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📁 CRC16的源程序
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tppabs="http://www.brokersys.com/snippets/#section1group26">www.brokersys.com/snippets/#section1group26</A> 
</P>
<P align=left>Robert Lee's optimized code for CRC computation:<BR><A 
href="javascript:if(confirm('http://www.optimalcode.com/excrc.zip%20%20\n\nThis%20file%20was%20not%20retrieved%20by%20Teleport%20Pro,%20because%20it%20is%20addressed%20on%20a%20domain%20or%20path%20outside%20the%20boundaries%20set%20for%20its%20Starting%20Address.%20%20\n\nDo%20you%20want%20to%20open%20it%20from%20the%20server?'))window.location='http://www.optimalcode.com/excrc.zip'" 
tppabs="http://www.optimalcode.com/excrc.zip">www.optimalcode.com/excrc.zip</A>&nbsp; 
</P>
<P>Checksum-Algorithms: XOR16, XOR32, CRC32<BR><A 
href="javascript:if(confirm('http://sunsite.icm.edu.pl/delphi/ftp/d20free/cipher.zip%20%20\n\nThis%20file%20was%20not%20retrieved%20by%20Teleport%20Pro,%20because%20it%20is%20addressed%20on%20a%20domain%20or%20path%20outside%20the%20boundaries%20set%20for%20its%20Starting%20Address.%20%20\n\nDo%20you%20want%20to%20open%20it%20from%20the%20server?'))window.location='http://sunsite.icm.edu.pl/delphi/ftp/d20free/cipher.zip'" 
tppabs="http://sunsite.icm.edu.pl/delphi/ftp/d20free/cipher.zip">http://sunsite.icm.edu.pl/delphi/ftp/d20free/cipher.zip</A> 
</P>
<P align=left>Steve Schafer's <A 
href="http://plum.ia.polsl.gliwice.pl/~DIP/efg/Library/UseNet/1999/0117.txt" 
tppabs="http://www.efg2.com/Lab/Library/UseNet/1999/0117.txt">UseNet Post</A> 
showing calculation of CRC-32 Lookup Table</P><B><FONT face=geneva,arial size=2>
<P></FONT></B><FONT size=3>Bj鰎n Kriedemann's</FONT><FONT face=geneva,arial 
size=2> </FONT><A 
href="http://plum.ia.polsl.gliwice.pl/~DIP/efg/Library/UseNet/1999/1028a.txt" 
tppabs="http://www.efg2.com/Lab/Library/UseNet/1999/1028a.txt">UseNet Post</A> 
with CRC Unit from April 1997 DDJ:&nbsp; CRC16, XYZModemCRC16, CRC32</P>
<P align=left>Lars Truijens's <A 
href="http://plum.ia.polsl.gliwice.pl/~DIP/efg/Library/UseNet/1999/0630b.txt" 
tppabs="http://www.efg2.com/Lab/Library/UseNet/1999/0630b.txt">UseNet Post</A> 
showing Delphi code for XModem CRC-16 (X<SUP>16</SUP> + X<SUP>12</SUP> + 
X<SUP>5</SUP> + 1) with a Lookup Table</P>
<P align=left>CRC-16 (X<SUP>16</SUP>+X<SUP>15</SUP>+X<SUP>2</SUP>+1) without 
lookup table, <A 
href="javascript:if(confirm('http://www.ibrtses.com/delphi/dcrc.html%20%20\n\nThis%20file%20was%20not%20retrieved%20by%20Teleport%20Pro,%20because%20it%20is%20addressed%20on%20a%20domain%20or%20path%20outside%20the%20boundaries%20set%20for%20its%20Starting%20Address.%20%20\n\nDo%20you%20want%20to%20open%20it%20from%20the%20server?'))window.location='http://www.ibrtses.com/delphi/dcrc.html'" 
tppabs="http://www.ibrtses.com/delphi/dcrc.html">www.ibrtses.com/delphi/dcrc.html</A> 
.</P>
<P align=left>A CRC Calculator Unit provides three speed-optimized functions to 
compute (or continue computation of) a Cyclic Redundancy Check (CRC). Applicable 
to XModem protocol (16-bit CRC), SEA's "ARC" utility, PKZip (32-bit CRC) and 
many others compatible software,&nbsp; <A 
href="javascript:if(confirm('http://sunsite.icm.edu.pl/delphi/ftp/d10free/crc.zip%20%20\n\nThis%20file%20was%20not%20retrieved%20by%20Teleport%20Pro,%20because%20it%20is%20addressed%20on%20a%20domain%20or%20path%20outside%20the%20boundaries%20set%20for%20its%20Starting%20Address.%20%20\n\nDo%20you%20want%20to%20open%20it%20from%20the%20server?'))window.location='http://sunsite.icm.edu.pl/delphi/ftp/d10free/crc.zip'" 
tppabs="http://sunsite.icm.edu.pl/delphi/ftp/d10free/crc.zip">http://SunSITE.ICM.edu.pl/delphi/ftp/d10free/crc.zip</A> 
.</P>
<P align=left>SWAG (Software Archive Group) CRC Snipets:&nbsp; Includes various 
CRC and Checksum routines<BR><A 
href="javascript:if(confirm('http://www.gdsoft.com/swag/downloads.html%20%20\n\nThis%20file%20was%20not%20retrieved%20by%20Teleport%20Pro,%20because%20it%20is%20addressed%20on%20a%20domain%20or%20path%20outside%20the%20boundaries%20set%20for%20its%20Starting%20Address.%20%20\n\nDo%20you%20want%20to%20open%20it%20from%20the%20server?'))window.location='http://www.gdsoft.com/swag/downloads.html'" 
tppabs="http://www.gdsoft.com/swag/downloads.html">www.gdsoft.com/swag/downloads.html</A> 
<BR><A 
href="javascript:if(confirm('http://www.gdsoft.com/swag/crc.zip%20%20\n\nThis%20file%20was%20not%20retrieved%20by%20Teleport%20Pro,%20because%20it%20is%20addressed%20on%20a%20domain%20or%20path%20outside%20the%20boundaries%20set%20for%20its%20Starting%20Address.%20%20\n\nDo%20you%20want%20to%20open%20it%20from%20the%20server?'))window.location='http://www.gdsoft.com/swag/crc.zip'" 
tppabs="http://www.gdsoft.com/swag/crc.zip">www.gdsoft.com/swag/crc.zip</A> 
(requires "<A 
href="javascript:if(confirm('ftp://ftp.gdsoft.com/pub/swag/swag.zip%20%20\n\nThis%20file%20was%20not%20retrieved%20by%20Teleport%20Pro,%20because%20it%20is%20addressed%20on%20a%20domain%20or%20path%20outside%20the%20boundaries%20set%20for%20its%20Starting%20Address.%20%20\n\nDo%20you%20want%20to%20open%20it%20from%20the%20server?'))window.location='ftp://ftp.gdsoft.com/pub/swag/swag.zip'" 
tppabs="ftp://ftp.gdsoft.com/pub/swag/swag.zip">Reader</A>" program to view)</P>
<P align=left>Algorithm of CRC-32 calculation for file<BR><A 
href="javascript:if(confirm('http://www.scalabium.com/faq/dct0048.htm%20%20\n\nThis%20file%20was%20not%20retrieved%20by%20Teleport%20Pro,%20because%20it%20is%20addressed%20on%20a%20domain%20or%20path%20outside%20the%20boundaries%20set%20for%20its%20Starting%20Address.%20%20\n\nDo%20you%20want%20to%20open%20it%20from%20the%20server?'))window.location='http://www.scalabium.com/faq/dct0048.htm'" 
tppabs="http://www.scalabium.com/faq/dct0048.htm">www.scalabium.com/faq/dct0048.htm</A>&nbsp;</P>
<P align=left>"Calculating CRC Checksums in C++" by Colin Mahoney in <A 
href="javascript:if(confirm('http://www.cuj.com/archive/1706%20%20\n\nThis%20file%20was%20not%20retrieved%20by%20Teleport%20Pro,%20because%20it%20is%20addressed%20on%20a%20domain%20or%20path%20outside%20the%20boundaries%20set%20for%20its%20Starting%20Address.%20%20\n\nDo%20you%20want%20to%20open%20it%20from%20the%20server?'))window.location='http://www.cuj.com/archive/1706'" 
tppabs="http://www.cuj.com/archive/1706">June 1999</A> <EM>C/C++ Users 
Journal.</EM></P>
<P>Algorithms Alfresco: Whirlpool (CRC Algorithms), Julian Bucknall unravels 
CRC, <EM>Delphi Magazine</EM>, <A 
href="javascript:if(confirm('http://www.itecuk.com/delmag/conts/conts48.htm%20%20\n\nThis%20file%20was%20not%20retrieved%20by%20Teleport%20Pro,%20because%20it%20is%20addressed%20on%20a%20domain%20or%20path%20outside%20the%20boundaries%20set%20for%20its%20Starting%20Address.%20%20\n\nDo%20you%20want%20to%20open%20it%20from%20the%20server?'))window.location='http://www.itecuk.com/delmag/conts/conts48.htm'" 
tppabs="http://www.itecuk.com/delmag/conts/conts48.htm">Issue 48</A>, August 
1999.&nbsp; <A 
href="javascript:if(confirm('http://www.itecuk.com/delmag/disks/dmag48.zip%20%20\n\nThis%20file%20was%20not%20retrieved%20by%20Teleport%20Pro,%20because%20it%20is%20addressed%20on%20a%20domain%20or%20path%20outside%20the%20boundaries%20set%20for%20its%20Starting%20Address.%20%20\n\nDo%20you%20want%20to%20open%20it%20from%20the%20server?'))window.location='http://www.itecuk.com/delmag/disks/dmag48.zip'" 
tppabs="http://www.itecuk.com/delmag/disks/dmag48.zip">Download Disk</A>.</P>
<P>Checksum example (assembly language)<BR><A 
href="javascript:if(confirm('http://www.delphi3000.com/article.asp?ID=298  \n\nThis file was not retrieved by Teleport Pro, because it is addressed on a domain or path outside the boundaries set for its Starting Address.  \n\nDo you want to open it from the server?'))window.location='http://www.delphi3000.com/article.asp?ID=298'" 
tppabs="http://www.delphi3000.com/article.asp?ID=298">www.delphi3000.com/article.asp?ID=298</A> 
&nbsp; </P>
<P>Split and Join&nbsp; (use CRCs to verify copy is correct after a file is 
split into separate floppy-size files and later rejoined)<BR><A 
href="javascript:if(confirm('http://www.undu.com/Articles/010511d.html%20%20\n\nThis%20file%20was%20not%20retrieved%20by%20Teleport%20Pro,%20because%20it%20is%20addressed%20on%20a%20domain%20or%20path%20outside%20the%20boundaries%20set%20for%20its%20Starting%20Address.%20%20\n\nDo%20you%20want%20to%20open%20it%20from%20the%20server?'))window.location='http://www.undu.com/Articles/010511d.html'" 
tppabs="http://www.undu.com/Articles/010511d.html">www.undu.com/Articles/010511d.html</A>&nbsp; 
</P>
<P align=left><A name=Literature></A><BIG><STRONG>Useful 
literature:</STRONG></BIG><BR>"Procedure for Computing CRC-32 Values," 
<EM>Microsoft Systems Journal</EM>, March 1995, pp. 107-108.</P>
<P align=left>"Byte-wise CRC Calculations" by Aram Perez in <EM>IEEE Micro</EM>, 
June 1983, pp. 40-50. Shows how to create a lookup table which is the best way 
to implement in software (versus the shifts that are done when implemented in 
hardware).&nbsp;</P>
<P align=left>"A Tutorial on CRC Computations" by Tenkasi V. Ramabadran and 
Sunil S. Gaitonde in <EM>IEEE Micro</EM>, August 1988, pp. 62-75.</P>
<P align=left>"Cyclic Redundancy Checks for Data Integrity or Identity" by 
William H. Press and Saul A. Teukolsky, <EM>Computers in Physics</EM>, Jul/Aug 
1989, pp. 88-91.</P>
<DIV align=center>
<CENTER>
<TABLE border=1>
  <TBODY>
  <TR>
    <TD><STRONG>Standard Name</STRONG></TD>
    <TD>CRC-CCITT (X25)</TD>
    <TD>CRC-16 (SDLC)</TD>
    <TD>CRC-32 (Ethernet)</TD></TR>
  <TR>
    <TD><STRONG>Width</STRONG></TD>
    <TD>16 bits</TD>
    <TD>16 bits</TD>
    <TD>32 bits</TD></TR>
  <TR>
    <TD><STRONG>Generator Polynomial</STRONG></TD>
    <TD vAlign=top>10001000000100001 
      <P>x<SUP>16 </SUP>+ x<SUP>12</SUP> + x<SUP>5</SUP> + 1</P></TD>
    <TD vAlign=top>11000000000000101 
      <P>x<SUP>16</SUP> + x<SUP>15</SUP> + x<SUP>2</SUP> + 1</P></TD>
    <TD vAlign=top>100000100110000010001110110110111 
      <P>x<SUP>32</SUP> + x<SUP>26</SUP> + x<SUP>23</SUP> + x<SUP>22</SUP> + 
      x<SUP>16</SUP> + x<SUP>12</SUP> + x<SUP>11</SUP> +&nbsp;<BR>x<SUP>10</SUP> 
      + x<SUP>8</SUP> + x<SUP>7</SUP> + x<SUP>5</SUP> + x<SUP>4</SUP> + 
      x<SUP>2</SUP> + x + 1</P></TD></TR>
  <TR>
    <TD><STRONG>Initial remainder</STRONG></TD>
    <TD>0xFFFF</TD>
    <TD>0x0000</TD>
    <TD>0xFFFFFFFF</TD></TR>
  <TR>
    <TD><STRONG>Final XOR value</STRONG></TD>
    <TD>0x0000</TD>
    <TD>0x0000</TD>
    <TD>0xFFFFFFFF</TD></TR></TBODY></TABLE></CENTER></DIV>
<P align=left>Other standard polynomials:<BR>CRC-12:&nbsp; x<SUP>12</SUP> + 
x<SUP>11</SUP> + x<SUP>3</SUP> + x<SUP>2</SUP> + x + 1</P>
<P align=left><FONT size=4><STRONG>Conclusions<BR></STRONG></FONT>CRC values, 
especially the CRC-32, are an extremely good way to verify the integrity of a 
string or even a&nbsp; file.</P>
<HR>

<P align=left><FONT size=4><STRONG>Keywords</STRONG><BR></FONT>cyclic redundancy 
check, CRC-16, CRC-32, APPTYPE CONSOLE, lookup table, XOR, Comp, Int64, 
IntToHex, Addr</P>
<P align=left><FONT size=4><STRONG>Files<BR></STRONG></FONT>Delphi 2/3/4/5 
Source and EXE (234 KB):&nbsp;&nbsp; <A 
href="http://plum.ia.polsl.gliwice.pl/~DIP/efg/Mathematics/CRCDelphi.ZIP" 
tppabs="http://www.efg2.com/Lab/Mathematics/CRCDelphi.ZIP">CRCDelphi.ZIP</A></P>
<P align=left>Borland C++ 5.02 "C" CRC-32 Source and EXE (45 KB):&nbsp; <A 
href="javascript:if(confirm('http://www.efg2.com/Lab/Mathematics/CRCC.ZIP%20%20\n\nThis%20file%20was%20not%20retrieved%20by%20Teleport%20Pro,%20because%20the%20server%20reports%20that%20this%20file%20cannot%20be%20found.%20%20\n\nDo%20you%20want%20to%20open%20it%20from%20the%20server?'))window.location='http://www.efg2.com/Lab/Mathematics/CRCC.ZIP'" 
tppabs="http://www.efg2.com/Lab/Mathematics/CRCC.ZIP">CRCC.ZIP</A><BR>Use the 
"make file" to compile:&nbsp; <FONT face="Arial Narrow">make -f 
crc32.mak</FONT><BR>(Modify <EM>.mak</EM> file to point to correct location of 
<EM>wildargs.obj</EM>.&nbsp; The <EM>.mak</EM> file automatically performs a 
test that the results will match those of PKZIP.)&nbsp; This command-line 
utility can be used with wildcards to find the CRC-32 of files in a directory, 
for example:&nbsp; <FONT face="Arial Narrow">crc32 *.*</FONT></P>
<P align=left>TP 5.5 program to <A 
href="http://plum.ia.polsl.gliwice.pl/~DIP/efg/Mathematics/CRCTable16.pas.txt" 
tppabs="http://www.efg2.com/Lab/Mathematics/CRCTable16.pas.txt">compute values 
for CRC-16 lookup table</A>.</P>
<P align=left>Felipe Rocha Machado's <A 
href="http://plum.ia.polsl.gliwice.pl/~DIP/efg/Mathematics/FelipeRochaMachado.TXT" 
tppabs="http://www.efg2.com/Lab/Mathematics/FelipeRochaMachado.TXT">comments</A> 
about printing 32-bit integers in D3.</P>
<P align=left>The Delphi&nbsp; 5 CDs (Version 3 through 5) have C code in 
\Info\Extras\Zlib\Src\CRC32.C</P>
<HR>

<P align=center><FONT size=1>Links verified 17 Jan 2001<BR>Updated <!--webbot bot="Timestamp" S-Type="EDITED" S-Format="%d %b %Y" startspan -->19 
Jun 2001<!--webbot bot="Timestamp" endspan i-checksum="15063" --></FONT></P>
<P align=center><IMG src="" 
tppabs="http://www.efg2.com/cgi-local/count.pl?L720CRC"><FONT size=1><BR>since 
29 Nov 1998</FONT></P>
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