Pre-launch Review
INTERPRETER
Scanned pages: 1002-1094
# Copyright: Public domain.# Filename: INTERPRETER.agc# Purpose: Part of the source code for Luminary 1A build 099.# It is part of the source code for the Lunar Module's (LM)# Apollo Guidance Computer (AGC), for Apollo 11.# Assembler: yaYUL# Contact: Ron Burkey <info@sandroid.org>.# Website: www.ibiblio.org/apollo.# Pages: 1002-1094# Mod history: 2009-05-25 RSB Adapted from the corresponding# Luminary131 file, using page# images from Luminary 1A.# 2011-01-06 JL Fixed pseudo-label indentation.# 2011-05-08 JL Removed workarounds.
# 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 001 of AGC program LMY99 by NASA 2021112-061# 16:27 JULY 14, 1969
# Page 1002# SECTION 1: DISPATCHER## ENTRY TO THE INTERPRETER. INTPRET SETS LOC TO THE FIRST INSTRUCTION, BANKSET TO THE BBANK OF THE# OBJECT INTERPRETIVE PROGRAM, AND INTBIT15 TO THE BIT15 CONTENTS OF FBANK. INTERPRETIVE PROGRAMS MAY BE IN# VIRTUALLY ALL BANKS PRESENT UNDER ANY SUPER-BANK SETTING, WITH THE RESTRICTION THAT PROGRAMS IN HIGH BANKS# (BIT15 OF FBANK = 1) DO NOT REFER TO LOWBANKS, AND VICE-VERSA. THE INTERPRETER DOES NOT SWITCH SUPERBANKS.# E-BANK SWITCHING OCCURS WHENEVER GENERAL ERASABLE (100-3777) IS ADDRESSED.
BLOCK 03
COUNT* $$/INTERINTPRET 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)) INT MPAC,MPAC +1SLOAD2 DXCH MPAC CAF ZERO # ZERO MPAC +2
# Page 1003# 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-EDITIING.
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 1004# 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 IFOCT40001 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 1005# 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. ADDRESSES LESS# 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.
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 EBANKITR10 INDEX CYR 7 INDJUMP -1
# Page 1006# THE FOLLOWING ROUTINE PROCESSES INTERPRETIVE INDEXED ADDRESSES. AN INTERPRETER INDEX REGISTER MAY# CONTAIN THE ADDRESS OF ANY ERASABLE REGISTER (0-42 BEING RELATIVE TO THE VAC AREA) OR ANY INTERPRETIVE PROGRAM# 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 ADDRWDITR11 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 1007ITR13 INDEX CYR 3 INDJUMP -1
# Page 1008# PUSH-UP ROUTINES. WHEN NO OPERAND ADDRESS IS GIVEN, THE APPROPRIATE OPERAND IS TAKEN FROM THE PUSH-DOWN# LIST. IN MOST CASES THE MODE OF THE RESULT (VECTOR OR SCALAR) OF THE LAST ARITHMETIC OPERATION PERFORMED# IS THE SAME AS THE TYPE OF OPERAND DESIRED (ALL ADD/SUBTRACT ETC.). EXCEPTIONS TO THIS GENERAL RULE ARE LISTED# 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 VECTOR# RESULT, VXSC WANTS A SCALAR.## 2. THE LOAD CODES SHOULD LOAD THE ACCUMULATOR INDEPENDENT OF THE RESULT OF THE LAST OPERATION. THIS# INCLUDES VLOAD, DLOAD, TLOAD, PDDL, AND PDVL (NO PUSHUP WITH SLOAD).## 3. SOME ARITHMETIC OPERATIONS REQUIRE A STANDARD TYPE OF OPERAND REGARDLESS OF THE PREVIOUS OPERATION.# 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 GREATEER 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 ADDRWDITR14 INDEX CYR 7 INDJUMP -1 # (THE INDEX MAKES THIS A TCF.)
OCT 2 # REVERSE PUSHUP DECREMENT. VECTOR TAKES 2REVCNT OCT 6 # WORDS, SCALAR TAKES 6. OCT 6NO.WDS OCT 2 # CONVENTIONAL DECREMENT IS 6 WORDS VECTOROCTAL3 OCT 3 # 2 IN DP, AND 3 IN TP. OCT 6
# Page 1009# 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 ADDRESSES# IN THE RANGE 0-52, ERASABLE ECADR CONSTANTS FROM 100-3777, AND FCADRS ABOVE THAT. ALL 15 BITS ARE AVAILABLE# 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 CYRITR7 INDEX A TCF MISCJUMP
# Page 1010# COMPLETE THE DISPATCHING OF UNARY AND SHORT SHIFT OPERATIONS.
OPJUMP3 TS FBANK # CALL IN BANK 0 (BIT5S 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 BANKMASKLVBUF ADRES VBUF
# Page 1011# 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 A SCALAR.
TCF SLOAD # 10 -- LOAD MPACIN 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 VECTOR LOAD. 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 1012# 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 1013# THE FOLLOWING JUMP TABLE APPLIES TO UNARY INSTRUCTIONS.
COUNT* $$/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 1014# 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 IS TAKEN AS A# STORE CODE WITH A CORRESPONDING ERASABLE ADDRESS. MOST OF THESE CODES ARE TWO ADDRESS, SPECIFYING THAT THE WORD# FOLLOWING THE STORE CODE IS TO BE USED AS AN ADDRESS FROM WHICH TO RE-LOAD MPAC. FOUR OPTIONS ARE AVAILABLE:## 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 ADDRESES MUST BE DIRECT HERE).## STODL AND STOVL WILL TAKE FROM THE PUSH-DOWN LIST IF NO LOAD ADDRESS IS GIVEN.
BLOCK 3
COUNT* $$/INTERSTADR CA BANKSET # THE STADR CODE (PUSHUP UP ON STORE TS FBANK # ADDRESS) ENTERS HERE. INCR LOCITR1 INDEX LOC # THE STORECODE WAS STORED COMPLEMENTED TO CS 0 # MAKE IT LOOK LIKE AN OPCODE PAIR. AD NEGONE # (YUL CAN'T 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. INDEX A TCF STORJUMP
# Page 1015# STORE CODE JUMP TABLE. CALLS THE APPROPRIATE STORING ROUTINE AND EXITS TO DANZIG OR TO ADDRESS WITH# 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 1016# STORE CODE ADDRESS PROCESSOR.
STORE,1 INDEX FIXLOC CS X1 TCF PRESTORE
STORE,2 INDEX FIXLOC CS X2PRESTORE 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 LOW8AHEAD5 ADS ADDRWD
# Page 1017# 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 1018# ROUTINES TO BEGIN PROCESSING OF THE SECOND ADDRES ASSOCIATED WITH ALL STORE-TYPE CODES EXCEPT STORE# 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 1019# THE FOLLOWING LOAD INSTRUCTIONS ARE PROVIDED FOR LOADING THE MULTI-PURPOSE ACCUMULATOR MPAC.
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 MPACTMODE 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 1020# 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 1021# 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 0STORE1 INDEX ADDRWD # SOME INDEX AND MISCELLANEOUS OPS END TS 0 # HERE.# Page 1022 TCF DANZIG
# Page 1023# SEQUENCE CHANGING AND SUBROUTINE CALLING OPTIONS.## THE FOLLOWING OPERATIONS ARE AVAILABLE FOR SEQUENCING CHANGING, BRANCHING, AND CALLING SUBROUTINES:# 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 CAF 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 1024 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 1025# 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 1026# SECTION 3 -- ADD/SUBTRACT PACKAGE.## THE FOLLOWING OPERATIONS ARE PROVIDED FOR ADDING TO AND SUBTRACTING FROM THE MULTI-PURPOSE ACCUMULATOR# 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 ABOVE.
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 0ENDVXV DAS MPAC # VXV FINISHES HERE. EXTEND BZF DANZIG
# Page 1027SETOVF TC OVERFLOW TCF DANZIG
# Page 1028DSU 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 # FORCE OVERFLOW. 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 1029BDSU EXTEND INDEX ADDRWD DCA 0 DXCH MPAC EXTEND DCOM TCF ENDVXV
# Page 1030# 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 1031# ARITHMETIC SUBROUTINES REQUIRED IN FIXED-FIXED.# 1. DMPSUB DOUBLE PRECISION MULTIPLY, MULTIPLY THE CONTENTS OF MPAC,+1 BY THE DP WORD WHOSE ADDRESS# 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 CAF 0 # ADRES OF ARGUMENT FOLLOWS TC DMP . 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 1032# 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 1033# THE DOT PRODUCT SUBROUTINE USUALLY FORMS THE DOT PRODUCT OF THE VECTOR IN MPAC WITH A STANDARD SIX# REGISTER VECTOR WHOSE ADDRESS IS IN ADDRWD. IN THIS CASE C(DOTINC) ARE SET TO 2. VXM, HOWEVER, SETS C(DOTINC) TO# 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 DMPSUBENDDOT 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 1034# 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 SP N-1# LOC+2 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 CAF 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 1035 DXCH MPAC # LOAD A(N) INTO MPAC DXCH VBUF # SAVING X IN VBUF TCF POLY2
POLYLOOP TS POLYCNT # SAVE DECREMENTD 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 1036# MISCELLANEOUS MULTI-PRECISION ROUTINES REQUIRED IN FIXED-FIXED BUT NOT USED BY THE INTERPRETER.
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 MPACARGZERO2 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 +2SHORTMP2 CAF ZERO # SO SUBSEQUENT DAS WILL WORK. XCH MPAC +1 TCF DMPSUB2
# Page 1037# 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 1038# 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, CHANGINGDMODE 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 1039# 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 1040# 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 VROUNDVROTATEX 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 1041# 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 ANSWER. 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 1042# 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 1043 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 ORIGINAL VALUE XCH L # SWAP A + L BANCK. 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 1044# 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 1045# THE FOLLOWING IS THE PROLOGUE TO V/SC. IF THE PRESENT MODE IS VECTOR, IT SAVES THE SCALAR AT X IN BUF# AND CALLS THE V/SC ROUTINE IN BANK 0. IF THE PRESENT MODE IS SCALAR, IT MOVES THE VECTOR AT X INTO MPAC, SAVING# 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 0V/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 # FINISH PROLOGUE AT COMMON SECTION.
# Page 1046# 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 ADDRWDCCSL CCS 1 TCF DANZIG TCF DANZIG TCF COMP TCF DANZIGCOMP 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 1047# 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 AND 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 SHIFT OF THE# ABSOLUTE VALUE OF THE COUNT IS DONE IN THE OPPOSITE DIRECTION.
BANK 00
COUNT* $$/INTERSHORTT 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 MP MPAC # SHIFT MAJOR PART INTO A,L AND PLACE IN# Page 1048 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 1049# 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 1050# 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 1051# 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 1052# TSLC -- TRIPLE SHIFT LEFT AND COUNT. SHIFTS MPAC LEFT UNTIL GREATER THAN .5 IN MAGNITUDE, LEAVING# 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 MPACTSLCTEST 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 1053# 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 1054# 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 VRIGHT2BIASLO 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 1055# 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 +1SLOPEHI 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 1056# 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 1057# SCALAR DIVISION INSTRUCTIONS, DDV AND BDDV, ARE EXECUTED HERE. AT THIS POINT, THE DIVIDEND IS IN MPAC# AND THE DIVISOR IS IN BUF.
DDV/BDDV CS ONE # INITIALIZATION TS DVSIGN # +-1 FOR POSITIVE QUOTIENT -- -0 FOR NEG. TS DVNORMCT # DIVIDENT 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 DVSIGNOVF+ 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 1058BUF+ 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 1059MPAC+ 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 1060BUFNORM 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 1061# 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 # OVEFLOW 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 THAY ARE NOW EQUAL.
# Page 1062# THE FOLLOWING IS A GENERAL PURPOSE DOUBLE PRECISION DIVISION ROUTINE. IT DIVIDES MPAC BY BUF AND LEAVES# 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 BUF# (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, RESPEC-# TIVELY, THE FOLLOWING APPROXIMATION IS OBTAINED BY MULTIPLYING ABOVE AND BELOW BY C - SD AND NEGLECTING TERMS OF# ORDER S-SQUARED (POSSIBLY INTRODUCING ERROR INTO THE LOW TWO BITS OF THE RESULT). SIGN AGREEMENT IS UNNECESSARY.## A + SB . (R - QD) 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 1063+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 THEENDMAXDV AD BUF # MAJOR PART NEVER GOES NEGATIVE.
# Page 1064FINALDV 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 # -0. TC Q TC Q
EXTEND DCS MPAC DXCH MPAC CAF ZERO # SO WE ALWAYS RETURN WITH C(A) = 0. TC Q
# Page 1065# 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. THE ASSUMPTIONS# ARE THE SAME AS THE GENERAL ROUTINE WITH THE ADDITION THAT SIGN AGREEMENT IS NECESSARY (B, C, & D POSITIVE).## 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 .5.
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 1066# 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 1067/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 1068# 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 1069SLOPELO 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 1070# THE FOLLOWING ROUTINE EXECUTES THE UNIT INSTRUCTION, WHICH TAKES THE UNIT OF THE VECTOR IN MPAC.
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 STORINGSMALL2 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 1071 TCF LARGE2
# Page 1072LARGE3 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 1073# IF THE LENGTH OF THE ARGUMENT VECTOR WAS LESS THAN 2(-28), EACH COMPONENT MUST BE SHIFTED LEFT AT LEAST# 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 = OCT15FOURTEEN = OCT16OCT16 = R1D1
# Page 1074# 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 1075# 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 1076# 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 PRECISION SET OF# 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 CONTENTS OF MPAC+2# 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 IS ALLOWED.# INPUT SCALING: THE BINARY POINT IS ASSUMED TO THE RIGHT OF BIT 15. THE ANSWER IS RETURNED WITH THE SAME SCALING.## 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 1077VDEF 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 1078# THE FOLLOWING SUBROUTINES ARE USED IN SQUARING MPAC, IN BOTH THE SCALAR AND VECTOR SENSE. THEY ARE# 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 1079# DOUBLE PRECISION SQUARE ROOT ROUTINE. TAKE THE SQUARE ROOT OF THE TRIPLE PRECISION (MPAC +2 USED ONLY# IN NORMALIZATION) CONTENTS OF MPAC AND LEAVE THE NORMALIZED RESULT IN MPAC (C(MPAC) GREATER THAN OR EQUAL TO# .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 DXCH LOC TC POODOO1 OCT 1302
# Page 1080SMPAC+ 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 POSMAXFIXROOT TS MPAC TS MPAC +1TCQBNK00 TC Q # RETURN TO CALLER TO UNNORMALIZE, ETC.
# Page 1081SRTEST 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 1082# TRIGONOMETRIC FUNCTION PACKAGE.# THE FOLLOWING TRIGONOMETRIC FUNCTIONS ARE AVAIALABLE 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 1083SN1 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 1084# 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 BEFORE 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 # IF SO.
# Page 1085ACOS3 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* # WHERE 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 MPACLDANZIG TCF DANZIG
# Page 1086ACOSSHR 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 EXTEND # IF OVERFLOW, CALL ANSWER ZERO BUT DCA LOC # SOUND AN ALARM. TC ALARM1 OCT 1301
CAF ZERO TCF ACOS=0
ACOSZERO CAF QUARTER # ACOS(0) = PI/2. TCF ACOS=0 +1 # SET MPAC AND EXIT VIA ESCAPE.
NEG12 DEC -12TCSUBTR TCF SUBTR
# Page 1087# THE FOLLOWING INSTRUCTIONS ARE AVAILABLE FOR SETTING, MODIFYING, AND BRANCHING ON INDEX REGISTERS:# 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 ADD TO INDEX REGISTER.# 9. XSU ERASABLE SUBTRACT FROM INDEX REGISTER.# 10. TIX BRANCH ON INDEX REGISTER AND DECREMENT.
BANK 01
COUNT* $$/INTERAXT TC TAGSUB # SELECT APPROPRIATE INDEX REGISTER. CA POLISHXSTORE 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 X1MSTORE1 INDEX POLISH TS 0 TCF DANZIG
# Page 1088XCHX 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 0XAD2 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 1089# 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 -38D.)
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 1090# 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 HIGH ORDER OF MPAC IS ZERO (SINGLE PRECISION).# 5. BOV BRANCH ON OVERFLOW.# 6. GOTO SIMPLE SEQUENCE CHANGE.
RTB/BHIZ CCS CYRRTB 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 1091BZE/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 BPL5B10 DEC 5 B+10 # SHIFTS OP CODE IN SWITCH INSTRUCTION ADR
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 1092# 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 1093 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 QSWSTORE INDEX SWWORD TS STATE # NEW SWITCH WORD.
# Page 1094 +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 0014SWSKIP INCR LOC
SW/ EQUALS SWITCHES
+13D TCF DANZIG # 11 -- NOOP.