TRIM_GIMBAL_CONTROL_SYSTEM.agc
### FILE="Main.annotation"
## Copyright: Public domain.
## Filename: TRIM_GIMBAL_CONTROL_SYSTEM.agc
## Purpose: The main source file for Luminary revision 069.
## It is part of the source code for the original release
## of the flight software for the Lunar Module's (LM) Apollo
## Guidance Computer (AGC) for Apollo 10. The actual flown
## version was Luminary 69 revision 2, which included a
## newer lunar gravity model and only affected module 2.
## This file is intended to be a faithful transcription, except
## that the code format has been changed to conform to the
## requirements of the yaYUL assembler rather than the
## original YUL assembler.
## Reference: pp. 1467-1478
## Assembler: yaYUL
## Contact: Ron Burkey <info@sandroid.org>.
## Website: www.ibiblio.org/apollo/index.html
## Mod history: 2016-12-13 MAS Created from Luminary 99.
## 2016-12-18 MAS Updated from comment-proofed Luminary 99 version.
## 2016-12-29 RRB Updated for Luminary 69.
## 2017-01-21 HG Fix operand BIT 12 -> BIT12
## NEGSUM -> NEGUSUM
## 2017-01-23 Fix operator TC -> TCF
## 2017-01-28 RSB Proofed comment text using octopus/prooferComments
## and fixed errors found.
## 2021-05-30 ABS GTSGO+DN -> GTSGO+ON
## MAXISHIFT -> MAXISHFT
## MINISHIFT -> MINISHFT
## Page 1467
BANK 21
EBANK= QDIFF
SETLOC DAPS4
BANK
COUNT* $$/DAPGT
# CONTROL REACHES THIS POINT UNDER EITHER OF THE FOLLOWING TWO CONDITIONS ONCE THE DESCENT ENGINE AND THE DIGITAL
# AUTOPILOT ARE BOTH ON:
# A) THE TRIM GIMBAL CONTROL LAW WAS ON DURING THE PREVIOUS Q,R-AXIS TIME5 INTERRUPT (OR THE DAPIDLER
# INITIALIZATION WAS SET FOR TRIM GIMBAL CONTROL AND THIS IS THE FIRST PASS), OR
# B) THE Q,R-AXES RCS AUTOPILOT DETERMINED THAT THE VEHICLE WAS ENTERING (OR HAD JUST ENTERED) A COAST
# ZONE WITH A SMALL OFFSET ANGULAR ACCELERATION.
# GTS IS THE ENTRY TO THE GIMBAL TRIM SYSTEM FOR CONTROLLING ATTITUDE ERRORS AND RATES AS WELL AS ACCELERATIONS.
GTS CAF NEGONE # MAKE THE NEXT PASS THROUGH THE DAP BE
TS COTROLER # THROUGH RCS CONTROL,
CAF FOUR # AND ENSURE THAT IT IS NOT A SKIP.
TS SKIPU
TS SKIPV
CAF TWO
TS INGTS # SET INDICATOR OF GTS CONTROL POSITIVE.
TS QGIMTIMR # SET TIMERS TO 200 MSEC TO AVOID BOTH
TS RGIMTIMR # RUNAWAY AND INTERFERENCE BY NULLING.
# THE DRIVE SETTING ALGORITHM
#
# DEL = SGN(OMEGA*K + ALPHA*ABS(ALPHA)/2).
#
# NEGUSUM = ERROR.K(2) + DEL(OMEGA.K.DEL + ALPHA(2)/2)(3/2) + ALPHA(OMEGA.K.DEL + ALPHA(2)/3)
#
# DRIVE = -SGN(NEGUSUM)
CA SR # SAVE THE SR. SHIFT IT LEFT TO CORRECT
AD A # FOR THE RIGHT SHIFT DUE TO EDITING.
TS SAVESR
GTSGO+ON CAF TWO # SET INDEXER FOR R-AXIS CALCULATIONS.
TS QRCNTR
CA AOSR
EXTEND
MP BIT3
CA EDOTR
TCF GTSQAXIS
GOQTRIMG CAF ZERO # SET INDEXER FOR Q-AXIS CALCULATIONS
TS QRCNTR
## Page 1468
CA AOSQ
EXTEND
MP BIT3
CA EDOTQ
GTSQAXIS DXCH WCENTRAL
EXTEND
INDEX QRCNTR # PICK UP K AND K(2) FOR THIS AXIS
DCA KQ
DXCH KCENTRAL
INDEX QRCNTR # QDIFF, RDIFF ARE STORED IN D.P.
CAE QDIFF
ALGORTHM EXTEND # Q(R)DIFF IS THETA (ERROR) SCALED AT PI.
MP K2CNTRAL # FORM K(2)*THETA IN D.P.
LXCH K2THETA
EXTEND # FORM K(2)*THETA*SF2 IN D.P.
MP BIT9
DXCH K2THETA
EXTEND
MP BIT9
ADS K2THETA +1
CAE WCENTRAL # GET OMEGA
EXTEND
MP KCENTRAL # FORM K*OMEGA IN D.P.
LXCH OMEGA.K
EXTEND # FORM OMEGA*K*SF1 IN D.P.
MP BIT12
DXCH OMEGA.K
EXTEND
MP BIT12
ADS OMEGA.K +1
CAE ACENTRAL # FORM ALPHA(2)/2 IN D.P.
EXTEND
SQUARE
DXCH A2CNTRAL
CAE ACENTRAL # GET ALPHA*ABS(ALPHA)/2, IF ALPHA GREATER
# THAN 0. OTHERWISE TAKE NEGATIVE OF ABOVE
EXTEND
BZMF +4
EXTEND
DCA A2CNTRAL
TCF +3
EXTEND
DCS A2CNTRAL
DXCH FUNCTION # SAVE AS SGN(ALPHA)*ALPHA(2)/2
## Page 1469
EXTEND
DCA OMEGA.K
DAS FUNCTION # FORM FUNCT1
CCS FUNCTION # DEL = +1 FOR FUNCT1 GREATER THAN ZERO.
TCF POSFNCT1 # OTHERWISE DEL = -1
TCF +2
TCF NEGFNCT1
CCS FUNCTION +1 # USE LOW ORDER WORD SINCE HIGH IS ZERO
POSFNCT1 CAF BIT1
TCF +2
NEGFNCT1 CS BIT1
TS DEL
CCS DEL # MAKE OMEGA*K REALLY DEL*OMEGA*K
TCF FUNCT2 # (NOTHING NEED BE DONE)
TCF FUNCT2
EXTEND
DCS OMEGA.K
DXCH OMEGA.K # CHANGE SIGN OF OMEGA*K
FUNCT2 EXTEND
DCA OMEGA.K
DXCH FUNCTION # DEL*OMEGA*K
EXTEND
DCA A2CNTRAL
DAS FUNCTION # DEL*OMEGA*K + ALPHA(2)/2
FUNCT3 CAE A2CNTRAL # CALCULATE (2/3)*ALPHA(2)/2 = ALPHA(2)/3
EXTEND
MP .66667
DXCH A2CNTRAL
XCH L
EXTEND
MP .66667
ADS A2CNTRAL +1
TS L
TCF +2
ADS A2CNTRAL
DXCH OMEGA.K # DEL*OMEGA*K + ALPHA(2)/3 = G
DAS A2CNTRAL
CAE A2CNTRAL # G*ALPHA IN D.P.
EXTEND
MP ACENTRAL
DXCH A2CNTRAL
XCH L
EXTEND
MP ACENTRAL
ADS A2CNTRAL +1
TS L
## Page 1470
TCF +2
ADS A2CNTRAL
DXCH A2CNTRAL # FIRST AND THIRD TERMS
DAS K2THETA # SUMMED IN D.P.
TCF RSTOFGTS
.66667 DEC .66667
BANK 16
EBANK= NEGUQ
SETLOC DAPS1
BANK
# THE WRCHN12 SUBROUTINE SETS BITS 9,10,11,12 OF CHANNEL 12 ON THE BASIS OF THE CONTENTS OF NEGUQ,NEGUR WHICH ARE
# THE NEGATIVES OF THE DESIRED ACCELERATION CHANGES. ACDT+C12 SETS Q(R)ACCDOT TO REFLECT THE NEW DRIVES.
#
# WARNING: ACDT+C12 AND WRCHN12 MUST BE CALLED WITH INTERRUPT INHIBITED.
BGIM OCTAL 07400
CHNL12 EQUALS ITEMP6
ACDT+C12 CS NEGUQ
EXTEND # GIMBAL DRIVE REQUESTS.
MP ACCDOTQ
LXCH QACCDOT
CS NEGUR
EXTEND
MP ACCDOTR
LXCH RACCDOT
CCS NEGUQ
CAF BIT10
TCF +2
CAF BIT9
TS CHNL12
CCS NEGUR
CAF BIT12
TCF +2
CAF BIT11
ADS CHNL12 # (STORED RESULT NOT USED AT PRESENT)
CS BGIM
EXTEND
RAND CHAN12
AD CHNL12
EXTEND
WRITE CHAN12
## Page 1471
CS CALLGMBL # TURN OFF REQUEST FOR ACDT+C12 EXECUTION.
MASK RCSFLAGS
TS RCSFLAGS
TC Q # RETURN TO CALLER.
BANK 21
EBANK= QDIFF
SETLOC DAPS4
BANK
## Page 1472
# SUBROUTINE TIMEGMBL: MOD 0, OCTOBER 1967, CRAIG WORK
#
# TIMEGMBL COMPUTES THE DRIVE TIME NEEDED FOR THE TRIM GIMBAL TO POSITION THE DESCENT ENGINE NOZZLE SO AS TO NULL
# THE OFFSET ANGULAR ACCELERATION ABOUT THE Q (OR R) AXIS. INSTEAD OF USING AOSQ(R), TIMEGMBL USES .4*AOSQ(R),
# SCALED AT PI/8. FOR EACH AXIS, THE DRIVE TIME IS COMPUTED AS ABS(ALPHA/ACCDOT). A ZERO
# ALPHA OR ACCDOT OR A ZERO QUOTIENT TURNS OFF THE GIMBAL DRIVE IMMEDIATELY. OTHERWISE, THE GIMBAL IS TURNED ON
# DRIVING IN THE CORRECT DIRECTION. THE Q(R)GIMTIMR IS SET TO TERMINATE THE DRIVE AND Q(R)ACCDOT
# IS STORED TO REFLECT THE NEW ACCELERATION DERIVATIVE. NEGUQ(R) WILL CONTAIN +1,+0,-1 FOR A Q(R)ACCDOT VALUE
# WHICH IS NEGATIVE, ZERO, OR POSITIVE.
#
# INPUTS: AOSQ,AOSR, SCALED AT P1/2, AND ACCDOTQ, ACCDOTR AT PI/2(7). PI/2(7).
#
# OUTPUTS: NEW GIMBAL DRIVE BITS IN CHANNEL 12,NEGUQ,NEGUR,QACCDOT AND RACCDOT, THE LAST SCALED AT PI/2(7).
# Q(R)GIMTIMR WILL BE SET TO TIME AND TERMINATE GIMBAL DRIVE(S)
#
# DEBRIS: A,L,Q, ITEMPS 2,3,6, RUPTREG2 AND ACDT+C12 DEBRIS.
#
# EXITS: VIA TC Q.
#
# ALARMS, ABORTS, : NONE
#
# SUBROUTINES: ACDT+C12, IBNKCALL
#
# WARNING: THIS SUBROUTINE WRITES INTO CHANNEL 12 AND USES THE ITEMPS. THEREFORE IT MAY ONLY BE CALLED WITH
# INTERRUPT INHIBITED.
#
# ERASABLE STORAGE CONFIGURATION (NEEDED BY THE INDEXING METHODS):
# NEGUQ ERASE +2 NEGATIVE OF Q-AXIS GIMBAL DRIVE
# (SPWORD) EQUALS NEGUQ +1 ANY S.P. ERASABLE NUMBER, NOW THRSTCMD
# NEGUR EQUALS NEGUQ +2 NEGATIVE OF R-AXIS GIMBAL DRIVE
#
# ACCDOTQ ERASE +2 Q-JERK TERM SCALED AT PI/2(7) RAD/SEC(3)
# (SPWORD) EQUALS ACCDOTQ +1 ANY S.P. ERASABLE NUMBER NOW QACCDOT
# ACCDOTR EQUALS ACCDOTQ +2 R-JERK TERM SCALED AT PI/2(7) RAD/SEC(3)
# ACCDOTQ, ACCDOTR ARE MAGNITUDES.
# AOSQ ERASE +4 Q-AXIS ACC., D.P. AT PI/2 R/SEC(2)
# AOSR EQUALS AOSQ +2 R-AXIS ACCELERATION SCALED AT PI/2 R/S2
QRNDXER EQUALS ITEMP6
OCT23146 OCTAL 23146 # DECIMAL .6
NZACCDOT EQUALS ITEMP3
TIMEGMBL CAF ONE # INITIALIZE ALLOWGTS.
TS ALLOWGTS
CAF TWO # SET UP LOOP FOR R AXIS.
LXCH Q # SAVE RETURN ADDRESS.
LXCH RUPTREG2
## Page 1473
TCF +2
TIMQGMBL CAF ZERO # NOW DO THE Q-AXIS
TS QRNDXER
INDEX QRNDXER
CA ACCDOTQ # ACCDOT IS PRESUMED TO BE AT PI/2(7).
EXTEND
BZMF TGOFFNOW # IS ACCDOT LESS THAN OR EQUAL TO 0?
TS NZACCDOT # NO. STORE NON-ZERO, POSITIVE ACCDOT.
ALPHATRY INDEX QRNDXER
CS AOSQ
EXTEND
BZF TGOFFNOW # IS ALPHA ZERO?
TS Q # SAVE A COPY OF -AOS.
EXTEND # NO. RESCALE FOR TIMEGMBL USE.
MP OCT23146 # OCTAL 23146 IS DECIMAL .6
AD Q # -1.6*AOS AT PI/2 = -.4*AOS AT PI/8.
TS L # WAS THERE OVERFLOW?
TCF SETNEGU # NO. COMPUTE DRIVE TIME.
CS A # RECOVER -SGN(AOS) IN THE A REGISTER.
INDEX QRNDXER # YES. START DRIVE WITHOUT WAITLIST.
XCH NEGUQ
TCF NOTALLOW # KNOCK DOWN THE ALLOWGTS FLAG.
SETNEGU EXTEND
BZMF POSALPH
COM
TS ITEMP2 # STORE -ABS(.4*AOS) SCALED AT PI/8.
CS BIT1
TCF POSALPH +2
POSALPH TS ITEMP2 # STORE -ABS(.4*AOS) SCALED AT PI/8.
CA BIT1
+2 INDEX QRNDXER # SGN(AOS) INTO NEGU
TS NEGUQ # STORE SGN(APLHA) AS NEGU
CA NZACCDOT
EXTEND
MP BIT12 # 2*ACCDOT, SCALED AT PI/8.
AD ITEMP2 # -ABS(ALPHA) + 2*ACCDOT, AT PI/8.
EXTEND
BZMF NOTALLOW # IS DRIVE TIME MORE THAN TWO SECONDS?
CS ITEMP2 # NO. COMPUTE DRIVE TIME.
EXTEND # ABS(ALPHA) AT PI/8.
MP OCT00240 # DECIMAL 10/1024
EXTEND # QUOTIENT IS DRIVE TIME AT WAITLIST.
DV NZACCDOT # ABS(ALPHA)/ACCDOT AT 2(14)/100
## Page 1474
EXTEND
BZF TGOFFNOW # DRIVE TIME MUST BE GREATER THAN ZERO.
TCF DRIVEON
TGOFFNOW CAF ZERO # TURN OFF GIMBAL NOW.
INDEX QRNDXER
TS NEGUQ
TCF DONEYET
NOTALLOW CAF OCT31
INDEX QRNDXER
TS QGIMTIMR
CAF ZERO # DRIVE TIME IS MORE THAN 2 SECONDS, SO
TS ALLOWGTS # DO NOT PERMIT FURTHER GTS ATTITUDE-RATE
# CONTROL UNTIL AOSTASK APPROVES.
TCF DONEYET # NO WAITLIST CALL IS MADE.
DRIVEON INDEX QRNDXER
TS QGIMTIMR # CHOOSE Q OR R AXIS.
DONEYET CCS QRNDXER
TCF TIMQGMBL
DXCH RUPTREG3 # PROTECT IBNKCALL ERASABLES. ACDT+C12
DXCH ITEMP2 # LEAVES ITEMPS2,3 ALONE.
TC IBNKCALL # TURN OF CHANNEL BITS, SET Q(R)ACCDOTS.
CADR ACDT+C12
DXCH ITEMP2 # RESTORE ERASABLES FOR IBNKCALL.
DXCH RUPTREG3
TC RUPTREG2 # RETURN TO CALLER.
OCT00240 OCTAL 00240 # DECIMAL 10/1024
## Page 1475
# THE FOLLOWING SECTION IS A CONTINUATION OF THE TRIM GIMBAL CONTROL FROM THE LAST GTS ENTRY. THE QUANTITY NEGUSUM
# IS COMPUTED FOR EACH AXIS (Q,R), .707*DEL*FUNCTION(3/2) + K2THETA = NEGUSUM. NEW DRIVES ARE ENTERED TO CH 12.
RSTOFGTS CCS FUNCTION
TCF GOODARG # FUNCTION IS POSITIVE. GET 3/2 POWER.
TCF +2 # HIGH ORDER WORD IS ZERO. TRY THE LOWER.
TCF ZEROOT # NEGATIVE. USE ZERO FOR 3/2 POWER.
CS FUNCTION +1 # IF ARG IS LESS THAN 2(-18), THEN THE 3/2
AD BIT11 # POWER IS LESS THAN 2(-27). USE ZERO.
EXTEND
BZMF ZEROHIGH # BRANCH IF ARG NOT LESS THAN 2(-18).
ZEROOT EXTEND
DCA ZERO
TCF NEGUSUM
ZEROHIGH CA FOURTEEN # ARG LESS THAN 2(-14) MEANS 3/2 POWER
# WILL BE LESS THAN 2(-21).
TS SHFTFLAG
CA TWO
TS ININDEX # INITIALIZE THE SHIFT LOOP.
# COLLECT THE 14 MOST SIGNIFICANT BITS OF
XCH FUNCTION +1 # THE 28 INTO THE HIGH ORDER WORD.
XCH FUNCTION
TCF SCALLOOP
GOODARG CA TWELVE
TS ININDEX # INITIALIZE THE SHIFT LOOP.
CA ZERO # THERE ARE SIGNIFICANT BITS IN THE HIGH
TS SHFTFLAG # ORDER WORD, SO SET SHFTFLAG TO ZERO.
TCF SCALLOOP
SCALSTRT CA FUNCTION
TCF SCALDONE
MULBUSH CA NEG2 # IF ARG IS NOT LESS THAN 1/4, INDEX IS
ADS ININDEX # ZERO, INDICATING NO SHIFT NEEDED.
EXTEND # BRANCH IF ARG IS NOT LESS THAN 1/4.
BZMF SCALSTRT # OTHERWISE COMPARE ARG WITH A REFERENCE
# WHICH IS 4 TIMES LARGER THAN THE LAST.
SCALLOOP CS FUNCTION
INDEX ININDEX
AD BIT15 # REFERENCE MAGNITUDE LESS OR EQUAL TO 1/4
EXTEND
BZMF MULBUSH # IF ARG IS NOT LESS THAN REFERENCE, GO
# AROUND THE MULBERRY BUSH ONCE MORE.
INDEX ININDEX
## Page 1476
CA BIT15 # THIS IS THE SCALE MAGNITUDE
XCH Q # 2**(-ININDEX) IS THE SHIFT DIVISOR.
EXTEND # RESCALE ARGUMENT.
DCA FUNCTION
EXTEND
DV Q
TS FUNCTION # ININDEX AND SHFTFLAG PRESERVE INFO FOR
# RESCALING AFTER ROOT PROCESS.
SCALDONE EXTEND # AFTER 3/2 POWER IS TAKEN, SCALE FACTOR
MP BIT13 # OF SQRT(1/2) WILL BE NEEDED, SO FACTOR
TS HALFARG # OF 1/2 IS INCLUDED NOW, BEFORE SQRT.
CA STARTER # INITIAL GUESS FOR SQRT ALGORITHM.
TC ROOTCYCL
TC ROOTCYCL
TC ROOTCYCL
EXTEND # SQRT(1/2)*SQRT(ARG) IN A.
MP FUNCTION # SQRT(1/2)*ARG*SQRT(ARG) IN A,L.
DXCH FUNCTION
DOSHIFT CA SHFTFLAG # HOW MANY SHIFT BITS ARE THERE?
AD ININDEX # 2**(-ININDEX) WAS SHIFT DIVISOR.
TS SR
AD SR # THIS MANY SHIFTS ARE REQUIRED.
SAVESHFT TS Q # Q BOUNDS ARE ZERO AND 24 (DECIMAL).
EXTEND
BZMF SUMNEGU # BRANCH IF SHIFTING IS UNNECESSARY.
CS FOURTEEN
AD Q
EXTEND # Q = 0(MOD 3), SO A REG IS NON-ZERO.
BZMF MINISHFT # BRANCH IF SMALL SHIFT SUFFICES.
MAXISHFT TS Q # 14 BIT SHIFT RIGHT NOW.
CA ZERO
XCH FUNCTION
TS FUNCTION +1
MINISHFT INDEX Q # C(Q) ARE GREATER THAN ZERO.
CA BIT15
TS Q # 2**(-Q) WILL BE SHIFT MULTIPLIER.
EXTEND
MP FUNCTION +1
XCH L
CA ZERO
DXCH FUNCTION # LOWER WORD SHIFTED NOW.
EXTEND
BZMF SUMNEGU # BRANCH IF UPPER WORD WAS ZERO.
## Page 1477
EXTEND # SHIFT UPPER WORD.
MP Q
DAS FUNCTION # NO OVERFLOW POSSIBLE.
SUMNEGU CS DEL # INCLUDE DEL FACTOR IN PRODUCT TERM.
EXTEND
BZMF SUMTERMS
EXTEND # DEL FACTOR IS MINUS ONE.
DCS FUNCTION
TCF NEGUSUM -1 # NOW ADD IN THE K2THETA TERM.
SUMTERMS EXTEND
BZF NEGUSUM # BRANCH IF DEL IS ZERO.
EXTEND # DEL FACTOR IS +1.
DCA FUNCTION
DAS K2THETA # NOW ADD IN THE K2THETA TERM.
NEGUSUM CCS K2THETA # TEST SIGN OF HIGH ORDER PART.
TCF NEGDRIVE
TCF +2
TCF POSDRIVE
CCS K2THETA +1 # SIGN TEST FOR LOW ORDER PART.
NEGDRIVE CA BIT1
TCF +2 # STOP GIMBAL DRIVE FOR A ZERO NEGUSUM.
POSDRIVE CS BIT1
TS L # SAVE FOR DRIVE REVERSAL TEST.
INDEX QRCNTR
XCH NEGUQ
EXTEND
MP L # MULTIPLY OLD NEGU AND NEW NEGU.
CCS L
TCF LOUPE # NON-ZERO GIMBAL DRIVE BEING CONTINUED.
TCF ZEROLOUP # NO REVERSAL PROBLEM HERE.
TCF REVERSAL # NON-ZERO GIMBAL DRIVE BEING REVERSED.
TCF ZEROLOUP # NO REVERSAL PROBLEM HERE.
REVERSAL INDEX QRCNTR # A ZERO-DRIVE PAUSE IS NEEDED HERE. ZERO
TS QACCDOT # IS IN A REGISTER FROM CCS ON (-1).
INDEX QRCNTR
CS GMBLBITA
EXTEND
WAND CHAN12
ZEROLOUP CS RCSFLAGS # SET UP REQUEST FOR ACDT+C12 CALL.
MASK CALLGMBL
## Page 1478
ADS RCSFLAGS
LOUPE CCS QRCNTR # HAVE BOTH AXES BEEN PROCESSED?
TCF GOQTRIMG # NO. DO Q AXIS NEXT.
CA SAVESR # RESTORE THE SR
TS SR
GOCLOSE EXTEND # TERMINATE THE JASK.
DCA CLOSEADR
DTCB
EBANK= AOSQ
CLOSEADR 2CADR CLOSEOUT # TERMINATE THE JASK.
TWELVE EQUALS OCT14
GMBLBITA OCTAL 01400 # INDEXED WRT GMBLBITB DO NOT MOVE ******
STARTER DEC .53033 # INITIAL VALUE FOR SQRT ALGORITHM.
GMBLBITB OCTAL 06000 # INDEXED WRT GMBLBITA DO NOT MOVE ******
# SUBROUTINE ROOTCYCL: BY CRAIG WORK,3 APRIL 68
#
# ROOTCYCL IS A SUBROUTINE WHICH EXECUTES ONE NEWTON SQUARE ROOT ALGORITHM ITERATION. THE INITIAL GUESS AT THE
# SQUARE ROOT IS PRESUMED TO BE IN THE A REGISTER AND ONE-HALF THE SQUARE IS TAKEN FROM HALFARG. THE NEW APPROXI-
# MATION TO THE SQUARE ROOT IS RETURNED IN THE A REGISTER. DEBRIS: A,L,SR,SCRATCH. ROOTCYCL IS CALLED FROM
# LOCATION (LOC) BY A TC ROOTCYCL, AND RETURNS (TC Q) TO LOC +1.
#
# WARNING: IF THE INITIAL GUESS IS NOT GREATER THAN THE SQUARE, DIVIDE OR ADD OVERFLOW IS A REAL POSSIBILITY.
ROOTCYCL TS SCRATCH # STORE X
TS SR # X/2 NOW IN SR
CA HALFARG # ARG/2 IN THE A REG
ZL # PREPARE FOR DIVISION
EXTEND
DV SCRATCH # (ARG/X)/2
AD SR # (X + ARG/X)/2 IN THE A REG
TC Q
