https://github.com/virtualagc/virtualagc
Revision 078c79d8734a9ed2860303a7c1662004284fe853 authored by Ron Burkey on 07 August 2022, 15:04:04 UTC, committed by Ron Burkey on 07 August 2022, 15:04:04 UTC
assembly listings from yaASM and yaLEMAP. Added some debugging messages to 'make install'. Tweaked debugging messages that VirtualAGC embeds in 'simulate'. Verified buildability in Mint 21, 20, 19, 17, and verified buildability using clang in Mint 17.
1 parent 6bb1acc
Tip revision: 078c79d8734a9ed2860303a7c1662004284fe853 authored by Ron Burkey on 07 August 2022, 15:04:04 UTC
Fixed a potential string-overflow bug in yaASM. Removed timestamps from
Fixed a potential string-overflow bug in yaASM. Removed timestamps from
Tip revision: 078c79d
INTERPRETER.agc
### FILE="Main.annotation"
## Copyright: Public domain.
## Filename: INTERPRETER.agc
## Purpose: A section of LUM69 revision 2.
## It is part of the reconstructed source code for the flown
## version of the flight software for the Lunar Module's (LM)
## Apollo Guidance Computer (AGC) for Apollo 10. The code has
## been recreated from a copy of Luminary revsion 069, using
## changes present in Luminary 099 which were described in
## Luminary memos 75 and 78. The code has been adapted such
## that the resulting bugger words exactly match those specified
## for LUM69 revision 2 in NASA drawing 2021152B, which gives
## relatively high confidence that the reconstruction is correct.
## Reference: pp. 997-1089
## Assembler: yaYUL
## Contact: Ron Burkey <info@sandroid.org>.
## Website: www.ibiblio.org/apollo/index.html
## Mod history: 2019-07-27 MAS Created from Luminary 69.
## 2021-05-30 ABS Added IRT0 location symbol to match Luminary 69.
## B5TOBB -> B5TOB8
## Page 997
# 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* $$/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 998
# 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 999
# 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 1000
# 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 EBANK
ITR10 INDEX CYR
7 INDJUMP -1
## Page 1001
# 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 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 1002
ITR13 INDEX CYR
3 INDJUMP -1
## Page 1003
# 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 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 1004
# 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 CYR
ITR7 INDEX A
TCF MISCJUMP
## Page 1005
# 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 # ITS 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 1006
# 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 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 1007
# 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 1008
# THE FOLLOWING JUMP TABLE APPIES 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 1009
# 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 ADDRESSES MUST BE DIRECT HERE).
# STODL AND STOVL WILL TAKE FROM THE PUSH-DOWN LIST IF NO LOAD ADDRESS IS GIVEN.
BLOCK 3
COUNT* $$/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 1010
# 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 1011
# 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 1012
# 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 1013
# ROUTINES TO BEGIN PROCESSING OF THE SECOND ADDRESS 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 1014
# 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 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 1015
# 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 1016
# 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 1017
TCF DANZIG
## Page 1018
# 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 AREA.
CCS A
CA POLISH # GENERAL ERASABLE.
TCF GOTOGE
## Page 1019
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 1020
# 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 1021
# 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 0
ENDVXV DAS MPAC # VXV FINISHES HERE.
EXTEND
BZF DANZIG
## Page 1022
SETOVF TC OVERFLOW
TCF DANZIG
## Page 1023
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 # 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 1024
BDSU EXTEND
INDEX ADDRWD
DCA 0
DXCH MPAC
EXTEND
DCOM
TCF ENDVXV
## Page 1025
# 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 1026
# 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 PRECISON 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 1027
# 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 NEEDNT TAKE THE TIME FOR VECTORS.
DOUBLE
TS L
TC Q
AD MPAC +1 # ADD ROUNDING 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 1028
# 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 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 1029
# 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, 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 1030
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 # USERS RESPONSIBILITY TO ASSURE NO OVFLOW
CCS POLYCNT
TCF POLYLOOP
TC POLYRET # RETURN CALLER
## Page 1031
# 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 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 1032
# 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 1033
# 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 1034
# 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 BASE ADDRESS OF NEXT COLUMN(ROW).
TC DOTSUB
DXCH VBUF # MOVE 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 1035
# 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 1036
# 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 1037
# THE 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 1038
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 # DONT INCREMENT IF NO OVERFLOW.
INCR L
XCH L
COM # MAKE NEGATIVE AGAIN.
TC Q
## Page 1039
# INTERPRETIVE INSTRUCTIONS WHOSE EXECUTION CONSISTS OF PRINCIPALLY CALLING SUBROUTINES.
DMP1 TC DMPSUB # DMP INSTRUCTION.
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 1040
# 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 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 # FINISH PROLOGUE AT COMMON SECTION.
## Page 1041
# 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 1042
# 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 SHIFT OF THE
# ABSOLUTE VALUE OF THE COUNT IS DONE IN THE OPPOSITE DIRECTION.
BANK 00
COUNT* $$/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
MP MPAC # SHIFT MAJOR PART INTO A,L AND PLACE IN
## Page 1043
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 1.
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 1044
# 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 IMMEDIATL
## Page 1045
# 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 1046
# 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 1047
# 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 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 1048
# THE FOLLOWING ROUTINES 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 1049
# GENERAL SHIFT RIGHT.
RIGHT CCS MODE # SEE 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 1050
# 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 1051
# 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 # SHIFTS WHOSE NET SHIFT COUNT IS NEGATIVE
COM
TS MPTEMP
LEFT CCS MODE # SINCE LEFT SHIFTING IS SONE 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 1052
# SCALAR DIVISION INSTRUCTIONS, DDV AND BDDV, ARE EXECUTED HERE. AT THIS POINT, THE DIVIDEND IS IN MPAC
# AND THE DIVISOR 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 1053
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 1054
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 MAXDV 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 1055
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 1056
# 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 1057
# 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 1058
+DOWN EXTEND
SU BUF # IF POSITIVE, REDUCE ONLY IF NECESSARY
EXTEND # SINCE THE COMPENSATING INCR MIGHT CAUSE
BZF +3 # OVERFLOW.
EXTEND # DONT 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 1059
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 # -0.
TC Q
TC Q
EXTEND
DCS MPAC
DXCH MPAC
CAF ZERO # SO WE ALWAYS RETURN WITH C(A) = 0.
TC Q
## Page 1060
# 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 BUF - 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 1061
# 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 1062
/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 1063
# 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 1064
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 1065
# 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 THE 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 1066
TCF LARGE2
## Page 1067
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 1068
# 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 = OCT15
FOURTEEN = OCT16
OCT16 = R1D1
## Page 1069
# 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 1070
# 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 1071
# 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 1072
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 1073
# 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 OVERFLOW.
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 1074
# 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 (TO 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 # ZERO - 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 1075
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)(SLOPEHI) + 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(MPAC/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 1076
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 1077
# 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, IE 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 1078
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 1079
# 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 1080
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* # 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 MPAC
LDANZIG TCF DANZIG
## Page 1081
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 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 -12
TCSUBTR TCF SUBTR
## Page 1082
# THE FOLLOWING INSTRUCTIONS ARE AVAILABLE FOR SETTING, MODIFYING, AND BRANCHING ON INDEX REGISTERS:
# 1. AXT ADDRESS TO INDEX TRUE.
# 1. 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 REIGSTER 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* $$/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 1083
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 1084
# 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 1085
# MISCELLANEOUS OPERATION CODES WITH DIRECT ADDRESSES. INCLUDED HERE ARE:
# 1. ITA STORE QPRET (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 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.
B5TOB8 OCT 360
TCF GOTO
## Page 1086
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
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 1087
# THE FOLLOWING OPERATIONS ARE AVAILABLE FOR ALTERING AND TESTING INTERPRETIVE 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 1088
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 1089
+13D RELINT # 11 - NOOP.
CAF BIT13
EXTEND # DISPATCH SEQUCE CHANGING OR BRANCHING
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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