CRC-16
XMODEM and Acorn CFS/RFS files have a 16-bit CRC (Cyclic Redundancy Check). The following code calculates these CRCs. I have put all my work together here so other people can use it.
The XMODEM CRC is CRC-16 with a start value of &0000 and uses a polynomic of &1021. These three values can be changed to create code to generate other variants of CRC-16. The same CRC is used by Acorn CFS/RFS, but the published code is different, and the CRC is stored high-byte,low-byte.
Contents
'C' code
/* Calculating XMODEM CRC-16 in 'C'
================================
Reference model for the translated code */
#define poly 0x1021
/* On entry, addr=>start of data
num = length of data
crc = incoming CRC */
int crc16(char *addr, int num, int crc)
{
int i;
for (; num>0; num--) /* Step through bytes in memory */
{
crc = crc ^ (*addr++ << 8); /* Fetch byte from memory, XOR into CRC top byte*/
for (i=0; i<8; i++) /* Prepare to rotate 8 bits */
{
crc = crc << 1; /* rotate */
if (crc & 0x10000) /* bit 15 was set (now bit 16)... */
crc = (crc ^ poly) & 0xFFFF; /* XOR with XMODEM polynomic */
/* and ensure CRC remains 16-bit value */
} /* Loop for 8 bits */
} /* Loop until num=0 */
return(crc); /* Return updated CRC */
}
An optimisation is to define poly as 0x11021 then the loop can use
crc ^= poly as the overflowed bit 16 is cleared by the additional 1.
Obviously, this depends on the compiler using 32-bit integers. If using
16-bit integers, bit 15 must be tested before it overflows:
{
if (crc & 0x8000) /* b15 is set... */
crc = (crc << 1) ^ poly; /* rotate and XOR with XMODEM polynomic */
else /* b15 is clear... */
crc = crc << 1; /* just rotate */
} /* Loop for 8 bits */
BBC BASIC
REM crc% = incoming CRC
REM start%=>start address
REM num% = number of bytes
:
FOR addr%=start% TO start%+num%-1
crc%=crc% EOR 256*?addr% :REM EOR with current byte
FOR bit%=1 TO 8 :REM Loop through 8 bits
crc%=crc%+crc% :REM Move crc% up one bit
IF crc% AND &10000:crc%=crc% EOR &11021 :REM EOR with XMODEM polynomic
NEXT bit% :REM Ensuring CRC remains a 16-bit value
NEXT addr%
:
REM crc% = outgoing CRC
The following is a highly crunched and speeded up version:
FORA%=mem%TOmem%+num%-1:S%=S%EOR256*?A%:FORB%=1TO8:S%=S%*2:IFS%AND&10000:S%=S%EOR&11021 NEXT:NEXT
6502
\ Calculating XMODEM CRC-16 in 6502 \ ================================= \ Calculate an XMODEM 16-bit CRC from data in memory. This code is as \ tight and as fast as it can be, moving as much code out of inner \ loops as possible. \ \ On entry, crc..crc+1 = incoming CRC \ addr..addr+1 => start address of data \ num..num+1 = number of bytes \ On exit, crc..crc+1 = updated CRC \ addr..addr+1 => end of data+1 \ num..num+1 = 0 \ \ Multiple passes over data in memory can be made to update the CRC. \ For XMODEM, initial CRC must be &0000. For Acorn CFS/RFS the CRC \ is stored in the header high-byte/low-byte. \ Opimisation based on Greg Cook's 6502 CRC-32 optimisation. \ Total 47 bytes \ .crc16 .bytelp LDX #8 :\ Prepare to rotate CRC 8 bits LDA (addr-8 AND &FF,X) :\ Fetch byte from memory : \ The following code updates the CRC with the byte in A ---------+ \ If used in isolation, requires LDX #8 here | EOR crc+1 :\ EOR byte into CRC top byte | .rotlp :\ | ASL crc+0:ROL A :\ Rotate CRC clearing bit 0 | BCC clear :\ b15 was clear, skip past | TAY :\ Hold CRC high byte in Y | LDA crc+0:EOR #&21:STA crc+0 :\ CRC=CRC EOR &1021, XMODEM polynomic TYA:EOR #&10 :\ Get CRC high byte back from Y | .clear :\ b15 was zero | DEX:BNE rotlp :\ Loop for 8 bits | STA crc+1 :\ Store CRC high byte | \ ---------------------------------------------------------------+ : INC addr+0:BNE next:INC addr+1 :\ Step to next byte .next : \ Now do a 16-bit decrement LDA num+0:BNE skip :\ num.lo<>0, not wrapping from 00 to FF DEC num+1 :\ Wrapping from 00 to FF, dec. high byte .skip DEC num+0:BNE bytelp :\ Dec. low byte, loop until num.lo=0 LDA num+1:BNE bytelp :\ Loop until num=0 RTS
Z80
\ Calculating XMODEM CRC-16 in Z80 \ ================================ \ Calculate an XMODEM 16-bit CRC from data in memory. This code is as \ tight and as fast as it can be, moving as much code out of inner \ loops as possible. Can be made shorter, but slower, by replacing \ JP with JR. \ \ On entry, crc..crc+1 = incoming CRC \ addr..addr+1 => start address of data \ num..num+1 = number of bytes \ On exit, crc..crc+1 = updated CRC \ addr..addr+1 => undefined \ num..num+1 = undefined \ \ Multiple passes over data in memory can be made to update the CRC. \ For XMODEM, initial CRC must be &0000. For Acorn CFS/RFS the CRC \ is stored in the header high-byte/low-byte. \ Total 47 bytes. \ .crc16 LD HL,(addr):LD BC,(num) :\ Address, Count LD DE,(crc) :\ Incoming CRC : \ Enter here with HL=>data, BC=count, DE=incoming CRC .bytelp PUSH BC :\ Save count LD A,(HL) :\ Fetch byte from memory : \ The following code updates the CRC with the byte in A ---------+ XOR D :\ XOR byte into CRC top byte | LD B,8 :\ Prepare to rotate 8 bits | .rotlp :\ | SLA E:ADC A,A :\ Rotate CRC | JP NC,clear :\ b15 was zero | LD D,A :\ Put CRC high byte back into D | LD A,E:XOR &21:LD E,A :\ CRC=CRC XOR &1021, XMODEM polynomic | LD A,D:XOR &10 :\ And get CRC top byte back into A | .clear :\ | DEC B:JP NZ,rotlp :\ Loop for 8 bits | LD D,A :\ Put CRC top byte back into D | \ ---------------------------------------------------------------+ : INC HL :\ Step to next byte POP BC:DEC BC :\ num=num-1 LD A,B:OR C:JP NZ,bytelp :\ Loop until num=0 LD (crc),DE :\ Store outgoing CRC RET
6809
\ Calculating XMODEM CRC-16 in 6809 \ ================================= \ Calculate an XMODEM 16-bit CRC from data in memory. This code is as \ tight and as fast as it can be, moving as much code out of inner \ loops as possible. \ \ On entry, crc..crc+1 = incoming CRC \ addr..addr+1 => start address of data \ num..num+1 = number of bytes \ On exit, crc..crc+1 = updated CRC \ addr..addr+1 => unchanged \ num..num+1 = unchanged \ \ Value order in memory is H,L (big endian) \ \ Multiple passes over data in memory can be made to update the CRC. \ For XMODEM, initial CRC must be &0000. For Acorn CFS/RFS the CRC \ is stored in the header high-byte/low-byte. \ Total 35 bytes (if above parameters are not in the direct page, otherwise 31). \ \ XMODEM polynomic POLYH EQU &10 POLYL EQU &21 .crc16 ldu addr :\ Start address (direct page or extended) ldx num :\ Count (DP or extended) ldd crc :\ Incoming CRC : .bl \ The following code updates the CRC with the byte in the operand of the eora statement --+ eora ,u+ :\ Fetch byte and XOR into CRC high byte | ldy #8 :\ Rotate loop counter | .rl | aslb :\ Shift CRC left, first low | rola :\ and than high byte | bcc cl :\ Justify or ... | eora #POLYH :\ CRC=CRC XOR polynomic, high | eorb #POLYL :\ and low byte | .cl | leay -1,y :\ Shift loop (8 bits) | bne rl | \ ----------------------------------------------------------------------------------------+ : leax -1,x :\ Byte loop bne bl : std crc :\ Store final CRC back rts
PDP-11
; Calculating XMODEM CRC-16 in PDP-11 ; =================================== ; Calculate an XMODEM 16-bit CRC from data in memory. This code is as ; tight and as fast as it can be, moving as much code out of inner ; loops as possible. ; ; On entry, crc..crc+1 = incoming CRC ; addr..addr+1 => start address of data ; num..num+1 = number of bytes ; On exit, crc..crc+1 = updated CRC ; addr..addr+1 => undefined ; num..num+1 = undefined ; ; Multiple passes over data in memory can be made to update the CRC. ; For XMODEM, initial CRC must be &0000. For Acorn CFS/RFS the CRC ; is stored in the header high-byte/low-byte. ; Total 56 bytes. ; .crc16 mov (addr),r1 ; Address mov (num),r2 ; Count mov (crc),r3 ; CRC ; ; Enter here with r1=>addr, r2=count, r3=CRC ; mov #&1021,r4 ; XMODEM polynomic .bytelp movb (r1)+,r0 ; Fetch byte from memory ; The following code updates the CRC with the byte in R0 -----+ bic #&FF00,r0 ; Ensure b8-b15 clear | swab r0 ; Move byte into b8-b15 | xor r0,r3 ; XOR into CRC high byte | mov #8,r0 ; Prepare to rotate 8 bits | .rotlp ; | clc ; | rol r3 ; Rotate CRC, clearing b0 | bcc clear ; b15 was zero | xor r4,r3 ; CRC=CRC xor &1021, XMODEM polynomic | .clear ; | sub #1,r0 ; | bne rotlp ; Loop for 8 bits | ; ------------------------------------------------------------+ ; sub #1,r2 ; num=num-1 bne bytelp ; Loop until num=0 mov r3,(crc) ; Store outgoing CRC rts pc
32-bit 80x86
; Calculating XMODEM CRC-16 in 32-bit 80x86 ; ========================================= ; Calculate a XMODEM 16-bit CRC from data in memory. This code is as ; tight and as fast as it can be, moving as much code out of inner ; loops as possible. ; ; On entry, crc..crc+3 = incoming CRC ; addr..addr+3 => start address of data ; num..num+3 = number of bytes ; On exit, crc..crc+3 = updated CRC ; addr..addr+3 = undefined ; num..num+3 = undefined ; ; Multiple passes over data in memory can be made to update the CRC. ; For XMODEM, initial CRC must be &0000. For Acorn CFS/RFS the CRC ; is stored in the header high-byte/low-byte. ; Opimisation based on Mike Cook's CRC32 optimisation. ; Total 71 bytes ; .crc16 MOV ESI,[addr] ; ESI=>start of data MOV EBX,[num] ; EBX= length of data MOV ECX,[crc] ; ECX= incoming CRC SHL ECX,16 ; Move CRC into b16-b31 ; .bytelp MOV AL,[ESI] ; Fetch byte from memory ; ; The following code updates the CRC with the byte in AL -----+ SHL EAX,24 ; Move byte to b8-b15 | XOR ECX,EAX ; XOR byte into top of CRC | MOV AL,8 ; Prepare to rotate 8 bits | .rotlp ; | SHL ECX,1 ; Rotate CRC | JNC clear ; b15 was zero | XOR ECX,&10210000 ; If b15 was set, XOR with XMODEM polymonic .clear ; | DEC AL:JNZ rotlp ; Loop for 8 bits | ; ------------------------------------------------------------+ ; INC SI ; Point to next byte DEC EBX:JNE bytelp ; num=num-1, loop until num=0 SHR ECX,16 ; Move CRC back into b0-b15 MOV [crc],ECX ; Store outgoing CRC RETF .addr:DD 0 .num:DD 0 .crc:DD 0
32016
ARM
\ Calculating XMODEM CRC-16 in ARM \ ================================ \ Calculate an XMODEM 16-bit CRC from data in memory. This code is as \ tight and as fast as it can be, moving as much code out of inner \ loops as possible. \ \ On entry, crc..crc+3 = incoming CRC \ addr..addr+3 => start address of data \ num..num+3 = number of bytes \ On exit, crc..crc+3 = updated CRC \ addr..addr+3 => undefined \ num..num+3 = undefined \ \ Multiple passes over data in memory can be made to update the CRC. \ For XMODEM, initial CRC must be &0000. For Acorn CFS/RFS the CRC \ is stored in the header high-byte/low-byte. \ Total 84 bytes. \ .crc16 LDR R0,addr:LDR R1,num :\ Address, Count LDR R2,crc :\ Incoming CRC \ \ Enter here with R0=addr, R1=num, R2=crc \ .crc16reg MOV R2,R2,LSL #16 :\ Move CRC to top of register LDR R3,xor :\ ZIP polynomic .bytelp LDRB R4,[R0],#1 :\ Get byte, inc address : \ The following code updates the CRC with the byte in R4 -----------+ \ If used in isolation, requires LDR R3,xor here | EOR R2,R2,R4,LSL #24 :\ EOR byte into CRC top byte | MOV R4,#8 :\ Prepare to rotate 8 bits | .rotlp :\ | MOVS R2,R2,LSL #1 :\ Rotate CRC | EORCS R2,R2,R3 :\ If b15 was set, EOR with ZIP polynomic SUBS R4,R4,#1:BNE rotlp :\ Loop for 8 bits | \ ------------------------------------------------------------------+ : SUBS R1,R1,#1:BNE bytelp :\ Loop until num=0 MOV R2,R2,LSR #16:STR R2,crc :\ Store outgoing CRC MOV R15,R14 .xor:EQUD &10210000 :\ ZIP polynomic .addr:EQUD 0:.num:EQUD 0 .crc:EQUD 0
Sample calling code
Multiple passes over data can be made, for instance, as an input file is copied to an output file. The following code demonstrates how to do this, copying from an open file on in% to an open file on out%, calculating an XMODEM CRC-16 as it goes.
S%=0 :REM CRC starts as &0000 REPEAT num%=EXT#in%-PTR#in% :REM Number of bytes to transfer IF num%>max% THEN num%=max% :REM If more than size of buffer max%, use max% PROCgbpb(rd%,in%,mem%,num%,0) :REM Read block of data PROCcrc :REM Update CRC PROCgbpb(wr%,out%,mem%,num%,0) :REM Write block of data UNTIL PTR#in%=EXT#in% :REM Loop until all done</pre>
The CRC is calculated with one of the following subroutines:
REM BASIC: DEFPROCcrc:FORA%=mem%TOmem%+num%-1:S%=S%EOR256*?A%:FORB%=1TO8:S%=S%*2:IFS%AND&10000:S%=S%EOR&11021 NEXT:NEXT:ENDPROC REM Assembler: DEFPROCcrc:!addr=mem%:!num=num%:!crc=S%:CALL Calc:S%=!crc:ENDPROC : REM With CRC-16 code previously assembled with: : REM Crunched assembler routines REM --------------------------- DEFPROCcrc65:DIM Calc 49:addr=&70:num=&72:crc=&74:FORP=0TO1 P%=Calc:[OPT P*2:.bl:LDX #8:LDA (addr-8 AND &FF,X) EOR crc+1:.rl:ASL crc:ROL A:BCC cl:TAY LDA crc:EOR #&21:STA crc:TYA:EOR #&10:.cl:DEX BNE rl:STA crc+1:INC addr:BNE nx:INC addr+1:.nx LDA num:BNE sk:DEC num+1:.sk:DEC num:BNE bl LDA num+1:BNE bl:RTS:]:NEXT:ENDPROC : DEFPROCcrc80:DIM Calc 49:addr=&70:num=&72:crc=&74:FORP=0TO1 P%=Calc:[OPT P*2:LD HL,(addr):LD BC,(num):LD DE,(crc) .bl:PUSH BC:LD A,(HL):XOR D:LD B,8 .rl:SLA E:ADC A,A:JP NC,cl:LD D,A:LD A,E:XOR &21 LD E,A:LD A,D:XOR &10:.cl:DEC B:LD D,A:JP NZ,rl INC HL:POP BC:DEC BC:LD A,B:OR C:JP NZ,bl LD (crc),DE:RET:]:NEXT:ENDPROC : DEFPROCcrc86:DIM Calc 71:FORP=0TO1 P%=Calc:[OPT P*2:MOV ESI,[addr]:MOV EBX,[num] MOV ECX,[crc]:SHL ECX,16:.bl:MOV AL,[ESI]:SHL EAX,24 XOR ECX,EAX:MOV AL,8:.rl:SHL ECX,1:JNC cl:XOR ECX,&10210000 .cl:DEC AL:JNZ rl:INC SI:DEC EBX:JNE blp:SHR ECX,16:MOV [crc],ECX RETF:.addr:DD 0:.num:DD 0:.crc:DD 0:]:NEXT:ENDPROC : DEFPROCcrcARM:DIM Calc 83:FORP=0TO1 P%=Calc:[OPT P*2:LDR R0,addr:LDR R1,num LDR R2,crc:MOV R2,R2,LSL #16:LDR R3,xor .bl:LDRB R4,[R0],#1:EOR R2,R2,R4,LSL #24:MOV R4,#8 .rl:MOVS R2,R2,LSL #1:EORCS R2,R2,R3 SUBS R4,R4,#1:BNE rl:SUBS R1,R1,#1:BNE bl MOV R2,R2,LSR #16:STR R2,crc:MOV R15,R14 .xor:EQUD &10210000:.addr:EQUD 0:.num:EQUD 0 .crc:EQUD 0:]:NEXT:ENDPROC :
External links
- Calculating CRC-16 at mdfs.net.
- 16-bit 6502 decrement code
