TRIM_GIMBAL_CNTROL_SYSTEM.agc
# Copyright: Public domain.
# Filename: TRIM_GIMBAL_CNTROL_SYSTEM.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: 1472-1485
# Mod history: 2009-05-27 RSB Adapted from the corresponding
# Luminary131 file, using page
# images from Luminary 1A.
#
# 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 1472
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 + ALPHA*ABS(ALPHA)/(2*K))
# 2 1/2 2 3/2
# NEGUSUM = ERROR*K + ALPHA*(DEL*OMEGA + ALPHA /(3*K)) + DEL*K (DEL*OMEGA + ALPHA /(2*K))
#
# 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+DN CAF TWO # SET INDEXER FOR R-AXIS CALCULATIONS.
TCF GOQTRIMG +1
GOQTRIMG CAF ZERO # SET INDEXER FOR Q-AXIS CALCULATIONS
TS QRCNTR
# Page 1473
# RSB 2009 ---------------------------------------------------------------------
# Everything between this line and the similar line below was simply filled-in
# as-is from Luminary 131, and then verified to assemble to the proper binary
# values. This area is blank on the Luminary 099 print-out, as if the
# printer ribbon had run out.
INDEX QRCNTR # AOS SCALED AT PI/2
CA AOSQ
EXTEND
MP BIT2 # RESCALE AOS TO PI/4
EXTEND
BZF GTSQAXIS -3 # USE FULL SCALE FOR LARGER AOS ESTIMATES.
INDEX A
CS LIMITS # LIMITS +1 CONTAINS NEGMAX.
XCH L # LIMITS -1 CONTAINS POSMAX.
CCS QRCNTR # PICK UP RATE FOR THIS AXIS. RATE CELLS
INDEX A # USE ADJACENT, NOT SEPARATED. AT PI/4
CA EDOTQ
GTSQAXIS DXCH WCENTRAL
INDEX QRCNTR # COLLECT K FOR THIS AXIS
CA KQ
TS KCENTRAL
EXTEND # CONTROL AUTHORITY ZERO. AVOID DRIVING
BZF POSDRIVE +1 # ENGINE BELL TO THE STOPS.
INDEX QRCNTR # QDIFF, RDIFF ARE STORED IN D.P.
CAE QDIFF
ALGORTHM EXTEND # Q(R)DIFF IS THETA (ERROR) SCALED AT PI.
MP KCENTRAL # FORM K*ERROR AT PI(2)/2(8), IN D.P.
LXCH K2THETA
EXTEND
MP BIT5 # RESCALE TO 4*PI(2)
DXCH K2THETA
EXTEND
MP BIT5 # FIRST TERM OF NEGUSUM IN K2THETA.
ADS K2THETA +1 # NO CARRY NEEDED D.P. AT 4*PI(2)
CS ACENTRAL # FORM ALPHA(2)/(2*K) AT 16*PI, IN D.P.,
EXTEND # LIMITING QUOTIENT TO AVOID OVERFLOW.
MP BIT14 # -ALPHA/2 IN A, SCALED AT PI/4
EXTEND
MP ACENTRAL # -ALPHA(2)/2 IN A,L, SCALED AT PI(2)/16)
AD KCENTRAL
EXTEND
BZMF HUGEQUOT # K-ALPHA(2)/2 SHOULD BE PNZ FO DIVISION
EXTEND
DCS A # ALPHA(2)/2 - K
AD KCENTRAL
# RSB 2009 ---------------------------------------------------------------------
EXTEND
DV KCENTRAL # HIGH ORDER OF QUOTIENT.
XCH A2CNTRAL
CA L # SHIFT UP THE REMAINDER.
LXCH 7 # ZERO LOW-ORDER DIVIDEND.
EXTEND
# Page 1474
DV KCENTRAL
XCH A2CNTRAL +1 # QUOTIENT STORED AT 16*PI, D.P.
TCF HAVEQUOT
HUGEQUOT CA POSMAX
TS L
DXCH A2CNTRAL # LIMITED QUOTIENT STORED AT 16*PI, D.P.
HAVEQUOT CA WCENTRAL
EXTEND
MP BIT9 # RESCALE OMEGA AT 16*PI IN D.P.
DXCH K2CNTRAL # LOWER WORD OVERLAYS OMEGA IN WCENTRAL
EXTEND
DCA K2CNTRAL
DXCH FUNCTION
CA ACENTRAL # GET ALPHA*ABS(ALPHA)/(2*K)
EXTEND
BZMF +4
EXTEND
DCA A2CNTRAL
TCF +3
EXTEND
DCS A2CNTRAL
DAS FUNCTION # OMEGA + ALPHA*ABS(ALPHA)/(2*K) AT 16*PI
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 # REPLACE OMEGA BY DEL*OMEGA
TCF FUNCT2 # POSITIVE DEL VALUE. PROCEED.
TCF DEFUNCT
TCF NEGFNCT2
DEFUNCT TS K2CNTRAL
TS K2CNTRAL +1
TCF FUNCT2
# Page 1475
NEG1/3 DEC -.33333
NEGFNCT2 EXTEND
DCS K2CNTRAL
DXCH K2CNTRAL
FUNCT2 EXTEND
DCA A2CNTRAL
DAS K2CNTRAL # DEL*OMEGA + ALPHA(2)/(2*K) AT 16*PI, D.P.
FUNCT3 CA A2CNTRAL
EXTEND
MP NEG1/3
DXCH A2CNTRAL
CA L
EXTEND
MP NEG1/3
ADS A2CNTRAL +1
TS L
TCF +2 # A2CNTRAL NOW CONTAINS -ALPHA(2)/(6*K),
ADS A2CNTRAL # SCALED AT 16*PI, IN D.P.
EXTEND
DCA K2CNTRAL # DEL*OMEGA + ALPHA(2)/(3*K) IN A2CNTRAL,
DAS A2CNTRAL # SCALED AT 16*PI, D.P.
CA A2CNTRAL
EXTEND
MP ACENTRAL
DAS K2THETA
CA A2CNTRAL +1
EXTEND
MP ACENTRAL # ACENTRAL MAY NOW BE OVERLAID.
ADS K2THETA +1
TS L
TCF +2 # TWO TERMS OF NEGUSUM ACCUMULATED, SO FAR
ADS K2THETA # SCALED AT 4*PI(2), IN D.P.
GETROOT CA K2CNTRAL # K*(DEL*OMEGA + ALPHA(2)/(2*K)) IS THE
EXTEND # TERM FOR WHICH A SQUARE ROOT IS NEEDED.
MP KCENTRAL # K AT PI/2(8)
DXCH FUNCTION
CA K2CNTRAL +1
EXTEND
MP KCENTRAL
ADS FUNCTION +1
TS L
TCF +2
ADS FUNCTION # DESIRED TERM IN FUNCTION, AT PI(2)/16
# Page 1476
CCS DEL
TCF RSTOFGTS
TCF NEGUSUM
TCF NEGATE
TCF NEGUSUM
NEGATE EXTEND
DCS K2CNTRAL
DXCH K2CNTRAL
TCF RSTOFGTS
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 1477
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 1478
# 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, AND 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 # INITIALZE ALLOWGTS.
TS ALLOWGTS
CAF TWO # SET UP LOOP FOR R AXIS.
LXCH Q # SAVE RETURN ADDRESS.
LXCH RUPTREG2
# Page 1479
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(ALPHA) AS NEGU
CA NZACCDOT
EXTEND
MP BIT12 # 2*ACCDOT, SCALED AT PI/8.
AD ITEMP2 # -ABS(ALPHS) + 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 1480
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 OFF 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 1481
# 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.
#
# THE SUBROUTINE GTSQRT ACCEPTS A DOUBLE PRECISION VALUE IN FUNCTION, FUNCTION +1 AND RETURNS A SINGLE-PRECISION
# SQUARE ROOT OF THE FOURTEEN MOST SIGNIFICANT BITS OF THE ARGUMENT. ALSO, THE CELL SHFTFLAG CONTAINS A BINARY
# EXPONENT S, SUCH THAT THE SQUARE ROOT (RETURNED IN THE A REGISTER) MUST BE SHIFTED RIGHT (MULTIPLIED BY 2 TO THE
# POWER (-S)) IN ORDER TO BE THE TRUE SQUARE ROOT OF THE FOURTEEN MOST SIGNIFICANT BITS OF FUNCTION, FUNCTION +1.
# SQUARE ROOT ERROR IS NOT MORE THAN 2 IN THE 14TH SIGNIFICANT BIT. CELLS CLOBBERED ARE A, L, SHFTFLAG, ININDEX,
# HALFARG, SCRATCH, SR, FUNCTION, FUNCTION +1. GTSQRT IS CALLED BY TC GTSQRT AND RETURNS VIA TC Q OR TC FUNCTION +1.
# ZERO OR NEGATIVE ARGUMENTS YIELD ZERO FOR SQUARE ROOTS.
GTSQRT CCS FUNCTION
TCF GOODARG # FUNCTION IS POSITIVE. TAKE SQUARE ROOT.
TCF +2 # HIGH ORDER WORD IS ZERO. TRY THE LOWER.
TCF ZEROOT # NEGATIVE. USE ZERO FOR 1/2 POWER.
CA FUNCTION +1
EXTEND
BZMF ZEROOT
TCF ZEROHIGH # PROCEED.
ZEROOT CA ZERO
TS SHFTFLAG
TC Q
ZEROHIGH XCH FUNCTION # 14 MOST SIGNIFICANT BITS ARE IN THE
XCH FUNCTION +1 # LOWER WORD. EXCHANGE THEM.
CA SEVEN
TCF GOODARG +1
GOODARG CA ZERO
TS SHFTFLAG
CA TWELVE # INITIALIZE THE SCALING LOOP.
TS ININDEX
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.
# Page 1482
INDEX ININDEX
CA BIT15 # THIS IS THE SCALE MAGNITUDE
XCH HALFARG # 2**(-ININDEX) IS THE SHIFT DIVISOR.
EXTEND # RESCALE ARGUMENT.
DCA FUNCTION
EXTEND
DV HALFARG
# ININDEX AND SHFTFLAG PRESERVE INFO FOR
# RESCALING AFTER ROOT PROCESS.
SCALDONE EXTEND
QXCH FUNCTION +1 # SAVE Q FOR RETURN
EXTEND
MP BIT14
TS HALFARG
MASK BIT13
CCS A
CA OCT11276
AD ROOTHALF # INITIAL GUESS IS ROOT 1/2 OR POSMAX
TC ROOTCYCL
TC ROOTCYCL
TC ROOTCYCL
TC FUNCTION +1
# ***************************************************************************
RSTOFGTS TC GTSQRT
PRODUCT XCH K2CNTRAL
EXTEND
MP K2CNTRAL
DXCH K2CNTRAL
EXTEND # THE PRODUCT OF
MP L # 1/2 2 1/2
ADS K2CNTRAL +1 # K *(DEL*OMEGA + ALPHA /(2*K))
TS L # AND
TCF +2 # 2
ADS K2CNTRAL # DEL*(DEL*OMEGA + ALPHA /(2*K)) NOW IN
# K2CNTRAL
DOSHIFT CA ININDEX
EXTEND # MULTIPLY IN THE FACTOR 2(-S), RETURNED
MP BIT14 # BY THE GTSQRT SUBROUTINE
ADS SHFTFLAG
EXTEND
BZF ADDITIN
INDEX SHFTFLAG
CA BIT15
# Page 1483
XCH K2CNTRAL
EXTEND
MP K2CNTRAL
DAS K2THETA
XCH K2CNTRAL
EXTEND
MP K2CNTRAL +1
ADS K2THETA +1
TS L
TCF +2
ADS K2THETA
TCF NEGUSUM
ADDITIN EXTEND
DCA K2CNTRAL
DAS K2THETA # NO 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
ADS RCSFLAGS
# Page 1484
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
ROOTHALF OCTAL 26501 # SQUARE ROOT OF 1/2
GMBLBITA OCTAL 01400 # INDEXED WRT GMBLBITB DO NOT MOVE *******
OCT11276 OCTAL 11276 # POSMAX -- ROOTHALF
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 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 APPROXIMATION
# 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
