INTERPRETER.agc

### FILE="Main.annotation"
## Copyright:	Public domain.
## Filename:	INTERPRETER.agc
## Purpose: 	Part of the source code for Luminary 1A build 099.
##		It is part of the source code for the Lunar Module's (LM)
##		Apollo Guidance Computer (AGC), for Apollo 11.
## Assembler:	yaYUL
## Contact:	Ron Burkey <info@sandroid.org>.
## Website:	www.ibiblio.org/apollo.
## Pages:	1002-1094
## Mod history:	2009-05-25 RSB	Adapted from the corresponding 
##				Luminary131 file, using page 
##				images from Luminary 1A.
##		2011-01-06 JL	Fixed pseudo-label indentation.
##		2011-05-08 JL	Removed workarounds.
##		2016-12-17 RSB	Proofed text comments with octopus/ProoferComments
##				and corrected the errors found.
##		2017-01-28 RSB	Back-ported some comment-text fixes made in Luminary 69.
##		2017-02-05 RSB	Back-ported comment corrections 
##				identified while proofing Artemis 072.
##		2017-03-13 RSB	Comment-text fixes noted in proofing Luminary 116.
##		2017-03-15 RSB	Comment-text fixes identified in 5-way
##				side-by-side diff of Luminary 69/99/116/131/210.
##		2021-05-30 ABS	Added IRT0 location symbol to match scans.
##				B5TOBB -> B5TOB8

## 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 2021112-61
##	16:27 JULY 14, 1969 

## Page 1002
# SECTION 1   DISPATCHER
#
# ENTRY TO THE INTERPRETER.  INTPRET SETS LOC TO THE FIRST INSTRUCTION, BANKSET TO THE BBANK OF THE
# OBJECT INTERPRETIVE PROGRAM, AND INTBIT15 TO THE BIT15 CONTENTS OF FBANK.  INTERPRETIVE PROGRAMS MAY BE IN
# VIRTUALLY ALL BANKS PRESENT UNDER ANY SUPER-BANK SETTING, WITH THE RESTRICTION THAT PROGRAMS IN HIGH BANKS
# (BIT15 OF FBANK = 1) DO NOT REFER TO LOWBANKS, AND VICE-VERSA.  THE INTERPRETER DOES NOT SWITCH SUPERBANKS.
# E-BANK SWITCHING OCCURS WHENEVER GENERAL ERASABLE (100-3777) IS ADDRESSED.

		BLOCK	03
		
		COUNT*	$$/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 1003
# AT THE END OF MOST INSTRUCTIONS, CONTROL IS GIVEN TO DANZIG TO DISPATCH THE NEXT OPERATION.

		TS	MPAC 	+2		# AND DECLARE DP MODE

NEWMODE		TS	MODE			# PROLOGUE FOR MODE-CHANGING INSTRUCTIONS.

DANZIG		CA	BANKSET			# SET BBANK BEFORE TESTING NEWJOB SO THAT
		TS 	BBANK			# IT MAY BE SAVED DIRECTLY BY CHANJOB.

NOIBNKSW	CCS	EDOP			# SEE IF AN ORDER CODE IS LEFT OVER FROM
		TCF	OPJUMP			# THE LAST PAIR RETRIEVED.  IF SO, EXECUTE.
						# EDOP IS SET TO ZERO ON ITS RE-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 1004
# PROCESS ADDRESSES WHICH MAY BE DIRECT, INDEXED, OR REFERENCE THE PUSHDOWN LIST.

ADDRESS		MASK	BIT1			# SEE IF ADDRESS IS INDEXED.  CYR CONTAINED
		CCS	A			# 400XX, SO BIT 1 IS NOW AS IT WAS IN CYR.
		TCF	INDEX			# FORM INDEXED ADDRESS.

DIRADRES	INDEX	LOC			# LOOK AHEAD TO NEXT WORD TO SEE 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 1005
# FINAL DIGESTION OF DIRECT ADDRESSES OF OP CODES WITH 01 PREFIX IS DONE HERE.   IN EACH CASE, THE
# REQUIRED 12-BIT SUB-ADDRESS IS LEFT IN ADDRWD, WITH ANY REQUIRED E OR F BANK SWITCHING DONE.  ADDRESSES LESS
# THAN 45D ARE TAKEN TO BE RELATIVE TO THE WORK AREA.  THE OP CODE IS NOW IN BITS 1-5 OF CYR WITH BIT 14 = 1.

		AD	-ENDVAC			# SEE IF ADDRESS RELATIVE TO WORK AREA.
		CCS	A
		AD	-ENDERAS		# IF NOT, SEE IF IN GENERAL ERASABLE.
		TCF	IERASTST
		
NETZERO		CA	FIXLOC			# IF SO, LEAVE THE MODIFIED ADDRESS IN
		ADS	ADDRWD			# ADDRWD AND DISPATCH.
ITR15		INDEX	CYR			# THIS INDEX MAKES THE NEXT INSTRUCTION
		7	INDJUMP -1		# TCF INDJUMP + OP, EDITING CYR.
		
IERASTST	EXTEND
		BZMF	GEADDR			# GO PROCESS GENERAL-ERASABLE ADDRESS.
		
		MASK	LOW10			# FIXED BANK ADDRESS. RESTORE AND ADD B15.
		AD	LOW10			# SWITCH BANKS AND LEAVE SUBADDRESS IN
		XCH	ADDRWD			# ADDRWD FOR OPERAND RETRIEVAL. (THIS
		AD	INTBIT15		# METHOD PRECLUDES USE OF THE LAST
		TS	FBANK			# LOCATION IN EACH FBANK.)
ITR12		INDEX	CYR
		7	INDJUMP -1
		
GEADDR		MASK	LOW8
		AD	OCT1400
		XCH	ADDRWD
		TS	EBANK
ITR10		INDEX	CYR
		7	INDJUMP -1

## Page 1006
# THE FOLLOWING ROUTINE PROCESSES INTERPRETIVE INDEXED ADDRESSES.  AN INTERPRETER INDEX REGISTER MAY
# CONTAIN THE ADDRESS OF ANY ERASABLE REGISTER (0-42 BEING RELATIVE TO THE VAC AREA) OR ANY INTERPRETIVE PROGRAM
# BANK, OR ANY INTEGER IN THAT RANGE.

DODLOAD*	CAF	DLOAD*			# STODL* COMES HERE TO PROCESS LOAD ADR.
		TS	CYR			# (STOVL* ENTERS HERE).
		
INDEX		CA	FIXLOC			# SET UP INDEX LOCATION.
		TS	INDEXLOC
		INCR	LOC			# (ADDRESS ALWAYS GIVEN).
		INDEX	LOC
		CS	0
		CCS	A			# INDEX 2 IF ADDRESS STORED COMPLEMENTED.
		INCR	INDEXLOC
		NOOP
		
		TS 	ADDRWD			# 14 BIT ADDRESS TO ADDRWD.
		MASK	HIGH4			# IF ADDRESS GREATER THAN 2K, ADD INTBIT15
		EXTEND
		BZF 	INDEX2
		CA	INTBIT15
		ADS	ADDRWD

INDEX2		INDEX	INDEXLOC
		CS	X1
		ADS	ADDRWD			# DO AUGMENT, IGNORING AND CORRECTING OVF.
		
		MASK	HIGH9			# SEE IF ADDRESS IS IN WORK AREA.
		EXTEND
		BZF	INDWORK
		MASK	HIGH4			# SEE IF IN FIXED BANK.
		EXTEND
		BZF	INDERASE

		CA	ADDRWD			# IN FIXED - SWITCH BANKS AND CREATE
		TS	FBANK			# SUB-ADDRESS.
		MASK	LOW10
		AD	2K
		TS	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 1007
ITR13		INDEX	CYR
		3	INDJUMP -1
		
## Page 1008
# PUSH-UP ROUTINES.  WHEN NO OPERAND ADDRESS IS GIVEN, THE APPROPRIATE OPERAND IS TAKEN FROM THE PUSH-DOWN
# LIST.  IN MOST CASES THE MODE OF THE RESULT (VECTOR OR SCALAR) OF THE LAST ARITHMETIC OPERATION PERFORMED
# IS THE SAME AS THE TYPE OF OPERAND DESIRED (ALL ADD/SUBTRACT ETC.).  EXCEPTIONS TO THIS GENERAL RULE ARE LISTED
# BELOW (NOTE THAT IN EVERY CASE THE MODE REGISTER IS LEFT INTACT):
#
#	1.	VXSC AND V/SC WANT THE OPPOSITE TYPE OF OPERAND, E.G., IF THE LAST OPERATION YIELDED A VECTOR
#		RESULT, VXSC WANTS A SCALAR.
#
#	2.	THE LOAD CODES SHOULD LOAD THE ACCUMULATOR INDEPENDENT OF THE RESULT OF THE LAST OPERATION.  THIS
#		INCLUDES VLOAD, DLOAD, TLOAD, PDDL, AND PDVL (NO PUSHUP WITH SLOAD).
#
#	3.	SOME ARITHMETIC OPERATIONS REQUIRE A STANDARD TYPE OF OPERAND REGARDLESS OF THE PREVIOUS OPERATION.
#		THIS INCLUDES SIGN WANTING DP AND TAD REQUIRING TP.

PUSHUP		CAF	OCT23		# IF THE LOW 5 BITS OF CYR ARE LESS THAN
		MASK	CYR		# 20, THIS OP REQUIRES SPECIAL ATTENTION.
		AD	-OCT10		# (NO -0).
		CCS	A
		TCF	REGUP		# FOR ALL CODES 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 1009
# TEST THE SECOND PREFIX BIT TO SEE IF THIS IS A MISCELLANEOUS OR A UNARY/SHORT SHIFT OPERATION.

OPJUMP2		CCS	CYR		# TEST SECOND PREFIX BIT.
		TCF	OPJUMP3		# TEST THIRD BIT TO SEE IF UNARY OR SHIFT.
		
-ENDVAC		DEC	-45

# THE FOLLOWING ROUTINE PROCESSES ADDRESSES OF SUFFIX CLASS 10.  THEY ARE BASICALLY WORK AREA ADDRESSES
# IN THE RANGE 0-52, ERASABLE ECADR CONSTANTS FROM 100-3777, AND FCADRS ABOVE THAT.  ALL 15 BITS ARE AVAILABLE
# IN CONTRAST TO SUFFIX 1, IN WHICH ONLY THE LOW ORDER 14 ARE AVAILABLE.

15BITADR	INCR	LOC		# (ENTRY HERE FROM STCALL).
		INDEX	LOC		# PICK UP ADDRESS WORD.
		CA	0
		TS	POLISH		# WE MAY NEED A SUBADDRESS LATER.
		
		CAF	LOW7+2K		# THESE INSTRUCTIONS ARE IN BANK 1.
		TS	FBANK
		MASK	CYR
ITR7		INDEX	A
		TCF 	MISCJUMP
		
## Page 1010
# 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 1011
# THE FOLLOWING IS THE JUMP TABLE FOR OP CODES WHICH MAY HAVE INDEXABLE ADDRESSES OR MAY PUSH UP.

INDJUMP		TCF	VLOAD		# 00 - LOAD MPAC WITH A VECTOR.
		TCF	TAD		# 01 - TRIPLE PRECISION ADD TO MPAC.
		TCF	SIGN		# 02 - COMPLEMENT MPAC (V OR SC) IF X NEG.
		TCF	VXSC		# 03 - VECTOR TIMES SCALAR.
		TCF	CGOTO		# 04 - COMPUTED GO TO.
		TCF	TLOAD		# 05 - LOAD MPAC WITH TRIPLE PRECISION.
		TCF	DLOAD		# 06 - LOAD MPAC WITH A DP SCALAR.
		TCF	V/SC		# 07 - VECTOR DIVIDED BY SCALAR.
		
		TCF	SLOAD		# 10 - LOAD MPACIN SINGLE PRECISION.
		TCF	SSP		# 11 - SET SINGLE PRECISION INTO X.
		TCF	PDDL		# 12 - PUSH DOWN MPAC AND RE-LOAD IN DP.
		TCF	MXV		# 13 - MATRIX POST-MULTIPLIED BY VECTOR.
		TCF	PDVL		# 14 - PUSH DOWN AND VECTOR LOAD.
		TCF	CCALL		# 15 - COMPUTED CALL.
		TCF	VXM		# 16 - MATRIX PRE-MULTIPLIED BY VECTOR.
		TCF	TSLC		# 17 - NORMALIZE MPAC (SCALAR ONLY).
		
		TCF	DMPR		# 20 - DP MULTIPLY AND ROUND.
		TCF	DDV		# 21 - DP DIVIDE BY.
		TCF	BDDV		# 22 - DP DIVIDE INTO.
		TCF	GSHIFT		# 23 - GENERAL SHIFT INSTRUCTION.
		TCF	VAD		# 24 - VECTOR ADD.
		TCF	VSU		# 25 - VECTOR SUBTRACT.
		TCF	BVSU		# 26 - VECTOR SUBTRACT FROM.
		TCF	DOT		# 27 - VECTOR DOT PRODUCT.
		
		TCF	VXV		# 30 - VECTOR CROSS PRODUCT.
		TCF	VPROJ		# 31 - VECTOR PROJECTION.
		TCF	DSU		# 32 - DP SUBTRACT.
		TCF	BDSU		# 33 - DP SUBTRACT FROM.
		TCF	DAD		# 34 - DP ADD.
		TCF			# 35 - AVAILABLE
		TCF	DMP1		# 36 - DP MULTIPLY.
		TCF	SETPD		# 37 - SET PUSH DOWN POINTER (DIRECT ONLY)
		
# CODES 10 AND 14 MUST NOT PUSH UP. CODE 04 MAY BE USED FOR VECTOR DECLARE BEFORE PUSHUP IF DESIRED.

## Page 1012
# THE FOLLOWING JUMP TABLE APPLIES TO INDEX, BRANCH, AND MISCELLANEOUS INSTRUCTIONS.

MISCJUMP	TCF	AXT		# 00 - ADDRESS TO INDEX TRUE.
		TCF	AXC		# 01 - ADDRESS TO INDEX COMPLEMENTED.
		TCF	LXA		# 02 - LOAD INDEX FROM ERASABLE.
		TCF	LXC		# 03 - LOAD INDEX FROM COMPLEMENT OF ERAS.
		TCF	SXA		# 04 - STORE INDEX IN ERASABLE.
		TCF	XCHX		# 05 - EXCHANGE INDEX WITH ERASABLE.
		TCF	INCR		# 06 - INCREMENT INDEX REGISTER.
		TCF	TIX		# 07 - TRANSFER ON INDEX.
		
		TCF	XAD		# 10 - INDEX REGISTER ADD FROM ERASABLE.
		TCF	XSU		# 11 - INDEX SUBTRACT FROM ERASABLE.
		TCF	BZE/GOTO	# 12 - BRANCH ZERO AND GOTO.
		TCF	BPL/BMN		# 13 - BRANCH PLUS AND BRANCH MINUS.
		TCF	RTB/BHIZ	# 14 - RETURN TO BASIC AND BRANCH HI ZERO.
		TCF	CALL/ITA	# 15 - CALL AND STORE QPRET.
		TCF	SW/		# 16 - SWITCH INSTRUCTIONS AND AVAILABLE.
		TCF	BOV(B)		# 17 - BRANCH ON OVERFLOW TO BASIC OR INT.

## Page 1013
# THE FOLLOWING JUMP TABLE 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 1014
# SECTION 2	LOAD AND STORE PACKAGE.
#
# A SET OF EIGHT STORE CODES IS PROVIDED AS THE PRIMARY METHOD OF STORING THE MULTI-PURPOSE
# ACCUMULATOR (MPAC).  IF IN THE DANZIG SECTION LOC REFERS TO AN ALGEBRAICALLY POSITIVE WORD, IT IS TAKEN AS A 
# STORE CODE WITH A CORRESPONDING ERASABLE ADDRESS.  MOST OF THESE CODES ARE TWO ADDRESS, SPECIFYING THAT THE WORD
# FOLLOWING THE STORE CODE IS TO BE USED AS AN ADDRESS FROM WHICH TO RE-LOAD MPAC.  FOUR OPTIONS ARE AVAILABLE:
#
#	1. STORE	STORE MPAC.  THE E ADDRESS MAY BE INDEXED.
#	2. STODL	STORE MPAC AND RE-LOAD IT IN DP WITH THE NEXT ADDRESS (THE LOAD MAY BE INDEXED).
#	3. STOVL	STORE MPAC AND RE-LOAD A VECTOR (AS ABOVE).
#	4. STCALL	STORE AND DO A CALL (BOTH 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 1015
# STORE CODE JUMP TABLE.  CALLS THE APPROPRIATE STORING ROUTINE AND EXITS TO DANZIG OR TO ADDRESS WITH
# A SUPPLIED OPERATION CODE.
#
# STORE STORE,1 AND STORE,2 RETURN TO DANZIG, THUS RESETTING THE EBANK TO ITS STATE AT INTPRET.

STORJUMP	TC	STORE		# STORE.
		TCF	DANZIG		# PICK UP NEW OP CODE(S).
		TC	STORE,1
		TCF	DANZIG
		TC	STORE,2
		TCF	DANZIG
		
		TC	STORE		# STODL.
		TCF	DODLOAD
		
		TC	STORE		# STODL WITH INDEXED LOAD ADDRESS.
		TCF	DODLOAD*
		
		TC	STORE		# STOVL.
		TCF	DOVLOAD
		
		TC	STORE		# STOVL WITH INDEXED LOAD ADDRESS.
		TCF	DOVLOAD*
		TC	STORE		# STOTC.
		CAF	CALLCODE
		TS	CYR
		TCF	15BITADR	# GET A 15 BIT ADDRESS.
		
## Page 1016
# STORE CODE ADDRESS PROCESSOR.

STORE,1		INDEX	FIXLOC
		CS	X1
		TCF	PRESTORE
		
STORE,2		INDEX	FIXLOC
		CS	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 1017
# STORING ROUTINES.  STORE DP, TP, OR VECTOR AS INDICATED BY MODE.

STARTSTO	EXTEND			# MPAC,+1 MUST BE STORED IN ANY EVENT.
# ITRACE (5) REFERS TO "STARTSTO".
		DCA	MPAC
		INDEX	ADDRWD
		DXCH	0
		
		CCS	MODE
		TCF	TSTORE
		TC	Q
		
VSTORE		EXTEND
		DCA	MPAC	 +3
		INDEX 	ADDRWD
		DXCH	2
		
		EXTEND
		DCA	MPAC	 +5
		INDEX	ADDRWD
		DXCH	4
		TC	Q
		
TSTORE		CA	MPAC 	+2
		INDEX	ADDRWD
		TS	2
		TC	Q
		
## Page 1018
# ROUTINES TO BEGIN PROCESSING OF THE SECOND 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 1019
# THE FOLLOWING LOAD INSTRUCTIONS ARE PROVIDED FOR LOADING THE MULTI-PURPOSE ACCUMULATOR MPAC.

TLOAD		INDEX 	ADDRWD
		CA	2		# LOAD A TRIPLE PRECISION ARGUMENT INTO
		TS	MPAC 	+2	# THE FIRST THREE MPAC REGISTERS, WITH THE
		EXTEND			# CONTENTS OF THE OTHER FOUR IRRELEVANT.
		INDEX	ADDRWD
		DCA	0
		DXCH	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 1020
# THE FOLLOWING INSTRUCTIONS ARE PROVIDED FOR STORING OPERANDS IN THE PUSHDOWN LIST:
#	1.	PUSH		PUSHDOWN AND NO LOAD.
#	2.	PDDL		PUSHDOWN AND DOUBLE PRECISION LOAD.
#	3.	PDVL		PUSHDOWN AND VECTOR LOAD.

PDDL		EXTEND
		INDEX	ADDRWD		# LOAD MPAC,+1, PUSHING THE FORMER
		DCA	0		# CONTENTS DOWN.
		DXCH	MPAC
		INDEX	PUSHLOC
		DXCH	0

		INDEX	MODE		# ADVANCE THE PUSHDOWN POINTER APPRO-
		CAF	NO.WDS		# PRIATELY.
		ADS	PUSHLOC

		CCS	MODE
		TCF	ENDTPUSH
		TCF	ENDDPUSH

		TS	MODE		# NOW DP.
ENDVPUSH	TS	MPAC 	+2
		DXCH	MPAC 	+3	# PUSH DOWN THE REST OF THE VECTOR HERE.
		INDEX	PUSHLOC
		DXCH	0 	-4

		DXCH	MPAC 	+5
		INDEX	PUSHLOC
		DXCH	0 	-2

		TCF	DANZIG

ENDDPUSH	TS	MPAC	+2	# SET MPAC +2 TO ZERO AND EXIT ON DP.
		TCF	DANZIG

ENDTPUSH	TS	MODE
		XCH	MPAC 	+2	# ON TRIPLE, SET MPAC +2 TO ZERO, PUSHING
 +2		INDEX	PUSHLOC		# DOWN THE OLD CONTENTS
		TS	0 	-1
		TCF	DANZIG

## Page 1021
# PDVL - PUSHDOWN AND VECTOR LOAD.

PDVL		EXTEND			# RELOAD MPAC AND PUSH DOWN ITS CONTENTS.
		INDEX	ADDRWD
		DCA	0
		DXCH	MPAC
		INDEX	PUSHLOC
		DXCH	0
		
		INDEX	MODE		# ADVANCE THE PUSHDOWN POINTER.
		CAF	NO.WDS
		ADS	PUSHLOC

		CCS	MODE		# TEST PAST MODE.
		TCF	TPDVL
		TCF	ENDVLOAD	# JUST LOAD LAST FOUR REGISTERS ON DP.

VPDVL		EXTEND			# PUSHDOWN AND RE-LOAD LAST TWO COMPONENTS
		INDEX	ADDRWD
		DCA	2
		DXCH	MPAC 	+3
		INDEX	PUSHLOC
		DXCH	0 	-4
		
		EXTEND
		INDEX 	ADDRWD
		DCA	4
		DXCH	MPAC 	+5
		INDEX	PUSHLOC
		DXCH	0 	-2
		
		TCF	DANZIG
		
TPDVL		EXTEND			# ON TP, WE MUST LOAD THE Y COMPONENT
		INDEX	ADDRWD		# BEFORE STORING MPAC +2 IN CASE THIS IS A
		DCA	2		# PUSHUP.
		DXCH	MPAC	+3
		
		CA	MPAC 	+2
		INDEX	PUSHLOC		# IN DP.
		TS	0 	-1
		TCF	ENDVLOAD +4
		
# SSP (STORE SINGLE PRECISION) IS EXECUTED HERE.

SSP		INCR	LOC		# PICK UP THE WORD FOLLOWING THE GIVEN
		INDEX	LOC		# ADDRESS AND STORE IT AT X.
		CA	0
STORE1		INDEX	ADDRWD		# SOME INDEX AND MISCELLANEOUS OPS END
		TS	0		# HERE.
## Page 1022
		TCF	DANZIG
		
## Page 1023
# SEQUENCE CHANGING AND SUBROUTINE CALLING OPTIONS.
#
# THE FOLLOWING OPERATIONS ARE AVAILABLE FOR SEQUENCING CHANGING, BRANCHING, AND CALLING SUBROUTINES:
#	1.	GOTO		GO TO.
#	2.	CALL		CALL SUBROUTINE SETTING QPRET.
#	3.	CGOTO		COMPUTED GO TO.
#	4.	CCALL		COMPUTED CALL.
#	7.	BPL		BRANCH IF MPAC POSITIVE OR ZERO.
#	8.	BZE		BRANCH IF MPAC ZERO.
#	9.	BMN		BRANCH IF MPAC NEGATIVE NON-ZERO.

CCALL		INCR	LOC		# MAINTAIN LOC FOR QPRET COMPUTATION.
		INDEX	LOC
		CAF	0		# GET BASE ADDRESS OF CADR LIST.
		INDEX	ADDRWD
		AD	0		# ADD INCREMENT.
		TS	FBANK		# SELECT DESIRED CADR.
		MASK	LOW10
		INDEX	A
		CAF	10000
		TS	POLISH

CALL		CA	BANKSET		# FOR ANY OF THE CALL OPTIONS, MAKE UP THE
		MASK	BANKMASK	# ADDRESS OF THE NEXT OP-CODE PAIR/STORE
		AD	BANKMASK	# CODE AND LEAVE IT IN QPRET.  NOTE THAT
		AD	LOC		# BANKMASK = -(2000 - 1).
		INDEX	FIXLOC
		TS	QPRET
		
GOTO		CA	POLISH		# BASIC BRANCHING SEQUENCE.
 +1		MASK 	HIGH4
		EXTEND
		BZF	GOTOERS		# SEE IF ADDRESS POINTS TO FIXED OR ERAS.
 +4		CA	BANKSET		# SET EBANK PART OF BBANK.  NEXT, SET UP
		TS	BBANK		# FBANK.  THE COMBINATION IS PICKED UP &
		CA	POLISH		# PUT INTO BANKSET AT INTPRET +2.
		TS	FBANK
		MASK 	LOW10
		AD	2K
		TS	LOC
		TCF	INTPRET +3
		
		EBANK=	1400		# SO YUL DOESN'T CUSS THE "CA 1400" BELOW.
		
GOTOERS		CA	POLISH		# THE GIVEN ADDRESS IS IN ERASABLE - SEE
		AD	-ENDVAC		# IF RELATIVE TO THE WORK AREA.
		CCS	A
		CA	POLISH		# GENERAL ERASABLE.
		TCF	GOTOGE

## Page 1024
		CA	FIXLOC		# WORK AREA.
		AD	POLISH
		INDEX	A		# USE THE GIVEN ADDRESS AS THE ADDRESS OF
		CA	0		# THE BRANCH ADDRESS.
		TS	POLISH
		TCF	GOTO 	+1	# ALLOWS ARBITRARY INDIRECTNESS LEVELS.
		
GOTOGE		TS	EBANK
		MASK	LOW8
		INDEX	A		# USE THE GIVEN ADDRESS AS THE ADDRESS OF
		CA	1400		# THE BRANCH ADDRESS.
		TS	POLISH
		TCF	GOTO 	+1
		
CGOTO		INDEX	LOC		# COMPUTED GO TO.  PICK UP ADDRESS OF CADR
		CA	1		# LIST.
		INDEX	ADDRWD		# ADD MODIFIER.
		AD	0
		TS	FBANK		# SELECT GOTO ADDRESS.
		MASK	LOW10
		INDEX	A
		CA	10000
		TS	POLISH
		TCF	GOTO 	+1	# WITH ADDRESS IN A.
		
SWBRANCH	CA	BANKSET		# SWITCH INSTRUCTIONS WHICH ELECT TO
		TS	FBANK		# BRANCH COME HERE TO DO SO.
		INDEX	LOC
		CA	1
		TS	POLISH
		TCF	GOTO 	+1
		
## Page 1025
# TRIPLE PRECISION BRANCHING ROUTINE.  IF CALLING TC IS AT L, RETURN IS AS FOLLOWS:
#	L+1	IF MPAC IS GREATER THAN ZERO.
#	L+2	IF MPAC IS EQUAL TO +0 OR -0.
#	L+3	IF MPAC IS LESS THAN ZERO.

BRANCH		CCS	MPAC
		TC	Q
		TCF	+2		# ON ZERO.
		TCF	NEG
		
		CCS	MPAC 	+1
		TC	Q
		TCF	+2
		TCF	NEG
		
		CCS	MPAC 	+2
		TC	Q
		TCF	+2
		TCF	NEG
		
Q+1		INDEX	Q
		TC	1
		
NEG		INDEX	Q		# IF FIRST NON-ZERO REGISTER WAS NEGATIVE.
		TC	2
		
Q+2		=	NEG

# ITRACE (3) REFERS TO "EXIT".

EXIT		CA	BANKSET		# RESTORE USER'S BANK SETTING, AND LEAVE
		TS	BBANK		# INTERPRETIVE MODE.
		INDEX	LOC
		TC	1

## Page 1026
# SECTION 3 - ADD/SUBTRACT PACKAGE.

#          THE FOLLOWING OPERATIONS ARE PROVIDED FOR ADDING TO AND SUBTRACTING FROM THE MULTI-PURPOSE ACCUMULATOR
# MPAC:

#	1.	DAD	DOUBLE PRECISION ADD.
#	2.	DSU	DOUBLE PRECISION SUBTRACT.
#	3.	BDSU	DOUBLE PRECISION SUBTRACT FROM.
#	4.	TAD	TRIPLE PRECISION ADD.
#	5.	VAD	VECTOR ADD.
#	6.	VSU	VECTOR SUBTRACT.
#	7.	BVSU	VECTOR SUBTRACT FROM.
# THE INTERPRETIVE OVERFLOW INDICATOR OVFIND IS SET NON-ZERO IF OVERFLOW OCCURS IN ANY OF THE ABOVE.

VSU		CAF	BIT15		# CHANGES 0 TO DCS.
		TCF	+2
		
VAD		CAF	PRIO30		# CHANGES 0 TO DCA.
		ADS	ADDRWD
		EXTEND
		INDEX	ADDRWD
		READ	HISCALAR	# DCA 2 OR DCS 2
		DAS 	MPAC 	+3
		EXTEND			# CHECK OVERFLOW.
		BZF	+2
		TC	OVERFLWY
		
		EXTEND
		INDEX	ADDRWD
		READ	CHAN5		# DCA 4 OR DCS 4
		DAS	MPAC 	+5
		EXTEND
		BZF	+2
		TC	OVERFLWZ
		
		EXTEND
		INDEX	ADDRWD
		READ	LCHAN		# DCA 0 OR DCS 0
		TCF	ENDVXV

DAD		EXTEND
		INDEX 	ADDRWD
		DCA	0
ENDVXV		DAS	MPAC		# VXV FINISHES HERE.
		EXTEND
		BZF	DANZIG
		
## Page 1027
SETOVF		TC	OVERFLOW
		TCF	DANZIG
		
## Page 1028
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 1029
BDSU		EXTEND
		INDEX	ADDRWD
		DCA	0
		DXCH	MPAC
		EXTEND
		DCOM
		TCF	ENDVXV
		
## Page 1030
# TRIPLE PRECISION ADD ROUTINE.

TAD		EXTEND
		INDEX	ADDRWD
		DCA	1		# ADD MINOR PARTS FIRST.
		DAS	MPAC 	+1
		INDEX	ADDRWD
		AD	0
		AD	MPAC
		TS	MPAC
		TCF	DANZIG
		
		TCF	SETOVF		# SET OVFIND IF SUCH OCCURS.
		
## Page 1031
# ARITHMETIC SUBROUTINES REQUIRED IN FIXED-FIXED.
#	1.  DMPSUB	DOUBLE PRECISION MULTIPLY. MULTIPLY THE CONTENTS OF MPAC,+1 BY THE DP WORD WHOSE ADDRESS
#			IS IN ADDRWD AND LEAVE A TRIPLE PRECISION RESULT IN MPAC.
#	2.  ROUNDSUB	ROUND THE TRIPLE 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 1032
# ROUND MPAC TO DOUBLE PRECISION, SETTING OVFIND ON THE RARE EVENT OF OVERFLOW.

ROUNDSUB	CAF	ZERO		# SET MPAC +2 = 0 FOR SCALARS AND CHANGE
 +1		TS	MODE		# MODE TO DP.

VROUND		XCH	MPAC 	+2	# BUT WE 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 1033
# THE DOT PRODUCT SUBROUTINE USUALLY FORMS THE DOT PRODUCT OF THE VECTOR IN MPAC WITH A STANDARD SIX
# REGISTER VECTOR WHOSE ADDRESS IS IN ADDRWD.  IN THIS CASE C(DOTINC) ARE SET TO 2.   VXM, HOWEVER, SETS C(DOTINC) TO
# 6 SO THAT DOTSUB DOTS MPAC WITH A COLUMN VECTOR OF THE MATRIX IN QUESTION IN THIS CASE.

PREDOT		CAF	TWO		# PROLOGUE TO SET DOTINC TO 2.
		TS	DOTINC

DOTSUB		EXTEND
		QXCH	DOTRET		# SAVE RETURN.
		TC	DMPSUB		# DOT X COMPONENTS.
		DXCH	MPAC 	+3	# POSITION Y COMPONENT OF MPAC FOR
		DXCH	MPAC		# MULTIPLICATION WHILE SAVING RESULT IN
		DXCH	BUF		# THREE WORD BUFFER, BUF.
		CA	MPAC 	+2
		TS	BUF 	+2

		CA	DOTINC		# ADVANCE ADDRWD TO Y COMPONENT OF
		ADS	ADDRWD		# OTHER ARGUMENT.
		TC	DMPSUB
		DXCH	MPAC 	+1	# ACCUMULATE PARTIAL PRODUCTS.
		DAS	BUF 	+1
		AD	MPAC
		AD	BUF
		TS	BUF
		TCF	+2
		TS	OVFIND		# IF OVERFLOW OCCURS.
		
		DXCH	MPAC 	+5	# MULTIPLY Z COMPONENTS.
		DXCH	MPAC
		CA	DOTINC
		ADS	ADDRWD
		TC	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 1034
# DOUBLE PRECISION POLYNOMIAL EVALUATOR
#	                          N        N-1
#	THIS ROUTINE EVALUATES A X  + A   X    + ... + A  X + A  LEAVING THE DP RESULT IN MPAC ON EXIT.
#	                        N      N-1              1      0
#
# THE ROUTINE HAS TWO ENTRIES
#
#	1.	ENTRY THRU POWRSERS.  THE COEFFICIENTS MAY BE EITHER IN FIXED OR ERASABLE, THE CALL IS BY
#		TC POWRSERS, AND THE RETURN IS TO LOC(TC POWRSERS)+1.  THE ENTERING DATA MUST BE AS FOLLOWS
#
#			A		SP	LOC-3		ADDRESS FOR REFERENCING COEF TABLE
#			L		SP	N-1		N IS THE DEGREE OF THE POWER SERIES
#			MPAC		DP	X		ARGUMENT
#			LOC-2N		DP	A(0)
#					...
#			LOC		DP	A(N)
#
#	2.	ENTRY THRU POLY.  THE CALL TO POLY AND THE ENTERING DATA MUST BE AS FOLLOWS
#
#			MPAC		DP	X		ARGUMENT
#			LOC		TC	POLY
#			LOC+1		SP	N-1
#			LOC+2		DP	A(0)
#					...
#			LOC+2N+2	DP	A(N)		RETURN IS TO LOC+2N+4

POWRSERS	EXTEND
		QXCH	POLYRET		# RETURN ADDRESS
		TS	POLISH		# POWER SERIES ADDRESS
		LXCH	POLYCNT		# N-1 TO COUNTER
		TCF	POLYCOM		# SKIP SET UP BY POLY

POLY		INDEX	Q
		CAF	0
		TS	POLYCNT		# N-1 TO COUNTER
		DOUBLE
		AD	Q
		TS	POLISH		# L(A(N))-3 TO POLISH
		AD	FIVE
		TS	POLYRET		# STORE RETURN ADDRESS

POLYCOM		CAF	LVBUF		# INCOMING X WILL BE MOVED TO VBUF, SO
		TS	ADDRWD		# SET ADDRWD SO DMPSUB WILL MPY BY VBUF.
		
		EXTEND
		INDEX	POLISH
		DCA	3
		
## Page 1035
		DXCH	MPAC		# LOAD A(N) INTO MPAC,
		DXCH	VBUF		# SAVING X IN VBUF
		TCF	POLY2
		
POLYLOOP	TS	POLYCNT		# SAVE 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 1036
# MISCELLANEOUS MULTI-PRECISION ROUTINES REQUIRED IN FIXED-FIXED BUT NOT USED BY THE INTERPRETER.

DPAGREE		CAF	ZERO		# DOUBLE PRECISION ENTRY -
		TS	MPAC 	+2	# ZERO LOW-ORDER WORD

TPAGREE		LXCH	Q		# FORCE SIGN AGREEMENT AMONG THE TRIPLE
		TC	BRANCH		# PRECISION CONTENTS OF MPAC.  RETURNING
		TCF	ARG+		# WITH SIGNUM OF THE INPUT IN A.
		TCF	ARGZERO

		CS	POSMAX		# IF NEGATIVE.
		TCF		+2

ARG+		CAF	POSMAX
		TS	Q
		EXTEND
		AUG	A		# FORMS +-1.0.
		AD	MPAC 	+2
		TS	MPAC 	+2
		CAF	ZERO
		AD	Q
		AD	MPAC 	+1
		TS	MPAC 	+1
		CAF	ZERO
		AD	Q		# Q STILL HAS POSMAX OR NEGMAX IN IT.
		AD	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 1037
# DMPNSUB MULTIPLIES THE DP FRACTION ARRIVING IN MPAC BY THE SP
# INTEGER ARRIVING IN A.  THE DP PRODUCT DEPARTS BOTH IN MPAC AND IN
# A AND L.  NOTE THAT DMPNSUB NORMALLY INCREASES THE MAGNITUDE OF THE
# CONTENTS OF MPAC.  THE CUSTOMER MUST INSURE THAT B(A) X B(MPAC,MPAC+1)
# AND B(A) X B(MPAC) ARE LESS THAN 1 IN MAGNITUDE, WHERE B, AS IS OBVIOUS,
# INDICATES THE ARRIVING CONTENTS.

DMPNSUB		TS	DMPNTEMP
		EXTEND
		MP	MPAC 	+1
		DXCH	MPAC		# LOW PRODUCT TO MPAC, HIGH FACTOR TO A
		EXTEND
		MP	DMPNTEMP
		CA	L
		ADS	MPAC		# COMPLETING THE PRODUCT IN MPAC
		EXTEND
		DCA	MPAC		# BRINGING THE PRODUCT INTO A AND L
		TC	Q

## Page 1038
# MISCELLANEOUS VECTOR OPERATIONS.  INCLUDED HERE ARE THE FOLLOWING:
#	1.	DOT	DP VECTOR DOT PRODUCT.
#	2.	VXV	DP VECTOR CROSS PRODUCT.
#	3.	VXSC	DP VECTOR TIMES SCALAR.
#	4.	V/SC	DP VECTOR DIVIDED BY SCALAR.
#	5.	VPROJ	DP VECTOR PROJECTION.  ( (MPAC.X)MPAC ).
#	6.	VXM	DP VECTOR POST-MULTIPLIED BY MATRIX.
#	7.	MXV	DP VECTOR PRE-MULTIPLIED BY MATRIX.

DOT		TC	PREDOT		# DO THE DOT PRODUCT AND EXIT, 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 1039
# COMMON PORTION OF MXV AND VXM.

VXM/MXV		TS	DOTINC
# ITRACE (2) REFERS TO "VXM/MXV".
		TC	MPACVBUF	# SAVE VECTOR IN MPAC FOR FURTHER USE.

		TC	DOTSUB		# GO DOT TO GET X COMPONENT OF ANSWER.
		EXTEND
		DCA	VBUF		# MOVE MPAC VECTOR BACK INTO MPAC, SAVING
		DXCH	MPAC		# NEW X COMPONENT IN BUF2.
		DXCH	BUF2
		EXTEND
		DCA	VBUF 	+2
		DXCH	MPAC 	+3
		EXTEND
		DCA	VBUF 	+4
		DXCH	MPAC 	+5
		CA	MATINC		# INITIALIZE ADDRWD FOR NEXT DOT PRODUCT.
		ADS	ADDRWD		# FORMS 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 1040
# VXSC - VECTOR TIMES SCALAR.

VXSC		CCS	MODE		# TEST PRESENT MODE.
		TCF	DVXSC		# SEPARATE ROUTINE WHEN SCALAR IS IN MPAC.
		TCF	DVXSC

VVXSC		TC	DMPSUB		# COMPUTE X COMPONENT
		TC	VROUND		# AND ROUND IT.
		DXCH	MPAC 	+3	# PUT Y COMPONENT INTO MPAC SAVING MPAC IN
		DXCH	MPAC		# MPAC +3.
		DXCH	MPAC 	+3

		TC	DMPSUB		# DO SAME FOR Y AND Z COMPONENTS.
		TC	VROUND
		DXCH	MPAC 	+5
		DXCH	MPAC
		DXCH	MPAC	+5

		TC	DMPSUB
		TC	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 1041
# DP VECTOR PROJECTION ROUTINE.

VPROJ		TC	PREDOT		# (MPAC.X)MPAC IS COMPUTED AND LEFT IN
		CS	FOUR		# MPAC.  DO DOT AND FALL INTO DVXSC.
		ADS	ADDRWD

# VXSC WHEN SCALAR ARRIVES IN MPAC AND VECTOR IS AT X.

DVXSC		EXTEND			# SAVE SCALAR IN MPAC +3 AND GET X
		DCA	MPAC		# COMPONENT OF ANSWER.
		DXCH	MPAC 	+3
		TC	DMPSUB
		TC	VROUND

		CAF	TWO		# ADVANCE ADDRWD TO Y COMPONENT OF X.
		ADS	ADDRWD
		EXTEND
		DCA	MPAC 	+3	# PUT SCALAR BACK INTO MPAC AND SAVE
		DXCH	MPAC		# X RESULT IN MPAC +5.
		DXCH	MPAC 	+5
		TC	DMPSUB
		TC	VROUND

		CAF	TWO
		ADS	ADDRWD		# TO Z COMPONENT.
		DXCH	MPAC 	+3	# BRING SCALAR BACK, PUTTING Y RESULT IN
		DXCH	MPAC		# THE PROPER PLACE.
		DXCH	MPAC 	+3
		TC	DMPSUB
		TC	VROUND

		DXCH	MPAC		# PUT Z COMPONENT IN PROPER PLACE, ALSO
		DXCH	MPAC 	+5	# POSITIONING X.
		DXCH	MPAC

		TCF	VMODE		# MODE HAS CHANGED TO VECTOR.

## Page 1042
#          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 1043
		TC OVERFLWY

		TC	DMPSUB
		DXCH	VBUF 	+4	# GO ADD -X2M3 TO X3M2 TO COMPLETE THE X
		TCF	ENDVXV		# COMPONENT (TAIL END OF DAD).

# THE MPACVBUF SUBROUTINE SAVES THE VECTOR IN MPAC IN VBUF WITHOUT CLOBBERING MPAC.

MPACVBUF	EXTEND			# CALLED BY MXV, VXM, AND UNIT.
		DCA	MPAC
		DXCH	VBUF
		EXTEND
		DCA	MPAC 	+3
		DXCH	VBUF 	+2
		EXTEND
		DCA	MPAC 	+5
		DXCH	VBUF 	+4
		TC	Q		# RETURN TO CALLER.

# DOUBLE PRECISION SIGN AGREE ROUTINE.  ARRIVE WITH INPUT IN A+L.  OUTPUT IS IN A + L.

ALSIGNAG	CCS	A		# TEST UPPER PART.
		TCF	UPPOS		# IT IS POSITIVE
		TC	Q		# ZERO
		TCF	UPNEG		# NEGATIVE
		TC	Q		# ZERO

UPPOS		XCH	L		# SAVE DECREMENTED UPPER PART.
		AD	HALF
		AD	HALF
		TS	A		# SKIPS ON OVERFLOW
		TCF	+2
		INCR	L		# RESTORE UPPER TO 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 1044
# 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 1045
# THE FOLLOWING IS THE PROLOGUE TO V/SC.  IF THE PRESENT MODE IS VECTOR, IT SAVES THE SCALAR AT X IN BUF
# AND CALLS THE V/SC ROUTINE IN BANK 0.  IF THE PRESENT MODE IS SCALAR, IT MOVES THE VECTOR AT X INTO MPAC, SAVING
# THE SCALAR IN MPAC IN BUF BEFORE CALLING THE V/SC ROUTINE IN BANK 0.

V/SC		CCS	MODE
		TCF	DV/SC		# MOVE VECTOR INTO MPAC.
		TCF	DV/SC

VV/SC		EXTEND
		INDEX	ADDRWD
		DCA	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 1046
# SIGN AND COMPLEMENT INSTRUCTIONS.

SIGN		INDEX 	ADDRWD		# CALL COMP INSTRUCTION IF WORD AT X IS
		CCS	0		# NEGATIVE NON-ZERO.
		TCF	DANZIG
		TCF	+2
		TCF	COMP		# DO THE COMPLEMENT.

		INDEX	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 1047
# THE FOLLOWING SHORT SHIFT CODES REQUIRE NO ADDRESS WORD:
#	1.	SR1 TO SR4	SCALAR SHIFT RIGHT.
#	2.	SR1R TO SR4R	SCALAR SHIFT RIGHT AND ROUND.
#	3.	SL1 TO SL4	SCALAR SHIFT LEFT.
#	4.	SL1R TO SL4R	SCALAR SHIFT LEFT AND ROUND.
#	5.	VSR1 TO VSR8	VECTOR SHIFT RIGHT (ALWAYS ROUNDS).
#	6.	VSL1 TO VSL8	VECTOR SHIFT LEFT (NEVER ROUNDS).
# THE FOLLOWING CODES REQUIRE 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 1048
		DXCH	MPAC		# MPAC,+1.
		CA	MPTEMP
		EXTEND
		MP	L		# ORIGINAL C(MPAC +1).
		DAS	MPAC 	+1	# GUARANTEED NO OVERFLOW.
		TCF	DANZIG

# MPAC SHIFT RIGHT AND ROUND SUBROUTINES.

MPACSRND	CA	MPAC 	+2	# WE HAVE TO DO ALL THREE MULTIPLIES SINCE
		EXTEND			# MPAC +1 AND MPAC +2 MIGHT HAVE SIGN
		MP	MPTEMP		# DISAGREEMENT WITH A SHIFT RIGHT OF 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 1049
# ROUTINE FOR SHORT SCALAR SHIFT LEFT (AND MAYBE ROUND).

TSSL		CA	SR		# GET SHIFT COUNT FOR SR.
 +1		TS	MPTEMP

 +2		EXTEND			# ENTRY HERE FROM SL FOR SCALARS.
		DCA	MPAC 	+1	# SHIFTING LEFT ONE PLACE AT A TIME IS
		DAS	MPAC 	+1	# FASTER THAN DOING THE WHOLE SHIFT WITH
		AD	MPAC		# MULTIPLIES ASSUMING THAT FREQUENCY OF
		AD	MPAC		# SHIFT COUNTS GOES DOWN RAPIDLY AS A
		TS	MPAC		# FUNCTION OF THEIR MAGNITUDE.
		TCF 	+2
		TS	OVFIND		# OVERFLOW.  (LEAVES OVERFLOW-CORRECTED
					# RESULT ANYWAY).
		CCS	MPTEMP		# LOOP ON DECREMENTED SHIFT COUNT.
		TCF	TSSL 	+1

		CCS	CYR		# SEE IF ROUND WANTED.
ROUND		TC	ROUNDSUB	# YES - ROUND AND EXIT.
		TCF	DANZIG		# SL LEAVES A ZERO IN CYR FOR NO ROUND.
		TCF	DANZIG		# NO - EXIT IMMEDIATL

## Page 1050
# VECTOR SHIFTING ROUTINES.

SHORTV		CAF	LOW3		# SAVE 3 BIT SHIFT COUNT - 1 WITHOUT
		MASK	CYR		# EDITING CYR.
		TS	MPTEMP
		CCS	CYR		# SEE IF LEFT OR RIGHT SHIFT.
		TCF	VSSL		# VECTOR SHIFT LEFT.
OCT176		OCT	176		# USED IN PROCESSED SHIFTS WITH - COUNT.

VSSR		INDEX	MPTEMP		# (ENTRY FROM SR).  PICK UP SHIFTING BIT.
		CAF	BIT14		# MPTEMP CONTAINS THE SHIFT COUNT - 1.
		TS	MPTEMP
		TC	VSHRRND		# SHIFT X COMPONENT.

		DXCH	MPAC		# SWAP X AND Y COMPONENTS.
		DXCH	MPAC 	+3
		DXCH	MPAC
		TC	VSHRRND		# SHIFT Y COMPONENT.

		DXCH	MPAC		# SWAP Y AND Z COMPONENTS.
		DXCH	MPAC 	+5
		DXCH	MPAC
		TC	VSHRRND		# SHIFT Z COMPONENT.

		TCF	VROTATEX	# RESTORE COMPONENTS TO PROPER PLACES.

## Page 1051
# VECTOR SHIFT LEFT - DONE ONE PLACE AT A TIME.

 -1		TS	MPTEMP		# SHIFTING LOOP.

VSSL		EXTEND
		DCA	MPAC
		DAS	MPAC
		EXTEND
		BZF	+2
		TC	OVERFLOW

		EXTEND
		DCA	MPAC 	+3
		DAS	MPAC 	+3
		EXTEND
		BZF	+2
		TC	OVERFLWY

		EXTEND
		DCA	MPAC 	+5
		DAS	MPAC 	+5
		EXTEND
		BZF	+2
		TC	OVERFLWZ

		CCS	MPTEMP		# LOOP ON DECREMENTED SHIFT COUNTER.
		TCF	VSSL 	-1
		TCF	DANZIG		# EXIT.

## Page 1052
# TSLC - TRIPLE SHIFT LEFT AND COUNT.  SHIFTS MPAC LEFT UNTIL GREATER THAN .5 IN MAGNITUDE, LEAVING
# THE COMPLEMENT OF THE NUMBER OF SHIFTS REQUIRED IN X.

TSLC2		TS	MPTEMP		# START BY ZEROING SHIFT COUNT (IN A NOW).
		TC	BRANCH		# EXIT WITH NO SHIFTING IF ARGUMENT ZERO.
		TCF	+2
		TCF	ENDTSLC		# STORES ZERO SHIFT COUNT IN THIS CASE.

		TC	TPAGREE		# MAY CAUSE UPSHIFT OF ONE EXTRA PLACE.

		CA	MPAC		# BEGIN NORMALIZATION LOOP.
		TCF	TSLCTEST

TSLCLOOP	INCR	MPTEMP		# INCREMENT SHIFT COUNTER.
		EXTEND
		DCA	MPAC 	+1
		DAS	MPAC 	+1
		AD	MPAC
		ADS	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 1053
# 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 1054
# 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 1055
# PROCESS SR AND SRR FOR SCALARS.

GENSCR		CA	MPTEMP		# SEE IF THE ORIGINAL SHIFT COUNT WAS LESS
 +1		AD	NEG12		# THAN 14D.
		EXTEND
		BZMF	DOSSHFT		# DO THE SHIFT IMMEDIATELY IF SO.

 +4		AD	NEGONE		# IF NOT, DECREMENT SHIFT COUNT BY 14D AND
		TS	MPTEMP		# SHIFT MPAC RIGHT 14 PLACES.
		CAF	ZERO
		XCH	MPAC
		XCH	MPAC 	+1
		TS	MPAC 	+2
		CCS	MPTEMP		# SEE IF FINISHED, DO FINAL DECREMENT.
		TS	MPTEMP
		TC	GENSCR	+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 1056
# PROCESS THE RIGHT- (SL(R) WITH A NEGATIVE COUNT), LEFT-, AND LEFT OPTIONS.

RIGHT-		CS	MPTEMP		# GET ABSOLUTE VALUE - 1 OF SHIFT COUNT
		AD	OCT176		# UNDERSTANDING THAT BIT8 (PSEUDO-SIGN)
		TS	MPTEMP		# WAS 1 INITIALLY.
		TCF	RIGHT		# DO NORMAL SHIFT RIGHT.

LEFT-		CS	OCT176		# SAME PROLOGUE TO LEFT FOR INDEXED RIGHT
		AD	MPTEMP		# 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 1057
# 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 1058
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 1059
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 1060
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 1061
# THE FOLLOWING ARE PROLOGUES TO SHIFT THE DIVIDEND ARRIVING IN A AND L BEFORE THE DIVIDE.

 -21D		LXCH	SR		# SPECIAL PROLOGUE FOR UNIT WHEN THE
		EXTEND			# LENGTH OF THE ARGUMENT WAS NOT LESS THAN
		MP	HALF		# .5.  IN THIS CASE, EACH COMPONENT MUST BE
		XCH	L		# SHIFTED RIGHT ONE TO PRODUCE A HALF-UNIT
		AD	SR		# VECTOR.
		XCH	L
		TCF	GENDDV 	+1	# WITH DP DIVIDEND IN A,L.

		DDOUBL			# PROLOGUE WHICH NORMALIZES THE DIVIDEND
		DDOUBL			# WHEN IT IS KNOWN THAT NO DIVISION
		DDOUBL			# 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 1062
# THE FOLLOWING IS A GENERAL PURPOSE DOUBLE PRECISION DIVISION ROUTINE.  IT DIVIDES MPAC BY BUF AND LEAVES
# THE RESULT IN MPAC.  THE FOLLOWING CONDITIONS MUST BE SATISFIED:
#
#	1.	THE DIVISOR (BUF) MUST BE POSITIVE AND NOT LESS THAN .5.
#
#	2.	THE DIVIDEND (MPAC) MUST BE POSITIVE WITH THE MAJOR PART OF MPAC STRICTLY LESS THAN THAT OF BUF
#		(A SPECIAL APPROXIMATION, MAXDV, IS USED WHEN THE MAJOR PARTS ARE EQUAL).
#
# UNDERSTANDING THAT A/B = Q + S(R/B) WHERE S = 2(-14) AND Q AND R ARE QUOTIENT AND REMAINDER, RESPEC-
# TIVELY, THE FOLLOWING APPROXIMATION IS OBTAINED BY MULTIPLYING ABOVE AND BELOW BY C - SD AND NEGLECTING TERMS OF
# ORDER S-SQUARED (POSSIBLY INTRODUCING ERROR INTO THE LOW TWO BITS OF THE RESULT).  SIGN AGREEMENT IS UNNECESSARY.
#
#	A + SB .      (R - QD)                                             A + SB
#	------ = Q + S(------) WHERE Q AND R ARE QUOTIENT AND REMAINDER OF ------ RESPECTIVELY.
#	C + SD        (  C   )                                                C

GENDDV		DXCH	MPAC		# WE NEED A AND B ONLY FOR FIRST DV.
 +1		EXTEND			# (SPECIAL UNIT PROLOGUE ENTERS HERE).
		DV	BUF		# A NOW CONTAINS Q AND L, R.
		DXCH	MPAC

		CS	MPAC		# FORM DIVIDEND FOR MINOR PART OF RESULT.
		EXTEND
		MP	BUF 	+1
		AD	MPAC 	+1	# OVERFLOW AT THIS POINT IS POSITIVE SINCE
		OVSK			# R IS POSITIVE IN EVERY CASE.
		TCF	+5

		EXTEND			# OVERFLOW CAN BE REMOVED BY SUBTRACTING C
		SU	BUF		# (BUF) ONCE SINCE R IS ALWAYS LESS THAN C
		INCR	MPAC		# IN THIS CASE.  INCR COMPENSATES SUBTRACT.
		TCF	+DOWN		# (SINCE C(A) IS STILL POSITIVE).

 +5		EXTEND			# C(A) CAN BE MADE LESS THAN C IN MAGNI-
		BZMF	-UP		# TUDE BY DIMINISHING IT BY C (SINCE C IS
					# NOT LESS THAN .5) UNLESS C(A) = 0.

## Page 1063
+DOWN		EXTEND
		SU	BUF		# IF POSITIVE, REDUCE ONLY IF NECESSARY
		EXTEND			# SINCE THE COMPENSATING INCR MIGHT CAUSE
		BZF	+3		# OVERFLOW.
		EXTEND			# 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 1064
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 1065
# IF THE MAJOR PARTS OF THE DIVISOR AND DIVIDEND ARE EQUAL, BUT THE MINOR PARTS ARE SUCH THAT THE
# DIVIDEND IS STRICTLY LESS THAN THE DIVISOR IN MAGNITUDE, THE FOLLOWING APPROXIMATION IS USED.  THE ASSUMPTIONS
# ARE THE SAME AS THE GENERAL ROUTINE WITH THE ADDITION THAT SIGN AGREEMENT IS NECESSARY (B, C, & D POSITIVE).
#
#	C + SB .          (C + B - D)
#	------ = 37777 + S(---------)
#	C + SD            (    C    )
#
# THE DIVISION MAY BE PERFORMED IMMEDIATELY SINCE B IS STRICTLY LESS THAN D AND C IS NOT LESS THAN .5.

MAXDV		CS	MPAC		# SEE IF MAXDV CASE STILL HOLDS AFTER
		AD	BUF		# NORMALIZATION.
		EXTEND
		BZF	+2
		TCF	GENDDV		# MPAC NOW LESS THAN 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 1066
# VECTOR DIVIDED BY SCALAR, V/SC, IS EXECUTED HERE.  THE VECTOR IS NOW IN MPAC WITH SCALAR IN BUF.

V/SC2		CS	ONE		# INITIALIZE DIVIDEND NORMALIZATION COUNT
		TS	DVNORMCT	# AND DIVISION SIGN REGISTER.
		TS	VBUF 	+5

		TC	VECAGREE	# FORCE SIGN AGREEMENT IN VECTOR

		DXCH	BUF
		TC	ALSIGNAG	# SIGN AGREE BUF
		DXCH	BUF
		CCS	BUF		# FORCE DIVISOR POSITIVE WITH MAJOR PART
		TCF	/BUF+		# NON-ZERO (IF POSSIBLE).
		TCF	+2
		TCF	/BUF-

		XCH	BUF	+1	# SHIFT VECTOR AND SCALAR LEFT 14.
		XCH	BUF
		XCH	MPAC  	+1
		XCH	MPAC
		EXTEND			# CHECK FOR OVERFLOW IN EACH CASE.
		BZF	+2
		TCF	DVOVF

		XCH	MPAC  	+4
		XCH	MPAC  	+3
		EXTEND
		BZF	+2
		TCF	DVOVF

		XCH	MPAC  	+6
		XCH	MPAC  	+5
		EXTEND
		BZF	+2
		TCF	DVOVF

		CCS	BUF
		TCF	/BUF+
		TCF	DVOVF		# ZERO DIVISOR - OVERFLOW.
		TCF	/BUF-
		TCF	DVOVF

/BUF-		EXTEND			# ON NEGATIVE, COMPLEMENT BUF AND MAINTAIN
		DCS	BUF		# DVSIGN IN VBUF +5.
		DXCH	BUF
		INCR	VBUF  	+5

## Page 1067
/BUF+		EXTEND
		DCA	BUF		# LEAVE ABS(ORIG DIVISOR) IN BUF2
		DXCH	BUF2		# FOR OVERFLOW TESTING
		TCF	/NORM		# NORMALIZE DIVISOR IN BUF.

/NORM2		EXTEND			# IF LESS THAN .5, AUGMENT DVNORMCT AND
		AUG	DVNORMCT	# DOUBLE DIVISOR.
		EXTEND
		DCA	BUF
		DAS	BUF

/NORM		CA	BUF		# SEE IF DIVISOR NORMALIZED.
		DOUBLE
		OVSK
		TCF	/NORM2		# DOUBLE AND TRY AGAIN IF NOT.

		TC	V/SCDV		# DO X COMPONENT DIVIDE.
		DXCH	MPAC 	+3	# SUPPLY ARGUMENTS IN USUAL SEQUENCE.
		DXCH	MPAC
		DXCH	MPAC 	+3

		TC	V/SCDV		# Y COMPONENT.
		DXCH	MPAC 	+5
		DXCH	MPAC
		DXCH	MPAC 	+5

		TC	V/SCDV		# Z COMPONENT.
		TCF	VROTATEX	# GO RE-ARRANGE COMPONENTS BEFORE EXIT.

## Page 1068
# SUBROUTINE USED BY V/SC TO DIVIDE VECTOR COMPONENT IN MPAC,+1 BY THE SCALAR GIVEN IN BUF.

V/SCDV		CA	VBUF 	+5	# REFLECTS SIGN OF SCALAR.
		TS	DVSIGN

		CCS	MPAC		# FORCE MPAC POSITIVE, EXITING ON ZERO.
		TCF	/MPAC+
		TCF	+2
		TCF	/MPAC-

		CCS	MPAC 	+1
		TCF	/MPAC+
		TC	Q
		TCF	/MPAC-
		TC	Q

/MPAC-		EXTEND			# USUAL COMPLEMENTING AND SETTING OF SIGN.
		DCS	MPAC
		DXCH	MPAC
		INCR	DVSIGN

/MPAC+		CS	ONE		# INITIALIZE NEAR-ONE SWITCH.
		TS	MAXDVSW

		CS	MPAC		# CHECK POSSIBLE OVERFLOW.
		AD	BUF2		# UNNORMALIZED INPUT DIVISOR.
		CCS	A
		TCF	DDVCALL		# NOT NEAR-ONE
		TCF	+2		# +0 IS JUST POSSIBLE
		TCF	DVOVF		# NO HOPE
		TS	MAXDVSW		# SIGNAL POSSIBLE NEAR-ONE CASE
		CS	MPAC 	+1	# SEE IF DIVISION CAN BE DONE
		AD	BUF2 	+1
		EXTEND
		BZMF	DVOVF

DDVCALL		DXCH	MPAC		# CALL PRE-DIVIDE NORMALIZATION.
		INDEX	DVNORMCT
		TCF	MAXTEST

## Page 1069
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 1070
# THE FOLLOWING ROUTINE EXECUTES THE UNIT INSTRUCTION, WHICH TAKES THE UNIT OF THE VECTOR IN MPAC.

UNIT		TC	VECAGREE	# FORCE SIGN AGREEMENT IN VECTOR
		TC	MPACVBUF	# SAVE ARGUMENT IN VBUF
		CAF	ZERO		# MUST SENSE OVERFLOW IN FOLLOWING DOT.
		XCH	OVFIND
		TS	TEM1
		TC	VSQSUB		# DOT MPAC WITH ITSELF.
		CA	TEM1
		XCH	OVFIND
		EXTEND
		BZF	+2
		TCF	DVOVF
		EXTEND
		DCA	MPAC		# LEAVE THE SQUARE OF THE LENGTH OF THE
		INDEX	FIXLOC		# ARGUMENT IN LVSQUARE.
		DXCH	LVSQUARE

		TC	SQRTSUB		# GO TAKE THE NORMALIZED SQUARE ROOT.

		CCS	MPAC		# CHECK FOR UNIT OVERFLOW.
		TCF	+5		# MPAC IS NOT LESS THAN .5 UNLESS
		TS	L
		INDEX	FIXLOC
		DXCH	LV
		TCF	DVOVF		# INPUT TO SQRTSUB WAS 0.

		CS	FOURTEEN	# SEE IF THE INPUT WAS SO SMALL 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 1071
		TCF	LARGE2

## Page 1072
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 1073
# IF THE LENGTH OF THE ARGUMENT VECTOR WAS LESS THAN 2(-28), EACH COMPONENT MUST BE SHIFTED LEFT AT LEAST
# 14 PLACES BEFORE THE DIVIDE. NOTE THAT IN THIS CASE, THE MAJOR PART OF EACH COMPONENT IS ZERO.

SMALL		TS	MPTEMP		# NEGATIVE OF PRE-DIVIDE SHIFT COUNT.

		CAF	ZERO		# SHIFT EACH COMPONENT LEFT 14.
		XCH	VBUF 	+1
		XCH	VBUF
		XCH	VBUF 	+3
		XCH	VBUF 	+2
		XCH	VBUF 	+5
		XCH	VBUF 	+4

		CS	MPTEMP
		INDEX	A
		CAF	BIT14
		EXTEND
		MP	MPAC
		TCF	SMALL2

THIRTEEN	=	OCT15
FOURTEEN	=	OCT16
OCT16		=	R1D1

## Page 1074
# THE FOLLOWING ROUTINE SETS UP THE CALL TO THE DIVIDE ROUTINES.

UNITDV		CCS	MPAC		# FORCE MPAC POSITIVE IF POSSIBLE, SETTING
		TCF	UMPAC+		# DVSIGN ACCORDING TO THE SIGN OF MPAC
		TCF	+2		# SINCE THE DIVISOR IS ALWAYS POSITIVE
		TCF	UMPAC-		# HERE.

		CCS	MPAC 	+1
		TCF	UMPAC+
		TC	Q		# EXIT IMMEDIATELY ON ZERO.
		TCF	UMPAC-
		TC	Q

UMPAC-		CS	ZERO		# IF NEGATIVE, SET -0 IN DVSIGN FOR FINAL
		TS	DVSIGN		# COMPLEMENT.
		EXTEND
		DCS	MPAC		# PICK UP ABSOLUTE VALUE OF ARG AND JUMP.
		INDEX	MPTEMP
		TCF	MAXTEST -1

UMPAC+		TS	DVSIGN		# SET DVSIGN FOR POSITIVE QUOTIENT.
		DXCH	MPAC
		INDEX	MPTEMP
		TCF	MAXTEST -1

## Page 1075
# MISCELLANEOUS UNARY OPERATIONS.

DSQ		TC	DSQSUB		# SQUARE THE DP CONTENTS OF MPAC.
		TCF	DANZIG

ABVALABS	CCS	MODE		# ABVAL OR ABS INSTRUCTION.
		TCF	ABS		# DO ABS ON SCALAR.
		TCF	ABS

ABVAL		TC	VSQSUB		# DOT MPAC WITH ITSELF.
		LXCH	MODE		# MODE IS NOW DP (L ZERO AFTER DAS).

		EXTEND			# STORE SQUARE OF LENGTH IN WORK AREA.
		DCA	MPAC
		INDEX	FIXLOC
		DXCH	LVSQUARE

## Page 1076
# PROGRAM DESCRIPTION - SUBROUTINE SQRT
#
# FUNCTIONAL DESCRIPTION - DOUBLE PRECISION SQUARE ROOT ROUTINE
#	THIS PROGRAM TAKES THE SQUARE ROOT OF THE 27 OR 28 MOST SIGNIFICANT BITS IN THE TRIPLE PRECISION SET OF
#	NUMBERS - MPAC, MPAC+1, AND MPAC+2.  THE ROOT IS RETURNED DOUBLE PRECISION IN MPAC AND MPAC+1.
#
# WARNING - THIS SUBROUTINE USES A TRIPLE PRECISION INPUT.  THE PROGRAMMER MUST ASSURE THE CONTENTS OF MPAC+2
#	ESPECIALLY IF THE CONTENTS OF MPAC IS SMALL OR ZERO.  FOR DETAILS SEE STG MEMO NO.949.
#
# CALLING SEQUENCE - IN INTERPRETIVE MODE I.E., FOLLOWING TC  INTPRET,SQRT   NO ADDRESS IS ALLOWED
#	INPUT SCALING  THE BINARY POINT IS ASSUMED TO THE RIGHT OF BIT 15.  THE ANSWER IS RETURNED WITH THE SAME SCALING
#
# SUBROUTINES - GENSCR, MPACSHR, SQRTSUB, ABORT
#
# ABORT EXIT MODE - ABORTS ON NEGATIVE INPUT -1.2X10E-4 (77775 OCTAL) OR LESS.
#	DISPLAYS ERROR CODE 1302
#		TC	ABORT
#		OCT	1302
#
# DEBRIS - LOCATIONS BUF, MPTEMP, ADDRWD ARE USED

SQRT		TC	SQRTSUB		# TAKE THE SQUARE ROOT OF MPAC.
		CCS	MPTEMP		# RETURNED NORMALIZED SQUARE ROOT.  SEE IF
		TCF	+2		# ANY UN-NORMALIZATION REQUIRED AND EXIT
		TCF	DANZIG		# IF NOT.

		AD	NEG12		# A RIGHT SHIFT OF MORE THAN 13 COULD BE
		EXTEND			# REQUIRED IF INPUT WAS ZERO IN MPAC,+1.
		BZMF	SQRTSHFT	# GOES HERE IN MOST CASES.
		ZL			# IF A LONG SHIFT IS REQUIRED, GO TO
		LXCH	ADDRWD		# GENERAL RIGHT SHIFT ROUTINES.
		TCF	GENSCR 	+4	# ADDRWD WAS ZERO TO PREVENT ROUND.

SQRTSHFT	INDEX	MPTEMP		# SELECT SHIFTING BIT AND EXIT THROUGH
		CAF	BIT15		# SHIFT ROUTINES.
		TS	MPTEMP
		CAF	ZERO		# TO ZERO MPAC +2 IN THE PROCESS.
		TCF	MPACSHR +3

ABS		TC	BRANCH		# TEST SIGN OF MPAC AND COMPLEMENT IF
		TCF	DANZIG
		TCF	DANZIG
		TCF	COMP

## Page 1077
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 1078
# THE FOLLOWING SUBROUTINES ARE USED IN SQUARING MPAC, IN BOTH THE SCALAR AND VECTOR SENSE.  THEY ARE
# SPECIAL CASES OF DMPSUB AND DOTSUB, PUT IN TO SAVE SOME TIME.

DSQSUB		CA	MPAC 	+1	# SQUARES THE SCALAR CONTENTS OF MPAC.
		EXTEND
		SQUARE
		TS	MPAC 	+2
		CAF	ZERO		# FORM 2(CROSS TERM).
		XCH	MPAC 	+1
		EXTEND
		MP	MPAC
		DDOUBL			# AND MAYBE 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 1079
# DOUBLE PRECISION SQUARE ROOT ROUTINE.  TAKE THE SQUARE ROOT OF THE TRIPLE PRECISION (MPAC +2 USED ONLY
# IN NORMALIZATION) CONTENTS OF MPAC AND LEAVE THE NORMALIZED RESULT IN MPAC (C(MPAC) GREATER THAN OR EQUAL TO
# .5).  THE RIGHT SHIFT COUNT (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 1080
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 1081
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 1082
# 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 1083
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 1084
# ARCSIN/ARCCOS ROUTINE.

ARCSIN		CAF	LASINEX		# COMPUTE ARCSIN BY USING THE IDENTITY
		TCF	+2		# ARCSIN(X) = PI/2 - ARCCOS(X).

ARCCOS		CAF	LDANZIG		# (EXITS IMMEDIATELY).
		TS	ESCAPE
		TC	BRANCH		# TEST SIGN OF INPUT.
		TCF	ACOSST		# START IMMEDIATELY IF POSITIVE.
		TCF	ACOSZERO	# ARCCOS(0) = PI/2 = .25.
		EXTEND			# IF NEGATIVE, USE THE IDENTITY
		DCS	MPAC		# ARCCOS(X) = PI - ARCCOS(-X), FORCING
		DXCH	MPAC		# ARGUMENT POSITIVE.
		CAF	TCSUBTR		# SET EXIT TO DO ABOVE BEFORE
		XCH	ESCAPE		# ARCSIN/ARCCOS CONSIDERATIONS.
		TS	ESCAPE2

ACOSST		CS	HALF		# TEST MAGNITUDE OF INPUT.
		AD	MPAC
		CCS	A
		TCF	ACOSOVF		# THIS IS PROBABLY AN OVERFLOW CASE.

LASINEX		TCF	ASINEX

		TCF	ACOSST2		# NO OVERFLOW - PROCEED.

		CCS	MPAC 	+1	# IF MAJOR PART IS .5, CALL ANSWER 0
		CAF	ZERO		# UNLESS MINOR PART NEGATIVE.
		TCF	ACOS=0

		TCF	ACOSST2

ACOS=0		TS	MPAC 	+1
		TS	MPAC
		TC	ESCAPE

ACOSST2		EXTEND			# NOW THAT ARGUMENT IS IN PROPER RANGE,
		DCS	MPAC		# BEGIN COMPUTATION.  USE HASTINGS
		AD	HALF		# APPROXIMATION ARCCOS(X) = SQRT(1-X)P(X)
		DXCH	MPAC		# IN A SCALED VERSION WHERE P(X) IS A
		DXCH	BUF2		# SEVENTH ORDER POLYNOMIAL.

		TC	SQRTSUB		# RETURNS WITH NORMALIZED SQUARE ROOT.

		CCS	MPTEMP		# SEE IF UN-NORMALIZATION REQUIRED.
		TCF	ACOSSHR		# IF SO.

## Page 1085
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 1086
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 1087
# 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 1088
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 1089
# SUBROUTINE TO CONVERT AN ERASABLE ADDRESS (11 BITS) TO AN EBANK SETTING AND SUBADDRESS.

15ADRERS	CS	POLISH
		AD	DEC45
		CCS	A		# DOES THE ADDRESS POINT TO THE WORK AREA?
		CA	FIXLOC		# YES.  ADD FIXLOC.  EBANK OK AS IS.
		TCF	+5

		CA	OCT1400		# NO. SET EBANK & MAKE UP SUBADDRESS.
		XCH	POLISH
		TS	EBANK
		MASK	LOW8
 +5		ADS	POLISH		# FALL INTO TAGSUB, AND RETURN VIA Q.

# SUBROUTINE WHICH SETS THE ADDRESS OF THE SPECIFIED INDEX IN INDEXLOC.  (ACTUALLY, THE ADDRESS -38D.)

TAGSUB		CA	FIXLOC
		TS	INDEXLOC

		CCS	CYR		# BIT 15 SPECIFIES INDEX.
		INCR	INDEXLOC	# 0 MEANS USE X2.
		TC	Q
		TC	Q		# 1 FOR X1.

## Page 1090
# MISCELLANEOUS OPERATION CODES WITH DIRECT ADDRESSES.  INCLUDED HERE ARE:
#	1.	ITA	STORE 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 1091
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 1092
# 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 1093
		CAF	BIT11
		EXTEND			# DISPATCH SWITCH BIT OPERATION AS IN BITS
		MP	POLISH		# 7-8 OF POLISH.
		MASK	B3TOB4		# GETS 4X2-BIT CODE.
		INDEX	A
		TCF	+1

 +1		CA	SWBIT		# 00 - SET SWITCH IN QUESTION.
		EXTEND
		ROR	QCHAN
		TCF	SWSTORE

 +5		CA	SWBIT		# 01 - INVERT SWITCH.
		EXTEND
		RXOR	QCHAN
		TCF	SWSTORE

 +9D		CS	SWBIT		# 10 - CLEAR.
		MASK	Q
SWSTORE		INDEX	SWWORD
		TS	STATE		# NEW SWITCH WORD.

## Page 1094
 +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.