perm filename FLOAT.PAL[AL,HE]2 blob
sn#309481 filedate 1977-10-13 generic text, type C, neo UTF8
COMMENT ā VALID 00012 PAGES
C REC PAGE DESCRIPTION
C00001 00001
C00003 00002 .SBTTL Floating point routines
C00004 00003 STRING TO FLOATING POINT NUMBER ROUTINE - "RELSCN".
C00007 00004 [CONTINUATION OF "RELSCN"]
C00010 00005 [CONTINUATION OF "RELSCN"]
C00012 00006 ROUTINES TO SET AND RESTORE OUTPUT FORMAT - "FORMAT"&"RSTFOR"
C00014 00007 FLOATING POINT NUMBER TO "F" FORMAT STRING ROUTINE - "CVF"
C00017 00008 FLOATING POINT NUMBER TO "E" FORMAT STRING ROUTINE - "CVE"
C00020 00009 [CONTINUATION OF "CVE"]
C00021 00010 FLOATING POINT NUMBER TO "E" OR "F" FORMAT STRING - "CVG"
C00023 00011 PRINTING ROUTINE USED BY "CVF" & "CVE"
C00026 00012 LOCAL STORAGE AREA
C00031 ENDMK
Cā;
.SBTTL Floating point routines
;The following pages contain floating point input-output routines.
;Coded by BES 9/74.
.IFNZ FLOAT
;STRING TO FLOATING POINT NUMBER ROUTINE - "RELSCN".
;THE FLOATING POINT NUMBER MUST BE OF THE FORM SIII.DDDESXX WHERE S IS
;THE SIGN OF THE NUMBER, III IS THE INTEGER FIELD, DDD IS THE DECIMAL
;FIELD, AND SXX IS THE EXPONENT AND ITS SIGN. THE LENGTH OF EACH
;FIELD IS VARIABLE BUT ONLY THE FIRST 8 DIGITS ARE USED IN COMPUTING
;THE F.P. NUMBER. EMPTY FIELDS ARE PERMITTED AND ALL LEADING SPACES
;AND ZEROS ARE IGNORED. THE LOCATION OF THE FIRST BYTE OF THE STRING
;MUST BE LOADED INTO R0 BEFORE CALLING "RELSCN". AFTER EXECUTION,
;THIS ROUTINE LEAVES THE F.P. NUMBER IN REGISTER AC0 AND R0 POINTS TO
;THE BYTE FOLLOWING THE LAST DIGIT. R1 CONTAINS AN ERROR CODE. IF NO
;NUMBER WAS FOUND, R1 IS -1 ELSE R1 IS 0. "RELSCN" IS CALLED IN THE
;"SIMPLE STYLE".
;REGISTERS USED:
;
; R0,R1,AC0 PASS ARGUMENTS
; NO OTHER REGISTERS AFFECTED
.STITLE FLOATING POINT TO/FROM STRING CONVERSION ROUTINES
;"DIGIT" CHECKS FOR ASC DIGIT AND CONVERTS TO INTEGER IF IT IS
.MACRO DIGIT NOTDIG
CMP R4,#60 ;COMPARE TO ASC ZERO
BLT NOTDIG ;SKIP IF OUT OF RANGE
CMP R4,#71 ;COMPARE TO ASC 9
BGT NOTDIG ;SKIP IF OUT OF RANGE
BIC #60,R4 ;MASK OUT ASC BASE
.ENDM
;"CKSIGN" CHECKS FOR A - OR + CHARACTER AND SETS SIGN APPROPRIATELY
.MACRO CKSIGN ISSIGN,NTSIGN,SIGN
CMP #53,R4 ;IGNOR "+" CHARACTER
BEQ ISSIGN
CMP #55,R4 ;CHECK IF ITS A "-" CHAR.
BNE NTSIGN ;EXIT IF ITS NOT
INC SIGN ;ELSE SET SIGN NON-ZERO
BR ISSIGN
.ENDM
;START OF "RELSCN"
.EVEN
RELSCN: MOV R2,-(SP) ;SAVE REGISTER
MOV R3,-(SP) ;SAVE REGISTER
MOV R4,-(SP)
CLR R2 ;RESET DIGIT COUNT
MOV #1,R3 ;SET DECIMAL POINT FLAG
[CONTINUATION OF "RELSCN"]
MOV #-1,R1 ;INDICATE NO DIGITS ENCOUNTERED
CLRF AC0 ;CLEAR THE NUMBER ACCUM
CLR MSIGN ;ASSUME MANTISSA POSITIVE
;PICK UP A CHARACTER AND CHECK FOR SIGN
PICK: MOVB (R0)+,R4 ;PICK UP A CHARACTER
TST R1 ;CHECK IF DIGIT ENCOUNTERED
BEQ CHKDG ;SKIP IF TRUE
CKSIGN PICK,CHKDG,MSIGN ;CHECK FOR + OR - SIGN
;CHECK IF CHARARCTER IS A DIGIT
CHKDG: DIGIT CHKDP ;SKIP TO CHKDP IF NOT A DIGIT
MULF TEN,AC0 ;MULT DIGIT SUM BY 10
ASH #2,R4 ;MULTIPLY INDEX BY 4
ADDF DGLST(R4),AC0 ;ADD THE F.P. TO ACCUM
CLR R1 ;INDICATE DIGIT ENCOUNTERED
SUB #4,R2 ;DECREMENT DIGIT COUNT
BR PICK ;GO GET ANOTHER CHARACTER
;CHECK IF THE CHARACTER IS A DECIMAL POINT
CHKDP: CMP #56,R4 ;COMPARE CHARACTER TO DECIMAL PT
BNE RNORM ;SKIP IF NOT D.P.
TST R3 ;CHECK IF DECIMAL POINT ALREADY SET
BEQ RNORM ;IF RESET THIS MUST BE A THE END OF THE MANT.
CLR R2 ;START COUNTING FRACTIONAL DIGITS
CLR R3 ;INDICATE D.P. SET
CLR R1 ;INDICATE DIGIT ENCOUNTERED
BR PICK ;GO GET ANOTHER CHARACTER
;CORRECT NUMBER FOR POWER OF TEN IF DIGITS FOUND
RNORM: TST R1 ;CHECK IF DIGITS FOUND
BNE CHKEX ;SKIP IF NONE
TST R3 ;CHECK IF DECIMAL POINT SET
BNE CHKEX ;DONT NORMALIZE IF NO D.P.
MULF TENLST(R2),AC0 ;CORRECT DECIMAL POINT
;CHECK IF E SIGN ENCOUNTERED
CHKEX: CMP #105,R4 ;COMPARE TO E CHARACTER
BNE CHKDN ;SKIP IF NOT E
TST R1 ;CHECK IF NO DIGITS BEFORE E
[CONTINUATION OF "RELSCN"]
BEQ EXCN
LDF TENLST,AC0 ;SET AC0=1 IF EXPONENT BUT NO DIGITS
CLR R1 ;INDICATE DIGITS ENCOUNTERED
EXCN: CLR ESIGN ;ASSUME EXPONENT POSITIVE
CLR R3 ;CLEAR EXPONENT ACCUMULATOR
MOVB (R0)+,R4 ;GET NEXT CHARACTER
CKSIGN PIC2,DIG2,ESIGN ;CHECK FOR SIGN CHARACTER
PIC2: MOVB (R0)+,R4 ;SIGN INCOUNTERED, GET NEXT CHAR.
DIG2: DIGIT NORM ;EXTRACT DIGIT
MUL #10.,R3 ;MULT EXPON REG BY 10.
ADD R4,R3 ;ADD DIGIT TO EXPONENT REG
JMP PIC2 ;GO GET ANOTHER CHARACTER
NORM: TST ESIGN ;CHECK SIGN OF EXPONENT
BEQ .+4
NEG R3 ;COMPLEMENT EXPONENT IF - SIGN
ASH #2,R3 ;MULT. INDEX BY 4 FOR F.P. NUMBERS
MULF TENLST(R3),AC0 ;ADJUST EXPONENT OF NUMBER
JMP CDONE ;EXIT ROUTINE
;CHECK IF END OF NUMBER
CHKDN: TST R4 ;COMPARE CHARACTER TO A NULL CHARACTER
BEQ CDONE ;EXIT IF IT IS, THIS IS THE END OF THE STR
TST R1 ;TEST IF ANY DIGITS YET
BLT PICK ;IF NONE, KEEP SCANNING
;NO MORE DIGITS - APPLY CORRECT SIGN TO NUMBER
CDONE: MOV (SP)+,R4 ;RESTORE REGISTERS
MOV (SP)+,R3
MOV (SP)+,R2
DEC R0 ;POINT TO BREAK CHARACTER
TST MSIGN ;TEST SIGN OF MANTISSA
BEQ .+4
NEGF AC0 ;COMPLEMENT NUMBER IF SIGN NEGATIVE
RTS PC ;RETURN
;ROUTINES TO SET AND RESTORE OUTPUT FORMAT - "FORMAT"&"RSTFOR"
;THE TOTAL NUMBER OF CHARACTERS TO BE WRITTEN (WIDTH) SHOULD BE
;LOADED INTO R0 AND THE NUMBER OF DECIMAL DIGITS (DIGITS) SHOULD
;BE LOADED INTO R1 BEFORE CALLING THIS ROUTINE. IN ALL CASES,
;WIDTH SHOULD BE GREATER THAN OR EQUAL TO DIGIT+2. "FORMAT" IS
;CALLED BY THE "SIMPLE METHOD".
;REGISTERS USED:
;
; R0,R1 PASS ARGUMENTS
; NO OTHER REGISTERS AFFECTED
FORMAT: MOV WIDTH,OLDW ;SAVE THE OLD WIDTH
MOV DIG,OLDD ; AND DIG
SUB #2,R0 ;SUBTRACT SPACES FOR SIGN AND . FROM WIDTH
MOV R0,WIDTH ;SAVE WIDTH OF I/O STRING - 2
MOV R1,DIG ;SAVE THE NUMBER OF DECI. DIGITS
CMP R0,R1 ;CHECK TO SEE THAT WIDTH.GE.DIGIT+2
BGE NFER ;SKIP IF SPACE ALLOWED, ELSE CORRECT
OUTSTR FERM ;TYPE OUT ERROR MESSAGE
MOV R1,WIDTH ;SET WIDTH=DIG+2
NFER: RTS PC ;RETURN
FERM: .ASCIZ /
FORMATTING ERROR
/
.EVEN
;ROUTINE TO RESTORE LAST FORMAT - "RSTFOR"
;THE PREVIOUS FORMAT BECOMES THE CURRENT FORMAT. THE CURRENT
;FORMAT IS LOST FOREVER. "RSTFOR" IS CALLED IN THE "SIMPLE
;METHOD".
;REGISTERS USED: NONE
RSTFOR: MOV OLDW,WIDTH ;RESTORE WIDTH
MOV OLDD,DIG ;RESTORE DIG
RTS PC ;RETURN
;FLOATING POINT NUMBER TO "F" FORMAT STRING ROUTINE - "CVF"
;"CVF" - THE STRING GENERATED BY THIS ROUTINE IS SIMILAR TO "F" FORMAT
;IN FORTRAN. IT IS ASSUMED THAT THE NUMBER TO BE CONVERTED IS IN
;REGISTER AC0 AND R0 CONTAINS A POINTER TO THE FIRST BYTE OF THE
;OUTPUT STRING. THE NUMBER OF CHARACTERS WRITTEN SHOULD FIRST BE SET
;IN A CALL TO "FORMAT", ELSE THE DEFAULT VALUES ARE USED. IF THE
;INTEGER PART OF THE NUMBER EXCEEDS THE FORMAT LIMITS THE FIRST
;CHARACTER WRITTEN IS A ">". AFTER COMPLETION, "CVF" LEAVES A NULL
;CHARACTER FOLLOWING THE NUMBER STRING. REGISTER R0 IS LEFT POINTING
;AT THE NULL CHARACTER.
;REGISTERS USED:
;
; R0,AC0 PASS ARGUMENTS
; R1,AC1 GARBAGED
CVF: MOV WIDTH,R1 ;GET THE TOTAL NUMBER OF CHAR TO BE WRITTEN
SUB DIG,R1 ;DETERMINE THE MAG. OF THE M.S. DIGIT
MOV R1,PT ;NOW HAVE # OF DIGITS BEFORE DECIMAL POINT
ASH #2,R1 ;X 4, USE AS INDEX INTO F.P. TABLE
DIVF TENLST(R1),AC0 ;NORMALIZE NUMBER TO BETWEEN 0 AND .99999999
MOV WIDTH,R1 ;TOTAL # OF DIGITS TO R1
MOV R2,-(SP) ;SAVE THE REGISTERS
MOV R3,-(SP)
JSR PC,PRTF ;TYPE OUT THE DIGITS
MOVB #0,(R0) ;PUT A NULL CHARACTER AFTER THE STRING
MOV (SP)+,R3 ;RESTORE THE REGISTERS
MOV (SP)+,R2
RTS PC ;RETURN
;FLOATING POINT NUMBER TO "E" FORMAT STRING ROUTINE - "CVE"
;"CVE" - SAME OPERATION AS "CVF" EXCEPT THAT OUTPUT IN FORTRAN "E" FORMAT
CVE: MOV R2,-(SP) ;SAVE THE REGISTERS
MOV R3,-(SP)
CLR EXPON ;RESET EXPONENT COUNT
MOV #1,PT ;SET COUNT TO PRINT 1 NUMBER BEFORE DECIMAL PT
MOV WIDTH,R1 ;SET COUNT FOR TOTAL NUMBER OF DIGITS TO BE SENT
SUB #4,R1 ;ADJUST FOR EXPONENT
TSTF AC0 ;CHECK IF NUMBER IS ZERO
CFCC ;TRANSFER CONDITIONAL CODES TO CPU
BEQ EPRT ;START PRINTING IF NUMBER IS 0.0
STF AC0,NUM ;GET THE NUMBER TO BE CONVERTED
DEC EXPON ;ADJUST EXPONENT FOR PRINTING 1 INT. DIGIT
MOV NUM,R2 ;LOAD THE EXPONENT AND MSB OF THE NUMBER
BIC #100000,R2 ;CONVERT TO ABSOLUTE VALUE
SUB #150,R2 ;ADJUST EXPONENT DOWN
BGE .+4
CLR R2 ;LEAVE IT POSITIVE
MUL #233,R2 ;USE EXPONENT AND MSB AS INDEX INTO TEN TABLE
CMP R2,#76. ;COMPARE TO 1.0@38
BLE .+6
MOV #76.,R2 ;IF LARGER, REPLACE BY 1.0@38
SUB #38.,R2 ;SHIFT INDEX INTO RANGE OF -38 TO +38
ADD R2,EXPON ;ADJUST EXPONENT COUNT
ASH #2,R2 ;MULT INDEX BY 4 FOR FLOATING POINT NUMBERS
DIVF TENLST(R2),AC0 ;NORMALIZE NUMBER INTO RANGE 0.0 TO 0.9999
STF AC0,AC1 ;GET ABSOLUTE VALUE OF NUMBER
ABSF AC1
CMPF TENLST,AC1 ;CHECK IF NUMBER LESS THAN 1.0
CFCC ;TRANSFER CONDITIONAL CODES TO CPU
BGT EPRT ;IF ITS BETWEEN 0.0 AND .99999, GO TO PNTF
DIVF TEN,AC0 ;ELSE MULT. BY 0.1 AND ADJUST EXPONENT
INC EXPON
[CONTINUATION OF "CVE"]
EPRT: JSR PC,PRTF ;GO PRINT MANTISSA
MOVB #105,(R0)+ ;PUT A "E" CHAR INTO THE STRING
MOVB #53,(R0)+ ;ASSUME EXPONENT POSITIVE A OUTPUT A "+"
MOV EXPON,R3 ;TEST SIGN OF EXPONENT
BGE XPRT ;SKIP IF POSITIVE
MOVB #55,-1(R0) ;REPLACE "+" WITH "-"
NEG R3 ;MAKE EXPONENT POSITIVE
XPRT: CLR R2 ;CLEAR FOR DIVISION
DIV #10.,R2 ;SEPARATES TENS AND UNITS DIGIT
BIS #60,R2 ;CONVERT TO ASC AND PUT IN I/O BUFFER
MOVB R2,(R0)+
BIS #60,R3
MOVB R3,(R0)+
MOVB #0,(R0) ;PUT IN A NULL CHARACTER
MOV (SP)+,R3 ;RESTORE THE REGISTERS
MOV (SP)+,R2
RTS PC ;RETURN
;FLOATING POINT NUMBER TO "E" OR "F" FORMAT STRING - "CVG"
;"CVG" - DETERMINES IF THE NUMBER IN AC0 CAN BE WRITTEN BY "CVF", IF
;IT CAN, THEN CVF IS CALLED, ELSE THE NUMBER IS PRINTED USING "CVE".
CVG: LDF AC0,AC1 ;COPY THE NUMBER
CFCC ;TRANSFER THE CONDITIONAL CODES TO CPU
ABSF AC1 ;CONVERT NUMBER TO ABSOLUTE VALUES
BEQ RUNF ;IF NUMBER = 0.0, EXECUTE CVF
MOV DIG,R1 ;GET THE NUMBER OF DECIMAL DIGITS TO BE TYPED
ASH #2,R1 ;MULT BY 4 TO USE A FLOATING POINT INDEX
MULF TENLST(R1),AC1 ;CHECK IF NUMBER SMALLER THAN 1.0@-DIG
CMPF TENLST,AC1 ;COMPARE TO 1.0
CFCC ;TRANSFER CONDITIONAL CODES TO CPU
BGT RUNE ;IF LESS THAN 1.0@-DIG, PRINT USING CVE
MOV WIDTH,R1 ;GET THE TOTAL NUMBER OF DIGITS TO BE PRINTED
ASH #2,R1 ;USE THIS AS A F.P. INDEX
NEG R1
MULF TENLST(R1),AC1 ;CHECK IF GREATER THAN WIDTH-DIG LONG
CMPF TENLST,AC1 ;COMPARE TO 1.0
CFCC ;TRANSFER CONDITIONAL CODES
BGE RUNF ;IF TOO LARGE, USE CVE
RUNE: JSR PC,CVE
RTS PC
RUNF: JSR PC,CVF
RTS PC
; PRINTING ROUTINE USED BY "CVF" & "CVE"
PRTF: TSTF AC0 ;TEST THE SIGN OF THE NUMBER
MOVB #40,MSIGN ;ASSUME SIGN POSITIVE
CFCC ;TRANSFER THE CONDITIONAL CODES TO CPU
ABSF AC0 ;CLEAR THE SIGN OF THE NUMBER
BGE .+10
MOVB #55,MSIGN ;IF NEGATIVE PUT IN "-" SIGN
MODF TEN,AC0 ;COMPUTE M.S. INTEGER DIGIT
CLR R3 ;INDICATE SIGN NOT YET WRITTEN
DIGLP: TST PT ;CHECK IF TIME TO PRINT DECIMAL POINT
BNE GETDG ;SKIP IF NOT
TST R3 ;HAVE WE PRINTED SIGN YET?
BNE WTDP ;SKIP IF WE HAVE
MOVB MSIGN,(R0)+ ;ELSE PRINT SIGN BEFORE DECIMAL POINT
INC R3 ;INDICATE SIGN PRINTED
WTDP: MOVB #56,(R0)+ ;PRINT DECIMAL POINT
GETDG: STCFI AC1,R2 ;SAVE M.S. INTEGER DIGIT
CFCC ;CHECK FOR NUMBER TOO LARGE TO INTEGERIZE
BCC CHKSZ
TOLGE: ADDF AC1,AC0 ;IF TWO LARGE, PUT IT BACK TOGETHER
MODF TENTH,AC0 ;SCALE DOWN AND TRY INTEGERIZING AGAIN
INC R1 ;PRINT OUT ONE MORE DIGIT
INC PT ;SHIFT DECIMAL POINT TO PUT IN EXTRA DIGIT
TST R3 ;CHECK IF SIGN AND D.P. ALREADY WRITTEN
BEQ GETDG ;GO CHECK IF IN RANGE IF NOT WRITTEN
CLR R3 ;CLEAR SIGN AND D.P.
SUB #2,R0 ;ADJUST BYTE POINTER
JMP GETDG ;GO CHECK IF IN RANGE AGAIN
CHKSZ: TST R2 ;TEST INTEGER
BLT TOLGE ;IF TOO LARGE, GO SCALE AGAIN
CMP R2,#9. ;CHECK IF LESS THAN 9
BGT TOLGE ;SCALE IF GREATER THAN 9
MODF TEN,AC0 ;START COMPUTING NEXT INTEGER DIGIT
TST R3 ;HAVE WE PRINTED SIGN YET?
BNE SETBS ;SKIP IF WE HAVE
TST R2 ;CHECK IF LEADING ZERO
BEQ WTSP ;IF IT IS GO WRITE A SPACE CHARACTER
MOVB MSIGN,(R0)+ ;FIRST CHARACTER, NOW PRINT SIGN
INC R3 ;INDICATE SIGN PRINTED
SETBS: BIS #60,R2 ;SET ASC ZERO BASE
JMP WTCH
WTSP: MOVB #40,R2 ;WRITE A SPACE CHARACTER
WTCH: MOVB R2,(R0)+ ;PUT CHARACTER IN I/O BUFFER
DEC PT ;DECREMENT DECIMAL POINT COUNT
SOB R1,DIGLP ;DONE WITH CHARACTERS?
RTS PC ;RETURN
;LOCAL STORAGE AREA
MSIGN: 0 ;SIGN OF CURRENT NUMBER
ESIGN: 0 ;SIGN OF EXPONENT
EXPON: 0
NUM: .WORD 0,0
WIDTH: 8. ;DEFAULT NUMBER OF CHARACTERS IN OUTPUT STRING
DIG: 3 ;DEFAULT NUMBER OF DECIMAL DIGITS
OLDW: 8. ;OLD VALUES OF WIDTH AND DIG
OLDD: 3
PT: 0 ;NUMBER OF DIGITS BEFORE DECIMAL POINT
;TABLE OF F.P. DIGITS FROM 0 TO 9.0
DGLST: .FLT2 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0
;TABLE OF POWERS OF TEN
.WORD 531,143735, 1410, 16352, 2252, 22045, 3124,126456
.WORD 4004,166075, 4646, 23514, 5517,130437, 6401,147263
.WORD 7242, 41140, 10112,151370, 10775,103666, 11636, 72322
.WORD 12506, 11006, 13367,113210, 14232,137025, 15101, 66632
.WORD 15761,144400, 16627, 16640, 17474,162410, 20354, 17113
.WORD 21223,111357, 22070, 73652, 22746,112625, 23620, 16575
.WORD 24464, 22334, 25341, 27023, 26214,136314, 27057,165777
.WORD 27733,163377, 30611, 70137, 31453,146167, 32326,137625
.WORD 33206, 33675, 34047,142654, 34721,133427, 35603, 11157
.WORD 36443,153412
TENTH: .FLT2 0.10
TENLST: .FLT2 1.0
TEN: .FLT2 10.0
.WORD 41710, 0, 42572, 0, 43434, 40000, 44303, 50000
.WORD 45164, 22000, 46030,113200, 46676,136040, 47556, 65450
.WORD 50425, 1371, 51272, 41667, 52150,152245, 53021,102347
.WORD 53665,163041, 54543, 57651, 55416, 15712, 56261,121274
.WORD 57136, 5553, 60012,143443, 60655, 74354, 61530,153447
.WORD 62407,103170, 63251, 64026, 64123,141034, 65004, 54521
.WORD 65645, 67646, 66516,145617, 67401, 37472, 70241,107410
.WORD 71111,171312, 71774, 67574, 72635,142656, 73505, 33431
.WORD 74366,102337, 75232, 11414, 76100,113717, 76760,136702
.WORD 77626, 73231
;This is the end of the floating package.
.ENDC