-*
-*
-*
-* MATRIX FORMAT:
-*
-* a11 a12
-*
-* a21 a22
-*
-* a11-a22 are single precision float variables (2 word).
-*
-*
-* IN MEMORY LAYOUT:
-*
-* a11
-* a11
-* a12
-* a12
-* a21
-* a21
-* a22
-* a22
-*
-*
-* JST M$INIT INITIALIZE MATRIX TO IDENTITY
-* DAC MATRIX ADDRESS
-*
-*
+* MATRIX - AFFINE TRANSFORM SUPPORT PACKAGE
+*
+*
+* AUTHOR:
+*
+* PHILIPP HACHTMANN
+*
+* VERSIONS:
+* 0.1 - INITIAL REVISION (22.12.2007
+*
+*
+* PURPOSE:
+*
+* THIS LIBRARY PROVIDES AFFINE TRANSFORMATION ROUTINES TO
+* PLOTTING ROUTINES AND OTHER SOFTWARE.
+*
+*
+* DATA REPRESENTATION:
+*
+*
+* MATRIX FORMAT: | A11 A12 |
+* M= | |
+* | A21 A22 |
+*
+* A11-A22 ARE SINGLE PRECISION FLOAT VALUES COMPLIANT TO THE
+* HONEYWELL MATHEMATICAL LIBARAY. EVERY VALUE USES TWO
+* 16 BIT MACHINE WORDS.
+* IF A MATRIX IS USED AS A DAC ARGUMENT, A POINTER TO THE FIRST
+* ELEMENT, A11, HAS TO BE USED.
+*
+*
+* VECTOR FORMAT: | A1 |
+* V= | |
+* | A2 |
+*
+* A1 AND A2 ARE SIGNED INTEGER VALUES. EVERY VALUE USES ONE
+* 16 BIT MACHINE WORD.
+* IF A VECTOR IS USED AS A DAC ARGUMENT, A POINTER TO THE FIRST
+* ELEMENT, A1, HAS TO BE USED.
+*
+*
+* AFFINE TRANSFORM FORMAT:
+*
+* AN AFFINE TRANSFORM CONSISTS OF A MATRIX FOR ROTATING AND SCALING
+* AND A VECTOR VOR RELOCATION OF THE RESULT.
+* A VECTOR IS TRANSFORMED BY FIRST MULTIPLYING THE MATRIX WITH IT
+* AND THEN ADDING THE RELOCATION VECTOR:
+*
+* | A11 A12 | | VI1 | | VT1 |
+* VO = MT * VI + VT = | | * | | + | |
+* | A21 A22 | | VI2 | | VT2 |
+*
+* | VI1*A11 + VI2*A12 + VT1 |
+* = | |
+* | VI1*A21 + VI2*A22 + VT2 |
+*
+* MT AND VT ARE THE TRANSFORMATION MATRIX AND VECTOR, VI THE INPUT
+* VECTOR, VO THE RESULT VECTOR.
+*
+* AN AFFINE TRANSFORM IS STORED AS A CONCATENATION OF A MATRIX AND
+* A VECTOR. HERE IS THE MEMORY LAYOUT:
+*
+* '000 : MT11 UPPER
+* '001 : MT11 LOWER
+* '002 : MT12 UPPER
+* '003 : MT12 LOWER
+* '004 : MT21 UPPER
+* '005 : MT21 LOWER
+* '006 : MT22 UPPER
+* '007 : MT22 LOWER
+* '010 : VT1
+* '011 : VT2
+*
+* FOR EVERY TRANSFORMATION, '12 WORDS HAVE TO BE RESERVED.
+* IN AN APPLICATION, A TRANFORMATION VARIABLE COULD BE
+* DECLARED WITH:
+*
+* TRANS BSS '12
+*
+*
+*
+*********************************************************************************
+*
+*
+*
+* M$INIT: INITIALISE MATRIX TO IDENTITY
+*
+* THE MATRIX ARGUMENT IS SET TO
+*
+* | 1.0 0.0 |
+* M= | |
+* | 0.0 1.0 |
+*
+* WICH RESULTS TO THE IDENTITY TRANSFORMATION.
+*
+* JST M$INIT
+* DAC MATRIX POINTER TO A MATRIX
+*
+*
+*
+* M$MUL: MATRIX MULTIPLICATION
+*
+* JST M$MUL
+* DAC TARGET POINTER TO TARGET MATRIX
+* DAC MATRIX1 POINTER TO LEFT MATRIX
+* DAC MATRIX2 POINTER TO RIGHT MATRIX
+* DAC 0 FOR FORTRAN IV COMPATIBILITY
+*
+*
+*
+* M$APLI: APPLY MATRIX TO VECTOR
+*
+* THIS ROUTINE CONVERTS THE VECTOR ELEMENTS TO FLOATING POINT VALUES,
+* APPLIES THE TRANSFORMATION TO THEM AND ROUNDS THE RESULTS BACK TO
+* INTEGER VALUES. THEN IT SAVES THE NEW VECTOR IN THE PLACE OF THE
+* OLD VECTOR.
+*
+* JST M$APLI
+* DAC MATRIX MATRIX TO APPLY
+* DAC VECTOR VECTOR TO TRANSFORM
+* DAC 0 FOR FORTRAN IV COMPATIBILITY
+*
+*
+* M$APII: APPLY MATRIX TO PAIR OF INTEGERS AS VECTOR
+*
+* THIS ROUTINE USES TWO DISTINCT INTEGER POINTERS INSTEAD OF ONE VECTOR
+* POINTER. THE REST OF THE BEHAVIOR IS EXACTLY LIKE M$APL.
+*
+* JST M$APLI
+* DAC MATRIX MATRIX TO APPLY
+* DAC X X COORDINATE OF ARGUMENT VECTOR
+* DAC Y Y COORDINATE OF ARGUMENT VECTOR
+*
+*
+* M$ROT: ROTATE MATRIX
+*
+* THIS ROUTINE TAKES A MATRIX AND ADDS A ROTATION TO IT.
+* INTERNALLY, THE ROUTINE CREATES A ROTATION MATRIX AND THEN
+* MULTIPLIES IT WITH THE ARGUMENT MATRIX. THE ROTATION IS SPECIFIED
+* COUNTERCLOCKWISE FORWARD, ANGLE IN RADIANT.
+* THE ANGLE ARGUMENT IS A SINGLE PRECISION FLOATING POINT NUMER
+* TAKING TWO WORDS TO STORE.
+*
+* JST M$ROT
+* DAC MATRIX MATRIX TO MODIFY
+* DAC ANGLE RADIANT ANGLE
+*
+*
+* M$SCLE: SCALE MATRIX
+*
+* THIS ROUTINE WORKS SIMILAR TO M$ROT BUT SCALES THE ARGUMENT MATRIX.
+* THE SCALE FACTOR IS A FLOATING POINT NUMBER. LIKE THE ROTATION ANGLE.
+*
+* JST M$SCLE
+* DAC MATRIX MATRIX TO MODIFY
+* DAC SCALE SCALE FACTOR
+*
+*
********************************************************************************
*
- SUBR M$INIT,INIT INITIALIZE MATRIX
+**** EXPORTED SYMBOLS
+*
+ SUBR MATRIX,INIT JUST A FANCY LABEL
+ SUBR M$INIT,INIT INITIALISE MATRIX
SUBR M$MUL,MUL MATRIX MULTIPLICATION
SUBR M$APLI,APLI APPLY MATRIX TO INTEGER VECTOR
SUBR M$APII,APII APPLY MATRIX TO PAIR OF INTEGERS
- SUBR M$ROT,XXX ADD ROTATION TO MATRIX ARGUMENT
+ SUBR M$ROT,ROT ADD ROTATION TO MATRIX
SUBR M$SCLE,SCLE SCALE MATRIX
*
- REL
- ORG '0
-*
-*
-*
-*
-*
+ SUBR A$INIT,AFIN INITIALISE AFFINE TRANSFORMATION
+*
+*
+********************************************************************************
+*
+*
+ REL RELOCATEABLE MODE
+*
+*
********************************************************************************
*
+*
+**** INITIALIZE AFFINE TRANSFORMATION
+*
+AFIN DAC **
+ LDA* AFIN
+ STA AFI1 STORE ARGUMENT POINTER
+ LDX AFIN LOAD INTO INDEX REGISTER, TOO
+ IRS AFIN TALLY RETURN ADDRESS
+*
+ JST INIT MATRIX INIT
+AFI1 DAC **
+*
+ CRA
+ STA 8,1 CLEAR FIRST VECTOR ELEMENT
+ STA 9,1 CLEAR SECOND VECTOR ELEMENT
+*
+ JMP* AFIN RETURN TO CALLER
+*
+*
+********************************************************************************
+*
*
+**** INITIALIZE MATRIX
+*
+* THIS ROUTINE SHOULD BE IMPROVED BY SUPPLYING
+* A FLOATING POINT 1.0 CONSTANT!
+*
+****************************************
+*
INIT DAC **
- LDX* INIT
-*
- LDA* INIT GET MATRIX BASE ADDRESS
- STA IM11
- ADD =6
- STA IM22
- IRS INIT
-*
- CRA
- STA 2,1
- STA 3,1
- STA 4,1
- STA 5,1
- CALL FLOAT
- DAC ONE
- CALL H$22
+ LDX* INIT LOAD INDEX REGISTER WITH ADDRESS OF MATRIX
+ LDA* INIT LOAD MATRIX ADDRESS
+ STA IM11 STORE POINTER TO FIRST ELEMENT (A11)
+ ADD =6 IM12,IM21 ARE NOT TO BE INITIALISED WITH FP DATA
+ STA IM22 STORE POINTER TO FOURTH ELEMENT (A22)
+ IRS INIT CORRECT RETURN ADDRESS
+*
+ CRA INITIALISE
+ STA 2,1 A12
+ STA 3,1
+ STA 4,1 A21
+ STA 5,1
+ CALL FLOAT GENERATE FLOATING POINT 1.0
+ DAC ONE CONSTANT INTEGER 1
+ CALL H$22 STORE FLOATING POINT
IM11 DEC 0
CALL H$22
IM22 DEC 0
*
- JMP* INIT
-ONE DEC 1
-*
-*
+ JMP* INIT RETURN.
+*
+*
********************************************************************************
+*
+*
+**** MATRIX MULTIPLICATION
+*
+* C = A * B
+*
+* | a11 a12 | | b11 b12 |
+* = | | * | |
+* | a21 a22 | | b21 b22 |
+*
+* | (a11*b11) (a21*b12) |
+* = | |
+* | (a12*b21) (a22*b22) |
+*
+* CALL:
+* JST MUL
+* DAC MC
+* DAC MA
+* DAC MB
*
-* C=A*B
-*
-* a11 a12 b11 b12 a11*b11 a21*b12
-* a21 a22 b21 b22 a12*b21 a22*b22
-*
-* JST MUL
-* DAC MC
-* DAC MA
-* DAC MB
-*
+****************************************
+*
MUL DAC **
LDX* MUL
*
IRS MUL
IRS MUL
*
-*
* a11 a12 b11 b12 a11*b11 a21*b12
* a21 a22 b21 b22 a12*b21 a22*b22
*
PC22 DEC 0
*
*
- JMP* MUL
+ JMP* MUL RETURN.
*
+*
********************************************************************************
*
*
+**** SCALE MATRIX
+*
SCLE DAC ** SCALE MATRIX
LDX* SCLE
*
JMP* SCLE
*
*
-*
-*
+********************************************************************************
+*
+*
+**** ROTATE MATRIX
+*
+* THIS ROUTINE IS NOT YET FINISHED!
+*
+****************************************
+*
+ROT DAC ** ENTRY
+ IRS ROT TALLY RETURN ADDRESS
+ JMP* ROT EXIT
+*
+*
********************************************************************************
*
*
-* Apply Pair of integers and round
+**** APPLY MATRIX TO PAIR OF INTEGERS
*
-* JST M$APII
-* DAC MATRIX
-* DAC X
-* DAC Y
-* DAC 0
+* SETS UP MATRIX POINTERS AND VECTOR POINTERS.
+* THEN IT CALLS APL, THE REAL WORKING ROUTINE.
+*
+* CALL:
+* JST M$APII
+* DAC MATRIX
+* DAC X
+* DAC Y
+* DAC 0 DON'T FORGET!
+*
+****************************************
*
APII DAC **
*
********************************************************************************
*
*
-* Apply to integer vector and round
+**** APPLY MATRIX TO VECTOR
+*
+* SETS UP MATRIX POINTERS AND VECTOR POINTERS. THEN IT CALLS APL,
+* THE REAL WORKING ROUTINE.
*
-* JST M$APLI
-* DAC MATRIX
-* DAC X Y MUST FOLLOW IN NEXT LOCATION!
+* CALL:
+* JST M$APLI
+* DAC MATRIX
+* DAC VECTOR
+* DAC 0 DON'T FORGET!
+*
+****************************************
*
APLI DAC **
-*
+*
LDA* APLI
STA MP11
ADD =2
STA YP2
IRS APLI
IRS APLI
- JST APL
- JMP* APLI
+ JST APL CALL INTERNAL ROUTINE
+ JMP* APLI RETURN.
*
*
-****************************************
+********************************************************************************
*
*
-APL DAC ** REAL APPLY ROUTINE
+**** INTERNAL ROUTINE OF M$APL AND M$APII.
+*
+* ALL DATA IS SET UP BY THE BOTH USER ROUTINES ABOVE.
+*
+****************************************
+*
+APL DAC **
*
CALL FLOAT LOAD SINGLE PRECISION FLOAT FROM 1-WORD INTEGER
XP1 DAC 0
STA* XP1
JMP* APL RETURN TO CALLER.
*
-****************************************
+*
+********************************************************************************
*
-RND DAC ** ROUND A/B AND RETURN WITH INTEGER IN A
- CALL A$22 ADD 0.5
- DAC HLF
- CALL C$21 CONVERT TO INTEGER
+*
+**** ROUND FLOAT TO INTEGER ROUTINE
+*
+* THERE IS NO CORRECTLY WORKING ROUNDING ROUTINE IN THE LIBRARY.
+* SO THIS IS A WORKAROUND. ADDS 0.5 TO THE VALUE AND USES ONE
+* ONE OF THE TRUNCATE AND CONVERT ROUTINES.
+* THE ARGUMENT IS IN REGISTERS A/B, THE RESULT IS PUT INTO A.
+*
+****************************************
+*
+RND DAC **
+ CALL A$22 ADD
+ DAC HLF 0.5
+ CALL C$21 TRUNCATE TO INTEGER
NOP
JMP* RND
+*
+*
+********************************************************************************
+*
+*
+**** CONSTANTS
+*
+ONE DEC 1
HLF OCT '040100 CONSTANT 0.5
OCT '000000
-*
-****************************************
-*
-TMP BSS 2
-*
-*
+*
+*
********************************************************************************
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+*
+**** VARIABLES
+*
+TMP BSS '10 SOME SPACE
*
*
********************************************************************************
*
+*
+**** END OF THE LINE
+*
END
*
+*
********************************************************************************
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projects / h316.git / blobdiff