| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/Asm/Apollo-11/Comanche055/ Datei vom 11.9.2026 mit Größe 76 kB |
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Quellcode-Bibliothek INTERPRETER.agc Sprache: Apollo |
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# Copyright: Public domain. # Filename: INTERPRETER.agc # Purpose: Part of the source code for Colossus 2A, AKA Comanche 055. # It is part of the source code for the Command Module's (CM) # Apollo Guidance Computer (AGC), for Apollo 11. # Assembler: yaYUL # Contact: Ron Burkey <info@sandroid.org>. # Website: www.ibiblio.org/apollo. # Pages: 1107-1199 # Mod history: 2009-05-08 RSB Adapted from the Luminary131/ file of the # same name, using Comanche055 page images. # 2009-05-20 RSB Corrections: P00D00 -> P00DOO, fixed a # "Page N" reference. # 2009-05-21 RSB Corrected definition of 5B10, which overflowed # integer arithmetic. # # This source code has been transcribed or otherwise adapted from digitized # images of a hardcopy from the MIT Museum. The digitization was performed # by Paul Fjeld, and arranged for by Deborah Douglas of the Museum. Many # thanks to both. The images (with suitable reduction in storage size and # consequent reduction in image quality as well) are available online at # www.ibiblio.org/apollo. If for some reason you find that the images are # illegible, contact me at info@sandroid.org about getting access to the # (much) higher-quality images which Paul actually created. # # Notations on the hardcopy document read, in part: # # Assemble revision 055 of AGC program Comanche by NASA # 2021113-051. 10:28 APR. 1, 1969 # # This AGC program shall also be referred to as # Colossus 2A # Page 1107 # SECTION 1: DISPATCHER # # ENTRY TO THE INTERPRETER. INTPRET SETS LOC TO THE FIRST INSTRUCTION, BANKSET TO THE BBANK OF TH # OBJECT INTERPRETIVE PROGRAM, AND INTBIT15 TO THE BIT15 CONTENTS OF FBANK. INTERPRETIVE PROG # VIRTUALLY ALL BANKS PRESENT UNDER ANY SUPER-BANK SETTING, WITH THE RESTRICTION THAT PROGRAM # (BIT15 OF FBANK = 1) DO NOT REFER TO LOWBANKS, AND VICE-VERSA. THE INTERPRETER DOES NOT SWITCH S # E-BANK SWITCHING OCCURS WHENEVER GENERAL ERASABLE (100-3777) IS ADDRESSED. BLOCK 03 COUNT 03/INTER INTPRET RELINT EXTEND # SET LOC TO THE WORD FOLLOWING THE TC. QXCH LOC +2 CA BBANK # INTERPRETIVE BRANCHES FINISH HERE. TS BANKSET MASK BIT15 # GET 15TH BIT FOR INDEXABLE ADDRESSES. TS INTBIT15 TS EDOP # MAKE SURE NO INSTRUCTIONS LEFT OVER TCF NEWOPS # PICK UP OP CODE PAIR AND BEGIN. INTRSM LXCH BBANK # RESUME SUSPENDED INTERPRETIVE JOB TCF INTPRET +3 # DLOAD LOADS MPAC, MPAC +1, LEAVING ZERO IN MPAC +2. DLOAD EXTEND INDEX ADDRWD DCA 0 # LOAD DP C(C(ADDRWD)) INTO MPAC,MPAX +1 SLOAD2 DXCH MPAC CAF ZERO # ZERO MPAC +2 # Page 1108 # AT THE END OF MOST INSTRUCTIONS, CONTROL IS GIVEN TO DANZIG TO DISPATCH THE NEXT OPERATION. TS MPAC +2 # AND DECLARE DP MODE NEWMODE TS MODE # PROLOGUE FOR MODE-CHANGING INSTRUCTIONS. DANZIG CA BANKSET # SET BBANK BEFORE TESTING NEWJOB SO THAT TS BBANK # IT MAY BE SAVED DIRECTLY BY CHANJOB. NOIBNKSW CCS EDOP # SEE IF AN ORDER CODE IS LEFT OVER FROM TCF OPJUMP # THE LAST PAIR RETRIEVED. IF SO, EXECUTE. # EDOP IS SET TO ZERO ON ITS RE-EDITING. CCS NEWJOB # SEE IF A JOB OF HIGHER PRIORITY IS TCF CHANG2 # PRESENT, AND IF SO, CHANGE JOBS. INCR LOC # ADVANCE THE LOCATION COUNTER. # ITRACE (1) REFERS TO "NEWOPS". NEWOPS INDEX LOC # ENTRY TO BEGIN BY PICKING OP CODE PAIR. CA 0 # MAY BE AN OPCODE PAIR OR A STORE CODE. CCS A # TEST SIGN AND GET DABS(A). TCF DOSTORE # PROCESS STORE CODE. LOW7 OCT 177 TS EDOP # OP CODE PAIR. LEAVE THE OTHER IN EDOP MASK LOW7 # WHERE CCS EDOP WILL HONOR IT NEXT. OPJUMP TS CYR # LOWWD ENTERS HERE IF A RIGHT-HAND OP CCS CYR # CODE IS TO BE PROCESSED. TEST PREFICES. TCF OPJUMP2 # TEST SECOND PREFIX BIT. TCF EXIT # +0 OP CODE IS EXIT # Page 1109 # PROCESS ADDRESSES WHICH MAY BE DIRECT, INDEXED, OR REFERENCE THE PUSHDOWN LIST. ADDRESS MASK BIT1 # SEE IF ADDRESS IS INDEXED. CYR CONTAINED CCS A # 400XX, SO BIT 1 IS NOW AS IT WAS IN CYR. TCF INDEX # FORM INDEXED ADDRESS. DIRADRES INDEX LOC # LOOK AHEAD TO NEXT WORD TO SEE IF OCT40001 CS 1 # ADDRESS IS GIVEN. CCS A TCF PUSHUP # IF NOT. NEG4 DEC -4 INCR LOC # IF SO, TO SHOW WE PICKED UP A WORD. TS ADDRWD # Page 1110 # FINAL DIGESTION OF DIRECT ADDRESSES OF OP CODES WITH 01 PREFIX IS DONE HERE. IN EACH CASE, THE # REQUIRED 12-BIT SUB-ADDRESS IS LEFT IN ADDRWD, WITH ANY REQUIRED E OR F BANK SWITCHING DONE. AD # 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 = AD -ENDVAC # SEE IF ADDRESS RELATIVE TO WORK AREA. CCS A AD -ENDERAS # IF NOT, SEE IF IN GENERAL ERASABLE. TCF IERASTST NETZERO CA FIXLOC # IF SO, LEAVE THE MODIFIED ADDRESS IN ADS ADDRWD # ADDRWD AND DISPATCH. ITR15 INDEX CYR # THIS INDEX MAKES THE NEXT INSTRUCTION 7 INDJUMP -1 # TCF INDJUMP + OP, EDITING CYR. IERASTST EXTEND BZMF GEADDR # GO PROCESS GENERAL-ERASABLE ADDRESS. MASK LOW10 # FIXED BANK ADDRESS. RESTORE AND ADD B15. AD LOW10 # SWITCH BANKS AND LEAVE SUBADDRESS IN XCH ADDRWD # ADDRWD FOR OPERAND RETRIEVAL. (THIS AD INTBIT15 # METHOD PRECLUDES USE OF THE LAST TS FBANK # LOCATION IN EACH FBANK.) ITR12 INDEX CYR 7 INDJUMP -1 GEADDR MASK LOW8 AD OCT1400 XCH ADDRWD TS EBANK ITR10 INDEX CYR 7 INDJUMP -1 # Page 1111 # THE FOLLOWING ROUTINE PROCESSES INTERPRETIVE INDEXED ADDRESSES. AN INTERPRETER INDEX REGI # CONTAIN THE ADDRESS OF ANY ERASABLE REGISTER (0-42 BEING RELATIVE TO THE VAC AREA) OR ANY INTER # BANK, OR ANY INTEGER IN THAT RANGE. DODLOAD* CAF DLOAD* # STODL* COMES HERE TO PROCESS LOAD ADR. TS CYR # (STOVL* ENTERS HERE). INDEX CA FIXLOC # SET UP INDEX LOCATION. TS INDEXLOC INCR LOC # (ADDRESS ALWAYS GIVEN). INDEX LOC CS 0 CCS A # INDEX 2 IF ADDRESS STORED COMPLEMENTED. INCR INDEXLOC NOOP TS ADDRWD # 14 BIT ADDRESS TO ADDRWD. MASK HIGH4 # IF ADDRESS GREATER THAN 2K, ADD INTBIT15 EXTEND BZF INDEX2 CA INTBIT15 ADS ADDRWD INDEX2 INDEX INDEXLOC CS X1 ADS ADDRWD # DO AUGMENT, IGNORING AND CORRECTING OVF. MASK HIGH9 # SEE IF ADDRESS IS IN WORK AREA. EXTEND BZF INDWORK MASK HIGH4 # SEE IF IN FIXED BANK. EXTEND BZF INDERASE CA ADDRWD # IN FIXED -- SWITCH BANKS AND CREATE TS FBANK # SUB-ADDRESS MASK LOW10 AD 2K TS ADDRWD ITR11 INDEX CYR 3 INDJUMP -1 INDWORK CA FIXLOC # MAKE ADDRWD RELATIVE TO WORK AREA. TCF ITR13 -1 INDERASE CA OCT1400 XCH ADDRWD TS EBANK MASK LOW8 -1 ADS ADDRWD # Page 1112 ITR13 INDEX CYR 3 INDJUMP -1 # Page 1113 # PUSH-UP ROUTINES. WHEN NO OPERAND ADDRESS IS GIVEN, THE APPROPRIATE OPERAND IS TAKEN FROM THE # LIST. IN MOST CASES THE MODE OF THE RESULT (VECTOR OR SCALAR) OF THE LAST ARITHMETIC OPERATION P # IS THE SAME AS THE TYPE OF OPERAND DESIRED (ALL ADD/SUBTRACT ETC.). EXCEPTIONS TO THIS GENERAL # BELOW (NOTE THAT IN EVERY CASE THE MODE REGISTER IS LEFT INTACT): # # 1. VXSC AND V/SC WANT THE OPPOSITE TYPE OF OPERAND, E.G., IF THE LAST OPERATION YIELDED A VECT # RESULT, VXSC WANTS A SCALAR. # # 2. THE LOAD CODES SHOULD LOAD THE ACCUMULATOR INDEPENDENT OF THE RESULT OF THE LAST OPERATIO # INCLUDES VLOAD, DLOAD, TLOAD, PDDL, AND PDVL (NO PUSHUP WITH SLOAD). # # 3. SOME ARITHMETIC OPERATIONS REQUIRE A STANDARD TYPE OF OPERAND REGARDLESS OF THE PREVIOU # THIS INCLUDES SIGN WANTING DP AND TAD REQUIRING TP. PUSHUP CAF OCT23 # IF THE LOW 5 BITS OF CYR ARE LESS THAN MASK CYR # 20, THIS OP REQUIRES SPECIAL ATTENTION. AD -OCT10 # (NO -0). CCS A TCF REGUP # FOR ALL CODES GREATER THAN OCT 7. -OCT10 OCT -10 AD NEG4 # WE NOW HAVE 7 -- OP CODE (MOD4). SEE IF CCS A # THE OP CODE (MOD4) IS THREE (REVERSE). INDEX A # NO -- THE MODE IS DEFINITE. PICK UP THE CS NO.WDS TCF REGUP +2 INDEX MODE # FOR VXSC AND V/SC WE WANT THE REQUIRED CS REVCNT # PUSHLOC DECREMENT WITHOUT CHANGING THE TCF REGUP +2 # MODE AT THIS TIME. REGUP INDEX MODE # MOST ALL OP CODES PUSHUP HERE. CS NO.WDS +2 ADS PUSHLOC TS ADDRWD ITR14 INDEX CYR 7 INDJUMP -1 # (THE INDEX MAKES THIS A TCF.) OCT 2 # REVERSE PUSHUP DECREMENT. VECTOR TAKES 2 REVCNT OCT 6 # WORDS, SCALAR TAKES 6. OCT 6 NO.WDS OCT 2 # CONVENTIONAL DECREMENT IS 6 WORDS VECTOR OCTAL3 OCT 3 # 2 IN DP, AND 3 IN TP. OCT 6 # Page 1114 # TEST THE SECOND PREFIX BIT TO SEE IF THIS IS A MISCELLANEOUS OR A UNARY/SHORT SHIFT OPERATION. OPJUMP2 CCS CYR # TEST SECOND PREFIX BIT. TCF OPJUMP3 # TEST THIRD BIT TO SEE IF UNARY OR SHIFT. -ENDVAC DEC -45 # THE FOLLOWING ROUTINE PROCESSES ADDRESSES OF SUFFIX CLASS 10. THEY ARE BASICALLY WORK AREA AD # IN THE RANGE 0-52, ERASABLE ECADR CONSTANTS FROM 100-3777, AND FCADRS ABOVE THAT. ALL 15 BITS A # IN CONTRAST TO SUFFIX 1, IN WHICH ONLY THE LOW ORDER 14 ARE AVAILABLE. 15BITADR INCR LOC # (ENTRY HERE FROM STCALL). INDEX LOC # PICK UP ADDRESS WORD. CA 0 TS POLISH # WE MAY NEED A SUBADDRESS LATER. CAF LOW7+2K # THESE INSTRUCTIONS ARE IN BANK 1. TS FBANK MASK CYR ITR7 INDEX A TCF MISCJUMP # Page 1115 # COMPLETE THE DISPATCHING OF UNARY AND SHORT SHIFT OPERATIONS. OPJUMP3 TS FBANK # CALL IN BANK 0 (BITS 11-15 OF A ARE 0.) # ITRACE (6) REFERS TO "OPJUMP3". CCS CYR # TEST THIRD PREFIX BIT. INDEX A # THE DECREMENTED UNARY CODE IS IN BITS TCF UNAJUMP # 1-4 OF A (ZERO, EXIT, HAS BEEN DETECTED) CCS MODE # IT'S A SHORT SHIFT CODE. SEE IF PRESENT TCF SHORTT # SCALAR OR VECTOR. TCF SHORTT TCF SHORTV # CALLS THE APPROPRIATE ROUTINE. FBANKMSK EQUALS BANKMASK LVBUF ADRES VBUF # Page 1116 # THE FOLLOWING IS THE JUMP TABLE FOR OP CODES WHICH MAY HAVE INDEXABLE ADDRESSES OR MAY PUSH UP. INDJUMP TCF VLOAD # 00 -- LOAD MPAC WITH A VECTOR. TCF TAD # 01 -- TRIPLE PRECISION ADD TO MPAC. TCF SIGN # 02 -- COMPLEMENT MPAC (V OR SC) IF X NEG. TCF VXSC # 03 -- VECTOR TIMES SCALAR. TCF CGOTO # 04 -- COMPUTED GO TO. TCF TLOAD # 05 -- LOAD MPAC WITH TRIPLE PRECISION. TCF DLOAD # 06 -- LOAD MPAC WITH A DP SCALAR. TCF V/SC # 07 -- VECTOR DIVIDED BY SCALAR. TCF SLOAD # 10 -- LOAD MPAC IN SINGLE PRECISION. TCF SSP # 11 -- SET SINGLE PRECISION INTO X. TCF PDDL # 12 -- PUSH DOWN MPAC AND RE-LOAD IN DP. TCF MXV # 13 -- MATRIX POST-MULTIPLIED BY VECTOR. TCF PDVL # 14 -- PUSH DOWN AND VECTORLOAD. TCF CCALL # 15 -- COMPUTED CALL. TCF VXM # 16 -- MATRIX PRE-MULTIPLIED BY VECTOR. TCF TSLC # 17 -- NORMALIZE MPAC (SCALAR ONLY). TCF DMPR # 20 -- DP MULTIPLY AND ROUND. TCF DDV # 21 -- DP DIVIDE BY. TCF BDDV # 22 -- DP DIVIDE INTO. TCF GSHIFT # 23 -- GENERAL SHIFT INSTRUCTION TCF VAD # 24 -- VECTOR ADD. TCF VSU # 25 -- VECTOR SUBTRACT. TCF BVSU # 26 -- VECTOR SUBTRACT FROM. TCF DOT # 27 -- VECTOR DOT PRODUCT. TCF VXV # 30 -- VECTOR CROSS PRODUCT. TCF VPROJ # 31 -- VECTOR PROJECTION. TCF DSU # 32 -- DP SUBTRACT. TCF BDSU # 33 -- DP SUBTRACT FROM. TCF DAD # 34 -- DP ADD. TCF # 35 -- AVAILABLE TCF DMP1 # 36 -- DP MULTIPLY. TCF SETPD # 37 -- SET PUSH DOWN POINTER (DIRECT ONLY) # CODES 10 AND 14 MUST NOT PUSH UP. CODE 04 MAY BE USED FOR VECTOR DECLARE BEFORE PUSHUP IF DESIRED. # Page 1117 # THE FOLLOWING JUMP TABLE APPLIES TO INDEX, BRANCH, AND MISCELLANEOUS INSTRUCTIONS. MISCJUMP TCF AXT # 00 -- ADDRESS TO INDEX TRUE. TCF AXC # 01 -- ADDRESS TO INDEX COMPLEMENTED. TCF LXA # 02 -- LOAD INDEX FROM ERASABLE. TCF LXC # 03 -- LOAD INDEX FROM COMPLEMENT OF ERAS. TCF SXA # 04 -- STORE INDEX IN ERASABLE. TCF XCHX # 05 -- EXCHANGE INDEX WITH ERASABLE. TCF INCR # 06 -- INCREMENT INDEX REGISTER. TCF TIX # 07 -- TRANSFER ON INDEX. TCF XAD # 10 -- INDEX REGISTER ADD FROM ERASABLE. TCF XSU # 11 -- INDEX SUBTRACT FROM ERASABLE. TCF BZE/GOTO # 12 -- BRANCH ZERO AND GOTO. TCF BPL/BMN # 13 -- BRANCH PLUS AND BRANCH MINUS. TCF RTB/BHIZ # 14 -- RETURN TO BASIC AND BRANCH HI ZERO. TCF CALL/ITA # 15 -- CALL AND STORE QPRET. TCF SW/ # 16 -- SWITCH INSTRUCTIONS AND AVAILABLE. TCF BOV(B) # 17 -- BRANCH ON OVERFLOW TO BASIC OR INT. # Page 1118 # THE FOLLOWING JUMP TABLE APPLIES TO UNARY INSTRUCTIONS COUNT 00/INTER BANK 0 # 00 -- EXIT -- DETECTED EARLIER. UNAJUMP TCF SQRT # 01 -- SQUARE ROOT. TCF SINE # 02 -- SIN. TCF COSINE # 03 -- COS. TCF ARCSIN # 04 -- ARC SIN. TCF ARCCOS # 05 -- ARC COS. TCF DSQ # 06 -- DP SQUARE. TCF ROUND # 07 -- ROUND TO DP. TCF COMP # 10 -- COMPLEMENT VECTOR OR SCALAR TCF VDEF # 11 -- VECTOR DEFINE. TCF UNIT # 12 -- UNIT VECTOR. TCF ABVALABS # 13 -- LENGTH OF VECTOR OR MAG OF SCALAR. TCF VSQ # 14 -- SQUARE OF LENGTH OF VECTOR. TCF STADR # 15 -- PUSH UP ON STORE CODE. TCF RVQ # 16 -- RETURN VIA QPRET. TCF PUSH # 17 -- PUSH MPAC DOWN. # Page 1119 # SECTION 2 LOAD AND STORE PACKAGE. # # A SET OF EIGHT STORE CODES IS PROVIDED AS THE PRIMARY METHOD OF STORING THE MULTI-PURPOSE # ACCUMULATOR (MPAC). IF IN THE DANZIG SECTION LOC REFERS TO AN ALGEBRAICALLY POSITIVE WORD, IT # STORE CODE WITH A CORRESPONDING ERASABLE ADDRESS. MOST OF THESE CODES ARE TWO ADDRESS, SPECIF # FOLLOWING THE STORE CODE IS TO BE USED AS AN ADDRESS FROM WHICH TO RE-LOAD MPAC. FOUR OPTIONS ARE # # 1. STORE STORE MPAC. THE E ADDRESS MAY BE INDEXED. # 2. STODL STORE MPAC AND RE-LOAD IT IN DP WITH THE NEXT ADDRESS (THE LOAD MAY BE INDEXED). # 3. STOVL STORE MPAC AND RE-LOAD A VECTOR (AS ABOVE). # 4. STCALL STORE AND DO A CALL (BOTH ADDRESSES MUST BE DIRECT HERE). # # STODL AND STOVL WILL TAKE FROM THE PUSH-DOWN LIST IF NO LOAD ADDRESS IS GIVEN. BLOCK 3 COUNT 03/INTER STADR CA BANKSET # THE STADR CODE (PUSHUP UP ON STORE TS FBANK # ADDRESS) ENTERS HERE. INCR LOC ITR1 INDEX LOC # THE STORECODE WAS STORED COMPLEMENTED TO CS 0 # MAKE IT LOOK LIKE AN OPCODE PAIR. AD NEGONE # (YUL CANT REMOVE 1 BECAUSE OF EARLY CCS) DOSTORE TS ADDRWD MASK LOW11 # ENTRY FROM DISPATCHER. SAVE THE ERASABLE XCH ADDRWD # ADDRESS AND JUMP ON THE STORE CODE NO. MASK B12T14 EXTEND MP BIT5 # EACH TRANSFER VECTOR ENTRY IS TWO WORDS. ITR0 INDEX A TCF STORJUMP # Page 1120 # STORE CODE JUMP TABLE. CALLS THE APPROPRIATE STORING ROUTINE AND EXITS TO DANZIG OR TO ADDRESS # A SUPPLIED OPERATION CODE. # # STORE STORE,1 AND STORE,2 RETURN TO DANZIG, THUS RESETTING THE EBANK TO ITS STATE AT INTPRET. STORJUMP TC STORE # STORE. TCF DANZIG # PICK UP NEW OP CODE(S). TC STORE,1 TCF DANZIG TC STORE,2 TCF DANZIG TC STORE # STODL. TCF DODLOAD TC STORE # STODL WITH INDEXED LOAD ADDRESS. TCF DODLOAD* TC STORE # STOVL. TCF DOVLOAD TC STORE # STOVL WITH INDEXED LOAD ADDRESS. TCF DOVLOAD* TC STORE # STOTC. CAF CALLCODE TS CYR TCF 15BITADR # GET A 15 BIT ADDRESS. # Page 1121 # STORE CODE ADDRESS PROCESSOR. STORE,1 INDEX FIXLOC CS X1 TCF PRESTORE STORE,2 INDEX FIXLOC CS X2 PRESTORE ADS ADDRWD # RESULTANT ADDRESS IS IN ERASABLE. STORE CS ADDRWD AD DEC45 CCS A # DOES THE ADDRESS POINT TO THE WORK AREA? CA FIXLOC # YES. TCF AHEAD5 CA OCT1400 # NO. SET EBANK & MAKE UP SUBADDRESS. XCH ADDRWD TS EBANK MASK LOW8 AHEAD5 ADS ADDRWD # Page 1122 # STORING ROUTINES. STORE DP, TP, OR VECTOR AS INDICATED BY MODE. STARTSTO EXTEND # MPAC,+1 MUST BE STORED IN ANY EVENT. # ITRACE (5) REFERS TO "STARTSTO". DCA MPAC INDEX ADDRWD DXCH 0 CCS MODE TCF TSTORE TC Q VSTORE EXTEND DCA MPAC +3 INDEX ADDRWD DXCH 2 EXTEND DCA MPAC +5 INDEX ADDRWD DXCH 4 TC Q TSTORE CA MPAC +2 INDEX ADDRWD TS 2 TC Q # Page 1123 # ROUTINES TO BEGIN PROCESSING OF THE SECOND ADDRESS ASSOCIATED WITH ALL STORE-TYPE CODES EXCE # ITSELF. DODLOAD CAF DLOADCOD TS CYR TCF DIRADRES # GO GET A DIRECT ADDRESS. DOVLOAD CAF VLOADCOD TS CYR TCF DIRADRES DOVLOAD* CAF VLOAD* TCF DODLOAD* +1 # PROLOGUE TO INDEX ROUTINE. # Page 1124 # THE FOLLOWING LOAD INSTRUCTIONS ARE PROVIDED FOR LOADING THE MULTI-PURPOSE ACCUMULATOR MPA TLOAD INDEX ADDRWD CA 2 # LOAD A TRIPLE PRECISION ARGUMENT INTO TS MPAC +2 # THE FIRST THREE MPAC REGISTERS, WITH THE EXTEND # CONTENTS OF THE OTHER FOUR IRRELEVANT. INDEX ADDRWD DCA 0 DXCH MPAC TMODE CAF ONE TCF NEWMODE # DECLARE TRIPLE PRECISION MODE. SLOAD ZL # LOAD A SINGLE PRECISION NUMBER INTO INDEX ADDRWD # MPAC, SETTING MPAC+1,2 TO ZERO. THE CA 0 # CONTENTS OF THE REMAINING MPAC REGISTERS TCF SLOAD2 # ARE IRRELEVANT. VLOAD EXTEND # LOAD A DOUBLE PRECISION VECTOR INTO INDEX ADDRWD # MPAC,+1, MPAC+3,4, AND MPAC+5,6. THE DCA 0 # CONTENTS OF MPAC +2 ARE IRRELEVANT. DXCH MPAC ENDVLOAD EXTEND # PDVL COMES HERE TO FINISH UP FOR DP, TP. INDEX ADDRWD DCA 2 DXCH MPAC +3 +4 EXTEND # TPDVL FINISHES HERE. INDEX ADDRWD DCA 4 DXCH MPAC +5 VMODE CS ONE # DECLARE VECTOR MODE. TCF NEWMODE # Page 1125 # THE FOLLOWING INSTRUCTIONS ARE PROVIDED FOR STORING OPERANDS IN THE PUSHDOWN LIST: # 1. PUSH PUSHDOWN AND NO LOAD. # 2. PDDL PUSHDOWN AND DOUBLE PRECISION LOAD. # 3. PDVL PUSHDOWN AND VECTOR LOAD. PDDL EXTEND INDEX ADDRWD # LOAD MPAC,+1, PUSHING THE FORMER DCA 0 # CONTENTS DOWN. DXCH MPAC INDEX PUSHLOC DXCH 0 INDEX MODE # ADVANCE THE PUSHDOWN POINTER APPRO- CAF NO.WDS # PRIATELY. ADS PUSHLOC CCS MODE TCF ENDTPUSH TCF ENDDPUSH TS MODE # NOW DP. ENDVPUSH TS MPAC +2 DXCH MPAC +3 # PUSH DOWN THE REST OF THE VECTOR HERE. INDEX PUSHLOC DXCH 0 -4 DXCH MPAC +5 INDEX PUSHLOC DXCH 0 -2 TCF DANZIG ENDDPUSH TS MPAC +2 # SET MPAC +2 TO ZERO AND EXIT ON DP. TCF DANZIG ENDTPUSH TS MODE XCH MPAC +2 # ON TRIPLE, SET MPAC +2 TO ZERO, PUSHING +2 INDEX PUSHLOC # DOWN THE OLD CONTENTS TS 0 -1 TCF DANZIG # Page 1126 # PDVL -- PUSHDOWN AND VECTOR LOAD PDVL EXTEND # RELOAD MPAC AND PUSH DOWN ITS CONTENTS. INDEX ADDRWD DCA 0 DXCH MPAC INDEX PUSHLOC DXCH 0 INDEX MODE # ADVANCE THE PUSHDOWN POINTER. CAF NO.WDS ADS PUSHLOC CCS MODE # TEST PAST MODE. TCF TPDVL TCF ENDVLOAD # JUST LOAD LAST FOUR REGISTERS ON DP. VPDVL EXTEND # PUSHDOWN AND RE-LOAD LAST TWO COMPONENTS INDEX ADDRWD DCA 2 DXCH MPAC +3 INDEX PUSHLOC DXCH 0 -4 EXTEND INDEX ADDRWD DCA 4 DXCH MPAC +5 INDEX PUSHLOC DXCH 0 -2 TCF DANZIG TPDVL EXTEND # ON TP, WE MUST LOAD THE Y COMPONENT INDEX ADDRWD # BEFORE STORING MPAC +2 IN CASE THIS IS A DCA 2 # PUSHUP. DXCH MPAC +3 CA MPAC +2 INDEX PUSHLOC # IN DP. TS 0 -1 TCF ENDVLOAD +4 # SSP (STORE SINGLE PRECISION) IS EXECUTED HERE. SSP INCR LOC # PICK UP THE WORD FOLLOWING THE GIVEN INDEX LOC # ADDRESS AND STORE IT AT X. CA 0 STORE1 INDEX ADDRWD # SOME INDEX AND MISCELLANEOUS OPS END TS 0 # HERE. # Page 1127 TCF DANZIG # Page 1128 # SEQUENCE CHANGING AND SUBROUTINE CALLING OPTIONS. # # THE FOLLOWING OPERATIONS ARE AVAILABLE FOR SEQUENCING CHANGING, BRANCHING, AND CALLING SUB # 1. GOTO GO TO. # 2. CALL CALL SUBROUTINE SETTING QPRET. # 3. CGOTO COMPUTED GO TO. # 4. CCALL COMPUTED CALL. # 7. BPL BRANCH IF MPAC POSITIVE OR ZERO. # 8. BZE BRANCH IF MPAC ZERO. # 9. BMN BRANCH IF MPAC NEGATIVE NON-ZERO. CCALL INCR LOC # MAINTAIN LOC FOR QPRET COMPUTATION INDEX LOC # Was CAF --- RSB 2009. CA 0 # GET BASE ADDRESS OF CADR LIST. INDEX ADDRWD AD 0 # ADD INCREMENT. TS FBANK # SELECT DESIRED CADR. MASK LOW10 INDEX A CAF 10000 TS POLISH CALL CA BANKSET # FOR ANY OF THE CALL OPTIONS, MAKE UP THE MASK BANKMASK # ADDRESS OF THE NEXT OP-CODE PAIR/STORE AD BANKMASK # CODE AND LEAVE IT IN QPRET. NOTE THAT AD LOC # BANKMASK = -(2000 - 1). INDEX FIXLOC TS QPRET GOTO CA POLISH # BASIC BRANCHING SEQUENCE. +1 MASK HIGH4 EXTEND BZF GOTOERS # SEE IF ADDRESS POINTS TO FIXED OR ERAS. +4 CA BANKSET # SET EBANK PART OF BBANK. NEXT, SET UP TS BBANK # FBANK. THE COMBINATION IS PICKED UP & CA POLISH # PUT INTO BANKSET AT INTPRET +2. TS FBANK MASK LOW10 AD 2K TS LOC TCF INTPRET +3 EBANK= 1400 # SO YUL DOESN'T CUSS THE "CA 1400" BELOW. GOTOERS CA POLISH # THE GIVEN ADDRESS IS IN ERASABLE -- SEE AD -ENDVAC # IF RELATIVE TO THE WORK ARA. CCS A CA POLISH # GENERAL ERASABLE. TCF GOTOGE # Page 1129 CA FIXLOC # WORK AREA. AD POLISH INDEX A # USE THE GIVEN ADDRESS AS THE ADDRESS OF CA 0 # THE BRANCH ADDRESS. TS POLISH TCF GOTO +1 # ALLOWS ARBITRARY INDIRECTNESS LEVELS. GOTOGE TS EBANK MASK LOW8 INDEX A # USE THE GIVEN ADDRESS AS THE ADDRESS OF CA 1400 # THE BRANCH ADDRESS. TS POLISH TCF GOTO +1 CGOTO INDEX LOC # COMPUTED GO TO. PICK UP ADDRESS OF CADR CA 1 # LIST INDEX ADDRWD # ADD MODIFIER. AD 0 TS FBANK # SELECT GOTO ADDRESS MASK LOW10 INDEX A CA 10000 TS POLISH TCF GOTO +1 # WITH ADDRESS IN A. SWBRANCH CA BANKSET # SWITCH INSTRUCTIONS WHICH ELECT TO TS FBANK # BRANCH COME HERE TO DO SO. INDEX LOC CA 1 TS POLISH TCF GOTO +1 # Page 1130 # TRIPLE PRECISION BRANCHING ROUTINE. IF CALLING TC IS AT L, RETURN IS AS FOLLOWS: # L+1 IF MPAC IS GREATER THAN ZERO. # L+2 IF MPAC IS EQUAL TO +0 OR -0. # L+3 IF MPAC IS LESS THAN ZERO. BRANCH CCS MPAC TC Q TCF +2 # ON ZERO. TCF NEG CCS MPAC +1 TC Q TCF +2 TCF NEG CCS MPAC +2 TC Q TCF +2 TCF NEG Q+1 INDEX Q TC 1 NEG INDEX Q # IF FIRST NON-ZERO REGISTER WAS NEGATIVE. TC 2 Q+2 = NEG # ITRACE (3) REFERS TO "EXIT". EXIT CA BANKSET # RESTORE USER'S BANK SETTING, AND LEAVE TS BBANK # INTERPRETIVE MODE. INDEX LOC TC 1 # Page 1131 # SECTION 3 -- ADD/SUBTRACT PACKAGE. # # THE FOLLOWING OPERATIONS ARE PROVIDED FOR ADDING TO AND SUBTRACTING FROM THE MULTI-PURPOSE A # MPAC: # 1. DAD DOUBLE PRECISION ADD. # 2. DSU DOUBLE PRECISION SUBTRACT. # 3. BDSU DOUBLE PRECISION SUBTRACT FROM. # 4. TAD TRIPLE PRECISION ADD. # 5. VAD VECTOR ADD. # 6. VSU VECTOR SUBTRACT. # 7. BVSU VECTOR SUBTRACT FROM. # THE INTERPRETIVE OVERFLOW INDICATOR OVFIND IS SET NON-ZERO IF OVERFLOW OCCURS IN ANY OF THE AB VSU CAF BIT15 # CHANGES 0 TO DCS. TCF +2 VAD CAF PRIO30 # CHANGES 0 TO DCA. ADS ADDRWD EXTEND INDEX ADDRWD READ HISCALAR # DCA 2 OR DCS 2 DAS MPAC +3 EXTEND # CHECK OVERFLOW. BZF +2 TC OVERFLWY EXTEND INDEX ADDRWD READ CHAN5 # DCA 4 OR DCS 4 DAS MPAC +5 EXTEND BZF +2 TC OVERFLWZ EXTEND INDEX ADDRWD READ LCHAN # DCA 0 OR DCS 0 TCF ENDVXV DAD EXTEND INDEX ADDRWD DCA 0 ENDVXV DAS MPAC # VXV FINISHES HERE. EXTEND BZF DANZIG # Page 1132 SETOVF TC OVERFLOW TCF DANZIG # Page 1133 DSU EXTEND INDEX ADDRWD DCS 0 TCF ENDVXV OVERFLWZ TS L # ENTRY FOR THIRD COMPONENT. CAF FIVE TCF +3 OVERFLWY TS L # ENTRY FOR SECOND COMPONENT. CAF THREE XCH L OVERFLOW INDEX A # ENTRY FOR 1ST COMP OR DP (L=0). CS LIMITS # PICK UP POSMAX OR NEGMAX. TS BUF EXTEND AUG A INDEX L ADS MPAC +1 TS 7 CAF ZERO AD BUF INDEX L ADS MPAC TS 7 TC Q # NO OVERFLOW EXIT. TCF SETOVF2 # SET OVFIND AND EXIT. BVSU EXTEND INDEX ADDRWD DCA 2 DXCH MPAC +3 EXTEND DCOM DAS MPAC +3 EXTEND BZF +2 TC OVERFLWY EXTEND INDEX ADDRWD DCA 4 DXCH MPAC +5 EXTEND DCOM DAS MPAC +5 EXTEND BZF +2 TC OVERFLWZ # Page 1134 BDSU EXTEND INDEX ADDRWD DCA 0 DXCH MPAC EXTEND DCOM TCF ENDVXV # Page 1135 # TRIPLE PRECISION ADD ROUTINE. TAD EXTEND INDEX ADDRWD DCA 1 # ADD MINOR PARTS FIRST. DAS MPAC +1 INDEX ADDRWD AD 0 AD MPAC TS MPAC TCF DANZIG TCF SETOVF # SET OVFIND IF SUCH OCCURS. # Page 1136 # ARITHMETIC SUBROUTINES REQUIRED IN FIXED-FIXED. # 1. DMPSUB DOUBLE PRECISION MULTIPLY, MULTIPLY THE CONTENTS OF MPAC,+1 BY THE DP WORD WHOSE A # IS IN ADDRWD AND LEAVE A TRIPLE-PRECISION RESULT IN MPAC. # 2. ROUNDSUB ROUND THE TRIPLE PRECISION CONTENTS OF MPAC TO DOUBLE PRECISION. # 3. DOTSUB TAKE THE DOT PRODUCT OF THE VECTOR IN MPAC AND THE VECTOR WHOSE ADDRESS IS IN ADDRWD # AND LEAVE THE TRIPLE PRECISION RESULT IN MPAC. # 4. POLY USING THE CONTENTS OF MPAC AS A DP ARGUMENT, EVALUATE THE POLYNOMIAL WHOSE DEGREE AND # COEFFICIENTS IMMEDIATELY FOLLOW THE TC POLY INSTRUCTION (SEE ROUTINE FOR DETAILS). DMP INDEX Q # BASIC SUBROUTINE FOR USE BY PINBALL, ETC # Was CAF --- RSB 2009. CA 0 INCR Q -1 TS ADDRWD # (PROLOGUE FOR SETTING ADDRWD.) DMPSUB INDEX ADDRWD # GET MINOR PART OF OPERAND AT C(ADDRWD). CA 1 TS MPAC +2 # THIS WORKS FOR SQUARING MPAC AS WELL. CAF ZERO # SET MPAC +1 TO ZERO SO WE CAN ACCUMULATE XCH MPAC +1 # THE PARTIAL PRODUCTS WITH DAS TS MPTEMP # INSTRUCTIONS. EXTEND MP MPAC +2 # MINOR OF MPAC X MINOR OF C(ADDRWD). XCH MPAC +2 # DISCARD MINOR PART OF ABOVE RESULT AND EXTEND # FORM MAJOR OF MPAC X MINOR OF C(ADDRWD). MP MPAC DAS MPAC +1 # GUARANTEED NO OVERFLOW. INDEX ADDRWD # GET MAJOR PART OF ARGUMENT AT C(ADDRWD). CA 0 XCH MPTEMP # SAVE AND BRING OUT MINOR OF MPAC. DMPSUB2 EXTEND MP MPTEMP # MAJOR OF C(ADDRWD) X MINOR OF MPAC. DAS MPAC +1 # ACCUMULATE, SETTING A TO NET OVERFLOW. XCH MPAC # SETTING MPAC TO 0 OR +-1. EXTEND MP MPTEMP # MAJOR OF MPAC X MAJOR OF C(ADDRWD). DAS MPAC # GUARANTEED NO OVERFLOW. TC Q # 49 MCT = .573 MS. INCLUDING RETURN. # Page 1137 # ROUND MPAC TO DOUBLE PRECISION, SETTING OVFIND ON THE RARE EVENT OF OVERFLOW. ROUNDSUB CAF ZERO # SET MPAC +2 = 0 FOR SCALARS AND CHANGE +1 TS MODE # MODE TO DP. VROUND XCH MPAC +2 # BUT WE NEEDN'T TAKE THE TIME FOR VECTORS. DOUBLE TS L TC Q AD MPAC +1 # ADD ROUDING BIT IF MPAC +2 WAS GREATER TS MPAC +1 # THAN .5 IN MAGNITUDE. TC Q AD MPAC # PROPAGATE INTERFLOW. TS MPAC TC Q SETOVF2 TS OVFIND # (RARE). TC Q # Page 1138 # THE DOT PRODUCT SUBROUTINE USUALLY FORMS THE DOT PRODUCT OF THE VECTOR IN MPAC WITH A STANDARD S # REGISTER VECTOR WHOSE ADDRESS IS IN ADDRWD. IN THIS CASE C(DOTINC) ARE SET TO 2. VXM, HOWEVER, S # 6 SO THAT DOTSUB DOTS MPAC WITH A COLUMN VECTOR OF THE MATRIX IN QUESTION IN THIS CASE. PREDOT CAF TWO # PROLOGUE TO SET DOTINC TO 2. TS DOTINC DOTSUB EXTEND QXCH DOTRET # SAVE RETURN TC DMPSUB # DOT X COMPONENTS. DXCH MPAC +3 # POSITION Y COMPONENT OF MPAC FOR DXCH MPAC # MULTIPLICATION WHILE SAVING RESULT IN DXCH BUF # THREE WORD BUFFER, BUF. CA MPAC +2 TS BUF +2 CA DOTINC # ADVANCE ADDRWD TO Y COMPONENT OF ADS ADDRWD # OTHER ARGUMENT. TC DMPSUB DXCH MPAC +1 # ACCUMULATE PARTIAL PRODUCTS. DAS BUF +1 AD MPAC AD BUF TS BUF TCF +2 TS OVFIND # IF OVERFLOW OCCURS. DXCH MPAC +5 # MULTIPLY Z COMPONENTS. DXCH MPAC CA DOTINC ADS ADDRWD TC DMPSUB ENDDOT DXCH BUF +1 # LEAVE FINAL ACCUMULATION IN MPAC. DAS MPAC +1 AD MPAC AD BUF TS MPAC TC DOTRET TC OVERFLOW # ON OVERFLOW HERE. TC DOTRET # Page 1139 # DOUBLE PRECISION POLYNOMIAL EVALUATOR # N N-1 # THIS ROUTINE EVALUATES A X + A X + ... + A X + A LEAVING THE DP RESULT IN MPAC ON EXIT. # N N-1 1 0 # # THE ROUTINE HAS TWO ENTRIES # # 1 ENTRY THRU POWRSERS. THE COEFFICIENTS MAY BE EITHER IN FIXED OR ERASABLE E. THE CALL IS BY # TC POWRSERS, AND THE RETURN IS TO LOC(TC POWRSERS)+1. THE ENTERING DATA MUST BE AS FOLLOWS: # A SP LOC-3 ADDRESS FOR REFERENCING COEF TABLE # L SP N-1 N IS THE DEGREE OF THE POWER SERIES # MPAC DP X ARGUMENT # LOC-2N DP A(0) # ... # LOC DP A(N) # # 2. ENTRY THRU POLY. THE CALL TO POLY AND THE ENTERING DATA MUST BE AS FOLLOWS # MPAC DP X ARGUMENT # LOC TC POLY # LOC+1 DP A(0) # ... # LOC+2N+2 DP A(N) RETURN IS TO LOC+2N+4 POWRSERS EXTEND QXCH POLYRET # RETURN ADDRESS TS POLISH # POWER SERIES ADDRESS LXCH POLYCNT # N-1 TO COUNTER TCF POLYCOM # SKIP SET UP BY POLY POLY INDEX Q # Was CAF --- RSB 2009. CA 0 TS POLYCNT # N-1 TO COUNTER DOUBLE AD Q TS POLISH # L(A(N))-3 TO POLISH AD FIVE TS POLYRET # STORE RETURN ADDRESS POLYCOM CAF LVBUF # INCOMING X WILL BE MOVED TO VBUF, SO TS ADDRWD # SET ADDRWD SO DMPSUB WILL MPY BY VBUF. EXTEND INDEX POLISH DCA 3 # Page 1140 DXCH MPAC # LOAD A(N) INTO MPAC DXCH VBUF # SAVING X IN VBUF TCF POLY2 POLYLOOP TS POLYCNT # SAVE DECREMENTED LOOP COUNTER CS TWO ADS POLISH # REGRESS COEFFICIENT POINTER POLY2 TC DMPSUB # MULTIPLY BY X EXTEND INDEX POLISH DCA 1 # ADD IN NEXT COEFFICIENT DAS MPAC # USER'S RESPONSIBILITY TO ASSURE NO OVFLOW CCS POLYCNT TCF POLYLOOP TC POLYRET # RETURN CALLER # Page 1141 # MISCELLANEOUS MULTI-PRECISION ROUTINES REQUIRED IN FIXED-FIXED BUT NOT USED BY THE INTERPR DPAGREE CAF ZERO # DOUBLE PRECISION ENTRY -- TS MPAC +2 # ZERO LOW-ORDER WORD TPAGREE LXCH Q # FORCE SIGN AGREEMENT AMONG THE TRIPLE TC BRANCH # PRECISION CONTENTS OF MPAC. RETURNING TCF ARG+ # WITH SIGNUM OF THE INPUT IN A. TCF ARGZERO CS POSMAX # IF NEGATIVE. TCF +2 ARG+ CAF POSMAX TS Q EXTEND AUG A # FORMS +-1.0. AD MPAC +2 TS MPAC +2 CAF ZERO AD Q AD MPAC +1 TS MPAC +1 CAF ZERO AD Q # Q STILL HAS POSMAX OR NEGMAX IN IT. AD MPAC ARGZERO2 TS MPAC # ALWAYS SKIPPING UNLESS ARGZERO. TS MPAC +1 TC L # RETURN VIA L. ARGZERO TS MPAC +2 # SET ALL THREE MPAC REGISTERS TO ZERO. TCF ARGZERO2 # SHORTMP MULTIPLIES THE TP CONTENTS OF MPAC BY THE SINGLE PRECISION NUMBER ARRIVING IN A. SHORTMP TS MPTEMP EXTEND MP MPAC +2 TS MPAC +2 SHORTMP2 CAF ZERO # SO SUBSEQUENT DAS WILL WORK. XCH MPAC +1 TCF DMPSUB2 # Page 1142 # DMPNSUB MULTIPLIES THE DP FRACTION ARRIVING IN MPAC BY THE SP # INTEGER ARRIVING IN A. THE DP PRODUCT DEPARTS BOTH IN MPAC AND IN # A AND L. NOTE THAT DMPNSUB NORMALLY INCREASES THE MAGNITUDE OF THE # CONTENTS OF MPAC. THE CUSTOMER MUST INSURE THAT B(A) X B(MPAC,MPAC+1) # AND B(A) X B(MPAC) ARE LESS THAN 1 IN MAGNITUDE, WHERE B, AS IS OBVIOUS, # INDICATES THE ARRIVING CONTENTS. DMPNSUB TS DMPNTEMP EXTEND MP MPAC +1 DXCH MPAC # LOW PRODUCT TO MPAC, HIGH FACTOR TO A EXTEND MP DMPNTEMP CA L ADS MPAC # COMPLETING THE PRODUCT IN MPAC EXTEND DCA MPAC # BRINGING THE PRODUCT INTO A AND L TC Q # Page 1143 # MISCELLANEOUS VECTOR OPERATIONS. INCLUDED HERE ARE THE FOLLOWING. # 1. DOT DP VECTOR DOT PRODUCT. # 2. VXV DP VECTOR CROSS PRODUCT. # 3. VXSC DP VECTOR TIMES SCALAR. # 4. V/SC DP VECTOR DIVIDED BY SCALAR. # 5. VPROJ DP VECTOR PROJECTION. ( (MPAC.X)MPAC ). # 6. VXM DP VECTOR POST-MULTIPLIED BY MATRIX. # 7. MXV DP VECTOR PRE-MULTIPLIED BY MATRIX. DOT TC PREDOT # DO THE DOT PRODUCT AND EXIT, CHANGING DMODE CAF ZERO # THE MODE TO DP SCALAR. TCF NEWMODE MXV CAF TWO # SET UP MATINC AND DOTINC FOR ROW TS MATINC # VECTORS. TCF VXM/MXV # GO TO COMMON PORTION. VXM CS TEN # SET MATINC AND DOTINC TO REFER TO MATRIX TS MATINC # AS THREE COLUMN VECTORS. CAF SIX # Page 1144 # COMMON PORTION OF MXV AND VXM. VXM/MXV TS DOTINC # ITRACE (2) REFERS TO "VXM/MXV". TC MPACVBUF # SAVE VECTOR IN MPAC FOR FURTHER USE. TC DOTSUB # GO DOT TO GET X COMPONENT OF ANSWER. EXTEND DCA VBUF # MOVE MPAC VECTOR BACK INTO MPAC, SAVING DXCH MPAC # NEW X COMPONENT IN BUF2. DXCH BUF2 EXTEND DCA VBUF +2 DXCH MPAC +3 EXTEND DCA VBUF +4 DXCH MPAC +5 CA MATINC # INITIALIZE ADDRWD FOR NEXT DOT PRODUCT. ADS ADDRWD # FORMS HAS ADDRESS OF NEXT COLUMN(ROW). TC DOTSUB DXCH VBUF # MORE GIVEN VECTOR BACK TO MPAC, SAVING Y DXCH MPAC # COMPONENT OF ANSWER IN VBUF +2. DXCH VBUF +2 DXCH MPAC +3 DXCH VBUF +4 DXCH MPAC +5 CA MATINC # FORM ADDRESS OF LAST COLUMN OR ROW. ADS ADDRWD TC DOTSUB DXCH BUF2 # ANSWER NOW COMPLETE. PUT COMPONENTS INTO DXCH MPAC # PROPER MPAC REGISTERS. DXCH MPAC +5 DXCH VBUF +2 DXCH MPAC +3 TCF DANZIG # EXIT. # Page 1145 # VXSC -- VECTOR TIMES SCALAR. VXSC CCS MODE # TEST PRESENT MODE. TCF DVXSC # SEPARATE ROUTINE WHEN SCALAR IS IN MPAC. TCF DVXSC VVXSC TC DMPSUB # COMPUTE X COMPONENT TC VROUND # AND ROUND IT. DXCH MPAC +3 # PUT Y COMPONENT INTO MPAC SAVING MPAC IN DXCH MPAC # MPAC +3. DXCH MPAC +3 TC DMPSUB # DO SAME FOR Y AND Z COMPONENTS. TC VROUND DXCH MPAC +5 DXCH MPAC DXCH MPAC +5 TC DMPSUB TC VROUND VROTATEX DXCH MPAC # EXIT USED TO RESTORE MPAC AFTER THIS DXCH MPAC +5 # TYPE OF ROTATION. CALLED BY VECTOR SHIFT DXCH MPAC +3 # RIGHT, V/SC, ETC. DXCH MPAC TCF DANZIG # Page 1146 # DP VECTOR PROJECTION ROUTINE. VPROJ TC PREDOT # (MPAC.X)MPAC IS COMPUTED AND LEFT IN CS FOUR # MPAC. DO DOT AND FALL INTO DVXSC. ADS ADDRWD # VXSC WHEN SCALAR ARRIVES IN MPAC AND VECTOR IS AT X. DVXSC EXTEND # SAVE SCALAR IN MPAC +3 AND GET X DCA MPAC # COMPONENT OF ANWER. DXCH MPAC +3 TC DMPSUB TC VROUND CAF TWO # ADVANCE ADDRWD TO Y COMPONENT OF X. ADS ADDRWD EXTEND DCA MPAC +3 # PUT SCALAR BACK INTO MPAC AND SAVE DXCH MPAC # X RESULT IN MPAC +5. DXCH MPAC +5 TC DMPSUB TC VROUND CAF TWO ADS ADDRWD # TO Z COMPONENT. DXCH MPAC +3 # BRING SCALAR BACK, PUTTING Y RESULT IN DXCH MPAC # THE PROPER PLACE. DXCH MPAC +3 TC DMPSUB TC VROUND DXCH MPAC # PUT Z COMPONENT IN PROPER PLACE, ALSO DXCH MPAC +5 # POSITIONING X. DXCH MPAC TCF VMODE # MODE HAS CHANGED TO VECTOR. # Page 1147 # VECTOR CROSS PRODUCT ROUTINE CALCULATES (X M -X M ,X M -X M ,X M -X M ) WHERE M IS THE VECTOR IN # 3 2 2 3 1 3 3 1 2 1 1 2 # MPAC AND X THE VECTOR AT THE GIVEN ADDRESS. VXV EXTEND DCA MPAC +5 # FORM UP M3X1, LEAVING M1 IN VBUF. DXCH MPAC DXCH VBUF TC DMPSUB # BY X1. EXTEND DCS MPAC +3 # CALCULATE -X1M2, SAVING X1M3 IN VBUF +2. DXCH MPAC DXCH VBUF +2 TC DMPSUB CAF TWO # ADVANCE ADDRWD TO X2. ADS ADDRWD EXTEND DCS MPAC +5 # PREPARE TO GET -X2M3, SAVING -X1M2 IN DXCH MPAC # MPAC +5. DXCH MPAC +5 TC DMPSUB EXTEND DCA VBUF # GET X2M1, SAVING -X2M3 IN VBUF +4. DXCH MPAC DXCH VBUF +4 TC DMPSUB CAF TWO # ADVANCE ADDRWD TO X3. ADS ADDRWD EXTEND DCS VBUF # GET -X3M1, ADDING X2M1 TO MPAC +5 TO DXCH MPAC # COMPLETE THE Z COMPONENT OF THE ANSWER. DAS MPAC +5 EXTEND BZF +2 TC OVERFLWZ TC DMPSUB DXCH VBUF +2 # MOVE X1M3 TO MPAC +3 SETTING UP FOR X3M2 DXCH MPAC +3 # AND ADD -X3M1 TO MPAC +3 TO COMPLETE THE DXCH MPAC # Y COMPONENT OF THE RESULT. DAS MPAC +3 EXTEND BZF +2 # Page 1148 TC OVERFLWY TC DMPSUB DXCH VBUF +4 # GO ADD -X2M3 TO X3M2 TO COMPLETE THE X TCF ENDVXV # COMPONENT (TAIL END OF DAD). # THE MPACVBUF SUBROUTINE SAVES THE VECTOR IN MPAC IN VBUF WITHOUT CLOBBERING MPAC. MPACVBUF EXTEND # CALLED BY MXV, VXM, AND UNIT. DCA MPAC DXCH VBUF EXTEND DCA MPAC +3 DXCH VBUF +2 EXTEND DCA MPAC +5 DXCH VBUF +4 TC Q # RETURN TO CALLER. # DOUBLE PRECISION SIGN AGREE ROUTINE. ARRIVE WITH INPUT IN A+L. OUTPUT IS IN A + L. ALSIGNAG CCS A # TEST UPPER PART. TCF UPPOS # IT IS POSITIVE TC Q # ZERO TCF UPNEG # NEGATIVE TC Q # ZERO UPPOS XCH L # SAVE DECREMENTED UPPER PART. AD HALF AD HALF TS A # SKIPS ON OVERFLOW TCF +2 INCR L # RESTORE UPPER TO ROIGINAL VALUE XCH L # SWAP A + L BACK. TC Q UPNEG XCH L # SAVE COMPLEMENTED + DECREMENTED UPPER PT AD NEGMAX AD NEGONE TS A TCF +2 # DON'T INCREMENT IF NO OVERFLOW. INCR L XCH L COM # MAKE NEGATIVE AGAIN. TC Q # Page 1149 # INTERPRETIVE INSTRUCTIONS WHOSE EXECUTION CONSISTS OF PRINCIPALLY CALLING SUBROUTINES. DMP1 TC DMPSUB # DMP INSTRUCTIONS TCF DANZIG DMPR TC DMPSUB TC ROUNDSUB +1 # (C(A) = +0). TCF DANZIG DDV EXTEND INDEX ADDRWD # MOVE DIVIDEND INTO BUF. DCA 0 TCF BDDV +4 BDDV EXTEND # MOVE DIVISOR INTO MPAC SAVING MPAC, THE INDEX ADDRWD # DIVIDEND, IN BUF. DCA 0 DXCH MPAC +4 DXCH BUF CAF ZERO # DIVIDE ROUTINES IN BANK 0. TS FBANK TCF DDV/BDDV SETPD CA ADDRWD # MUST SET TO WORK AREA, OR EBANK TROUBLE. TS PUSHLOC TCF NOIBNKSW # NO FBANK SWITCH REQUIRED. TSLC CAF ZERO # SHIFTING ROUTINES LOCATED IN BANK 00. TS FBANK TCF TSLC2 GSHIFT CAF LOW7 # USED AS MASK AT GENSHIFT. THIS PROCESSES TS FBANK # ANY SHIFT INSTRUCTION (EXCEPT TSLC) WITH TCF GENSHIFT # AN ADDRESS (ROUTINES IN BANK 0). # Page 1150 # THE FOLLOWING IS THE PROLOGUE TO V/SC. IF THE PRESENT MODE IS VECTOR, IT SAVES THE SCALAR AT X IN B # AND CALLS THE V/SC ROUTINE IN BANK 0. IF THE PRESENT MODE IS SCALAR, IT MOVES THE VECTOR AT X INTO M # THE SCALAR IN MPAC IN BUF BEFORE CALLING THE V/SC ROUTINE IN BANK 0. V/SC CCS MODE TCF DV/SC # MOVE VECTOR INTO MPAC. TCF DV/SC VV/SC EXTEND INDEX ADDRWD DCA 0 V/SC1 DXCH BUF # IN BOTH CASES, VECTOR IS NOW IN MPAC AND CAF ZERO # SCALAR IN BUF. TS FBANK TCF V/SC2 DV/SC EXTEND INDEX ADDRWD DCA 2 DXCH MPAC +3 EXTEND INDEX ADDRWD DCA 4 DXCH MPAC +5 CS ONE # CHANGE MODE TO VECTOR. TS MODE EXTEND INDEX ADDRWD DCA 0 DXCH MPAC TCF V/SC1 # Page 1151 # SIGN AND COMPLEMENT INSTRUCTIONS. SIGN INDEX ADDRWD # CALL COMP INSTRUCTION IF WORD AT X IS CCS 0 # NEGATIVE NON-ZERO. TCF DANZIG TCF +2 TCF COMP # DO THE COMPLEMENT. INDEX ADDRWD CCSL CCS 1 TCF DANZIG TCF DANZIG TCF COMP TCF DANZIG COMP EXTEND # COMPLEMENT DP MPAC IN EVERY CASE. DCS MPAC DXCH MPAC CCS MODE # EITHER COMPLEMENT MPAC +3 OR THE REST OF TCF DCOMP # THE VECTOR ACCUMULATOR. TCF DCOMP EXTEND # VECTOR COMPLEMENT. DCS MPAC +3 DXCH MPAC +3 EXTEND DCS MPAC +5 DXCH MPAC +5 TCF DANZIG DCOMP CS MPAC +2 TS MPAC +2 TCF DANZIG # Page 1152 # THE FOLLOWING SHORT SHIFT CODES REQUIRE NO ADDRESS WORD: # 1. SR1 TO SR4 SCALAR SHIFT RIGHT. # 2. SR1R TO SR4R SCALAR SHIFT RIGHT AND ROUND. # 3. SL1 TO SL4 SCALAR SHIFT LEFT. # 4. SL1R TO SL4R SCALAR SHIFT LEFT AND ROUND. # 5. VSR1 TO VSR8 VECTOR SHIFT RIGHT (ALWAYS ROUNDS). # 6. VSL1 TO VSL8 VECTOR SHIFT LEFT (NEVER ROUNDS). # THE FOLLOWING CODES REQUIRE AN ADDRESS WHICH MAY BE INDEXED:* # 1. SR SCALAR SHIFT RIGHT. # 2. SRR SCALAR SHIFT RIGHT AND ROUND. # 3. SL SCALAR SHIFT LEFT. # 4. SLR SCALAR SHIFT LEFT AND ROUND. # 5. VSR VECTOR SHIFT RIGHT. # 6. VSL VECTOR SHIFT LEFT. # * IF THE ADDRESS IS INDEXED, AND THE INDEX MODIFICATION RESULTS IN A NEGATIVE SHIFT COUNT, A SHI # ABSOLUTE VALUE OF THE COUNT IS DONE IN THE OPPOSITE DIRECTION. BANK 00 COUNT 00/INTER SHORTT CAF SIX # SCALAR SHORT SHIFTS COME HERE. THE SHIFT MASK CYR # COUNT-1 IS NOW IN BITS 2-3 OF CYR. THE TS SR # ROUNDING BIT IS IN BIT1 AT THIS POINT. CCS CYR # SEE IF RIGHT OR LEFT SHIFT DESIRED. TCF TSSL # SHIFT LEFT. SRDDV DEC 20 # MPTEMP SETTING FOR SR BEFORE DDV. TSSR INDEX SR # GET SHIFTING BIT. CAF BIT14 TS MPTEMP CCS CYR # SEE IF A ROUND IS DESIRED. RIGHTR TC MPACSRND # YES -- SHIFT RIGHT AND ROUND. TCF NEWMODE # SET MODE TO DP (C(A) = 0). MPACSHR CA MPTEMP # DO A TRIPLE PRECISION SHIFT RIGHT. EXTEND MP MPAC +2 +3 TS MPAC +2 # (EXIT FROM SQRT AND ABVAL). CA MPTEMP EXTEND # Page 1153 MP MPAC # SHIFT MAJOR PART INTO A,L AND PLACE IN DXCH MPAC # MPAC,+1. CA MPTEMP EXTEND MP L # ORIGINAL C(MPAC +1). DAS MPAC +1 # GUARANTEED NO OVERFLOW. TCF DANZIG # MPAC SHIFT RIGHT AND ROUND SUBROUTINES MPACSRND CA MPAC +2 # WE HAVE TO DO ALL THREE MULTIPLIES SINCE EXTEND # MPAC +1 AND MPAC +2 MIGHT HAVE SIGN MP MPTEMP # DISAGREEMENT WITH A SHIFT RIGHT OF L. XCH MPAC +1 EXTEND MP MPTEMP XCH MPAC +1 # TRIAL MINOR PART. AD L VSHR2 DOUBLE # (FINISH VECTOR COMPONENT SHIFT RIGHT TS MPAC +2 # AND ROUND.) TCF +2 ADS MPAC +1 # GUARANTEED NO OVERFLOW. CAF ZERO TS MPAC +2 XCH MPAC # SETTING TO ZERO SO FOLLOWING DAS WORKS. EXTEND MP MPTEMP DAS MPAC # AGAIN NO OVERFLOW. TC Q VSHRRND CA MPTEMP # ENTRY TO SHIFT RIGHT AND ROUND MPAC WHEN EXTEND # MPAC CONTAINS A VECTOR COMPONENT. MP MPAC +1 TS MPAC +1 XCH L TCF VSHR2 # GO ADD ONE IF NECESSARY AND FINISH. # Page 1154 # ROUTINE FOR SHORT SCALAR SHIFT LEFT (AND MAYBE ROUND). TSSL CA SR # GET SHIFT COUNT FOR SR. +1 TS MPTEMP +2 EXTEND # ENTRY HERE FROM SL FOR SCALARS. DCA MPAC +1 # SHIFTING LEFT ONE PLACE AT A TIME IS DAS MPAC +1 # FASTER THAN DOING THE WHOLE SHIFT WITH AD MPAC # MULTIPLIES ASSUMING THAT FREQUENCY OF AD MPAC # SHIFT COUNTS GOES DOWN RAPIDLY AS A TS MPAC # FUNCTION OF THEIR MAGNITUDE. TCF +2 TS OVFIND # OVERFLOW. (LEAVES OVERFLOW-CORRECTED # RESULT ANYWAY). CCS MPTEMP # LOOP ON DECREMENTED SHIFT COUNT. TCF TSSL +1 CCS CYR # SEE IF ROUND WANTED. ROUND TC ROUNDSUB # YES -- ROUND AND EXIT. TCF DANZIG # SL LEAVES A ZERO IN CYR FOR NO ROUND. TCF DANZIG # NO -- EXIT IMMEDIATELY # Page 1155 # VECTOR SHIFTING ROUTINES. SHORTV CAF LOW3 # SAVE 3 BIT SHIFT COUNT -- 1 WITHOUT MASK CYR # EDITING CYR. TS MPTEMP CCS CYR # SEE IF LEFT OR RIGHT SHIFT. TCF VSSL # VECTOR SHIFT LEFT. OCT176 OCT 176 # USED IN PROCESSED SHIFTS WITH - COUNT. VSSR INDEX MPTEMP # (ENTRY FROM SR). PICK UP SHIFTING BIT. CAF BIT14 # MPTEMP CONTAINS THE SHIFT COUNT - 1. TS MPTEMP TC VSHRRND # SHIFT X COMPONENT. DXCH MPAC # SWAP X AND Y COMPONENTS. DXCH MPAC +3 DXCH MPAC TC VSHRRND # SHIFT Y COMPONENT. DXCH MPAC # SWAP Y AND Z COMPONENTS. DXCH MPAC +5 DXCH MPAC TC VSHRRND # SHIFT Z COMPONENT. TCF VROTATEX # RESTORE COMPONENTS TO PROPER PLACES. # Page 1156 # VECTOR SHIFT LEFT -- DONE ONE PLACE AT A TIME. -1 TS MPTEMP # SHIFTING LOOP. VSSL EXTEND DCA MPAC DAS MPAC EXTEND BZF +2 TC OVERFLOW EXTEND DCA MPAC +3 DAS MPAC +3 EXTEND BZF +2 TC OVERFLWY EXTEND DCA MPAC +5 DAS MPAC +5 EXTEND BZF +2 TC OVERFLWZ CCS MPTEMP # LOOP ON DECREMENTED SHIFT COUNTER. TCF VSSL -1 TCF DANZIG # EXIT. # Page 1157 # TSLC -- TRIPLE SHIFT LEFT AND COUNT. SHIFTS MPAC LEFT UNTIL GREATER THAN .5 IN MAGNITUDE, LEAVI # THE COMPLEMENT OF THE NUMBER OF SHIFTS REQUIRED IN X. TSLC2 TS MPTEMP # START BY ZEROING SHIFT COUNT (IN A NOW). TC BRANCH # EXIT WITH NO SHIFTING IF ARGUMENT ZERO. TCF +2 TCF ENDTSLC # STORES ZERO SHIFT COUNT IN THIS CASE. TC TPAGREE # MAY CAUSE UPSHIFT OF ONE EXTRA PLACE. CA MPAC # BEGIN NORMALIZATION LOOP. TCF TSLCTEST TSLCLOOP INCR MPTEMP # INCREMENT SHIFT COUNTER. EXTEND DCA MPAC +1 DAS MPAC +1 AD MPAC ADS MPAC TSLCTEST DOUBLE # SEE IF (ANOTHER) SHIFT IS REQUIRED OVSK TCF TSLCLOOP # YES -- INCREMENT COUNT AND SHIFT AGAIN. ENDTSLC CS MPTEMP TCF STORE1 # STORE SHIFT COUNT AND RETURN TO DANZIG. # Page 1158 # THE FOLLOWING ROUTINE PROCESSES THE GENERAL SHIFT INSTRUCTIONS SR, SRR, SL, AND SLR. # THE GIVEN ADDRESS IS DECODED AS FOLLOWS: # BITS 1-7 SHIFT COUNT (SUBADDRESS) LESS THAN 125 DECIMAL. # BIT 8 PSEUDO SIGN BIT (DETECTS CHANGE IN SIGN IN INDEXED SHIFTS). # BIT 9 0 FOR LEFT SHIFT, AND 1 FOR RIGHT SHIFT. # BIT 10 1 FOR TERMINAL ROUND ON SCALAR SHIFTS, 0 OTHERWISE # BITS 11-13 0. # BIT 14 1. # BIT 15 0. # THE ABOVE ENCODING IS DONE BY THE YUL SYSTEM. GENSHIFT MASK ADDRWD # GET SHIFT COUNT, TESTING FOR ZERO. CCS A # (ARRIVES WITH C(A) = LOW7). TCF GENSHFT2 # IF NON-ZERO, PROCEED WITH DECREMENTED CT CAF BIT10 # ZERO SHIFT COUNT. NO SHIFTS NEEDED BUT MASK ADDRWD # WE MIGHT HAVE TO ROUND MPAC ON SLR AND CCS A # SRR (SCALAR ONLY). TC ROUNDSUB TCF DANZIG GENSHFT2 TS MPTEMP # DECREMENTED SHIFT COUNT TO MPTEMP. CAF BIT8 # TEST MEANING OF LOW SEVEN BIT COUNT IN EXTEND # MPTEMP NOW. MP ADDRWD MASK LOW2 # JUMPS ON SHIFT DIRECTION (BIT8) AND INDEX A TCF +1 # ORIGINAL SHIFT DIRECTION (BIT 9) TCF RIGHT- # NEGATIVE SHIFT COUNT FOR SL OR SLR. TCF LEFT # SL OR SLR. TCF LEFT- # NEGATIVE SHIFT COUNT WITH SR OR SRR. # Page 1159 # GENERAL SHIFT RIGHT RIGHT CCS MODE # SET IF VECTOR OR SCALAR. TCF GENSCR TCF GENSCR CA MPTEMP # SEE IF SHIFT COUNT LESS THAN 14D. VRIGHT2 AD NEG12 EXTEND BZMF VSSR # IF SO, BRANCH AND SHIFT IMMEDIATELY. AD NEGONE # IF NOT, REDUCE MPTEMP BY A TOTAL OF 14. TS MPTEMP # AND DO A SHIFT RIGHT AND ROUND BY 14. CAF ZERO # THE ROUND AT THIS STAGE MAY INTRODUCE A TS L # ONE BIT ERROR IN A SHIFT RIGHT 15D. XCH MPAC XCH MPAC +1 TC SETROUND # X COMPONENT NOW SHIFTED, SO MAKE UP THE DAS MPAC # ROUNDING QUANTITY (0 IN A AND 0 OR +-1 # IN L). XCH MPAC +3 # REPEAT THE ABOVE PROCESS FOR Y AND Z/ XCH MPAC +4 TC SETROUND DAS MPAC +3 # NO OVERFLOW ON THESE ADDS. XCH MPAC +5 XCH MPAC +6 TC SETROUND DAS MPAC +5 CCS MPTEMP # SEE IF DONE, DOING FINAL DECREMENT. TS MPTEMP TCF VRIGHT2 BIASLO DEC .2974 B-1 # SQRT CONSTANT TCF DANZIG SETROUND DOUBLE # MAKES UP ROUNDING QUANTITY FROM ARRIVING TS MPAC +2 # C(A). L IS ZERO INITIALLY. CAF ZERO XCH L TC Q # RETURN AND DO THE DAS, RESETTING L TO 0. # Page 1160 # PROCESS SR AND SRR FOR SCALARS. GENSCR CA MPTEMP # SEE IF THE ORIGINAL SHIFT COUNT WAS LESS +1 AD NEG12 # THAN 14D. EXTEND BZMF DOSSHFT # DO THE SHIFT IMMEDIATELY IF SO. +4 AD NEGONE # IF NOT, DECREMENT SHIFT COUNT BY 14D AND TS MPTEMP # SHIFT MPAC RIGHT 14 PLACES. CAF ZERO XCH MPAC XCH MPAC +1 TS MPAC +2 CCS MPTEMP # SEE IF FINISHED, DO FINAL DECREMENT. TS MPTEMP TC GENSCR +1 SLOPEHI DEC .5884 # SQRT CONSTANT. CAF BIT10 # FINISHED WITH SHIFT. SEE IF ROUND MASK ADDRWD # WANTED. CCS A TC ROUNDSUB TCF DANZIG # DO SO AND/OR EXIT. DOSSHFT INDEX MPTEMP # PICK UP SHIFTING BIT. CAF BIT14 TS MPTEMP CAF BIT10 # SEE IF TERMINAL ROUND DESIRED. MASK ADDRWD CCS A TCF RIGHTR # YES. TCF MPACSHR # JUST SHIFT RIGHT. # Page 1161 # PROCESS THE RIGHT- (SL(R) WITH A NEGATIVE COUNT), LEFT-, AND LEFT OPTIONS. RIGHT- CS MPTEMP # GET ABSOLUTE VALUE - 1 OF SHIFT COUNT AD OCT176 # UNDERSTANDING THAT BIT8 (PSEUDO-SIGN) TS MPTEMP # WAS 1 INITIALLY. TCF RIGHT # DO NORMAL SHIFT RIGHT. LEFT- CS OCT176 # SAME PROLOGUE TO LEFT FOR INDEXED RIGHT AD MPTEMP # SHIFT WHOSE NET SHIFT COUNT IS NEGATIVE COM TS MPTEMP LEFT CCS MODE # SINCE LEFT SHIFTING IS DONE ONE PLACE AT TCF GENSCL # A TIME, NO COMPARISON WITH 14 NEED BE TCF GENSCL # DONE. FOR SCALARS, SEE IF TERMINAL ROUND TCF VSSL # DESIRED. FOR VECTORS, SHIFT IMMEDIATELY. GENSCL CS ADDRWD # PUT ROUNDING BIT (BIT 10 OF ADDRWD) INTO EXTEND # BIT 15 OF CYR WHERE THE ROUNDING BIT OF MP BIT6 # A SHORT SHIFT LEFT WOULD BE TS CYR TCF TSSL +2 # DO THE SHIFT. # Page 1162 # SCALAR DIVISION INSTRUCTIONS, DDV AND BDDV, ARE EXECUTED HERE. AT THIS POINT, THE DIVIDEND IS # AND THE DIVISOR IS IN BUF. DDV/BDDV CS ONE # INITIALIZATION TS DVSIGN # +-1 FOR POSITIVE QUOTIENT -- -0 FOR NEG. TS DVNORMCT # DIVIDEND NORMALIZATION COUNT. TS MAXDVSW # NEAR-ONE DIVIDE FLAG. CCS BUF # FORCE BUF POSITIVE WITH THE MAJOR PART TCF BUFPOS # NON-ZERO. TCF +2 TCF BUFNEG BUFZERO TS MPAC +2 # ZERO THIS. TC TPAGREE # FORCE SIGN AGREEMENT BEFORE OVERFLOW CCS MPAC # TEST TO SEE IF MPAC NON-ZERO. (TOO BIG) TCF OVF+ # MAJOR PART OF DIVIDEND IS POSITIVE NON-0 TCF +2 TCF OVF+ -1 # MAJOR PART OF DIVIDEND IS NEG. NON-ZERO XCH BUF +1 # SHIFT DIVIDEND AND DIVISOR LEFT 14 XCH BUF XCH MPAC +1 XCH MPAC CCS BUF # TRY AGAIN ON FORMER MINOR PART. TCF BUF+ TCF +2 # OVERFLOW ON ZERO DIVISOR. TCF BUF- CS MPAC # SIGN OF MPAC DETERMINES SIGN OF RESULT. SGNDVOVF EXTEND BZMF +2 INCR DVSIGN # NEGMAX IN MPAC PERHAPS. DVOVF CAF POSMAX # ON DIVISION OVERFLOW OF ANY SORT, SET TS MPAC # SET DP MPAC TO +-POSMAX. TC FINALDV +3 CAF ONE # SET OVERFLOW INDICATOR AND EXIT. TS OVFIND TC DANZIG -1 INCR DVSIGN OVF+ CS BUF +1 # LOAD LOWER ORDER PART OF DIVISOR. TCF SGNDVOVF # GET SIGN OF RESULT. BUF- EXTEND # IF BUF IS NEGATIVE, COMPLEMENT IT AND DCS BUF # MAINTAIN DVSIGN FOR FINAL QUOTIENT SIGN. DXCH BUF INCR DVSIGN # NOW -0. # Page 1163 BUF+ CCS MPAC # FORCE MPAC POSITIVE, CHECKING FOR ZERO TCF MPAC+ # DIVIDEND IN THE PROCESS. TCF +2 TCF MPAC- CCS MPAC +1 TCF MPAC+ TCF DANZIG # EXIT IMMEDIATELY ON ZERO DIVIDEND. TCF MPAC- TCF DANZIG MPAC- EXTEND # FORCE MPAC POSITIVE AS BUF IN BUF-. DCS MPAC DXCH MPAC INCR DVSIGN # NOW +1 OR -0. # Page 1164 MPAC+ CS MPAC # CHECK FOR DIVISION OVERFLOW. IF THE AD NEGONE # MAJOR PART OF THE DIVIDEND IS LESS THAN AD BUF # THE MAJOR PART OF THE DIVISOR BY AT CCS A # LEAST TWO, WE CAN PROCEED IMMEDIATELY TCF DVNORM # WITHOUT NORMALIZATION PRODUCING A DVMAX. -1/2+2 OCT 60001 # USED IN SQRTSUB. TCF +1 # IF THE ABOVE DOES NOT HOLD, FORCE SIGN CAF HALF # AGREEMENT IN NUMERATOR AND DENOMINATOR DOUBLE # TO FACILITATE OVERFLOW AND NEAR-ONE AD MPAC +1 # CHECKING. TS MPAC +1 CAF ZERO AD POSMAX ADS MPAC CAF HALF # SAME FOR BUF. DOUBLE AD BUF +1 TS BUF +1 CAF ZERO AD POSMAX ADS BUF CS MPAC # CHECK MAGNITUDE OF SIGN-CORRECTED AD BUF # OPERANDS. CCS A TCF DVNORM # DIVIDE OK -- WILL NOT BECOME MAXOV CASE. LBUF2 ADRES BUF2 TCF DVOVF # DIVISOR NOT LESS THAN DIVIDEND -- OVF. TS MAXDVSW # IF THE MAJOR PARTS OF THE DIVIDEND AND CS MPAC +1 # DIVISOR ARE EQUAL, A SPECIAL APPROXIMA- AD BUF +1 # TION IS USED (PROVIDED THE DIVISION IS EXTEND # POSSIBLE, OF COURSE). BZMF DVOVF TCF DVNORM # IF NO OVERFLOW. # Page 1165 BUFNORM EXTEND # ADD -1 TO AUGMENT SHIFT COUNT AND SHIFT AUG DVNORMCT # LEFT ONE PLACE. EXTEND DCA BUF DAS BUF DVNORM CA BUF # SEE IF DIVISOR NORMALIZED YET. DOUBLE OVSK TCF BUFNORM # NO -- SHIFT LEFT ONE AND TRY AGAIN. DXCH MPAC # CALL DIVIDEND NORMALIZATION SEQUENCE INDEX DVNORMCT # PRIOR TO DOING THE DIVIDE. TC MAXTEST TS MPAC +2 # RETURNS WITH DIVISION DONE AND C(A) = 0. TCF DANZIG BUFPOS CCS A TCF BUF+ # TO BUF+ IF BUF IS GREATER THAN +1. CS BUF +1 # IF BUF IS +1, FORCING SIGN AGREEMENT EXTEND # MAY CAUSE BUF TO BECOME ZERO. BZMF BUF+ # BRANCH IF SIGNS AGREE. CA HALF # SIGNS DISAGREE. FORCE AGREEMENT. +6 DOUBLE ADS BUF +1 CA ZERO TS BUF TCF BUFZERO BUFNEG CCS A TCF BUF- # TO BUF- IF BUF IS LESS THAN -1. CA BUF +1 # IF BUF IS -1, FORCING SIGN AGREEMENT EXTEND # MAY CAUSE BUF TO BECOME ZERO. BZMF BUF- # BRANCH IF SIGNS AGREE. CS HALF # SIGNS DISAGREE. FORCE AGREEMENT. TCF BUFPOS +6 # Page 1166 # THE FOLLOWING ARE PROLOGUES TO SHIFT THE DIVIDEND ARRIVING IN A AND L BEFORE THE DIVIDE. -21D LXCH SR # SPECIAL PROLOGUE FOR UNIT WHEN THE EXTEND # LENGTH OF THE ARGUMENT WAS NOT LESS THAN MP HALF # .5. IN THIS CASE, EACH COMPONENT MUST BE XCH L # SHIFTED RIGHT ONE TO PRODUCE A HALF-UNIT AD SR # VECTOR. XCH L TCF GENDDV +1 # WITH DP DIVIDEND IN A,L. DDOUBL # PROLOGUE WHICH NORMALIZES THE DIVIDEND DDOUBL # WHEN IT IS KNOWN THAT NO DIVISION DDOUBL # OVERFLOW WILL OCCUR. DDOUBL DDOUBL DDOUBL DDOUBL DDOUBL DDOUBL DDOUBL DDOUBL DDOUBL DDOUBL DXCH MPAC MAXTEST CCS MAXDVSW # 0 IF MAJORS MIGHT BE =, -1 OTHERWISE. BIASHI DEC .4192 B-1 # SQRT CONSTANTS. TCF MAXDV # CHECK TO SEE IF THEY ARE NOW EQUAL. # Page 1167 # THE FOLLOWING IS A GENERAL PURPOSE DOUBLE PRECISION DIVISION ROUTINE. IT DIVIDES MPAC BY BUF A # THE RESULT IN MPAC. THE FOLLOWING CONDITIONS MUST BE SATISFIED: # # 1. THE DIVISOR (BUF) MUST BE POSITIVE AND NOT LESS THAN .5. # # 2. THE DIVIDEND (MPAC) MUST BE POSITIVE WITH THE MAJOR PART OF MPAC STRICTLY LESS THAN THAT OF # (A SPECIAL APPROXIMATION, MAXDV, IS USED WHEN THE MAJOR PARTS ARE EQUAL). # # UNDERSTANDING THAT A/B = Q + S(R/B) WHERE S = 2(-14) AND Q AND R ARE QUOTIENT AND REMAINDER, RESPE # TIVELY, THE FOLLOWING APPROXIMATION IS OBTAINED BY MULTIPLYING ABOVE AND BELOW BY C - SD AND NE # ORDER S-SQUARED (POSSIBLY INTRODUCING ERROR INTO THE LOW TWO BITS OF THE RESULT). SIGN AGREEM # # A + SB . (R - CD) A + SB # ------ = Q + S(------) WHERE Q AND R ARE QUOTIENT AND REMAINDER OF ------ RESPECTIVELY. # C + SD ( C } C GENDDV DXCH MPAC # WE NEED A AND B ONLY FOR FIRST DV. +1 EXTEND # (SPECIAL UNIT PROLOGUE ENTERS HERE). DV BUF # A NOW CONTAINS Q AND L, R. DXCH MPAC CS MPAC # FORM DIVIDEND FOR MINOR PART OF RESULT. EXTEND MP BUF +1 AD MPAC +1 # OVERFLOW AT THIS POINT IS POSITIVE SINCE OVSK # R IS POSITIVE IN EVERY CASE. TCF +5 EXTEND # OVERFLOW CAN BE REMOVED BY SUBTRACTING C SU BUF # (BUF) ONCE SINCE R IS ALWAYS LESS THAN C INCR MPAC # IN THIS CASE. INCR COMPENSATES SUBTRACT. TCF +DOWN # (SINCE C(A) IS STILL POSITIVE). +5 EXTEND # C(A) CAN BE MADE LESS THAN C IN MAGNI- BZMF -UP # TUDE BY DIMINISHING IT BY C (SINCE C IS # NOT LESS THAN .5) UNLESS C(A) = 0. # Page 1168 +DOWN EXTEND SU BUF # IF POSITIVE, REDUCE ONLY IF NECESSARY EXTEND # SINCE THE COMPENSATING INCR MIGHT CAUSE BZF +3 # OVERFLOW. EXTEND # DON'T SUBTRACT UNLESS RESULT IS POSITIVE BZMF ENDMAXDV # OR ZERO. +3 INCR MPAC # KEEP SUBTRACT HERE AND COMPENSATE. TCF FINALDV -UP EXTEND # IF ZERO, SET MINOR PART OF RESULT TO BZF FINALDV +3 # ZERO. EXTEND # IF NEGATIVE, ADD C TO A, SUBTRACTING ONE DIM MPAC # TO COMPENSATE. DIM IS OK HERE SINCE THE ENDMAXDV AD BUF # MAJOR PART NEVER GOES NEGATIVE. # Page 1169 FINALDV ZL # DO DV TO OBTAIN MINOR PART OF RESULT. EXTEND DV BUF +3 TS MPAC +1 CCS DVSIGN # LEAVE RESULT POSITIVE UNLESS C(DVSIGN). TC Q TC Q TC Q EXTEND DCS MPAC DXCH MPAC CAF ZERO # SO WE ALWAYS RETURN WITH C(A) = 0. TC Q # Page 1170 # IF THE MAJOR PARTS OF THE DIVISOR AND DIVIDEND ARE EQUAL, BUT THE MINOR PARTS ARE SUCH THAT THE # DIVIDEND IS STRICTLY LESS THAN THE DIVISOR IN MAGNITUDE, THE FOLLOWING APPROXIMATION IS USED # ARE THE SAME AS THE GENERAL ROUTINE WITH THE ADDITION THAT SIGN AGREEMENT IS NECESSARY (B, C, &&nb # # C + SB . (C + B - D) # ------ = 37777 + S(---------) # C + SD ( C ) # # THE DIVISION MAY BE PERFORMED IMMEDIATELY SINCE B IS STRICTLY LESS THAN D AND C IS NOT LESS THAN . MAXDV CS MPAC # SEE IF MAXDV CASE STILL HOLDS AFTER AD BUF # NORMALIZATION. EXTEND BZF +2 TCF GENDDV # MPAC NOW LESS THAN BUFF -- DIVIDE AS USUAL. +2 CAF POSMAX # SET MAJOR PART OF RESULT. TS MPAC CS BUF +1 # FORM DIVIDEND OF MINOR PART OF RESULT. AD MPAC +1 TCF ENDMAXDV # GO ADD C AND DO DIVIDE, ATTACHING SIGN # BEFORE EXITING. # Page 1171 # VECTOR DIVIDED BY SCALAR, V/SC, IS EXECUTED HERE. THE VECTOR IS NOW IN MPAC WITH SCALAR IN BUF. V/SC2 CS ONE # INITIALIZE DIVIDEND NORMALIZATION COUNT TS DVNORMCT # AND DIVISION SIGN REGISTER. TS VBUF +5 TC VECAGREE # FORCE SIGN AGREEMENT IN VECTOR DXCH BUF TC ALSIGNAG # SIGN AGREE BUF DXCH BUF CCS BUF # FORCE DIVISOR POSITIVE WITH MAJOR PART TCF /BUF+ # NON-ZERO (IF POSSIBLE). TCF +2 TCF /BUF- XCH BUF +1 # SHIFT VECTOR AND SCALAR LEFT 14. XCH BUF XCH MPAC +1 XCH MPAC EXTEND # CHECK FOR OVERFLOW IN EACH CASE. BZF +2 TCF DVOVF XCH MPAC +4 XCH MPAC +3 EXTEND BZF +2 TCF DVOVF XCH MPAC +6 XCH MPAC +5 EXTEND BZF +2 TCF DVOVF CCS BUF TCF /BUF+ TCF DVOVF # ZERO DIVISOR - OVERFLOW. TCF /BUF- TCF DVOVF /BUF- EXTEND # ON NEGATIVE, COMPLEMENT BUF AND MAINTAIN DCS BUF # DVSIGN IN VBUF +5. DXCH BUF INCR VBUF +5 # Page 1172 /BUF+ EXTEND DCA BUF # LEAVE ABS(ORIG DIVISOR) IN BUF2 DXCH BUF2 # FOR OVERFLOW TESTING TCF /NORM # NORMALIZE DIVISOR IN BUF. /NORM2 EXTEND # IF LESS THAN .5, AUGMENT DVNORMCT AND AUG DVNORMCT # DOUBLE DIVISOR. EXTEND DCA BUF DAS BUF /NORM CA BUF # SEE IF DIVISOR NORMALIZED. DOUBLE OVSK TCF /NORM2 # DOUBLE AND TRY AGAIN IF NOT. TC V/SCDV # DO X COMPONENT DIVIDE. DXCH MPAC +3 # SUPPLY ARGUMENTS IN USUAL SEQUENCE. DXCH MPAC DXCH MPAC +3 TC V/SCDV # Y COMPONENT. DXCH MPAC +5 DXCH MPAC DXCH MPAC +5 TC V/SCDV # Z COMPONENT. TCF VROTATEX # GO RE-ARRANGE COMPONENTS BEFORE EXIT. # Page 1173 # SUBROUTINE USED BY V/SC TO DIVIDE VECTOR COMPONENT IN MPAC,+1 BY THE SCALAR GIVEN IN BUF. V/SCDV CA VBUF +5 # REFLECTS SIGN OF SCALAR. TS DVSIGN CCS MPAC # FORCE MPAC POSITIVE, EXITING ON ZERO. TCF /MPAC+ TCF +2 TCF /MPAC- CCS MPAC +1 TCF /MPAC+ TC Q TCF /MPAC- TC Q /MPAC- EXTEND # USUAL COMPLEMENTING AND SETTING OF SIGN. DCS MPAC DXCH MPAC INCR DVSIGN /MPAC+ CS ONE # INITIALIZE NEAR-ONE SWITCH. TS MAXDVSW CS MPAC # CHECK POSSIBLE OVERFLOW. AD BUF2 # UNNORMALIZED INPUT DIVISOR. CCS A TCF DDVCALL # NOT NEAR-ONE TCF +2 # +0 IS JUST POSSIBLE TCF DVOVF # NO HOPE TS MAXDVSW # SIGNAL POSSIBLE NEAR-ONE CASE CS MPAC +1 # SEE IF DIVISION CAN BE DONE AD BUF2 +1 EXTEND BZMF DVOVF DDVCALL DXCH MPAC # CALL PRE-DIVIDE NORMALIZATION. INDEX DVNORMCT TCF MAXTEST # Page 1174 SLOPELO DEC .8324 VECAGREE XCH Q # SAVE Q IN A DXCH MPAC TC ALSIGNAG # SIGNAGREE MPAC DXCH MPAC DXCH MPAC +3 TC ALSIGNAG # SIGN AGREE MPAC +3 DXCH MPAC +3 DXCH MPAC +5 TC ALSIGNAG # SIGNAGREE MPAC +5 DXCH MPAC +5 TC A # Page 1175 # THE FOLLOWING ROUTINE EXECUTES THE UNIT INSTRUCTION, WHICH TAKES THE UNIT OF THE VECTOR IN MPA UNIT TC VECAGREE # FORCE SIGN AGREEMENT IN VECTOR TC MPACVBUF # SAVE ARGUMENT IN VBUF CAF ZERO # MUST SENSE OVERFLOW IN FOLLOWING DOT. XCH OVFIND TS TEM1 TC VSQSUB # DOT MPAC WITH ITSELF. CA TEM1 XCH OVFIND EXTEND BZF +2 TCF DVOVF EXTEND DCA MPAC # LEAVE THE SQUARE OF THE LENGTH OF THE INDEX FIXLOC # ARGUMENT IN LVSQUARE. DXCH LVSQUARE TC SQRTSUB # GO TAKE THE NORMALIZED SQUARE ROOT. CCS MPAC # CHECK FOR UNIT OVERFLOW. TCF +5 # MPAC IS NOT LESS THAN .5 UNLESS TS L INDEX FIXLOC DXCH LV TCF DVOVF # INPUT TO SQRTSUB WAS 0. CS FOURTEEN # SEE IF THE INPUT WAS SO SMALL THAT THE AD MPTEMP # FIRST TWO REGISTERS OF THE SQUARE WERE 0 CCS A COM # IF SO, SAVE THE NEGATIVE OF THE SHIFT TCF SMALL # COUNT -15D. TCF LARGE # (THIS IS USUALLY THE CASE.) CS THIRTEEN # IF THE SHIFT COUNT WAS EXACTLY 14, SET TS MPTEMP # THE PRE-DIVIDE NORM COUNT TO -13D. CA MPAC # SHIFT THE LENGTH RIGHT 14 BEFORE STORING SMALL2 TS L # (SMALL EXITS TO THIS POINT). CAF ZERO TCF LARGE2 # GO TO STORE LENGTH AND PROCEED. LARGE CCS MPTEMP # MOST ALL CASES COME HERE. TCF LARGE3 # SEE IF NO NORMALIZATION WAS REQUIRED BY CS SRDDV # SQRT, AND IF SO, SET UP FOR A SHIFT TS MPTEMP # RIGHT 1 BEFORE DIVIDING TO PRODUCE EXTEND # THE DESIRED HALF UNIT VECTOR. DCA MPAC # Page 1176 TCF LARGE2 # Page 1177 LARGE3 COM # LEAVE NEGATIVE OF SHIFT COUNT-1 FOR TS MPTEMP # PREDIVIDE LEFT SHIFT. COM # PICK UP REQUIRED SHIFTING BIT TO UNNORM- INDEX A # ALIZE THE SQRT RESULT. CAF BIT14 TS BUF EXTEND MP MPAC +1 XCH BUF EXTEND # (UNNORMALIZE THE SQRT FOR LV). MP MPAC XCH L AD BUF XCH L LARGE2 INDEX FIXLOC DXCH LV # LENGTH NOW STORED IN WORK AREA. CS ONE TS MAXDVSW # NO MAXDV CASES IN UNIT. DXCH VBUF # PREPARE X COMPONENT FOR DIVIDE, SETTING DXCH MPAC # LENGTH OF VECTOR AS DIVISOR IN BUF. DXCH BUF TC UNITDV DXCH VBUF +2 # DO Y AND Z IN USUAL FASHION SO WE CAN DXCH MPAC # EXIT THROUGH VROTATEX. DXCH MPAC +3 TC UNITDV DXCH VBUF +4 DXCH MPAC DXCH MPAC +5 TC UNITDV TCF VROTATEX # AND EXIT. # Page 1178 # IF THE LENGTH OF THE ARGUMENT VECTOR WAS LESS THAN 2(-28), EACH COMPONENT MUST BE SHIFTED LEFT A # 14 PLACES BEFORE THE DIVIDE, NOTE THAT IN THIS CASE, THE MAJOR PART OF EACH COMPONENT IS ZERO. SMALL TS MPTEMP # NEGATIVE OF PRE-DIVIDE SHIFT COUNT. CAF ZERO # SHIFT EACH COMPONENT LEFT 14. XCH VBUF +1 XCH VBUF XCH VBUF +3 XCH VBUF +2 XCH VBUF +5 XCH VBUF +4 CS MPTEMP INDEX A CAF BIT14 EXTEND MP MPAC TCF SMALL2 THIRTEEN = OCT15 FOURTEEN = OCT16 OCT16 = R1D1 # Page 1179 # THE FOLLOWING ROUTINE SETS UP THE CALL TO THE DIVIDE ROUTINES. UNITDV CCS MPAC # FORCE MPAC POSITIVE IF POSSIBLE, SETTING TCF UMPAC+ # DVSIGN ACCORDING TO THE SIGN OF MPAC TCF +2 # SINCE THE DIVISOR IS ALWAYS POSITIVE TCF UMPAC- # HERE. CCS MPAC +1 TCF UMPAC+ TC Q # EXIT IMMEDIATELY ON ZERO. TCF UMPAC- TC Q UMPAC- CS ZERO # IF NEGATIVE, SET -0 IN DVSIGN FOR FINAL TS DVSIGN # COMPLEMENT. EXTEND DCS MPAC # PICK UP ABSOLUTE VALUE OF ARG AND JUMP. INDEX MPTEMP TCF MAXTEST -1 UMPAC+ TS DVSIGN # SET DVSIGN FOR POSITIVE QUOTIENT. DXCH MPAC INDEX MPTEMP TCF MAXTEST -1 # Page 1180 # MISCELLANEOUS UNARY OPERATIONS. DSQ TC DSQSUB # SQUARE THE DP CONTENTS OF MPAC. TCF DANZIG ABVALABS CCS MODE # ABVAL OR ABS INSTRUCTION. TCF ABS # DO ABS ON SCALAR. TCF ABS ABVAL TC VSQSUB # DOT MPAC WITH ITSELF. LXCH MODE # MODE IS NOW DP (L ZERO AFTER DAS). EXTEND # STORE SQUARE OF LENGTH IN WORK AREA. DCA MPAC INDEX FIXLOC DXCH LVSQUARE # Page 1181 # PROGRAM DESCRIPTION -- SUBROUTINE SQRT # # FUNCTIONAL DESCRIPTION -- DOUBLE PRECISION SQUARE ROOT ROUTINE # THIS PROGRAM TAKES THE SQUARE ROOT OF THE 27 OR 28 MOST SIGNIFICANT BITS IN THE TRIPLE PRECISIO # NUMBERS -- MPAC, MPAC+1, AND MPAC+2. THE ROOT IS RETURNED DOUBLE PRECISION IN MPAC AND MPAC+1 # # WARNING -- THIS SUBROUTINE USES A TRIPLE PRECISION INPUT. THE PROGRAMMER MUST ASSURE THE CONT # ESPECIALLY IF THE CONTENTS OF MPAC IS SMALL OR ZERO. FOR DETAILS SEE STG MEMO NO.949. # # CALLING SEQUENCE -- IN INTERPRETIVE MODE, I.E., FOLLOWING `TC INTPRET', `SQRT', NO ADDRESS I # INPUT SCALING: THE BINARY POINT IS ASSUMED TO THE RIGHT OF BIT 15. THE ANSWER IS RETURNED WITH T # # SUBROUTINES -- GENSCR, MPACSHR, SQRTSUB, ABORT # # ABORT EXIT MODE -- ABORTS ON NEGATIVE INPUT -1.2X10E-4 (77775 OCTAL) OR LESS. # DISPLAYS ERROR CODE 1302 # TC ABORT # OCT 1302 # # DEBRIS -- LOCATIONS BUF, MPTEMP, ADDRWD ARE USED SQRT TC SQRTSUB # TAKE THE SQUARE ROOT OF MPAC. CCS MPTEMP # RETURNED NORMALIZED SQUARE ROOT. SEE IF TCF +2 # ANY UN-NORMALIZATION REQUIRED AND EXIT TCF DANZIG # IF NOT. AD NEG12 # A RIGHT SHIFT OF MORE THAN 13 COULD BE EXTEND # REQUIRED IF INPUT WAS ZERO IN MPAC,+1. BZMF SQRTSHFT # GOES HERE IN MOST CASES. ZL # IF A LONG SHIFT IS REQUIRED, GO TO LXCH ADDRWD # GENERAL RIGHT SHIFT ROUTINES. TCF GENSCR +4 # ADDRWD WAS ZERO TO PREVENT ROUND. SQRTSHFT INDEX MPTEMP # SELECT SHIFTING BIT AND EXIT THROUGH CAF BIT15 # SHIFT ROUTINES. TS MPTEMP CAF ZERO # TO ZERO MPAC +2 IN THE PROCESS. TCF MPACSHR +3 ABS TC BRANCH # TEST SIGN OF MPAC AND COMPLEMENT IF TCF DANZIG TCF DANZIG TCF COMP # Page 1182 VDEF CS FOUR # VECTOR DEFINE -- ESSENTIALLY TREATS ADS PUSHLOC # SCALAR IN MPAC AS X COMPONENT, PUSHES UP EXTEND # FOR Y AND THEN AGAIN FOR Z. INDEX A DCA 2 DXCH MPAC +3 EXTEND INDEX PUSHLOC DCA 0 DXCH MPAC +5 TCF VMODE # MODE IS NON VECTOR. VSQ TC VSQSUB # DOT MPAC WITH ITSELF. TCF DMODE # MODE IS NOW DP. PUSH EXTEND # PUSH DOWN MPAC LEAVING IT LOADED. DCA MPAC INDEX PUSHLOC # PUSH DOWN FIRST TWO REGISTERS IN EACH DXCH 0 INDEX MODE # INCREMENT PUSHDOWN POINTER. CAF NO.WDS ADS PUSHLOC CCS MODE TCF TPUSH # PUSH DOWN MPAC +2. TCF DANZIG # DONE FOR DP. EXTEND # ON VECTOR, PUSH DOWN Y AND Z COMPONENTS. DCA MPAC +3 INDEX PUSHLOC DXCH 0 -4 EXTEND DCA MPAC +5 INDEX PUSHLOC DXCH 0 -2 TCF DANZIG TPUSH CA MPAC +2 TCF ENDTPUSH +2 RVQ INDEX FIXLOC # RVQ -- RETURN IVA QPRET. CA QPRET TS POLISH TCF GOTO +4 # (ASSUME QPRET POINTS TO FIXED ONLY.) # Page 1183 # THE FOLLOWING SUBROUTINES ARE USED IN SQUARING MPAC, IN BOTH THE SCALAR AND VECTOR SENSE. THEY # SPECIAL CASES OF DMPSUB AND DOTSUB, PUT IN TO SAVE SOME TIME. DSQSUB CA MPAC +1 # SQUARES THE SCALAR CONTENTS OF MPAC. EXTEND SQUARE TS MPAC +2 CAF ZERO # FORM 2(CROSS TERM). XCH MPAC +1 EXTEND MP MPAC DDOUBL # AND MAYBE OVEFLOW. DAS MPAC +1 # AND SET A TO NET OVERFLOW. XCH MPAC EXTEND SQUARE DAS MPAC TC Q VSQSUB EXTEND # DOTS THE VECTOR IN MPAC WITH ITSELF. QXCH DOTRET TC DSQSUB # SQUARE THE X COMPONENT. DXCH MPAC +3 DXCH MPAC DXCH BUF # SO WE CAN END IN DOTSUB. CA MPAC +2 TS BUF +2 TC DSQSUB # SQUARE Y COMPONENT. DXCH MPAC +1 DAS BUF +1 AD MPAC AD BUF TS BUF TCF +2 TS OVFIND # IF OVERFLOW. DXCH MPAC +5 DXCH MPAC TC DSQSUB # SQUARE Z COMPONENT. TCF ENDDOT # END AS IN DOTSUB. # Page 1184 # DOUBLE PRECISION SQUARE ROOT ROUTINE. TAKE THE SQUARE ROOT OF THE TRIPLE PRECISION (MPAC +2 US # IN NORMALIZATION) CONTENTS OF MPAC AND LEAVE THE NORMALIZED RESULT IN MPAC (C(MPAC) GREATER T # .5). THE RIGHT SHIFT COUNT (TC UNNORMALIZE) IS LEFT IN MPTEMP. SQRTSUB CAF ZERO # START BY ZEROING RIGHT SHIFT COUNT. TS MPTEMP CCS MPAC # CHECK FOR POSITIVE ARGUMENT, SHIFTING TCF SMPAC+ # FIRST SIGNIFICANT MPAC REGISTER INTO TCF +2 # MPAC ITSELF. TCF SQRTNEG # SEE IF MAG OF ARGUMENT LESS THAN 10(-4). XCH MPAC +2 # MPAC IS ZERO -- SHIFT LEFT 14. XCH MPAC +1 TS MPAC CAF SEVEN # AUGMENT RIGHT SHIFT COUNTER. TS MPTEMP CCS MPAC # SEE IF MPAC NOW PNZ. TCF SMPAC+ TCF +2 TCF ZEROANS # NEGATIVE BUT LESS THAN 10(-4) IN MAG. XCH MPAC +1 # XERO -- SHIFT LEFT 14 AGAIN. TS MPAC CAF SEVEN # AUGMENT RIGHT SHIFT COUNTER. ADS MPTEMP CCS MPAC TCF SMPAC+ TC Q # SQRT(0) = 0. TCF ZEROANS TCF FIXROOT # DO NOT LEAVE SQRTSUB WITH -0 IN MPAC. SQRTNEG CCS A # ARGUMENT IS NEGATIVE, BUT SEE IF SIGN- TCF SQRTABRT # CORRECTED ARGUMENT IS LESS THAN 10(-4) CCS MPAC +1 # IN MAGNITUDE. IF SO, CALL ANSWER ZERO. ZEROANS CAF ZERO # FORCE ANSWER TO ZERO HERE. TCF FIXROOT TCF SQRTABRT TCF FIXROOT SQRTABRT TC POODOO OCT 1302 # Page 1185 SMPAC+ AD -1/2+2 # SEE IF ARGUMENT GREATER THAN OR EQUAL TO EXTEND # .5. BZMF SRTEST # IF SO, SEE IF LESS THAN .25. DXCH MPAC # WE WILL TAKE THE SQUARE ROOT OF MPAC/2. LXCH SR # SHIFT RIGHT 1 AND GO TO THE SQRT ROUTINE EXTEND MP HALF DXCH MPAC XCH SR ADS MPAC +1 # GUARANTEED NO OVERFLOW. ARGHI CAF SLOPEHI # ARGUMENT BETWEEN .25 AND .5, GET A EXTEND # LINEAR APPROXIMATION FOR THIS RANGE. MP MPAC AD BIASHI # X0/2 = (MPAC/2)(SLOPHI) + BIASHI/2. +4 TS BUF # X0/2 (ARGLO ENTERS HERE). CA MPAC # SINGLE-PRECISION THROUGHOUT. ZL EXTEND DV BUF # (MPAC/2)/(X0/2) EXTEND MP HALF ADS BUF # X1 = X0/2 + .5(MPAX/2)/(X0/2) EXTEND MP HALF # FORM UP X1/2. DXCH MPAC # SAVE AND BRING OUT ARGUMENT. EXTEND # TAKE DP QUOTIENT WITH X1. DV BUF TS BUF +1 # SAVE MAJOR PART OF QUOTIENT. CAF ZERO # FORM MINOR PART OF QUOTIENT USING XCH L # (REMAINDER,0). EXTEND DV BUF TS L # IN PREPARATION FOR DAS. CA BUF +1 DAS MPAC # X2 = X1/2 + (MPAC/2)X1 EXTEND # OVERFLOWS IF ARG. NEAR POSMAX. BZF TCQBNK00 CAF POSMAX FIXROOT TS MPAC TS MPAC +1 TCQBNK00 TC Q # RETURN TO CALLER TO UNNORMALIZE, ETC. # Page 1186 SRTEST AD QUARTER # ARGUMENT WAS LESS THAN .5, SEE IF LESS EXTEND # THAN .25. BZMF SQRTNORM # IF SO, BEGIN NORMALIZATION. DXCH MPAC # IF BETWEEN .5 AND .25, SHIFT RIGHT 1 AND LXCH SR # START AT ARGLO. EXTEND MP HALF DXCH MPAC XCH SR ADS MPAC +1 # NO OVERFLOW. ARGLO CAF SLOPELO # (NORMALIZED) ARGUMENT BETWEEN .125 AND EXTEND # .25 MP MPAC AD BIASLO TCF ARGHI +4 # BEGIN SQUARE ROOT. SQRTNM2 EXTEND # SHIFT LEFT 2 AND INCREMENT RIGHT SHIFT DCA MPAC +1 # COUNT (FOR TERMINAL UNNORMALIZATION). DAS MPAC +1 AD MPAC ADS MPAC # (NO OVERFLOW). SQRTNORM INCR MPTEMP # FIRST TIME THROUGH, JUST SHIFT LEFT 1 EXTEND # (PUTS IN EFFECTIVE RIGHT SHIFT SINCE DCA MPAC +1 # WE WANT MPAC/2). DAS MPAC +1 AD MPAC ADS MPAC # (AGAIN NO OVERFLOW). DOUBLE TS CYL NORMTEST CCS CYL # SEE IF ARGUMENT NOW NORMALIZED AT CCS CYL # GREATER THAN .125. TCF SQRTNM2 # NO -- SHIFT LEFT 2 MORE AND TRY AGAIN. TCF ARGHI # YES -- NOW BETWEEN .5 AND .25. TCF ARGLO # ARGUMENT NOW BETWEEN .25 AND .125. # Page 1187 # TRIGONOMETRIC FUNCTION PACKAGE. # THE FOLLOWING TRIGONOMETRIC FUNCTIONS ARE AVAILABLE AS INTERPRETIVE OPERATIONS: # 1. SIN COMPUTES (1/2)SINE(2 PI MPAC). # 2. COS COMPUTES (1/2)COSINE(2 PI MPAC). # 3. ASIN COMPUTES (1/2PI)ARCSINE(2 MPAC). # 4. ACOS COMPUTES (1/2PI)ARCCOSINE(2 MPAC). # # SIN-ASIN AND COS-ACOS ARE MUTUALLY INVERSE, I.E., SIN(ASIN(X)) = X. COSINE TC BRANCH # FINDS COSINE USING THE IDENTITY TCF +3 # COS(X) = SIN(PI/2 - ABS(X)). TCF PRESINE TCF PRESINE +3 EXTEND DCS MPAC DXCH MPAC PRESINE CAF QUARTER # PI/2 SCALED. ADS MPAC SINE DXCH MPAC # DOUBLE ARGUMENT. DDOUBL OVSK # SEE IF OVERFLOW PRESENT. TCF +3 # IF NOT, ARGUMENT OK AS IS. EXTEND # IF SO, WE LOST (OR GAINED) PI, SO DCOM # COMPLEMENT MPAC USING THE IDENTITY # SIN(X-(+)PI) = SIN(-X). +3 DXCH MPAC CA MPAC # SEE IF ARGUMENT GREATER THAN .5 IN DOUBLE # MAGNITUDE. IF SO, REDUCE IT TO LESS THAN TS L # .5 (+-PI/2 SCALED) AS FOLLOWS: TCF SN1 INDEX A # IF POSITIVE, FORM PI - X, IF NEGATIVE CAF NEG1/2 +1 # USE -PI -X. DOUBLE EXTEND SU MPAC # GUARANTEED NO OVERFLOW. TS MPAC CS MPAC +1 TS MPAC +1 # Page 1188 SN1 EXTEND # SET UP TO EVALUATE HASTINGS POLYNOMIAL DCA MPAC DXCH BUF2 TC DSQSUB # SQUARE MPAC. TC POLY # EVALUATE FOURTH ORDER POLYNOMIAL. DEC 3 2DEC +.3926990796 2DEC -.6459637111 2DEC +.318758717 2DEC -.074780249 2DEC +.009694988 CAF LBUF2 # MULTIPLY BY ARGUMENT AND SHIFT LEFT 2. TC DMPSUB -1 EXTEND DCA MPAC +1 DAS MPAC +1 AD MPAC ADS MPAC # NEITHER SHIFT OVERFLOWS. EXTEND DCA MPAC +1 DAS MPAC +1 AD MPAC ADS MPAC TCF DANZIG # Page 1189 # ARCSIN/ARCCOS ROUTINE. ARCSIN CAF LASINEX # COMPUTE ARCSIN BY USING THE IDENTITY TCF +2 # ARCSIN(X) = PI/2 - ARCCOS(X). ARCCOS CAF LDANZIG # (EXITS IMMEDIATELY). TS ESCAPE TC BRANCH # TEST SIGN OF INPUT. TCF ACOSST # START IMMEDIATELY IF POSITIVE. TCF ACOSZERO # ARCCOS(0) = PI/2 = .25. EXTEND # IF NEGATIVE, USE THE IDENTITY DCS MPAC # ARCCOS(X) = PI - ARCCOS(-X), FORCING DXCH MPAC # ARGUMENT POSITIVE. CAF TCSUBTR # SET EXIT TO DO ABOVE BEFROE XCH ESCAPE # ARCSIN/ARCCOS CONSIDERATIONS. TS ESCAPE2 ACOSST CS HALF # TEST MAGNITUDE OF INPUT. AD MPAC CCS A TCF ACOSOVF # THIS IS PROBABLY AN OVERFLOW CASE. LASINEX TCF ASINEX TCF ACOSST2 # NO OVERFLOW -- PROCEED. CCS MPAC +1 # IF MAJOR PART IS .5, CALL ANSWER 0 CAF ZERO # UNLESS MINOR PART NEGATIVE. TCF ACOS=0 TCF ACOSST2 ACOS=0 TS MPAC +1 TS MPAC TC ESCAPE ACOSST2 EXTEND # NOW THAT ARGUMENT IS IN PROPER RANGE, DCS MPAC # BEGIN COMPUTATION. USE HASTINGS AD HALF # APPROXIMATION ARCCOS(X) = SQRT(1-X)P(X) DXCH MPAC # IN A SCALED VERSION WHERE P(X) IS A DXCH BUF2 # SEVENTH ORDER POLYNOMIAL. TC SQRTSUB # RETURNS WITH NORMALIZED SQUARE ROOT. CCS MPTEMP # SEE IF UN-NORMALIZATION REQUIRED. TCF ACOSSHR # Page 1190 ACOS3 DXCH MPAC # SET UP FOR POLYNOMIAL EVALUATION. DXCH BUF2 DXCH MPAC TC POLY DEC 6 2DEC +.353553385 # COEFFICIENTS ARE C 2(+I)/PISQRT(2) WHERE 2DEC* -.0483017006 B+1* # I 2DEC* +.0200273085 B+2* # WEHRE C STANDS FOR ORIGINAL COEFFS. 2DEC* -.0112931863 B+3* 2DEC* +.00695311612 B+4* 2DEC* -.00384617957 B+5* 2DEC* +.001501297736 B+6* 2DEC* -.000284160334 B+7* CAF LBUF2 # DO FINAL MULTIPLY AND GO TO ANY TC DMPSUB -1 # EPILOGUE SEQUENCES. TC ESCAPE SUBTR EXTEND # EPILOGUE FOR NEGATIVE INPUTS TO ARCCOS. DCS MPAC AD HALF # FORMS PI - ARCCOS(-X) = ARCCOS(X). DXCH MPAC TC ESCAPE2 # GO TO POSSIBLE ARCSIN EPILOGUE. ASINEX EXTEND DCS MPAC # ARCSIN EPILOGUE -- GET ARCSIN(X) AD QUARTER # = PI/2 - ARCCOS(X). DXCH MPAC LDANZIG TCF DANZIG # Page 1191 ACOSSHR INDEX A # THE SHIFT RIGHT IS LESS THAN 14 SINCE CAF BIT14 # THE INPUT WAS NON-ZERO DP. TS MPTEMP TC VSHRRND # DP SHIFT RIGHT AND ROUND. TCF ACOS3 # PROCEED. ACOSOVF EXTEND # IF MAJOR PART WAS ONLY 1 MORE THAN .5, BZF ACOS=0 # CALL ANSWER ZERO. ACOSABRT TC ALARM # IF OVERFLOW, CALL ANSWER ZERO BUT OCT 1301 # SOUND AN ALARM. CAF ZERO TCF ACOS=0 ACOSZERO CAF QUARTER # ACOS(0) = PI/2. TCF ACOS=0 +1 # SET MPAC AND EXIT VIA ESCAPE. NEG12 DEC -12 TCSUBTR TCF SUBTR # Page 1192 # THE FOLLOWING INSTRUCTIONS ARE AVAILABLE FOR SETTING, MODIFYING, AND BRANCHING ON INDEX REG # 1. AXT ADDRESS TO INDEX TRUE. # 2. AXC ADDRESS TO INDEX COMPLEMENTED. # 3. LXA LOAD INDEX FROM ERASABLE. # 4. LXC LOAD INDEX COMPLEMENTED FROM ERASABLE. # 5. SXA STORE INDEX IN ERASABLE. # 6. XCHX EXCHANGE INDEX REGISTER WITH ERASABLE. # 7. INCR INCREMENT INDEX REGISTER. # 8. XAD ERASABLE ERASABLE ADD TO INDEX REGISTER. # 9. XSU ERASABLE SUBTRACT FROM INDEX REGISTER. # 10. TIX BRANCH ON INDEX REGISTER AND DECREMENT. BANK 01 COUNT 01/INTER AXT TC TAGSUB # SELECT APPROPRIATE INDEX REGISTER. CA POLISH XSTORE INDEX INDEXLOC # CONTAINS C(FIXLOC) OR C(FIXLOC)+1 TS X1 TCF DANZIG AXC TC TAGSUB CS POLISH TC XSTORE LXA TC 15ADRERS # LOAD INDEX REGISTER FROM ERASABLE. INDEX POLISH CA 0 TCF XSTORE LXC TC 15ADRERS # LOAD NDX REG FROM ERASABLE COMPLEMENTED. INDEX POLISH CS 0 TCF XSTORE SXA TC 15ADRERS # STORE INDEX REGISTER IN ERASABLE. INDEX INDEXLOC CA X1 MSTORE1 INDEX POLISH TS 0 TCF DANZIG # Page 1193 XCHX TC 15ADRERS # EXCHANGE INDEX REGISTER WITH ERASABLE. INDEX POLISH CA 0 INDEX INDEXLOC XCH X1 TCF MSTORE1 XAD TC 15ADRERS # ADD ERASABLE TO INDEX REGISTER. INDEX POLISH CA 0 XAD2 INDEX INDEXLOC ADS X1 # IGNORING OVERFLOWS. TCF DANZIG INCR TC TAGSUB # INCREMENT INDEX REGISTER. CA POLISH TCF XAD2 XSU TC 15ADRERS # SUBTRACT ERASABLE FROM INDEX REGISTER. INDEX POLISH CS 0 TCF XAD2 TIX TC TAGSUB # BRANCH AND DECREMENT ON INDEX. INDEX INDEXLOC CS S1 INDEX INDEXLOC AD X1 EXTEND # NO OPERATION IF DECREMENTED INDEX IS BZMF DANZIG # NEGATIVE OR ZERO. DOTIXBR INDEX INDEXLOC XCH X1 # IGNORING OVERFLOWS. TCF GOTO # DO THE BRANCH USING THE CADR IN POLISH. # Page 1194 # SUBROUTINE TO CONVERT AN ERASABLE ADDRESS (11 BITS) TO AN EBANK SETTING AND SUBADDRESS. 15ADRERS CS POLISH AD DEC45 CCS A # DOES THE ADDRESS POINT TO THE WORK AREA? CA FIXLOC # YES. ADD FIXLOC. EBANK OK AS IS. TCF +5 CA OCT1400 # NO. SET EBANK & MAKE UP SUBADDRESS. XCH POLISH TS EBANK MASK LOW8 +5 ADS POLISH # FALL INTO TAGSUB, AND RETURN VIA Q. # SUBROUTINE WHICH SETS THE ADDRESS OF THE SPECIFIED INDEX IN INDEXLOC. (ACTUALLY, THE ADDRESS TAGSUB CA FIXLOC TS INDEXLOC CCS CYR # BIT 15 SPECIFIES INDEX. INCR INDEXLOC # 0 MEANS USE X2. TC Q TC Q # 1 FOR X1. # Page 1195 # MISCELLANEOUS OPERATION CODES WITH DIRECT ADDRESSES. INCLUDED HERE ARE: # 1. ITA STORE CPRET (RETURN ADDRESS) IN ERASABLE. # 2. CALL CALL A SUBROUTINE, LEAVING RETURN IN QPRET. # 3. RTB RETURN TO BASIC LANGUAGE AT THE GIVEN ADDRESS. # 4. BHIZ BRANCH IF THE HIGHORDER OF MPAC IS ZERO (SINGLE PRECISION). # 5. BOV BRANCH ON OVERFLOW. # 6. GOTO SIMPLE SEQUENCE CHANGE. RTB/BHIZ CCS CYR RTB CA POLISH TC SWCALL -1 # SO A "TC Q" FROM ROUTINE LEADS TO DANZIG BHIZ CCS MPAC TCF DANZIG TCF GOTO TCF DANZIG TCF GOTO BOV(B) CCS OVFIND # BRANCH ON OVERFLOW TO BASIC OR INTERP. TCF +2 TCF DANZIG TS OVFIND CCS CYR TCF RTB # IF BASIC. B5TOBB OCT 360 TCF GOTO # Page 1196 BZE/GOTO CCS CYR # SEE WHICH OP-CODE IS DESIRED. TC BRANCH # DO BZE. TCF DANZIG TCF GOTO # DO GOTO. TCF DANZIG BPL/BMN CCS CYR TCF BPL 5B10 #DEC 5 B+10 # SHIFTS OP CODE IN SWITCH INSTRUCTION ADR DEC 5 B-4 # RSB 2009 TC BRANCH # DO BMN TCF DANZIG TCF DANZIG TCF GOTO # ONLY IF NNZ. BPL TC BRANCH TCF GOTO # IF POSITIVE OR ZERO. TCF GOTO TCF DANZIG CALL/ITA CCS CYR TCF CALL TC CCSHOLE TC 15ADRERS # STORE QPRET. (TAGSUB AFTER 15ADRERS IS INDEX FIXLOC # SLOW IN THIS CASE, BUT SAVES STORAGE.) CA QPRET TCF MSTORE1 # Page 1197 # THE FOLLOWING OPERATIONS ARE AVAILABLE FOR ALTERING AND TESTING INTERPRETATIVE SWITCHES: # 00 BONSET SET A SWITCH AND DO A GOTO IF IT WAS ON. # 01 SETGO SET A SWITCH AND DO A GOTO. # 02 BOFSET SET A SWITCH AND DOA GOTO IF IT WAS OFF # 03 SET SET A SWITCH. # 04 BONINV INVERT A SWITCH AND BRANCH IF IT WAS ON. # 05 INVGO INVERT A SWITCH AND DO A GOTO. # 06 BOFINV INVERT A SWITCH AND BRANCH IF IT WAS OFF # 07 INVERT INVERT A SWITCH. # 10 BONCLR CLEAR A SWITCH AND BRANCH IF IT WAS ON. # 11 CLRGO CLEAR A SWITCH AND DO A GOTO. # 12 BOFCLR CLEAR A SWITCH AND BRANCH IF IT WAS OFF. # 13 CLEAR CLEAR A SWITCH. # 14 BON BRANCH IF A SWITCH WAS ON. # 16 BOFF BRANCH IF A SWITCH WAS OFF. # THE ADDRESS SUPPLIED WITH THE SWITCH INSTRUCTION IS INTERPRETED AS FOLLOWS: # BITS 1-4 SWITCH BIT NUMBER (1-15). # BITS 5-8 SWITCH OPERATION NUMBER # BITS 9- SWITCH WORD NUMBER (UP TO 64 SWITCH WORDS). # THE ADDRESS ITSELF IS MADE UP BY THE YUL SYSTEM ASSEMBLER. THE BRANCH INSTRUCTIONS REQUIRE TWO # ADDRESSES, THE SECOND TAKEN AS THE DIRECT (OR INDIRECT IF IN ERASABLE) ADDRESS OF THE BRANCH. SWITCHES CAF LOW4 # LEAVE THE SWITCH BIT IN SWBIT. MASK POLISH INDEX A CAF BIT15 # (NUMBER FROM LEFT TO RIGHT.) TS SWBIT CAF BIT7 # LEAVE THE SWITCH NUMBER IN SWWORD. EXTEND MP POLISH TS SWWORD INHINT # DURING SWITCH CHANGE SO RUPT CAN USE TOO INDEX A # LEAVE THE SWITCH WORD ITSELF IN L. CA STATE TS Q # Q WILL BE USED AS A CHANNEL. # Page 1198 CAF BIT11 EXTEND # DISPATCH SWITCH BIT OPERATION AS IN BITS MP POLISH # 7-8 OF POLISH. MASK B3TOB4 # GETS 4X2-BIT CODE. INDEX A TCF +1 +1 CA SWBIT # 00 -- SET SWITCH IN QUESTION. EXTEND ROR QCHAN TCF SWSTORE +5 CA SWBIT # 01 -- INVERT SWITCH. EXTEND RXOR QCHAN TCF SWSTORE +9D CS SWBIT # 10 -- CLEAR. MASK Q SWSTORE INDEX SWWORD TS STATE # NEW SWITCH WORD. # Page 1199 +13D RELINT # 11 -- NOOP. CAF BIT13 EXTEND # DISPATCH SEQUENCE CHANGING OR BRANCING MP POLISH # CODE. MASK B3TOB4 INDEX A TCF +1 # ORIGINALLY STORED IN BITS 5-6 +1 CS Q # 00 -- BRANCH IF ON. TEST MASK SWBIT CCS A TCF SWSKIP +5 TCF SWBRANCH # 01 -- GO TO. TCF SWSKIP # HERE ONLY ON BIT 15. TC CCSHOLE TC CCSHOLE +9D CA Q # 10 -- BRANCH IF OFF. TCF TEST B3TOB4 OCT 0014 SWSKIP INCR LOC SW/ EQUALS SWITCHES +13D TCF DANZIG # 11 -- NOOP.
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2026-10-11