046463,002095: 00,2672           56154                           XCH      MPAC                                  
046464,002096: 00,2673           00006                           EXTEND                                         #  CHECK FOR OVERFLOW IN EACH CASE.
046465,002097: 00,2674           12676                           BZF      +2                                    
046466,002098: 00,2675           12405                           TCF      DVOVF                                 
046467,002099: 
046468,002100: 00,2676           56160                           XCH      MPAC       +4                         
046469,002101: 00,2677           56157                           XCH      MPAC       +3                         
046470,002102: 00,2700           00006                           EXTEND                                         
046471,002103: 00,2701           12703                           BZF      +2                                    
046472,002104: 00,2702           12405                           TCF      DVOVF                                 
046473,002105: 
046474,002106: 00,2703           56162                           XCH      MPAC       +6                         
046475,002107: 00,2704           56161                           XCH      MPAC       +5                         
046476,002108: 00,2705           00006                           EXTEND                                         
046477,002109: 00,2706           12710                           BZF      +2                                    
046478,002110: 00,2707           12405                           TCF      DVOVF                                 
046479,002111: 
046480,002112: 00,2710           10130                           CCS      BUF                                   
046481,002113: 00,2711           12721                           TCF      /BUF+                                 
046482,002114: 00,2712           12405                           TCF      DVOVF                                 #  ZERO DIVISOR - OVERFLOW.
046483,002115: 00,2713           12715                           TCF      /BUF-                                 
046484,002116: 00,2714           12405                           TCF      DVOVF                                 
046485,002117: 
046486,002118: 00,2715           00006        /BUF-              EXTEND                                         #  ON NEGATIVE, COMPLEMENT BUF AND MAINTAIN
046487,002119: 00,2716           40131                           DCS      BUF                                   #  DVSIGN IN VBUF +5.
046488,002120: 00,2717           52131                           DXCH     BUF                                   
046489,002121: 00,2720           24127                           INCR     VBUF       +5                         
046490,002122: 

Page 1058

046492,002124: 00,2721           00006        /BUF+              EXTEND                                         
046493,002125: 00,2722           30131                           DCA      BUF                                   #  LEAVE ABS(ORIG DIVISOR) IN BUF2
046494,002126: 00,2723           52134                           DXCH     BUF2                                  #  FOR OVERFLOW TESTING
046495,002127: 00,2724           12732                           TCF      /NORM                                 #  NORMALIZE DIVISOR IN BUF.
046496,002128: 
046497,002129: 00,2725           00006        /NORM2             EXTEND                                         #  IF LESS THAN .5, AUGMENT DVNORMCT AND
046498,002130: 00,2726           24137                           AUG      DVNORMCT                              #  DOUBLE DIVISOR.
046499,002131: 00,2727           00006                           EXTEND                                         
046500,002132: 00,2730           30131                           DCA      BUF                                   
046501,002133: 00,2731           20131                           DAS      BUF                                   
046502,002134: 
046503,002135: 00,2732           30130        /NORM              CA       BUF                                   #  SEE IF DIVISOR NORMALIZED.
046504,002136: 00,2733           60000                           DOUBLE                                         
046505,002137: 00,2734           54000                           OVSK                                           
046506,002138: 00,2735           12725                           TCF      /NORM2                                #  DOUBLE AND TRY AGAIN IF NOT.
046507,002139: 
046508,002140: 00,2736           02750                           TC       V/SCDV                                #  DO X COMPONENT DIVIDE.
046509,002141: 00,2737           52160                           DXCH     MPAC       +3                         #  SUPPLY ARGUMENTS IN USUAL SEQUENCE.
046510,002142: 00,2740           52155                           DXCH     MPAC                                  
046511,002143: 00,2741           52160                           DXCH     MPAC       +3                         
046512,002144: 
046513,002145: 00,2742           02750                           TC       V/SCDV                                #  Y COMPONENT.
046514,002146: 00,2743           52162                           DXCH     MPAC       +5                         
046515,002147: 00,2744           52155                           DXCH     MPAC                                  
046516,002148: 00,2745           52162                           DXCH     MPAC       +5                         
046517,002149: 
046518,002150: 00,2746           02750                           TC       V/SCDV                                #  Z COMPONENT.
046519,002151: 00,2747           17432                           TCF      VROTATEX                              #  GO RE-ARRANGE COMPONENTS BEFORE EXIT.
046520,002152: 

Page 1059

046522,002154:                                                                                                  #           SUBROUTINE USED BY V/SC TO DIVIDE VECTOR COMPONENT IN MPAC,+1 BY THE SCALAR GIVEN IN BUF.
046523,002155: 
046524,002156: 00,2750           30127        V/SCDV             CA       VBUF       +5                         #  REFLECTS SIGN OF SCALAR.
046525,002157: 00,2751           54136                           TS       DVSIGN                                
046526,002158: 
046527,002159: 00,2752           10154                           CCS      MPAC                                  #  FORCE MPAC POSITIVE, EXITING ON ZERO.
046528,002160: 00,2753           12767                           TCF      /MPAC+                                
046529,002161: 00,2754           12756                           TCF      +2                                    
046530,002162: 00,2755           12763                           TCF      /MPAC-                                
046531,002163: 
046532,002164: 00,2756           10155                           CCS      MPAC       +1                         
046533,002165: 00,2757           12767                           TCF      /MPAC+                                
046534,002166: 00,2760           00002                           TC       Q                                     
046535,002167: 00,2761           12763                           TCF      /MPAC-                                
046536,002168: 00,2762           00002                           TC       Q                                     
046537,002169: 
046538,002170: 00,2763           00006        /MPAC-             EXTEND                                         #  USUAL COMPLEMENTING AND SETTING OF SIGN.
046539,002171: 00,2764           40155                           DCS      MPAC                                  
046540,002172: 00,2765           52155                           DXCH     MPAC                                  
046541,002173: 00,2766           24136                           INCR     DVSIGN                                
046542,002174: 
046543,002175: 00,2767           44753        /MPAC+             CS       ONE                                   #  INITIALIZE NEAR-ONE SWITCH.
046544,002176: 00,2770           54140                           TS       MAXDVSW                               
046545,002177: 
046546,002178: 00,2771           40154                           CS       MPAC                                  #  CHECK POSSIBLE OVERFLOW.
046547,002179: 00,2772           60133                           AD       BUF2                                  #  UNNORMALIZED INPUT DIVISOR.
046548,002180: 00,2773           10000                           CCS      A                                     
046549,002181: 00,2774           13004                           TCF      DDVCALL                               #  NOT NEAR-ONE
046550,002182: 00,2775           12777                           TCF      +2                                    #  +0 IS JUST POSSIBLE
046551,002183: 00,2776           12405                           TCF      DVOVF                                 #  NO HOPE
046552,002184: 00,2777           54140                           TS       MAXDVSW                               #  SIGNAL POSSIBLE NEAR-ONE CASE
046553,002185: 00,3000           40155                           CS       MPAC       +1                         #  SEE IF DIVISION CAN BE DONE
046554,002186: 00,3001           60134                           AD       BUF2       +1                         
046555,002187: 00,3002           00006                           EXTEND                                         
046556,002188: 00,3003           62405                           BZMF     DVOVF                                 
046557,002189: 
046558,002190: 00,3004           52155        DDVCALL            DXCH     MPAC                                  #  CALL PRE-DIVIDE NORMALIZATION.
046559,002191: 00,3005           50137                           INDEX    DVNORMCT                              
046560,002192: 00,3006           12565                           TCF      MAXTEST                               
046561,002193: 

Page 1060

046563,002195: 00,3007           32506        SLOPELO            DEC      .8324                                 
046564,002196: 
046565,002197: 00,3010           56002        VECAGREE           XCH      Q                                     #  SAVE Q IN A
046566,002198: 00,3011           52155                           DXCH     MPAC                                  
046567,002199: 00,3012           07556                           TC       ALSIGNAG                              #  SIGNAGREE MPAC
046568,002200: 00,3013           52155                           DXCH     MPAC                                  
046569,002201: 00,3014           52160                           DXCH     MPAC       +3                         
046570,002202: 00,3015           07556                           TC       ALSIGNAG                              #  SIGN AGREE MPAC +3
046571,002203: 00,3016           52160                           DXCH     MPAC       +3                         
046572,002204: 00,3017           52162                           DXCH     MPAC       +5                         
046573,002205: 00,3020           07556                           TC       ALSIGNAG                              #  SIGNAGREE MPAC +5
046574,002206: 00,3021           52162                           DXCH     MPAC       +5                         
046575,002207: 00,3022           00000                           TC       A                                     
046576,002208: 

Page 1061

046578,002210:                                                                                                  #           THE FOLLOWING ROUTINE EXECUTES THE UNIT INSTRUCTION, WHICH TAKES THE UNIT OF THE VECTOR IN MPAC.
046579,002211: 
046580,002212: 00,3023           03010        UNIT               TC       VECAGREE                              #  FORCE SIGN AGREEMENT IN VECTOR
046581,002213: 00,3024           07544                           TC       MPACVBUF                              #  SAVE ARGUMENT IN VBUF
046582,002214: 00,3025           34755                           CAF      ZERO                                  #  MUST SENSE OVERFLOW IN FOLLOWING DOT.
046583,002215: 00,3026           56121                           XCH      OVFIND                                
046584,002216: 00,3027           54141                           TS       TEM1                                  
046585,002217: 00,3030           03317                           TC       VSQSUB                                #  DOT MPAC WITH ITSELF.
046586,002218: 00,3031           30141                           CA       TEM1                                  
046587,002219: 00,3032           56121                           XCH      OVFIND                                
046588,002220: 00,3033           00006                           EXTEND                                         
046589,002221: 00,3034           13036                           BZF      +2                                    
046590,002222: 00,3035           12405                           TCF      DVOVF                                 
046591,002223: 00,3036           00006                           EXTEND                                         
046592,002224: 00,3037           30155                           DCA      MPAC                                  #  LEAVE THE SQUARE OF THE LENGTH OF THE
046593,002225: 00,3040           50120                           INDEX    FIXLOC                                #  ARGUMENT IN LVSQUARE.
046594,002226: 00,3041           52043                           DXCH     LVSQUARE                              
046595,002227: 
046596,002228: 00,3042           03343                           TC       SQRTSUB                               #  GO TAKE THE NORMALIZED SQUARE ROOT.
046597,002229: 
046598,002230: 00,3043           10154                           CCS      MPAC                                  #  CHECK FOR UNIT OVERFLOW.
046599,002231: 00,3044           13051                           TCF      +5                                    #  MPAC IS NOT LESS THAN .5 UNLESS
046600,002232: 00,3045           54001                           TS       L                                     
046601,002233: 00,3046           50120                           INDEX    FIXLOC                                
046602,002234: 00,3047           52045                           DXCH     LV                                    
046603,002235: 00,3050           12405                           TCF      DVOVF                                 #  INPUT TO SQRTSUB WAS 0.
046604,002236: 
046605,002237: 00,3051           44317                           CS       FOURTEEN                              #  SEE IF THE INPUT WAS SO SMALL THE THE
046606,002238: 00,3052           60135                           AD       MPTEMP                                #  FIRST TWO REGISTERS OF THE SQUARE WERE 0
046607,002239: 00,3053           10000                           CCS      A                                     
046608,002240: 00,3054           40000                           COM                                            #  IF SO, SAVE THE NEGATIVE OF THE SHIFT
046609,002241: 00,3055           13133                           TCF      SMALL                                 #  COUNT -15D.
046610,002242: 
046611,002243: 00,3056           13065                           TCF      LARGE                                 #  (THIS IS USUALLY THE CASE.)
046612,002244: 
046613,002245: 00,3057           44761                           CS       THIRTEEN                              #  IF THE SHIFT COUNT WAS EXACTLY 14, SET
046614,002246: 00,3060           54135                           TS       MPTEMP                                #  THE PRE-DIVIDE NORM COUNT TO -13D.
046615,002247: 
046616,002248: 00,3061           30154                           CA       MPAC                                  #  SHIFT THE LENGTH RIGHT 14 BEFORE STORING
046617,002249: 00,3062           54001        SMALL2             TS       L                                     #  (SMALL EXITS TO THIS POINT).
046618,002250: 00,3063           34755                           CAF      ZERO                                  
046619,002251: 00,3064           13112                           TCF      LARGE2                                #  GO TO STORE LENGTH AND PROCEED.
046620,002252: 
046621,002253: 00,3065           10135        LARGE              CCS      MPTEMP                                #  MOST ALL CASES COME HERE.
046622,002254: 00,3066           13074                           TCF      LARGE3                                #  SEE IF NO NORMALIZATION WAS REQUIRED BY
046623,002255: 
046624,002256: 00,3067           42024                           CS       SRDDV                                 #  SQRT, AND IF SO, SET UP FOR A SHIFT
046625,002257: 00,3070           54135                           TS       MPTEMP                                #  RIGHT 1 BEFORE DIVIDING TO PRODUCE
046626,002258: 00,3071           00006                           EXTEND                                         #  THE DESIRED HALF UNIT VECTOR.
046627,002259: 00,3072           30155                           DCA      MPAC                                  

Page 1062

046629,002261: 00,3073           13112                           TCF      LARGE2                                
046630,002262: 

Page 1063

046632,002264: 00,3074           40000        LARGE3             COM                                            #  LEAVE NEGATIVE OF SHIFT COUNT-1 FOR
046633,002265: 00,3075           54135                           TS       MPTEMP                                #  PREDIVIDE LEFT SHIFT.
046634,002266: 
046635,002267: 00,3076           40000                           COM                                            #  PICK UP REQUIRED SHIFTING BIT TO UNNORM-
046636,002268: 00,3077           50000                           INDEX    A                                     #  ALIZE THE SQRT RESULT.
046637,002269: 00,3100           34736                           CAF      BIT14                                 
046638,002270: 00,3101           54130                           TS       BUF                                   
046639,002271: 00,3102           00006                           EXTEND                                         
046640,002272: 00,3103           70155                           MP       MPAC       +1                         
046641,002273: 00,3104           56130                           XCH      BUF                                   
046642,002274: 00,3105           00006                           EXTEND                                         #  (UNNORMALIZE THE SQRT FOR LV).
046643,002275: 00,3106           70154                           MP       MPAC                                  
046644,002276: 00,3107           56001                           XCH      L                                     
046645,002277: 00,3110           60130                           AD       BUF                                   
046646,002278: 00,3111           56001                           XCH      L                                     
046647,002279: 
046648,002280: 00,3112           50120        LARGE2             INDEX    FIXLOC                                
046649,002281: 00,3113           52045                           DXCH     LV                                    #  LENGTH NOW STORED IN WORK AREA.
046650,002282: 
046651,002283: 00,3114           44753                           CS       ONE                                   
046652,002284: 00,3115           54140                           TS       MAXDVSW                               #  NO MAXDV CASES IN UNIT.
046653,002285: 
046654,002286: 00,3116           52123                           DXCH     VBUF                                  #  PREPARE X COMPONENT FOR DIVIDE, SETTING
046655,002287: 00,3117           52155                           DXCH     MPAC                                  #  LENGTH OF VECTOR AS DIVISOR IN BUF.
046656,002288: 00,3120           52131                           DXCH     BUF                                   
046657,002289: 00,3121           03151                           TC       UNITDV                                
046658,002290: 
046659,002291: 00,3122           52125                           DXCH     VBUF       +2                         #  DO Y AND Z IN USUAL FASHION SO WE CAN
046660,002292: 00,3123           52155                           DXCH     MPAC                                  #  EXIT THROUGH VROTATEX.
046661,002293: 00,3124           52160                           DXCH     MPAC       +3                         
046662,002294: 00,3125           03151                           TC       UNITDV                                
046663,002295: 
046664,002296: 00,3126           52127                           DXCH     VBUF       +4                         
046665,002297: 00,3127           52155                           DXCH     MPAC                                  
046666,002298: 00,3130           52162                           DXCH     MPAC       +5                         
046667,002299: 00,3131           03151                           TC       UNITDV                                
046668,002300: 00,3132           17432                           TCF      VROTATEX                              #  AND EXIT.
046669,002301: 

Page 1064

046671,002303:                                                                                                  #           IF THE LENGTH OF THE ARGUMENT VECTOR WAS LESS THAN 2(-28), EACH COMPONENT MUST BE SHIFTED LEFT AT LEAST
046672,002304:                                                                                                  #  14 PLACES BEFORE THE DIVIDE. NOTE THAT IN THIS CASE, THE MAJOR PART OF EACH COMPONENT IS ZERO.
046673,002305: 
046674,002306: 00,3133           54135        SMALL              TS       MPTEMP                                #  NEGATIVE OF PRE-DIVIDE SHIFT COUNT.
046675,002307: 
046676,002308: 00,3134           34755                           CAF      ZERO                                  #  SHIFT EACH COMPONENT LEFT 14.
046677,002309: 00,3135           56123                           XCH      VBUF       +1                         
046678,002310: 00,3136           56122                           XCH      VBUF                                  
046679,002311: 00,3137           56125                           XCH      VBUF       +3                         
046680,002312: 00,3140           56124                           XCH      VBUF       +2                         
046681,002313: 00,3141           56127                           XCH      VBUF       +5                         
046682,002314: 00,3142           56126                           XCH      VBUF       +4                         
046683,002315: 
046684,002316: 00,3143           40135                           CS       MPTEMP                                
046685,002317: 00,3144           50000                           INDEX    A                                     
046686,002318: 00,3145           34736                           CAF      BIT14                                 
046687,002319: 00,3146           00006                           EXTEND                                         
046688,002320: 00,3147           70154                           MP       MPAC                                  
046689,002321: 00,3150           13062                           TCF      SMALL2                                
046690,002322: 
046691,002323: 00,3151     4761               THIRTEEN           =        OCT15                                 
046692,002324: 00,3151     4317               FOURTEEN           =        OCT16                                 
046693,002325: 00,3151     4317               OCT16              =        R1D1                                  
046694,002326: 

Page 1065

046696,002328:                                                                                                  #           THE FOLLOWING ROUTINE SETS UP THE CALL TO THE DIVIDE ROUTINES.
046697,002329: 
046698,002330: 00,3151           10154        UNITDV             CCS      MPAC                                  #  FORCE MPAC POSITIVE IF POSSIBLE, SETTING
046699,002331: 00,3152           13170                           TCF      UMPAC+                                #  DVSIGN ACCORDING TO THE SIGN OF MPAC
046700,002332: 00,3153           13155                           TCF      +2                                    #  SINCE THE DIVISOR IS ALWAYS POSITIVE
046701,002333: 00,3154           13162                           TCF      UMPAC-                                #  HERE.
046702,002334: 
046703,002335: 00,3155           10155                           CCS      MPAC       +1                         
046704,002336: 00,3156           13170                           TCF      UMPAC+                                
046705,002337: 00,3157           00002                           TC       Q                                     #  EXIT IMMEDIATELY ON ZERO.
046706,002338: 00,3160           13162                           TCF      UMPAC-                                
046707,002339: 00,3161           00002                           TC       Q                                     
046708,002340: 
046709,002341: 00,3162           44755        UMPAC-             CS       ZERO                                  #  IF NEGATIVE, SET -0 IN DVSIGN FOR FINAL
046710,002342: 00,3163           54136                           TS       DVSIGN                                #  COMPLEMENT.
046711,002343: 00,3164           00006                           EXTEND                                         
046712,002344: 00,3165           40155                           DCS      MPAC                                  #  PICK UP ABSOLUTE VALUE OF ARG AND JUMP.
046713,002345: 00,3166           50135                           INDEX    MPTEMP                                
046714,002346: 00,3167           12564                           TCF      MAXTEST    -1                         
046715,002347: 
046716,002348: 00,3170           54136        UMPAC+             TS       DVSIGN                                #  SET DVSIGN FOR POSITIVE QUOTIENT.
046717,002349: 00,3171           52155                           DXCH     MPAC                                  
046718,002350: 00,3172           50135                           INDEX    MPTEMP                                
046719,002351: 00,3173           12564                           TCF      MAXTEST    -1                         
046720,002352: 

Page 1066

046722,002354:                                                                                                  #           MISCELLANEOUS UNARY OPERATIONS.
046723,002355: 
046724,002356: 00,3174           03300        DSQ                TC       DSQSUB                                #  SQUARE THE DP CONTENTS OF MPAC.
046725,002357: 00,3175           16073                           TCF      DANZIG                                
046726,002358: 
046727,002359: 00,3176           10163        ABVALABS           CCS      MODE                                  #  ABVAL OR ABS INSTRUCTION.
046728,002360: 00,3177           13226                           TCF      ABS                                   #  DO ABS ON SCALAR.
046729,002361: 00,3200           13226                           TCF      ABS                                   
046730,002362: 
046731,002363: 00,3201           03317        ABVAL              TC       VSQSUB                                #  DOT MPAC WITH ITSELF.
046732,002364: 00,3202           22163                           LXCH     MODE                                  #  MODE IS NOW DP (L ZERO AFTER DAS).
046733,002365: 
046734,002366: 00,3203           00006                           EXTEND                                         #  STORE SQUARE OF LENGTH IN WORK AREA.
046735,002367: 00,3204           30155                           DCA      MPAC                                  
046736,002368: 00,3205           50120                           INDEX    FIXLOC                                
046737,002369: 00,3206           52043                           DXCH     LVSQUARE                              
046738,002370: 

Page 1067

046740,002372:                                                                                                  #  PROGRAM DESCRIPTION- SUBROUTINE SQRT
046741,002373:                                                                                                  #  FUNCTIONAL DESCRIPTION-DOUBLE PRECISION SQUARE ROOT ROUTINE
046742,002374:                                                                                                  #      THIS PROGRAM TAKES THE SQUARE ROOT OF THE 27 OR 28 MOST SIGNIFICANT BITS IN THE TRIPLE PRECISION SET OF
046743,002375:                                                                                                  #      NUMBERS-MPAC,MPAC+1,AND MPAC+2.  THE ROOT IS RETURNED DOUBLE        PRECISION IN MPAC AND MPAC+1.
046744,002376:                                                                                                  #  WARNING- THIS SUBROUTINE USES A TRIPLE PRECISION INPUT. THE PROGRAMMER  MUST ASSURE THE CONTENTS OF MPAC+2
046745,002377:                                                                                                  #      ESPECIALLY IF THE CONTENTS OF MPAC IS SMALL OR ZERO.  FOR DETAILS SEE STG MEMO NO.949.
046746,002378:                                                                                                  #  CALLING SEQUENCE- IN INTERPRETIVE MODE I.E., FOLLOWING TC  INTPRET,SQRT   NO ADDRESS IS ALLOWED
046747,002379:                                                                                                  #  INPUT SCALING  THE BINARY POINT IS ASSUMED TO THE RIGHT OF BIT 15. THE  ANSWER IS RETURNED WITH THE SAME SCALING
046748,002380:                                                                                                  #  SUBROUTINES- GENSCR,MPACSHR, SQRTSUB,ABORT
046749,002381:                                                                                                  #  ABORT EXIT MODE- ABORTS ON NEGATIVE INPUT -1.2X10E-4 (77775  OCTAL)     OR LESS.
046750,002382:                                                                                                  #      DISPLAYS ERROR CODE 1302
046751,002383:                                                                                                  #                  TC   ABORT
046752,002384:                                                                                                  #                  OCT  1302
046753,002385:                                                                                                  #  DEBRIS -  LOCATIONS BUF,MPTEMP,ADDRWD ARE USED
046754,002386: 00,3207           03343        SQRT               TC       SQRTSUB                               #  TAKE THE SQUARE ROOT OF MPAC.
046755,002387: 00,3210           10135                           CCS      MPTEMP                                #  RETURNED NORMALIZED SQUARE ROOT. SEE IF
046756,002388: 00,3211           13213                           TCF      +2                                    #  ANY UN-NORMALIZATION REQUIRED AND EXIT
046757,002389: 00,3212           16073                           TCF      DANZIG                                #  IF NOT.
046758,002390: 
046759,002391: 00,3213           63733                           AD       NEG12                                 #  A RIGHT SHIFT OF MORE THAN 13 COULD BE
046760,002392: 00,3214           00006                           EXTEND                                         #  REQUIRED IF INPUT WAS ZERO IN MPAC,+1.
046761,002393: 00,3215           63221                           BZMF     SQRTSHFT                              #  GOES HERE IN MOST CASES.
046762,002394: 00,3216           22007                           ZL                                             #  IF A LONG SHIFT IS REQUIRED, GO TO
046763,002395: 00,3217           22116                           LXCH     ADDRWD                                #  GENERAL RIGHT SHIFT ROUTINES.
046764,002396: 00,3220           12303                           TCF      GENSCR     +4                         #  ADDRWD WAS ZERO TO PREVENT ROUND.
046765,002397: 
046766,002398: 00,3221           50135        SQRTSHFT           INDEX    MPTEMP                                #  SELECT SHIFTING BIT AND EXIT THROUGH
046767,002399: 00,3222           34735                           CAF      BIT15                                 #  SHIFT ROUTINES.
046768,002400: 00,3223           54135                           TS       MPTEMP                                
046769,002401: 00,3224           34755                           CAF      ZERO                                  #  TO ZERO MPAC +2 IN THE PROCESS.
046770,002402: 00,3225           12036                           TCF      MPACSHR    +3                         
046771,002403: 
046772,002404: 00,3226           06735        ABS                TC       BRANCH                                #  TEST SIGN OF MPAC AND COMPLEMENT IF
046773,002405: 00,3227           16073                           TCF      DANZIG                                
046774,002406: 00,3230           16073                           TCF      DANZIG                                
046775,002407: 00,3231           17702                           TCF      COMP                                  
046776,002408: 

Page 1068

046778,002410: 00,3232           44751        VDEF               CS       FOUR                                  #  VECTOR DEFINE - ESSENTIALLY TREATS
046779,002411: 00,3233           26166                           ADS      PUSHLOC                               #  SCALAR IN MPAC AS X COMPONENT, PUSHES UP
046780,002412: 00,3234           00006                           EXTEND                                         #  FOR Y AND THEN AGAIN FOR Z.
046781,002413: 00,3235           50000                           INDEX    A                                     
046782,002414: 00,3236           30003                           DCA      2                                     
046783,002415: 00,3237           52160                           DXCH     MPAC       +3                         
046784,002416: 00,3240           00006                           EXTEND                                         
046785,002417: 00,3241           50166                           INDEX    PUSHLOC                               
046786,002418: 00,3242           30001                           DCA      0                                     
046787,002419: 00,3243           52162                           DXCH     MPAC       +5                         
046788,002420: 00,3244           16533                           TCF      VMODE                                 #  MODE IS NON VECTOR.
046789,002421: 
046790,002422: 00,3245           03317        VSQ                TC       VSQSUB                                #  DOT MPAC WITH ITSELF.
046791,002423: 00,3246           17344                           TCF      DMODE                                 #  MODE IS NOW DP.
046792,002424: 
046793,002425: 00,3247           00006        PUSH               EXTEND                                         #  PUSH DOWN MPAC LEAVING IT LOADED.
046794,002426: 00,3250           30155                           DCA      MPAC                                  
046795,002427: 00,3251           50166                           INDEX    PUSHLOC                               #  PUSH DOWN FIRST TWO REGISTERS IN EACH
046796,002428: 00,3252           52001                           DXCH     0                                     
046797,002429: 
046798,002430: 00,3253           50163                           INDEX    MODE                                  #  INCREMENT PUSHDOWN POINTER.
046799,002431: 00,3254           36256                           CAF      NO.WDS                                
046800,002432: 00,3255           26166                           ADS      PUSHLOC                               
046801,002433: 
046802,002434: 00,3256           10163                           CCS      MODE                                  
046803,002435: 00,3257           13272                           TCF      TPUSH                                 #  PUSH DOWN MPAC +2.
046804,002436: 00,3260           16073                           TCF      DANZIG                                #  DONE FOR DP.
046805,002437: 
046806,002438: 00,3261           00006                           EXTEND                                         #  ON VECTOR, PUSH DOWN Y AND Z COMPONENTS.
046807,002439: 00,3262           30160                           DCA      MPAC       +3                         
046808,002440: 00,3263           50166                           INDEX    PUSHLOC                               
046809,002441: 00,3264           51775                           DXCH     0          -4                         
046810,002442: 00,3265           00006                           EXTEND                                         
046811,002443: 00,3266           30162                           DCA      MPAC       +5                         
046812,002444: 00,3267           50166                           INDEX    PUSHLOC                               
046813,002445: 00,3270           51777                           DXCH     0          -2                         
046814,002446: 00,3271           16073                           TCF      DANZIG                                
046815,002447: 
046816,002448: 00,3272           30156        TPUSH              CA       MPAC       +2                         
046817,002449: 00,3273           16566                           TCF      ENDTPUSH   +2                         
046818,002450: 
046819,002451: 00,3274           50120        RVQ                INDEX    FIXLOC                                #  RVQ - RETURN IVA QPRET.
046820,002452: 00,3275           30052                           CA       QPRET                                 
046821,002453: 00,3276           54117                           TS       POLISH                                
046822,002454: 00,3277           16664                           TCF      GOTO       +4                         #  (ASSUME QPRET POINTS TO FIXED ONLY.)
046823,002455: 

Page 1069

046825,002457:                                                                                                  #           THE FOLLOWING SUBROUTINES ARE USED IN SQUARING MPAC, IN BOTH THE SCALAR AND VECTOR SENSE. THEY ARE
046826,002458:                                                                                                  #  SPECIAL CASES OF DMPSUB AND DOTSUB, PUT IN TO SAVE SOME TIME.
046827,002459: 
046828,002460: 00,3300           30155        DSQSUB             CA       MPAC       +1                         #  SQUARES THE SCALAR CONTENTS OF MPAC.
046829,002461: 00,3301           00006                           EXTEND                                         
046830,002462: 00,3302           70000                           SQUARE                                         
046831,002463: 00,3303           54156                           TS       MPAC       +2                         
046832,002464: 00,3304           34755                           CAF      ZERO                                  #  FORM 2(CROSS TERM).
046833,002465: 00,3305           56155                           XCH      MPAC       +1                         
046834,002466: 00,3306           00006                           EXTEND                                         
046835,002467: 00,3307           70154                           MP       MPAC                                  
046836,002468: 00,3310           20001                           DDOUBL                                         #  AND MAYBE OVERFLOW.
046837,002469: 00,3311           20156                           DAS      MPAC       +1                         #  AND SET A TO NET OVERFLOW.
046838,002470: 00,3312           56154                           XCH      MPAC                                  
046839,002471: 00,3313           00006                           EXTEND                                         
046840,002472: 00,3314           70000                           SQUARE                                         
046841,002473: 00,3315           20155                           DAS      MPAC                                  
046842,002474: 00,3316           00002                           TC       Q                                     
046843,002475: 
046844,002476: 00,3317           00006        VSQSUB             EXTEND                                         #  DOTS THE VECTOR IN MPAC WITH ITSELF.
046845,002477: 00,3320           22137                           QXCH     DOTRET                                
046846,002478: 00,3321           03300                           TC       DSQSUB                                #  SQUARE THE X COMPONENT.
046847,002479: 00,3322           52160                           DXCH     MPAC       +3                         
046848,002480: 00,3323           52155                           DXCH     MPAC                                  
046849,002481: 00,3324           52131                           DXCH     BUF                                   #  SO WE CAN END IN DOTSUB.
046850,002482: 00,3325           30156                           CA       MPAC       +2                         
046851,002483: 00,3326           54132                           TS       BUF        +2                         
046852,002484: 
046853,002485: 00,3327           03300                           TC       DSQSUB                                #  SQUARE Y COMPONENT.
046854,002486: 00,3330           52156                           DXCH     MPAC       +1                         
046855,002487: 00,3331           20132                           DAS      BUF        +1                         
046856,002488: 00,3332           60154                           AD       MPAC                                  
046857,002489: 00,3333           60130                           AD       BUF                                   
046858,002490: 00,3334           54130                           TS       BUF                                   
046859,002491: 00,3335           13337                           TCF      +2                                    
046860,002492: 00,3336           54121                           TS       OVFIND                                #  IF OVERFLOW.
046861,002493: 
046862,002494: 00,3337           52162                           DXCH     MPAC       +5                         
046863,002495: 00,3340           52155                           DXCH     MPAC                                  
046864,002496: 00,3341           03300                           TC       DSQSUB                                #  SQUARE Z COMPONENT.
046865,002497: 00,3342           17217                           TCF      ENDDOT                                #  END AS IN DOTSUB.
046866,002498: 

Page 1070

046868,002500:                                                                                                  #           DOUBLE PRECISION SQUARE ROOT ROUTINE. TAKE THE SQUARE ROOT OF THE TRIPLE PRECISION (MPAC +2 USED ONLY
046869,002501:                                                                                                  #  IN NORMALIZATION) CONTENTS OF MPAC AND LEAVE THE NORMALIZED RESULT IN MPAC (C(MPAC) GREATER THAN OR EQUAL TO
046870,002502:                                                                                                  #  .5). THE RIGHT SHIFT COUNT (TO UNNORMALIZE) IS LEFT IN MPTEMP.
046871,002503: 
046872,002504: 00,3343           34755        SQRTSUB            CAF      ZERO                                  #  START BY ZEROING RIGHT SHIFT COUNT.
046873,002505: 00,3344           54135                           TS       MPTEMP                                
046874,002506: 
046875,002507: 00,3345           10154                           CCS      MPAC                                  #  CHECK FOR POSITIVE ARGUMENT, SHIFTING
046876,002508: 00,3346           13405                           TCF      SMPAC+                                #  FIRST SIGNIFICANT MPAC REGISTER INTO
046877,002509: 00,3347           13351                           TCF      +2                                    #  MPAC ITSELF.
046878,002510: 00,3350           13373                           TCF      SQRTNEG                               #  SEE IF MAG OF ARGUMENT LESS THAN 10(-4).
046879,002511: 
046880,002512: 00,3351           56156                           XCH      MPAC       +2                         #  MPAC IS ZERO - SHIFT LEFT 14.
046881,002513: 00,3352           56155                           XCH      MPAC       +1                         
046882,002514: 00,3353           54154                           TS       MPAC                                  
046883,002515: 00,3354           34757                           CAF      SEVEN                                 #  AUGMENT RIGHT SHIFT COUNTER.
046884,002516: 00,3355           54135                           TS       MPTEMP                                
046885,002517: 
046886,002518: 00,3356           10154                           CCS      MPAC                                  #  SEE IF MPAC NOW PNZ.
046887,002519: 00,3357           13405                           TCF      SMPAC+                                
046888,002520: 00,3360           13362                           TCF      +2                                    
046889,002521: 00,3361           13376                           TCF      ZEROANS                               #  NEGATIVE BUT LESS THAN 10(-4) IN MAG.
046890,002522: 
046891,002523: 00,3362           56155                           XCH      MPAC       +1                         #  ZERO - SHIFT LEFT 14 AGAIN.
046892,002524: 00,3363           54154                           TS       MPAC                                  
046893,002525: 00,3364           34757                           CAF      SEVEN                                 #  AUGMENT RIGHT SHIFT COUNTER.
046894,002526: 00,3365           26135                           ADS      MPTEMP                                
046895,002527: 
046896,002528: 00,3366           10154                           CCS      MPAC                                  
046897,002529: 00,3367           13405                           TCF      SMPAC+                                
046898,002530: 00,3370           00002                           TC       Q                                     #  SQRT(0) = 0.
046899,002531: 00,3371           13376                           TCF      ZEROANS                               
046900,002532: 00,3372           13453                           TCF      FIXROOT                               #  DO NOT LEAVE SQRTSUB WITH -0 IN MPAC.
046901,002533: 
046902,002534: 00,3373           10000        SQRTNEG            CCS      A                                     #  ARGUMENT IS NEGATIVE, BUT SEE IF SIGN-
046903,002535: 00,3374           13402                           TCF      SQRTABRT                              #  CORRECTED ARGUMENT IS LESS THAN 10(-4)
046904,002536: 
046905,002537: 00,3375           10155                           CCS      MPAC       +1                         #  IN MAGNITUDE. IF SO, CALL ANSWER ZERO.
046906,002538: 00,3376           34755        ZEROANS            CAF      ZERO                                  #  FORCE ANSWER TO ZERO HERE.
046907,002539: 00,3377           13453                           TCF      FIXROOT                               
046908,002540: 00,3400           13402                           TCF      SQRTABRT                              
046909,002541: 00,3401           13453                           TCF      FIXROOT                               
046910,002542: 
046911,002543: 00,3402           52165        SQRTABRT           DXCH     LOC                                   
046912,002544: 00,3403           05727                           TC       POODOO1                               
046913,002545: 00,3404           21302                           OCT      21302                                 
046914,002546: 
046915,002547: 00,3405           62444        SMPAC+             AD       -1/2+2                                #  SEE IF ARGUMENT GREATER THAN OR EQUAL TO

Page 1071

046917,002549: 00,3406           00006                           EXTEND                                         #  .5.
046918,002550: 00,3407           63456                           BZMF     SRTEST                                #  IF SO, SEE IF LESS THAN .25.
046919,002551: 
046920,002552: 00,3410           52155                           DXCH     MPAC                                  #  WE WILL TAKE THE SQUARE ROOT OF MPAC/2.
046921,002553: 00,3411           22021                           LXCH     SR                                    #  SHIFT RIGHT 1 AND GO TO THE SQRT ROUTINE
046922,002554: 00,3412           00006                           EXTEND                                         
046923,002555: 00,3413           74736                           MP       HALF                                  
046924,002556: 00,3414           52155                           DXCH     MPAC                                  
046925,002557: 00,3415           56021                           XCH      SR                                    
046926,002558: 00,3416           26155                           ADS      MPAC       +1                         #  GUARANTEED NO OVERFLOW.
046927,002559: 
046928,002560: 00,3417           32314        ARGHI              CAF      SLOPEHI                               #  ARGUMENT BETWEEN .25 AND .5. GET A
046929,002561: 00,3420           00006                           EXTEND                                         #  LINEAR APPROXIMATION FOR THIS RANGE.
046930,002562: 00,3421           70154                           MP       MPAC                                  
046931,002563: 00,3422           62566                           AD       BIASHI                                #  X0/2 = (MPAC/2)(SLOPEHI) + BIASHI/2.
046932,002564: 
046933,002565: 00,3423           54130                 +4        TS       BUF                                   #  X0/2 (ARGLO ENTERS HERE).
046934,002566: 00,3424           30154                           CA       MPAC                                  #  SINGLE-PRECISION THROUGHOUT.
046935,002567: 00,3425           22007                           ZL                                             
046936,002568: 00,3426           00006                           EXTEND                                         
046937,002569: 00,3427           10130                           DV       BUF                                   #  (MPAC/2)/(X0/2)
046938,002570: 00,3430           00006                           EXTEND                                         
046939,002571: 00,3431           74736                           MP       HALF                                  
046940,002572: 00,3432           26130                           ADS      BUF                                   #  X1 = X0/2 + .5(MPAC/2)/(X0/2).
046941,002573: 
046942,002574: 00,3433           00006                           EXTEND                                         
046943,002575: 00,3434           74736                           MP       HALF                                  #  FORM UP X1/2.
046944,002576: 00,3435           52155                           DXCH     MPAC                                  #  SAVE AND BRING OUT ARGUMENT.
046945,002577: 00,3436           00006                           EXTEND                                         #  TAKE DP QUOTIENT WITH X1.
046946,002578: 00,3437           10130                           DV       BUF                                   
046947,002579: 00,3440           54131                           TS       BUF        +1                         #  SAVE MAJOR PART OF QUOTIENT.
046948,002580: 00,3441           34755                           CAF      ZERO                                  #  FORM MINOR PART OF QUOTIENT USING
046949,002581: 00,3442           56001                           XCH      L                                     #  (REMAINDER,0).
046950,002582: 00,3443           00006                           EXTEND                                         
046951,002583: 00,3444           10130                           DV       BUF                                   
046952,002584: 00,3445           54001                           TS       L                                     #  IN PREPARATION FOR DAS.
046953,002585: 00,3446           30131                           CA       BUF        +1                         
046954,002586: 00,3447           20155                           DAS      MPAC                                  #  X2 = X1/2 + (MPAC/2)X1
046955,002587: 
046956,002588: 00,3450           00006                           EXTEND                                         #  OVERFLOWS IF ARG. NEAR POSMAX.
046957,002589: 00,3451           13455                           BZF      TCQBNK00                              
046958,002590: 00,3452           34733                           CAF      POSMAX                                
046959,002591: 00,3453           54154        FIXROOT            TS       MPAC                                  
046960,002592: 00,3454           54155                           TS       MPAC       +1                         
046961,002593: 00,3455           00002        TCQBNK00           TC       Q                                     #  RETURN TO CALLER TO UNNORMALIZE, ETC.
046962,002594: 

Page 1072

046964,002596: 00,3456           64737        SRTEST             AD       QUARTER                               #  ARGUMENT WAS LESS THAN .5, SEE IF LESS
046965,002597: 00,3457           00006                           EXTEND                                         #  THAN .25.
046966,002598: 00,3460           63502                           BZMF     SQRTNORM                              #  IF SO, BEGIN NORMALIZATION.
046967,002599: 
046968,002600: 00,3461           52155                           DXCH     MPAC                                  #  IF BETWEEN .5 AND .25, SHIFT RIGHT 1 AND
046969,002601: 00,3462           22021                           LXCH     SR                                    #  START AT ARGLO.
046970,002602: 00,3463           00006                           EXTEND                                         
046971,002603: 00,3464           74736                           MP       HALF                                  
046972,002604: 00,3465           52155                           DXCH     MPAC                                  
046973,002605: 00,3466           56021                           XCH      SR                                    
046974,002606: 00,3467           26155                           ADS      MPAC       +1                         #  NO OVERFLOW.
046975,002607: 
046976,002608: 00,3470           33007        ARGLO              CAF      SLOPELO                               #  (NORMALIZED) ARGUMENT BETWEEN .125 AND
046977,002609: 00,3471           00006                           EXTEND                                         #  .25
046978,002610: 00,3472           70154                           MP       MPAC                                  
046979,002611: 00,3473           62270                           AD       BIASLO                                
046980,002612: 00,3474           13423                           TCF      ARGHI      +4                         #  BEGIN SQUARE ROOT.
046981,002613: 
046982,002614: 00,3475           00006        SQRTNM2            EXTEND                                         #  SHIFT LEFT 2 AND INCREMENT RIGHT SHIFT
046983,002615: 00,3476           30156                           DCA      MPAC       +1                         #  COUNT (FOR TERMINAL UNNORMALIZATION).
046984,002616: 00,3477           20156                           DAS      MPAC       +1                         
046985,002617: 00,3500           60154                           AD       MPAC                                  
046986,002618: 00,3501           26154                           ADS      MPAC                                  #  (NO OVERFLOW).
046987,002619: 
046988,002620: 00,3502           24135        SQRTNORM           INCR     MPTEMP                                #  FIRST TIME THROUGH, JUST SHIFT LEFT 1
046989,002621: 00,3503           00006                           EXTEND                                         #  (PUTS IN EFFECTIVE RIGHT SHIFT SINCE
046990,002622: 00,3504           30156                           DCA      MPAC       +1                         #  WE WANT MPAC/2).
046991,002623: 00,3505           20156                           DAS      MPAC       +1                         
046992,002624: 00,3506           60154                           AD       MPAC                                  
046993,002625: 00,3507           26154                           ADS      MPAC                                  #  (AGAIN NO OVERFLOW).
046994,002626: 00,3510           60000                           DOUBLE                                         
046995,002627: 00,3511           54022                           TS       CYL                                   
046996,002628: 
046997,002629: 00,3512           10022        NORMTEST           CCS      CYL                                   #  SEE IF ARGUMENT NOW NORMALIZED AT
046998,002630: 00,3513           10022                           CCS      CYL                                   #  GREATER THAN .125.
046999,002631: 00,3514           13475                           TCF      SQRTNM2                               #  NO - SHIFT LEFT 2 MORE AND TRY AGAIN.
047000,002632: 00,3515           13417                           TCF      ARGHI                                 #  YES - NOW BETWEEN .5 AND .25.
047001,002633: 00,3516           13470                           TCF      ARGLO                                 #  ARGUMENT NOW BETWEEN .25 AND .125.
047002,002634: 

Page 1073

047004,002636:                                                                                                  #  TRIGONOMETRIC FUNCTION PACKAGE.
047005,002637: 
047006,002638:                                                                                                  #           THE FOLLOWING TRIGONOMETRIC FUNCTIONS ARE AVAILABLE AS INTERPRETIVE OPERATIONS:
047007,002639: 
047008,002640:                                                                                                  #           1.  SIN                COMPUTES (1/2)SINE(2 PI MPAC).
047009,002641:                                                                                                  #           2.  COS                COMPUTES (1/2)COSINE(2 PI MPAC).
047010,002642: 
047011,002643:                                                                                                  #           3.  ASIN               COMPUTES (1/2PI)ARCSINE(2 MPAC).
047012,002644:                                                                                                  #           4.  ACOS               COMPUTES (1/2PI)ARCCOSINE(2 MPAC).
047013,002645: 
047014,002646:                                                                                                  #  SIN-ASIN AND COS-ACOS ARE MUTUALLY INVERSE, IE SIN(ASIN(X)) = X.
047015,002647: 
047016,002648: 00,3517           06735        COSINE             TC       BRANCH                                #  FINDS COSINE USING THE IDENTITY
047017,002649: 00,3520           13523                           TCF      +3                                    #  COS(X) = SIN(PI/2 - ABS(X)).
047018,002650: 00,3521           13526                           TCF      PRESINE                               
047019,002651: 00,3522           13526                           TCF      PRESINE                               
047020,002652: 
047021,002653: 00,3523           00006                 +3        EXTEND                                         
047022,002654: 00,3524           40155                           DCS      MPAC                                  
047023,002655: 00,3525           52155                           DXCH     MPAC                                  
047024,002656: 
047025,002657: 00,3526           34737        PRESINE            CAF      QUARTER                               #  PI/2 SCALED.
047026,002658: 00,3527           26154                           ADS      MPAC                                  
047027,002659: 
047028,002660: 
047029,002661: 00,3530           52155        SINE               DXCH     MPAC                                  #  DOUBLE ARGUMENT.
047030,002662: 00,3531           20001                           DDOUBL                                         
047031,002663: 00,3532           54000                           OVSK                                           #  SEE IF OVERFLOW PRESENT.
047032,002664: 00,3533           13536                           TCF      +3                                    #  IF NOT, ARGUMENT OK AS IS.
047033,002665: 
047034,002666: 00,3534           00006                           EXTEND                                         #  IF SO, WE LOST (OR GAINED) PI, SO
047035,002667: 00,3535           40001                           DCOM                                           #  COMPLEMENT MPAC USING THE IDENTITY
047036,002668:                                                                                                  #  SIN(X-(+)PI) = SIN(-X).
047037,002669: 00,3536           52155                 +3        DXCH     MPAC                                  
047038,002670: 00,3537           30154                           CA       MPAC                                  #  SEE IF ARGUMENT GREATER THAN .5 IN
047039,002671: 00,3540           60000                           DOUBLE                                         #  MAGNITUDE. IF SO, REDUCE IT TO LESS THAN
047040,002672: 00,3541           54001                           TS       L                                     #  .5 (+-PI/2 SCALED) AS FOLLOWS:
047041,002673: 00,3542           13553                           TCF      SN1                                   
047042,002674: 
047043,002675: 00,3543           50000                           INDEX    A                                     #  IF POSITIVE, FORM PI - X, IF NEGATIVE
047044,002676: 00,3544           34735                           CAF      NEG1/2     +1                         #  USE -PI - X.
047045,002677: 00,3545           60000                           DOUBLE                                         
047046,002678: 00,3546           00006                           EXTEND                                         
047047,002679: 00,3547           60154                           SU       MPAC                                  #  GUARANTEED NO OVERFLOW.
047048,002680: 00,3550           54154                           TS       MPAC                                  
047049,002681: 00,3551           40155                           CS       MPAC       +1                         
047050,002682: 00,3552           54155                           TS       MPAC       +1                         
047051,002683: 

Page 1074

047053,002685: 00,3553           00006        SN1                EXTEND                                         #  SET UP TO EVALUATE HASTINGS POLYNOMIAL
047054,002686: 00,3554           30155                           DCA      MPAC                                  
047055,002687: 00,3555           52134                           DXCH     BUF2                                  
047056,002688: 00,3556           03300                           TC       DSQSUB                                #  SQUARE MPAC.
047057,002689: 
047058,002690: 00,3557           07234                           TC       POLY                                  #  EVALUATE FOURTH ORDER POLYNOMIAL.
047059,002691: 00,3560           00003                           DEC      3          B-14                       
047060,002692: 00,3561           14441 37325                     2DEC     +.3926990796                            
047061,002693: 
047062,002694: 00,3563           53250 60764                     2DEC     -.6459637111                            
047063,002695: 
047064,002696: 00,3565           12146 21276                     2DEC     +.318758717                            
047065,002697: 
047066,002698: 00,3567           75466 71471                     2DEC     -.074780249                            
047067,002699: 
047068,002700: 00,3571           00236 32757                     2DEC     +.009694988                            
047069,002701: 
047070,002702: 
047071,002703: 00,3573           32470                           CAF      LBUF2                                 #  MULTIPLY BY ARGUMENT AND SHIFT LEFT 2.
047072,002704: 00,3574           07120                           TC       DMPSUB     -1                         
047073,002705: 
047074,002706: 00,3575           00006                           EXTEND                                         
047075,002707: 00,3576           30156                           DCA      MPAC       +1                         
047076,002708: 00,3577           20156                           DAS      MPAC       +1                         
047077,002709: 00,3600           60154                           AD       MPAC                                  
047078,002710: 00,3601           26154                           ADS      MPAC                                  #  NEITHER SHIFT OVERFLOWS.
047079,002711: 00,3602           00006                           EXTEND                                         
047080,002712: 00,3603           30156                           DCA      MPAC       +1                         
047081,002713: 00,3604           20156                           DAS      MPAC       +1                         
047082,002714: 00,3605           60154                           AD       MPAC                                  
047083,002715: 00,3606           26154                           ADS      MPAC                                  
047084,002716: 00,3607           16073                           TCF      DANZIG                                
047085,002717: 

Page 1075

047087,002719:                                                                                                  #           ARCSIN/ARCCOS ROUTINE.
047088,002720: 
047089,002721: 00,3610           33631        ARCSIN             CAF      LASINEX                               #  COMPUTE ARCSIN BY USING THE IDENTITY
047090,002722: 00,3611           13613                           TCF      +2                                    #  ARCSIN(X) = PI/2 - ARCCOS(X).
047091,002723: 
047092,002724: 00,3612           33713        ARCCOS             CAF      LDANZIG                               #  (EXITS IMMEDIATELY).
047093,002725: 00,3613           54136                           TS       ESCAPE                                
047094,002726: 00,3614           06735                           TC       BRANCH                                #  TEST SIGN OF INPUT.
047095,002727: 00,3615           13625                           TCF      ACOSST                                #  START IMMEDIATELY IF POSITIVE.
047096,002728: 00,3616           13731                           TCF      ACOSZERO                              #  ARCCOS(0) = PI/2 = .25.
047097,002729: 00,3617           00006                           EXTEND                                         #  IF NEGATIVE, USE THE IDENTITY
047098,002730: 00,3620           40155                           DCS      MPAC                                  #  ARCCOS(X) = PI - ARCCOS(-X), FORCING
047099,002731: 00,3621           52155                           DXCH     MPAC                                  #  ARGUMENT POSITIVE.
047100,002732: 00,3622           33734                           CAF      TCSUBTR                               #  SET EXIT  TO DO ABOVE BEFORE
047101,002733: 00,3623           56136                           XCH      ESCAPE                                #  ARCSIN/ARCCOS CONSIDERATIONS.
047102,002734: 00,3624           54137                           TS       ESCAPE2                               
047103,002735: 
047104,002736: 00,3625           44736        ACOSST             CS       HALF                                  #  TEST MAGNITUDE OF INPUT.
047105,002737: 00,3626           60154                           AD       MPAC                                  
047106,002738: 00,3627           10000                           CCS      A                                     
047107,002739: 00,3630           13721                           TCF      ACOSOVF                               #  THIS IS PROBABLY AN OVERFLOW CASE.
047108,002740: 
047109,002741: 00,3631           13707        LASINEX            TCF      ASINEX                                
047110,002742: 
047111,002743: 00,3632           13642                           TCF      ACOSST2                               #  NO OVERFLOW - PROCEED.
047112,002744: 
047113,002745: 00,3633           10155                           CCS      MPAC       +1                         #  IF MAJOR PART IS .5, CALL ANSWER 0
047114,002746: 00,3634           34755                           CAF      ZERO                                  #  UNLESS MINOR PART NEGATIVE.
047115,002747: 00,3635           13637                           TCF      ACOS=0                                
047116,002748: 
047117,002749: 00,3636           13642                           TCF      ACOSST2                               
047118,002750: 
047119,002751: 00,3637           54155        ACOS=0             TS       MPAC       +1                         
047120,002752: 00,3640           54154                           TS       MPAC                                  
047121,002753: 00,3641           00136                           TC       ESCAPE                                
047122,002754: 
047123,002755: 00,3642           00006        ACOSST2            EXTEND                                         #  NOW THAT ARGUMENT IS IN PROPER RANGE,
047124,002756: 00,3643           40155                           DCS      MPAC                                  #  BEGIN COMPUTATION. USE HASTINGS
047125,002757: 00,3644           64736                           AD       HALF                                  #  APPROXIMATION ARCCOS(X) = SQRT(1-X)P(X)
047126,002758: 00,3645           52155                           DXCH     MPAC                                  #  IN A SCALED VERSION WHERE P(X) IS A
047127,002759: 00,3646           52134                           DXCH     BUF2                                  #  SEVENTH ORDER POLYNOMIAL.
047128,002760: 
047129,002761: 00,3647           03343                           TC       SQRTSUB                               #  RETURNS WITH NORMALIZED SQUARE ROOT.
047130,002762: 
047131,002763: 00,3650           10135                           CCS      MPTEMP                                #  SEE IF UN-NORMALIZATION REQUIRED.
047132,002764: 00,3651           13714                           TCF      ACOSSHR                               #  IF SO.
047133,002765: 

Page 1076

047135,002767: 00,3652           52155        ACOS3              DXCH     MPAC                                  #  SET UP FOR POLYNOMIAL EVALUATION.
047136,002768: 00,3653           52134                           DXCH     BUF2                                  
047137,002769: 00,3654           52155                           DXCH     MPAC                                  
047138,002770: 
047139,002771: 00,3655           07234                           TC       POLY                                  
047140,002772: 00,3656           00006                           DEC      6          B-14                       
047141,002773: 00,3657           13240 23630                     2DEC     +.353553385                            #  COEFFICIENTS ARE C 2(+I)/PISQRT(2) WHERE
047142,002774: 
047143,002775: 00,3661           74721 47775                     2DEC*    -.0483017006 B+1*                       #                    I
047144,002776: 
047145,002777: 00,3663           02440 20237                     2DEC*    +.0200273085 B+2*                       #       WHERE C STANDS FOR ORIGINAL COEFFS.
047146,002778: 
047147,002779: 00,3665           75067 70742                     2DEC*    -.0112931863 B+3*                       
047148,002780: 
047149,002781: 00,3667           03436 26756                     2DEC*    +.00695311612 B+4*                       
047150,002782: 
047151,002783: 00,3671           74037 57640                     2DEC*    -.00384617957 B+5*                       
047152,002784: 
047153,002785: 00,3673           03046 07143                     2DEC*    +.001501297736 B+6*                       
047154,002786: 
047155,002787: 00,3675           76654 42244                     2DEC*    -.000284160334 B+7*                       
047156,002788: 
047157,002789: 
047158,002790: 00,3677           32470                           CAF      LBUF2                                 #  DO FINAL MULTIPLY AND GO TO ANY
047159,002791: 00,3700           07120                           TC       DMPSUB     -1                         #  EPILOGUE SEQUENCES.
047160,002792: 00,3701           00136                           TC       ESCAPE                                
047161,002793: 
047162,002794: 00,3702           00006        SUBTR              EXTEND                                         #  EPILOGUE FOR NEGATIVE INPUTS TO ARCCOS.
047163,002795: 00,3703           40155                           DCS      MPAC                                  
047164,002796: 00,3704           64736                           AD       HALF                                  #  FORMS PI - ARCCOS(-X) = ARCCOS(X).
047165,002797: 00,3705           52155                           DXCH     MPAC                                  
047166,002798: 00,3706           00137                           TC       ESCAPE2                               #  GO TO POSSIBLE ARCSIN EPILOGUE.
047167,002799: 
047168,002800: 00,3707           00006        ASINEX             EXTEND                                         
047169,002801: 00,3710           40155                           DCS      MPAC                                  #  ARCSIN EPILOGUE - GET ARCSIN(X)
047170,002802: 00,3711           64737                           AD       QUARTER                               #  = PI/2 - ARCCOS(X).
047171,002803: 00,3712           52155                           DXCH     MPAC                                  
047172,002804: 00,3713           16073        LDANZIG            TCF      DANZIG                                
047173,002805: 

Page 1077

047175,002807: 00,3714           50000        ACOSSHR            INDEX    A                                     #  THE SHIFT RIGHT IS LESS THAN 14 SINCE
047176,002808: 00,3715           34736                           CAF      BIT14                                 #  THE INPUT WAS NON-ZERO DP.
047177,002809: 00,3716           54135                           TS       MPTEMP                                
047178,002810: 00,3717           02073                           TC       VSHRRND                               #  DP SHIFT RIGHT AND ROUND.
047179,002811: 00,3720           13652                           TCF      ACOS3                                 #  PROCEED.
047180,002812: 
047181,002813: 00,3721           00006        ACOSOVF            EXTEND                                         #  IF MAJOR PART WAS ONLY 1 MORE THAN .5,
047182,002814: 00,3722           13637                           BZF      ACOS=0                                #  CALL ANSWER ZERO.
047183,002815: 
047184,002816: 00,3723           00006        ACOSABRT           EXTEND                                         #  IF OVERFLOW, CALL ANSWER ZERO BUT
047185,002817: 00,3724           30165                           DCA      LOC                                   #  SOUND AN ALARM.
047186,002818: 00,3725           05733                           TC       ALARM1                                
047187,002819: 00,3726           01301                           OCT      1301                                  
047188,002820: 
047189,002821: 00,3727           34755                           CAF      ZERO                                  
047190,002822: 00,3730           13637                           TCF      ACOS=0                                
047191,002823: 
047192,002824: 00,3731           34737        ACOSZERO           CAF      QUARTER                               #  ACOS(0) = PI/2.
047193,002825: 00,3732           13640                           TCF      ACOS=0     +1                         #  SET MPAC AND EXIT VIA ESCAPE.
047194,002826: 
047195,002827: 00,3733           77763        NEG12              DEC      -12        B-14                       
047196,002828: 00,3734           13702        TCSUBTR            TCF      SUBTR                                 
047197,002829: 

Page 1078

047199,002831:                                                                                                  #           THE FOLLOWING INSTRUCTIONS ARE AVAILABLE FOR SETTING, MODIFYING, AND BRANCHING ON INDEX REGISTERS:
047200,002832: 
047201,002833:                                                                                                  #           1.  AXT                ADDRESS TO INDEX TRUE.
047202,002834:                                                                                                  #           1.  AXC                ADDRESS TO INDEX COMPLEMENTED.
047203,002835:                                                                                                  #           3.  LXA                LOAD INDEX FROM ERASABLE.
047204,002836:                                                                                                  #           4.  LXC                LOAD INDEX COMPLEMENTED FROM ERASABLE.
047205,002837:                                                                                                  #           5.  SXA                STORE INDEX IN ERASABLE.
047206,002838:                                                                                                  #           6.  XCHX               EXCHANGE INDEX REIGSTER WITH ERASABLE.
047207,002839: 
047208,002840:                                                                                                  #           7.  INCR               INCREMENT INDEX REGISTER.
047209,002841:                                                                                                  #           8.  XAD                ERASABLE ADD TO INDEX REGISTER.
047210,002842:                                                                                                  #           9.  XSU                ERASABLE SUBTRACT FROM INDEX REGISTER.
047211,002843: 
047212,002844:                                                                                                  #          10.  TIX                BRANCH ON INDEX REGISTER AND DECREMENT.
047213,002845: 
047214,002846: 01,2350                                           BANK     01                                    
047215,002847: 
047216,002848: 01,2350                                           COUNT*   $$/INTER                              
047217,002849: 01,2350           02445        AXT                TC       TAGSUB                                #  SELECT APPROPRIATE INDEX REGISTER.
047218,002850: 01,2351           30117                           CA       POLISH                                
047219,002851: 01,2352           50130        XSTORE             INDEX    INDEXLOC                              #  CONTAINS C(FIXLOC) OR C(FIXLOC)+1.
047220,002852: 01,2353           54046                           TS       X1                                    
047221,002853: 01,2354           16073                           TCF      DANZIG                                
047222,002854: 
047223,002855: 01,2355           02445        AXC                TC       TAGSUB                                
047224,002856: 01,2356           40117                           CS       POLISH                                
047225,002857: 01,2357           02352                           TC       XSTORE                                
047226,002858: 
047227,002859: 01,2360           02433        LXA                TC       15ADRERS                              #  LOAD INDEX REGISTER FROM ERASABLE.
047228,002860: 01,2361           50117                           INDEX    POLISH                                
047229,002861: 01,2362           30000                           CA       0                                     
047230,002862: 01,2363           12352                           TCF      XSTORE                                
047231,002863: 
047232,002864: 01,2364           02433        LXC                TC       15ADRERS                              #  LOAD NDX REG FROM ERASABLE COMPLEMENTED.
047233,002865: 01,2365           50117                           INDEX    POLISH                                
047234,002866: 01,2366           40000                           CS       0                                     
047235,002867: 01,2367           12352                           TCF      XSTORE                                
047236,002868: 
047237,002869: 01,2370           02433        SXA                TC       15ADRERS                              #  STORE INDEX REGISTER IN ERASABLE.
047238,002870: 01,2371           50130                           INDEX    INDEXLOC                              
047239,002871: 01,2372           30046                           CA       X1                                    
047240,002872: 01,2373           50117        MSTORE1            INDEX    POLISH                                
047241,002873: 01,2374           54000                           TS       0                                     
047242,002874: 01,2375           16073                           TCF      DANZIG                                
047243,002875: 

Page 1079

047245,002877: 01,2376           02433        XCHX               TC       15ADRERS                              #  EXCHANGE INDEX REGISTER WITH ERASABLE.
047246,002878: 01,2377           50117                           INDEX    POLISH                                
047247,002879: 01,2400           30000                           CA       0                                     
047248,002880: 01,2401           50130                           INDEX    INDEXLOC                              
047249,002881: 01,2402           56046                           XCH      X1                                    
047250,002882: 01,2403           12373                           TCF      MSTORE1                               
047251,002883: 
047252,002884: 01,2404           02433        XAD                TC       15ADRERS                              #  ADD ERASABLE TO INDEX REGISTER.
047253,002885: 01,2405           50117                           INDEX    POLISH                                
047254,002886: 01,2406           30000                           CA       0                                     
047255,002887: 01,2407           50130        XAD2               INDEX    INDEXLOC                              
047256,002888: 01,2410           26046                           ADS      X1                                    #  IGNORING OVERFLOWS.
047257,002889: 01,2411           16073                           TCF      DANZIG                                
047258,002890: 
047259,002891: 01,2412           02445        INCR               TC       TAGSUB                                #  INCREMENT INDEX REGISTER.
047260,002892: 01,2413           30117                           CA       POLISH                                
047261,002893: 01,2414           12407                           TCF      XAD2                                  
047262,002894: 
047263,002895: 01,2415           02433        XSU                TC       15ADRERS                              #  SUBTRACT ERASABLE FROM INDEX REGISTER.
047264,002896: 01,2416           50117                           INDEX    POLISH                                
047265,002897: 01,2417           40000                           CS       0                                     
047266,002898: 01,2420           12407                           TCF      XAD2                                  
047267,002899: 
047268,002900: 01,2421           02445        TIX                TC       TAGSUB                                #  BRANCH AND DECREMENT ON INDEX.
047269,002901: 01,2422           50130                           INDEX    INDEXLOC                              
047270,002902: 01,2423           40050                           CS       S1                                    
047271,002903: 01,2424           50130                           INDEX    INDEXLOC                              
047272,002904: 01,2425           60046                           AD       X1                                    
047273,002905: 01,2426           00006                           EXTEND                                         #  NO OPERATION IF DECREMENTED INDEX IS
047274,002906: 01,2427           66073                           BZMF     DANZIG                                #  NEGATIVE OR ZERO.
047275,002907: 
047276,002908: 01,2430           50130        DOTIXBR            INDEX    INDEXLOC                              
047277,002909: 01,2431           56046                           XCH      X1                                    #  IGNORING OVERFLOWS.
047278,002910: 
047279,002911: 01,2432           16660                           TCF      GOTO                                  #  DO THE BRANCH USING THE CADR IN POLISH.
047280,002912: 

Page 1080

047282,002914:                                                                                                  #           SUBROUTINE TO CONVERT AN ERASABLE ADDRESS (11 BITS) TO AN EBANK SETTING AND SUBADDRESS.
047283,002915: 
047284,002916: 01,2433           40117        15ADRERS           CS       POLISH                                
047285,002917: 01,2434           64772                           AD       DEC45                                 
047286,002918: 01,2435           10000                           CCS      A                                     #  DOES THE ADDRESS POINT TO THE WORK AREA?
047287,002919: 01,2436           30120                           CA       FIXLOC                                #  YES.  ADD FIXLOC.  EBANK OK AS IS.
047288,002920: 01,2437           12444                           TCF      +5                                    
047289,002921: 
047290,002922: 01,2440           35007                           CA       OCT1400                               #  NO.  SET EBANK & MAKE UP SUBADDRESS.
047291,002923: 01,2441           56117                           XCH      POLISH                                
047292,002924: 01,2442           54003                           TS       EBANK                                 
047293,002925: 01,2443           74357                           MASK     LOW8                                  
047294,002926: 01,2444           26117                 +5        ADS      POLISH                                #  FALL INTO TAGSUB, AND RETURN VIA Q.
047295,002927: 
047296,002928:                                                                                                  #           SUBROUTINE WHICH SETS THE ADDRESS OF THE SPECIFIED INDEX IN INDEXLOC. (ACTUALLY, THE ADDRESS -38D.)
047297,002929: 
047298,002930: 01,2445           30120        TAGSUB             CA       FIXLOC                                
047299,002931: 01,2446           54130                           TS       INDEXLOC                              
047300,002932: 
047301,002933: 01,2447           10020                           CCS      CYR                                   #  BIT 15 SPECIFIES INDEX.
047302,002934: 01,2450           24130                           INCR     INDEXLOC                              #  0 MEANS USE X2.
047303,002935: 01,2451           00002                           TC       Q                                     
047304,002936: 01,2452           00002                           TC       Q                                     #  1 FOR X1.
047305,002937: 

Page 1081

047307,002939:                                                                                                  #           MISCELLANEOUS OPERATION CODES WITH DIRECT ADDRESSES. INCLUDED HERE ARE:
047308,002940: 
047309,002941:                                                                                                  #           1.  ITA                STORE QPRET (RETURN ADDRESS) IN ERASABLE.
047310,002942:                                                                                                  #           2.  CALL               CALL A SUBROUTINE, LEAVING RETURN IN QPRET.
047311,002943:                                                                                                  #           3.  RTB                RETURN TO BASIC LANGUAGE AT THE GIVEN ADDRESS.
047312,002944:                                                                                                  #           4.  BHIZ               BRANCH IF THE HIGH ORDER OF MPAC IS ZERO (SINGLE PRECISION).
047313,002945:                                                                                                  #           5.  BOV                BRANCH ON OVERFLOW.
047314,002946:                                                                                                  #           6.  GOTO               SIMPLE SEQUENCE CHANGE.
047315,002947: 
047316,002948: 01,2453           10020        RTB/BHIZ           CCS      CYR                                   
047317,002949: 01,2454           30117        RTB                CA       POLISH                                
047318,002950: 01,2455           04621                           TC       SWCALL     -1                         #  SO A "TC Q" FROM ROUTINE LEADS TO DANZIG
047319,002951: 
047320,002952: 01,2456           10154        BHIZ               CCS      MPAC                                  
047321,002953: 01,2457           16073                           TCF      DANZIG                                
047322,002954: 01,2460           16660                           TCF      GOTO                                  
047323,002955: 01,2461           16073                           TCF      DANZIG                                
047324,002956: 01,2462           16660                           TCF      GOTO                                  
047325,002957: 
047326,002958: 01,2463           10121        BOV(B)             CCS      OVFIND                                #  BRANCH ON OVERFLOW TO BASIC OR INTERP.
047327,002959: 01,2464           12466                           TCF      +2                                    
047328,002960: 01,2465           16073                           TCF      DANZIG                                
047329,002961: 01,2466           54121                           TS       OVFIND                                
047330,002962: 01,2467           10020                           CCS      CYR                                   
047331,002963: 01,2470           12454                           TCF      RTB                                   #  IF BASIC.
047332,002964: 01,2471           00360        B5TOBB             OCT      360                                   
047333,002965: 01,2472           16660                           TCF      GOTO                                  
047334,002966: 

Page 1082

047336,002968: 01,2473           10020        BZE/GOTO           CCS      CYR                                   #  SEE WHICH OP-CODE IS DESIRED.
047337,002969: 01,2474           06735                           TC       BRANCH                                #  DO BZE.
047338,002970: 01,2475           16073                           TCF      DANZIG                                
047339,002971: 01,2476           16660                           TCF      GOTO                                  #  DO GOTO.
047340,002972: 01,2477           16073                           TCF      DANZIG                                
047341,002973: 
047342,002974: 01,2500           10020        BPL/BMN            CCS      CYR                                   
047343,002975: 01,2501           12507                           TCF      BPL                                   
047344,002976: 01,2502           12000        5B10               DEC      5          B+10                       #  SHIFTS OP CODE IN SWITCH INSTRUCTION ADR
047345,002977: 
047346,002978: 01,2503           06735                           TC       BRANCH                                #  DO BMN.
047347,002979: 01,2504           16073                           TCF      DANZIG                                
047348,002980: 01,2505           16073                           TCF      DANZIG                                
047349,002981: 01,2506           16660                           TCF      GOTO                                  #  ONLY IF NNZ.
047350,002982: 
047351,002983: 01,2507           06735        BPL                TC       BRANCH                                
047352,002984: 01,2510           16660                           TCF      GOTO                                  #  IF POSITIVE OR ZERO.
047353,002985: 01,2511           16660                           TCF      GOTO                                  
047354,002986: 01,2512           16073                           TCF      DANZIG                                
047355,002987: 
047356,002988: 01,2513           10020        CALL/ITA           CCS      CYR                                   
047357,002989: 01,2514           16652                           TCF      CALL                                  
047358,002990: 
047359,002991: 01,2515           05706                           TC       CCSHOLE                               
047360,002992: 01,2516           02433                           TC       15ADRERS                              #  STORE QPRET. (TAGSUB AFTER 15ADRERS IS
047361,002993: 01,2517           50120                           INDEX    FIXLOC                                #  SLOW IN THIS CASE, BUT SAVES STORAGE.)
047362,002994: 01,2520           30052                           CA       QPRET                                 
047363,002995: 01,2521           12373                           TCF      MSTORE1                               
047364,002996: 

Page 1083

047366,002998:                                                                                                  #           THE FOLLOWING OPERATIONS ARE AVAILABLE FOR ALTERING AND TESTING INTERPRETIVE SWITCHES:
047367,002999: 
047368,003000:                                                                                                  #  00       BONSET                 SET A SWITCH AND DO A GOTO IF IT WAS ON.
047369,003001:                                                                                                  #  01       SETGO                  SET A SWITCH AND DO A GOTO.
047370,003002:                                                                                                  #  02       BOFSET                 SET A SWITCH AND DO A GOTO IF IT WAS OFF
047371,003003:                                                                                                  #  03       SET                    SET A SWITCH.
047372,003004: 
047373,003005:                                                                                                  #  04       BONINV                 INVERT A SWITCH AND BRANCH IF IT WAS ON.
047374,003006:                                                                                                  #  05       INVGO                  INVERT A SWITCH AND DO A GOTO.
047375,003007:                                                                                                  #  06       BOFINV                 INVERT A SWITCH AND BRANCH IF IT WAS OFF
047376,003008:                                                                                                  #  07       INVERT                 INVERT A SWITCH.
047377,003009: 
047378,003010:                                                                                                  #  10       BONCLR                 CLEAR A SWITCH AND BRANCH IF IT WAS ON.
047379,003011:                                                                                                  #  11       CLRGO                  CLEAR A SWITCH AND DO A GOTO.
047380,003012:                                                                                                  #  12       BOFCLR                 CLEAR A SWITCH AND BRANCH IF IT WAS OFF.
047381,003013:                                                                                                  #  13       CLEAR                  CLEAR A SWITCH.
047382,003014: 
047383,003015:                                                                                                  #  14       BON                    BRANCH IF A SWITCH WAS ON.
047384,003016:                                                                                                  #  16       BOFF                   BRANCH IF A SWITCH WAS OFF.
047385,003017: 
047386,003018: 
047387,003019:                                                                                                  #           THE ADDRESS SUPPLIED WITH THE SWITCH INSTRUCTION IS INTERPRETED AS FOLLOWS:
047388,003020: 
047389,003021:                                                                                                  #           BITS 1-4    SWITCH BIT NUMBER (1-15).
047390,003022:                                                                                                  #           BITS 5-8    SWITCH OPERATION NUMBER.
047391,003023:                                                                                                  #           BITS 9-     SWITCH WORD NUMBER (UP TO 64 SWITCH WORDS).
047392,003024: 
047393,003025:                                                                                                  #           THE ADDRESS ITSELF IS MADE UP BY THE YUL SYSTEM ASSEMBLER. THE BRANCH INSTRUCTIONS REQUIRE TWO
047394,003026:                                                                                                  #  ADDRESSES, THE SECOND TAKEN AS THE DIRECT (OR INDIRECT IF IN ERASABLE) ADDRESS OF THE BRANCH.
047395,003027: 
047396,003028: 
047397,003029: 01,2522           34762        SWITCHES           CAF      LOW4                                  #  LEAVE THE SWITCH BIT IN  SWBIT  .
047398,003030: 01,2523           70117                           MASK     POLISH                                
047399,003031: 01,2524           50000                           INDEX    A                                     
047400,003032: 01,2525           34735                           CAF      BIT15                                 #  (NUMBER FROM LEFT TO RIGHT.)
047401,003033: 01,2526           54131                           TS       SWBIT                                 
047402,003034: 
047403,003035: 01,2527           34745                           CAF      BIT7                                  #  LEAVE THE SWITCH NUMBER IN SWWORD.
047404,003036: 01,2530           00006                           EXTEND                                         
047405,003037: 01,2531           70117                           MP       POLISH                                
047406,003038: 01,2532           54130                           TS       SWWORD                                
047407,003039: 
047408,003040: 01,2533           00004                           INHINT                                         #  DURING SWITCH CHANGE SO RUPT CAN USE TOO
047409,003041: 01,2534           50000                           INDEX    A                                     #  LEAVE THE SWITCH WORD ITSELF IN L.
047410,003042: 01,2535           30074                           CA       STATE                                 
047411,003043: 01,2536           54002                           TS       Q                                     #  Q WILL BE USED AS A CHANNEL.

Page 1084

047413,003045: 01,2537           34741                           CAF      BIT11                                 
047414,003046: 01,2540           00006                           EXTEND                                         #  DISPATCH SWITCH BIT OPERATION AS IN BITS
047415,003047: 01,2541           70117                           MP       POLISH                                #  7-8 OF POLISH.
047416,003048: 01,2542           72602                           MASK     B3TOB4                                #  GETS 4X2-BIT CODE.
047417,003049: 01,2543           50000                           INDEX    A                                     
047418,003050: 01,2544           12545                           TCF      +1                                    
047419,003051: 
047420,003052: 01,2545           30131                 +1        CA       SWBIT                                 #  00 - SET SWITCH IN QUESTION.
047421,003053: 01,2546           00006                           EXTEND                                         
047422,003054: 01,2547           04002                           ROR      QCHAN                                 
047423,003055: 01,2550           12557                           TCF      SWSTORE                               
047424,003056: 
047425,003057: 01,2551           30131                 +5        CA       SWBIT                                 #  01 - INVERT SWITCH.
047426,003058: 01,2552           00006                           EXTEND                                         
047427,003059: 01,2553           06002                           RXOR     QCHAN                                 
047428,003060: 01,2554           12557                           TCF      SWSTORE                               
047429,003061: 
047430,003062: 01,2555           40131                 +9D       CS       SWBIT                                 #  10 - CLEAR.
047431,003063: 01,2556           70002                           MASK     Q                                     
047432,003064: 01,2557           50130        SWSTORE            INDEX    SWWORD                                
047433,003065: 01,2560           54074                           TS       STATE                                 #  NEW SWITCH WORD.
047434,003066: 

Page 1085

047436,003068: 01,2561           00003                 +13D      RELINT                                         #  11 - NOOP.
047437,003069: 01,2562           34737                           CAF      BIT13                                 
047438,003070: 01,2563           00006                           EXTEND                                         #  DISPATCH SEQUCE CHANGING OR BRANCHING
047439,003071: 01,2564           70117                           MP       POLISH                                #  CODE.
047440,003072: 01,2565           72602                           MASK     B3TOB4                                
047441,003073: 01,2566           50000                           INDEX    A                                     
047442,003074: 01,2567           12570                           TCF      +1                                    #  ORIGINALLY STORED IN BITS 5-6.
047443,003075: 
047444,003076: 01,2570           40002                 +1        CS       Q                                     #  00 - BRANCH IF ON.
047445,003077: 01,2571           70131        TEST               MASK     SWBIT                                 
047446,003078: 01,2572           10000                           CCS      A                                     
047447,003079: 01,2573           12603                           TCF      SWSKIP                                
047448,003080: 
047449,003081: 01,2574           16727                 +5        TCF      SWBRANCH                              #  01 - GO TO.
047450,003082: 
047451,003083: 01,2575           12603                           TCF      SWSKIP                                #  HERE ONLY ON BIT 15.
047452,003084: 
047453,003085: 01,2576           05706                           TC       CCSHOLE                               
047454,003086: 01,2577           05706                           TC       CCSHOLE                               
047455,003087: 
047456,003088: 01,2600           30002                 +9D       CA       Q                                     #  10 - BRANCH IF OFF.
047457,003089: 01,2601           12571                           TCF      TEST                                  
047458,003090: 
047459,003091: 01,2602           00014        B3TOB4             OCT      0014                                  
047460,003092: 01,2603           24164        SWSKIP             INCR     LOC                                   
047461,003093: 
047462,003094: 01,2604  01,2522               SW/                EQUALS   SWITCHES                              
047463,003095: 
047464,003096: 01,2604           16073                 +13D      TCF      DANZIG                                #  11 - NOOP.

End of include-file INTERPRETER.agc.  Parent file is MAIN.agc