LUNAR_LANDING_GUIDANCE_EQUATIONS.agc
### FILE="Main.annotation"
## Copyright: Public domain.
## Filename: LUNAR_LANDING_GUIDANCE_EQUATIONS.agc
## Purpose: A section of a reconstructed, mixed version of Sundance
## It is part of the reconstructed source code for the Lunar
## Module's (LM) Apollo Guidance Computer (AGC) for Apollo 9.
## No original listings of this program are available;
## instead, this file was created via disassembly of dumps
## of various revisions of Sundance core rope modules.
## Assembler: yaYUL
## Contact: Ron Burkey <info@sandroid.org>.
## Website: www.ibiblio.org/apollo/index.html
## Mod history: 2020-06-17 MAS Created from Luminary 69.
## 2021-05-30 ABS DEC -> DEC* for extended address fields.
## Sundance 292
EBANK= E2DPS
COUNT* $$/F2DPS
# ****************************************************************************************************************
# LUNAR LANDING FLIGHT SEQUENCE TABLES
# ****************************************************************************************************************
# FLIGHT SEQUENCE TABLES ARE ARRANGED BY PHASE. THEY ARE REFERENCED USING AS AN INDEX THE REGISTER WCHPHASE:
# WCHPHASE -1 ---> DISPLAY ROUTINES
# WCHPHASE +0 ---> ROUTINE FOR STARTING NEW GUIDANCE PHASES
# WCHPHASE +1 ---> GUIDANCE EQUATIONS
# WCHPHASE +2 ---> WINDOW VECTOR COMPUTATIONS
# WCHPHASE +3 ---> EXIT CRITERION
# WCHPHASE +4 ---> POST GUIDANCE EQUATION COMPUTATIONS
# WCHPHASE +5 ---> INDICES FOR REFERENCING TARGET PARAMETERS
# WCHPHASE +6 ---> AUGMENT FOR TTF/8
# ***************************************************************************************************************
# IGNITION ALGORITHM:
# -1 NO DISPLAYS
IGNALG TCF TTFINCR # +0
TCF TTF/8CL # +1
TCF EXGSUB # +2
DEC 0 # +3
TCF CGCALC # +4
OCT 0 # +5
DEC 108 E2 B-17 # +6
# BRAKING QUADRATIC:
TCF P63DISPS # -1
BRAKQUAD TCF TTFINCR # +0
TCF TTF/8CL # +1
TCF EXBRAK # +2
DEC -20 E2 B-17 # +3
TCF CGCALC # +4
OCT 0 # +5
DEC 0 # +6
# BRAKING LINEAR:
TCF P63DISPS # -1
BRAKLING TCF LINSET # +0
TCF LINGUID # +1
TCF EXBRAK # +2
DEC -2 E2 B-17 # +3
TCF RGVGCALC # +4
OCT 0 # +5
DEC 0 # +6
# APPROACH QUADRATIC:
TCF P64DISPS # -1
APPRQUAD TCF STARTP64 # +0
TCF TTF/8CL # +1
TCF EXNORM # +2
DEC -10 E2 B-17 # +3
TCF REDESIG # +4
OCT 30 # +5
DEC -158 E2 B-17 # +6
# APPROACH LINEAR:
TCF P64DISPS # -1
APPRLING TCF LINSET # +0
TCF LINGUID # +1
TCF EXNORM # +2
DEC -2 E2 B-17 # +3
TCF RGVGCALC # +4
OCT 30 # +5
DEC 0 # +6
# VERTICAL:
TCF VERTDISP # -1
VERTICAL TCF P65START # +0
TCF VERTGUID # +1
TCF EXVERT # +2
OCT 37777 # +3
TCF RGVGCALC # +4
# ****************************************************************************************************************
# ENTRY POINTS: ?GUIDSUB FOR THE IGNITION ALGORITHM, LUNLAND FOR SERVOUT
# ****************************************************************************************************************
# IGNITION ALGORITHM ENTRY: DELIVERS N PASSES OF QUADRATIC QUIDANCE
?GUIDSUB EXIT
CAF ONE # N = 2
GUIDSUB TS NGUIDSUB
TCF GUILDRET
# NORMAL ENTRY: CONTROL COMES HERE FROM SERVOUT
LUNLAND TC 2PHSCHNG
OCT 00035 # GROUP 5: RETAIN ONLY PIPA TASK
OCT 05022 # GROUP 2: PROTECT GUIDANCE WITH PRIO 21
OCT 21000 # JUST HIGHER THAN SERVICER'S PRIORITY
TC GUILDEN
# ****************************************************************************************************************
# INITIALIZATION FOR THIS PASS
# ****************************************************************************************************************
COUNT* $$/F2DPS
GUILDRET INDEX WCHPHASE
CA 5
TS TARGTDEX
COM
INDEX FIXLOC
TS X1
EXTEND
DCA TPIP
DXCH TPIPOLD
TC FASTCHNG
EXTEND
DCA PIPTIME
DXCH TPIP
EXTEND
DCA TTF/8
DXCH TTF/8TMP
CCS FLPASS0
TCF TTFINCR
BRSPOT1 INDEX WCHPHASE
CA 6
ADS TTF/8TMP
INDEX WCHPHASE
TCF 0
# ****************************************************************************************************************
# ROUTINES TO START NEW PHASES
# ****************************************************************************************************************
P65START TC NEWMODEX
DEC 65
CS TWO
TS WCHVERT
TC DOWNFLAG # PERMIT X-AXIS OVERRIDE
CADR XOVINFLG
TCF TTFINCR
STARTP64 TC NEWMODEX
DEC 64
CA BIT12 # ENABLE RUPT10
EXTEND
WOR CHAN13
TC DOWNFLAG # INITIALIZE REDESIGNATION FLAG
ADRES REDFLAG
TCF TTFINCR
# ****************************************************************************************************************
# SET LINEAR GUIDANCE COEFFICIENTS
# ****************************************************************************************************************
LINSET TC INTPRET
VLOAD VSU* # - - -
ACG # JLING = (ACG - ADG)/TTF
ADG,1
V/SC
TTF/8TMP # TTF/8 NOT YET UPDATED
STORE JLING # JLING IS IN UMITS OF 2(-18) M/CS/CS/CS
EXIT
# (CONTINUE TO TTFINCR)
# ****************************************************************************************************************
# INCREMENT TTF/8, UPDATE LAND FOR LUNAR ROTATION, DO OTHER USEFUL THINGS
# ****************************************************************************************************************
#
# TTFINCR COMPUTATIONS ARE AS FOLLOWS:-
# TTF/8 UPDATED FOR TIME SINCE LAST PASS:
# TTF/8 = TTF/8 + (TPIP - TPIPOLD)/8
# LANDING SITE VECTOR UPDATED FOR LUNAR ROTATION:
# - - - -
# LAND = /LAND/ UNIT(LAND - LAND(TPIP - TPIPOLD) * WM)
# SLANT RANGE TO LANDING SITE, FOR DISPLAY:
# - -
# RANGEDSP = ABVAL(LAND - R)
TTFINCR TC INTPRET
DLOAD DSU
TPIP
TPIPOLD
SLR PUSH # SHIFT SCALES DELTA TIME TO 2(17) CSECS
11D
VXSC VXV
LAND
WM
BVSU RTB
LAND
NORMUNIT
VXSC VSL1
/LAND/
STORE LANDTEMP
VSU ABVAL
R
STORE RANGEDSP
VLOAD VXV
R
WM
VAD VSR2 # RESCALE TO UNITS OF 2(9) M/CS
V
STODL ANGTERM
EXIT
DXCH MPAC
DAS TTF/8TMP # NOW HAVE INCREMENTED TTF/8 IN TTF/8TMP
TC FASTCHNG
EXTEND
DCA TTF/8TMP
DXCH TTF/8
EXTEND
DCA LANDTEMP
DXCH LAND
EXTEND
DCA LANDTEMP +2
DXCH LAND +2
EXTEND
DCA LANDTEMP +4
DXCH LAND +4
TC TDISPSET
BRSPOT2 INDEX WCHPHASE
TCF 4
# ****************************************************************************************************************
# LANDING SITE PERTURBATION EQUATIONS
# ****************************************************************************************************************
REDESIG TC FASTCHNG
CA FLAGWRD6 # IS REDFLAG SET?
MASK REDFLBIT
CCS A
TCF +3
TS ELINCR1
TS AZINCR1
CA TREDES # YES: HAS TREDES REACHED ZERO?
EXTEND
BZF CGCALC # YES: SKIP REDESIGNATION LOGIC
INHINT
CA ELINCR1
TS ELINCR
CA AZINCR1
TS AZINCR
TC FASTCHNG
CA ZERO
TS ELINCR1
TS AZINCR1
RELINT
TS ELINCR +1
TS AZINCR +1
TC INTPRET
SETPD VLOAD
0
LAND
VSU RTB # - -
R # PUSH DOWN UNIT (LAND - R)
NORMUNIT
MXV VSL1
XNBPIP
STODL 20D
20D
DMP BDSU
ELINCR
24D
PDDL VSR1
AZINCR
DAD PDDL
22D
24D
DMP DAD
ELINCR
20D
VDEF VXM
XNBPIP
PUSH DLOAD
0
DSU
DEPRCRIT
BMN DLOAD
REDES1
DEPRCRIT
STORE 0
REDES1 DLOAD DSU
LAND
R
DDV VXSC
0
VAD UNIT
R
VXSC VSL1
/LAND/
STORE LANDTEMP
VSU RTB
R
NORMUNIT
DOT SL1
XNBPIP
VCOMP ASIN
EXIT # LOOKANGL WILL BE COMPUTED AT RGVGCALC
CAF 360DEGS
TC SHORTMP
CAF BIT14
TS L
CAF ZERO
DAS MPAC
DXCH MPAC
TC ALSIGNAG
TS GEFF
TC FASTCHNG
EXTEND
DCA LANDTEMP
DXCH LAND
EXTEND
DCA LANDTEMP +2
DXCH LAND +2
EXTEND
DCA LANDTEMP +4
DXCH LAND +4
# ***************************************************************************************************************
# ERECT GUIDANCE-STABLE MEMBER TRANSFORMATION MATRIX
# ***************************************************************************************************************
CGCALC TC INTPRET
VLOAD UNIT
LAND
STOVL CG # FIRST ROW
ANGTERM
VXSC VAD # REMEMBER THAT ANGTERM IS DOUBLE-SIZED
TTF/8
LAND
VSU RTB
R
NORMUNIT
VXV RTB
LAND
NORMUNIT
STOVL CG +6 # SECOND ROW
CG
VXV VSL1
CG +6
STORE CG +14
EXIT
# ****************************************************************************************************************
# COMPUTE STATE IN GUIDANCE COORDINATES
# ****************************************************************************************************************
# RGVGCALC COMPUTATIONS ARE AS FOLLOWS:-
# VELOCITY RELATIVE TO THE SURFACE:
# - - - -
# ANGTERM = V + R * WM
# STATE IN GUIDANCE COORDINATES:
# - * - -
# RGU = CG (R - LAND)
# - * - - -
# VGU = CG (V - WM * R)
# HORIZONTAL VELOCITY FOR DISPLAY:
# VHORIZ = 8 ABVAL (0, VG , VG )
# 2 1
# DEPRESSION ANGLE FOR DISPLAY:
# - - -
# LOOKANGL = ARCSIN(UNIT(R - LAND).XMBPIP)
RGVGCALC TC INTPRET # ENTER HERE TO RECOMPUTE RG AND VG
VLOAD VSU
R # - -
LAND # PUSH DOWN R - LAND
MXV VSL1
CG
STOVL RGU
ANGTERM
MXV
CG # NO SHIFT SINCE ANGTERM IS DOUBLE SIZED
STORE VGU
PDDL VDEF # FORM (0,VG ,VG ) IN UNITS OF 2(10) M/CS
ZEROVECS # 2 1
ABVAL SL3
STODL VHORIZ # VHORIZ FOR DISPLAY DURING P65, P66, P67
EXIT
BRSPOT3 INDEX WCHPHASE
TCF 1
#****************************************************************************************************************
# LINEAR GUIDANCE EQUATION
#****************************************************************************************************************
LINGUID TC INTPRET
VLOAD VXSC # - - -
JLING # ACG = ADG + JLING TTF
TTF/8
VAD* GOTO
ADG,1
AFCCALC +2
#****************************************************************************************************************
# TTF/4 COMPUTATION
#****************************************************************************************************************
TTF/8CL EXTEND
INDEX TARGTDEX
DCA JDG2TTF # A(3) = 8 JDG TO TABLTTF
DXCH TABLTTF +6 # 2
EXTEND
INDEX TARGTDEX
DCA ADG2TTF # A(2) = 6 ADG TO TABLTTF
DXCH TABLTTF +4 # 2
EXTEND
DCA VGU +4
DXCH MPAC
CAF 3/4DP
TC SHORTMP
EXTEND
INDEX TARGTDEX
DCA VDG2TTF
DAS MPAC
DXCH MPAC # A(1) = (6 VGU + 18 VDG )/8 TO TABLTTF
DXCH TABLTTF +2 # 2 2
EXTEND
DCS RGU +4
DXCH MPAC
EXTEND
INDEX TARGTDEX
DCA RDG +4
DAS MPAC
CAF 3/8
TC SHORTMP
DXCH MPAC # A(0) = -24 (RGU - RDG )/64 TO TABLTTF
DXCH TABLTTF # 2 2
CA BIT8
TS TABLTTF +10 # FRACTIONAL PRECISION FOR TTF TO TABLE
EXTEND
DCA TTF/8
DXCH MPAC # LOADS TTF/8 (INITIAL GUESS) INTO MPAC
EXTEND
DCA TABLTTFL
TC ROOTPSRS # YIELDS TTF/8 IN MPAC
EXTEND
DCA MPAC # FETCH TTF/8 KEEPING IT IN MPAC
DXCH TTF/8 # CORRECTED TTF/8
TC TDISPSET
# (CONTINUE TO QUADGUID)
# ****************************************************************************************************************
# MAIN GUIDANCE EQUATION
# ****************************************************************************************************************
# AS PUBLISHED:-
# - - - -
# - - 6(VDG + VG) 12(RDG - RG)
# ACG = ADG + ----------- + ------------
# TTF (TTF)(TTF)
# AS HERE PROGRAMMED:-
# - -
# 3 (1/4(RDG - RG) - - )
# - (------------- + VDG + VG)
# - 4 ( TTF/8 ) -
# ACG = ---------------------------- + ADG
# TTF/8
QUADGUID TC INTPRET
VLOAD* VSU
RDG,1
RGU
V/SC VSR2
TTF/8
VAD* VAD
VDG,1
VGU
V/SC VXSC
TTF/8
3/4DP
AFCCALC VAD*
ADG,1 # CURRENT TARGET ACCELERATION
STORE ACG
AFCCALC1 VXM VSL1 # VERTGUID COMES HERE
CG
PDVL V/SC
GDT/2
GSCALE
BVSU STADR
STORE UNFC/2 # UNFC/2 NEED NOT BE UNITIZED
ABVAL
AFCCALC2 STORE /AFC/ # MAGNITUDE OF AFC FOR THROTTLE
EXIT
TC FASTCHNG
INCR FLPASS0 # INCREMENT PASS COUNTER
# (CONTINUE TO EXTLOGIC)
# ****************************************************************************************************************
# PREPARE TO EXIT
# ****************************************************************************************************************
# DECIDE (1) HOW TO EXIT, AND (2) WHETHER TO SWITCH PHASES
EXTLOGIC INDEX WCHPHASE
CS 3
AD TTF/8
EXTEND
INDEX WCHPHASE
BZMF 2
CA WCHPHASE # PREPARE FOR PHASE SWITCHING LOGIC
TS WCHPHOLD
TC FASTCHNG
CA WCHPHOLD
AD BIT4
ZL # +0
DXCH WCHPHASE # ADVANCING WCHPHASE AND RESETTING FLPASS0
INDEX WCHPHOLD
TCF 2
# ****************************************************************************************************************
# ROUTINES FOR EXITING FROM LANDING GUIDANCE
# ****************************************************************************************************************
# 1. EXGSUB IS THE RETURN WHEN GUIDSUB IS CALLED BY THE IGNITION ALGORITHM.
# 2. EXBRAK IN THE EXIT USED DURING THE BRAKING PHASE. IN THIS CASE UNIT(R) IS THE WINDOW POINTING VECTOR.
# 3. EXNORM IS THE EXIT USED AT OTHER TIMES DURING THE BURN.
# (EXOVFLOW IS A SUBROUTINE OF EXBRAK AND EXNORM CALLED WHEN OVERFLOW OCCURRED ANYWHERE IN GUIDANCE.)
EXGSUB CCS NGUIDSUB
TCF GUIDSUB
INCR NIGNLOOP
CS BIT5
AD NIGNLOOP
EXTEND
BZMF +3
TC ALARM
OCT 01412
+3 TC INTPRET
GOTO
DDUMCALC
EXBRAK TC INTPRET
VLOAD GOTO
UNIT/R/
STEER?
EXNORM TC INTPRET
VLOAD VSU
LAND
R
RTB
NORMUNIT
STORE 20D # UNIT(LAND - R) IS TENTATIVE CHOICE
VXV DOT
XNBPIP
CG +6
STORE 18D # PROJ 1/8 REAL SIZE
DSU BMN
PROJMAX
+4
VLOAD GOTO
20D
STEER?
DLOAD
18D
DSU BPL
PROJMIN
+4
VLOAD GOTO
CG +12D
STEER?
DLOAD DSU
18D
PROJMAX
VXSC PDDL
CG +12D
18D
DSU VXSC
PROJMIN
20D
VSU
V/SC
PROJDIV
STEER? STORE UNWC/2
BOFF EXIT # IF STEERSW DOWN NO OUTPUTS
STEERSW
DISPEXIT -1
EXVERT CA OVFIND # IF OVERFLOW ANYWHERE IN GUIDANCE
EXTEND # DON'T CALL THROTTLE OR FINDCDUW
BZF +4
EXOVFLOW TC ALARM # SOUND THE ALARM NON-ABORTIVELY.
OCT 01410
TCF DISPEXIT
GDUMP1 TC THROTTLE
TC INTPRET
CALL
FINDCDUW -2
EXIT
# (CONTINUE TO DISPEXIT)
# ****************************************************************************************************************
# GUIDANCE LOOP DISPLAYS
# ****************************************************************************************************************
DISPEXIT EXTEND # KILL GROUP 2: DISPLAYS WILL BE
DCA NEG0 # RESTORED BY NEXT GUIDANCE CYCLE
DXCH -PHASE2
CS FLAGWRD8 # IF FLUNDISP SET, NO DISPLAY THIS PASS
MASK FLUNDBIT
EXTEND
BZF ENDLLJOB # TO PICK UP THE TAG
INDEX WCHPHASE
TCF 0 -1
P63DISPS CAF V06N63
DISPCOMN TC BANKCALL
CADR GODSPR
ENDLLJOB TCF ENDOFJOB
P64DISPS CS FLAGWRD6 # NO: IS REDFLAG SET?
MASK REDFLBIT
EXTEND
BZF REDES-OK # YES: DO STATIC DISPLAY
CAF V06N64 # OTHERWISE USE FLASHING DISPLAY
TC BANKCALL
CADR REFLASHR
TCF GOTOPOOH # TERMINATE
TCF P64CEED # PROCEED PERMIT REDESIGNATIONS
TCF P64DISPS # RECYCLE
TCF ENDLLJOB # TO PICK UP THE TAG
P64CEED CAF ZERO
TS ELINCR1
TS AZINCR1
TC UPFLAG # ENABLE REDESIGNATION LOGIC
ADRES REDFLAG
TCF ENDOFJOB
REDES-OK CAF V06N64
TCF DISPCOMN
VERTDISP CAF FOUR
TC BANKCALL
CADR ALTCHK
TCF VERTDSP2
CAF V06N60
TC BANKCALL
CADR REFLASHR
TCF GOTOPOOH
TCF LANDJUNK
TCF VERTDISP
TCF ENDLLJOB
VERTDSP2 CAF V06N60
TCF DISPCOMN
# ****************************************************************************************************************
# GUIDANCE FOR VERTICAL DESCENT
# ****************************************************************************************************************
VERTGUID CCS WCHVERT
TCF DISPEXIT # POSITIVE P67, WHICH SKIPS ALL GUIDANCE
TCF P66VERT # +0
# THE P65 GUIDANCE EQUATION IS AS FOLLOWS:-
# - -
# - VDGVERT - VGU -
# ACG = ------------- , WHERE VDGVERT = (-3FPS,0,0)
# TAUVERT
P65VERT EXTEND # NEGATIVE
DCS +3FPS
DXCH VDGVERT
TC INTPRET
VLOAD PDDL
ZEROVECS
VDGVERT
VDEF VSU # FORM (VDGVERT,0,0), LEAVING DP 0 IN PDL
VGU
V/SC GOTO
TAUVERT
AFCCALC1
# THE R.O.D. EQUATION IS AS FOLLOWS:-
# (VDGVERTX - VGUX)/TAUVERT - GMOON
# /AFC/ = ---------------------------------
# UNIT/R/ . XNB
P66VERT XCH RODCOUNT # RESTART COULD CAUSE RODCOUNTS TO BE LOST
EXTEND
MP +1FPS
DAS VDGVERT
TC FASTCHNG
TC INTPRET
DLOAD DSU
VDGVERT
VGU
DDV DSU
TAUROD
MOONG
PDVL DOT # HAVE ACC IN UNITS OF 2(-2) M/CS/CS
XNBPIP
UNIT/R/
BDDV STADR
STORE /AFC/
BOVB EXIT
EXOVFLOW
TC THROTTLE
TCF DISPEXIT
# ****************************************************************************************************************
# REDESIGNATOR TRAP
# ****************************************************************************************************************
BANK 21
SETLOC F2DPS*21
BANK
COUNT* $$/F2DPS
PITFALL XCH BANKRUPT
EXTEND
QXCH QRUPT
TC CHECKMM # IF NOT IN P64, NO REASON TO CONTINUE
DEC 64
TCF RESUME
EXTEND
READ CHAN31
COM
MASK ALL4BITS
TS ELVIRA
CAF TWO
TS ZERLINA
CAF FIVE
TC TWIDDLE
ADRES REDESMON
TCF RESUME
## Sundance 302
# REDESIGNATION MONITOR (INITIATED BY PITFALL)
PREMON1 TS ZERLINA
PREMON2 CAF SEVEN
TC VARDELAY
REDESMON EXTEND
READ 31
COM
MASK ALL4BITS
XCH ELVIRA
TS L
CCS ELVIRA # DO ANY BITS APPEAR THIS PASS?
TCF PREMON2 # Y: CONTINUE MONITOR
CCS L # N: ANY LAST PASS?
TCF COUNT'EM # Y: COUNT 'EM, RESET RUPT, TERMINATE
CCS ZERLINA # N: HAS ZERLINA REACHED ZERO YET?
TCF PREMON1 # N: DIMINISH ZERLINA, CONTINUE
RESETRPT CAF BIT12 # Y: RESET RUPT, TERMINATE
EXTEND
WOR CHAN13
TCF TASKOVER
COUNT'EM CA L
MASK -AZBIT
CCS A
-AZ CS AZEACH
ADS AZINCR1
CA L
MASK +AZBIT
CCS A
+AZ CA AZEACH
ADS AZINCR1
CA L
MASK -ELBIT
CCS A
-EL CS ELEACH
ADS ELINCR1
CA L
MASK +ELBIT
CCS A
+EL CA ELEACH
ADS ELINCR1
TCF RESETRPT
# THESE EQUIVALENCIES ARE BASED ON GSOP CHAPTER 4, REVISION 16 OF P64LM
+ELBIT = BIT2 # -PITCH
-ELBIT = BIT1 # +PITCH
+AZBIT = BIT5
-AZBIT = BIT6
ALL4BITS OCT 00063
AZEACH DEC .03491 # 2 DEGREES
ELEACH DEC .00873 # 1/2 DEGREE
# ****************************************************************************************************************
# R.O.D. TRAP
# ************************************************************************
BANK 21
SETLOC RODTRAP
BANK
COUNT* $$/F2DPS # ****************************************
DESCBITS MASK BIT7 # COME HERE FROM MARKRUPT CODING WITH BIT
CCS A # 7 OR 6 OF CHANNEL 16 IN A: BIT 7 MEANS
CS TWO # - RATE INCREMENT, BIT 6 + INCREMENT
AD ONE
ADS RODCOUNT
TCF RESUME # TRAP IS RESET WHEN SWITCH IS RELEASED
## Sundance 292
BANK 31
SETLOC F2DPS*31
BANK
COUNT* $$/F2DPS
# ****************************************************************************************************************
# DOUBLE PRECISION ROOT FINDER SUBROUTINE (BY ALLAN KLUMPP)
# ****************************************************************************************************************
# N N-1
# ROOTPSRS FINDS ONE ROOT OF THE POWER SERIES A X + A X + ... + A X + A
# N N-1 1 0
# USING NEWTON'S METHOD STARTING WITH AN INITIAL GUESS FOR THE ROOT. THE ENTERING DATA MUST BE AS FOLLOWS:
# A SP LOC-3 ADRES FOR REFERENCING PWR COF TABL
# L SP N-1 N IS THE DEGREE OF THE POWER SERIES
# MPAC DP X INITIAL GUESS FOR ROOT
# LOC-2N DP A(0)
# ...
# LOC DP A(N)
# LOC+2 SP PRECROOT PREC RQD OF ROOT (AS FRACT OF 1ST GUESS)
# THE DP RESULT IS LEFT IN MPAC UPON EXIT, AND A SP COUNT OF THE ITERATIONS TO CONVERGENCE IS LEFT IN MPAC+2.
# RETURN IS NORMALLY TO LOC(TC ROOTPSRS)+3. IF ROOTPSRS FAILS TO CONVERGE IN 32 PASSES, RETURN IS TO LOC+1 AND
# OUTPUTS ARE NOT TO BE TRUSTED.
# PRECAUTION: ROOTPSRS MAKES NO CHECKS FOR OVERFLOW OR FOR IMPROPER USAGE. IMPROPER USAGE COULD
# PRECLUDE CONVERGENCE OR REQUIRE EXCESSIVE ITERATIONS. AS A SPECIFIC EXAMPLE, ROOTPSRS FORMS A DERIVATIVE
# COEFFICIENT TABLE BY MULTIPLYING EACH A(I) BY I, WHERE I RANGES FROM 1 TO N. IF AN ELEMENT OF THE DERIVATIVE
# COEFFICIENT TABLE = 1 OR > 1 IN MAGNITUDE, ONLY THE EXCESS IS RETAINED. ROOTPSRS MAY CONVERGE ON THE CORRECT
# ROOT NONETHELESS, BUT IT MAY TAKE AN EXCESSIVE NUMBER OF ITERATIONS. THEREFORE THE USER SHOULD RECOGNIZE:
# 1. USER'S RESPONSIBILITY TO ASSURE THAT I X A(I) < 1 IN MAGNITUDE FOR ALL I.
# 2. USER'S RESPONSIBILITY TO ASSURE OVERFLOW WILL NOT OCCUR IN EVALUATING EITHER THE RESIDUAL OR THE DERIVATIVE
# POWER SERIES. THIS OVERFLOW WOULD BE PRODUCED BY SUBROUTINE POWRSERS, CALLED BY ROOTPSRS, AND MIGHT NOT
# PRECLUDE EVENTUAL CONVERGENCE.
# 3. AT PRESENT, ERASABLE LOCATIONS ARE RESERVED ONLY FOR N UP TO 5. AN N IN EXCESS OF 5 WILL PRODUCE CHAOS.
# ALL ERASABLES USED BY ROOTPSRS ARE UNSWITCHED LOCATED IN THE REGION FROM MPAC-33 OCT TO MPAC+7.
# 4. THE ITERATION COUNT RETURNED IN MPAC+2 MAY BE USED TO DETECT ABNORMAL PERFORMANCE.
# STORE ENTERING DATA, INITLIZE ERASABLES
ROOTPSRS EXTEND
QXCH RETROOT # RETURN ADRES
TS PWRPTR # PWR TABL POINTER
DXCH MPAC +3 # PWR TABL ADRES, N-1
CA DERTABLL
TS DERPTR # DER TABL POINTER
TS MPAC +5 # DER TABL ADRES
CCS MPAC +4 # NO POWER SERIES OF DEGREE 1 OR LESS
TS MPAC +6 # N-2
CA ZERO # MODE USED AS ITERATION COUNTER. MODE
TS MODE # MUST BE POS SO ABS WON'T COMP MPAC+3 ETC
# COMPUTE CRITERION TO STOP ITERATING
EXTEND
DCA MPAC # FETCH ROOT GUESS, KEEPING IT IN MPAC
DXCH ROOTPS # AND IN ROOTPS
INDEX MPAC +3 # PWR TABL ADRES
CA 5 # PRECROOT TO A
TC SHORTMP # YIELDS DP PRODUCT IN MPAC
TC USPRCADR
CADR ABS # YIELDS ABVAL OF CRITERION ON DX IN MPAC
DXCH MPAC
DXCH DXCRIT # CRITERION
# SET UP DER COF TABL
EXTEND
INDEX PWRPTR
DCA 3
DXCH MPAC # A(N) TO MPAC
CA MPAC +4 # N-1 TO A
DERCLOOP TS PWRCNT # LOOP COUNTER
AD ONE
TC DMPNSUB # YIELDS DERCOF = I X A(I) IN MPAC
EXTEND
INDEX PWRPTR
DCA 1
DXCH MPAC # A(I-1) TO MPAC, FETCHING DERCOF
INDEX DERPTR
DXCH 3 # DERCOF TO DER TABL
CS TWO
ADS PWRPTR # DECREMENT PWR POINTER
CS TWO
ADS DERPTR # DECREMENT DER POINTER
CCS PWRCNT
TCF DERCLOOP
# CONVERGE ON ROOT
ROOTLOOP EXTEND
DCA ROOTPS # FETCH CURRENT ROOT
DXCH MPAC # LEAVE IN MPAC
EXTEND
DCA MPAC +5 # LOAD A, L WITH DER TABL ADRES, N-2
TC POWRSERS # YIELDS DERIVATIVE IN MPAC
EXTEND
DCA ROOTPS
DXCH MPAC # CURRENT ROOT TO MPAC, FETCHING DERIVTIVE
DXCH BUF # LEAVE DERIVATIVE IN BUF AS DIVISOR
EXTEND
DCA MPAC +3 # LOAD A, L WITH PWR TABL ADRES, N-1
TC POWRSERS # YIELDS RESIDUAL IN MPAC
TC USPRCADR
CADR DDV/BDDV # YIELDS -DX IN MPAC
EXTEND
DCS MPAC # FETCH DX, LEAVING -DX IN MPAC
DAS ROOTPS # CORRECTED ROOT NOW IN ROOTPS
TC USPRCADR
CADR ABS # YIELDS ABS(DX) IN MPAC
EXTEND
DCS DXCRIT
DAS MPAC # ABS(DX)-ABS(DXCRIT) IN MPAC
INCR MODE # INCREMENT ITERATION COUNTER
CCS MPAC # TEST HI ORDER DX
TCF ROOTLOOP
TCF TESTLODX
TCF ROOTSTOR
TESTLODX CCS MPAC +1 # TEST LO ORDER DX
TCF ROOTLOOP
TCF ROOTSTOR
TCF ROOTSTOR
ROOTSTOR DXCH ROOTPS
DXCH MPAC
CA MODE
TS MPAC +2 # STORE SP ITERATION COUNT IN MPAC+2
TC RETROOT
DERTABLL ADRES DERCOFN -3
# ****************************************************************************************************************
# TRASHY LITTLE SUBROUTINES
# ****************************************************************************************************************
TDISPSET CA TTF/8
EXTEND
MP TSCALINV
DXCH TTFDISP
CA TTF/8
EXTEND
MP SCTTFDSP
TS L
AD 99+LINT
EXTEND
BZMF +11
CS L
AD -LINT
EXTEND
BZMF +3
TS TREDES
TC Q
CA ZERO
TCF -3
CA 99+LINT
TCF -10
# ****************************************************************************************************************
# SPECIALIZED "PHASCHNG" SUBROUTINE
# ****************************************************************************************************************
EBANK= PHSNAME2
FASTCHNG CA EBANK3 # SPECIALIZED 'PHASCHNG' ROUTINE
XCH EBANK
DXCH L
TS PHSNAME2
LXCH EBANK
EBANK= E2DPS
TC A
# ****************************************************************************************************************
# PARAMETER TABLE INDIRECT ADDRESSES
# ****************************************************************************************************************
RDG = RBRFG
VDG = VBRFG
ADG = ABRFG
VDG2TTF = VBRFG*
ADG2TTF = ABRFG*
JDG2TTF = JBRFG*
# ****************************************************************************************************************
# LUNAR LANDING CONSTANTS
# ***************************************************************************************************************
# LUNAR LANDING TARGET PARAMETERS
#
ABRFG 2DEC* -3.43285501 E-5 B+4*
2DEC* +0.00000000 E+0 B+4*
2DEC* -2.74418853 E-4 B+4*
RBRFG 2DEC* +3.12375000 E+3 B-24*
2DEC* +0.00000000 E+0 B-24*
2DEC* -1.07834375 E+4 B-24*
VBRFG 2DEC* -4.92340088 E-1 B-10*
2DEC* +0.00000000 E+0 B-10*
2DEC* +1.80714798 E+0 B-10*
VBRFG* 2DEC* +4.06608200 E+0 B-10*
ABRFG* 2DEC* -1.64651359 E-3 B+4*
JBRFG* 2DEC* -2.69203326 E-8 B+18*
AAPFG 2DEC* +1.52399999 E-6 B+4*
2DEC* +0.00000000 E+0 B+4*
2DEC* -1.98119999 E-5 B+4*
RAPFG 2DEC* +2.35092239 E+1 B-24*
2DEC* +0.00000000 E+0 B-24*
2DEC* -5.28319999 E-1 B-24*
VAPFG 2DEC* -9.44879999 E-3 B-10*
2DEC* +0.00000000 E+0 B-10*
2DEC* +3.96239999 E-3 B-10*
VAPFG* 2DEC* +8.91539999 E-3 B-10*
AAPFG* 2DEC* -1.18871999 E-4 B+04*
JAPFG* 2DEC* +8.37250411 E-8 B+18*
TABLTTFL ADRES TABLTTF +3 # ADDRESS FOR REFERENCING TTF TABLE
DEC 2 # DEGREE - ONE
TSCALINV = BIT4
99+LINT DEC +119
-LINT DEC -20
SCTTFDSP DEC .08 # RESCALES FROM 2(-17) CS TO WHOLE SECONDS
360DEGS DEC +360
TAUVERT 2DEC 600 B-14
TAUROD 2DEC 300 B-12
GSCALE 2DEC 100 B-11
3/8 DEC .375000000
2/3DP 2DEC .666666667
3/4DP 2DEC .750000000
WMREF 2DEC 0.0
2DEC* .26616994890062991 E-7 B+18* # RAD/CS.
2DEC 0.0
MOONG 2DEC -1.6226 E-4 B2
+1FPS DEC .3048 E-2 B+4
+3FPS 2DEC +0.9144 E-2 B-10
+5FPS 2DEC +1.524 E-2 B-10
DEPRCRIT 2DEC -.02 B-2 # DEPRESSION ANGLE CRITERION
PROJMAX 2DEC .42262 B-3 # SIN(25')/8 TO COMPARE WITH PROJ
PROJMIN 2DEC .25882 B-3 # SIN(15')/8 TO COMPARE WITH PROJ
PROJDIV 2DEC .1638 B-3
V06N63 VN 0663 # P63
V06N64 VN 0664 # P64
V06N60 VN 0660 # P65, P66, P67
# ****************************************************************************************************************
# ****************************************************************************************************************
