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| <h1><img src="../../boost.png" alt="boost.png (6897 bytes)" |
| align="middle" width="277" height="86">Header <cite><<a |
| href="../../boost/crc.hpp">boost/crc.hpp</a>></cite></h1> |
| |
| <p>The header <cite><<a |
| href="../../boost/crc.hpp">boost/crc.hpp</a>></cite> supplies two |
| class templates in namespace <code>boost</code>. These templates define |
| objects that can compute the <dfn>CRC</dfn>, or cyclic redundancy code |
| (or check), of a given stream of data. The header also supplies |
| function templates to compute a CRC in one step.</p> |
| |
| <h2><a name="contents">Contents</a></h2> |
| |
| <ol> |
| <li><a href="#contents">Contents</a></li> |
| <li><a href="#header">Header Synopsis</a></li> |
| <li><a href="#rationale">Rationale</a></li> |
| <li><a href="#background">Background</a> |
| <ul> |
| <li><a href="#parameters">CRC Parameters</a></li> |
| </ul></li> |
| <li><a href="#crc_basic">Theoretical CRC Computer</a></li> |
| <li><a href="#crc_optimal">Optimized CRC Computer</a></li> |
| <li><a href="#usage">Computer Usage</a></li> |
| <li><a href="#crc_func">CRC Function</a></li> |
| <li><a href="#a_crc_func">Augmented-CRC Functions</a></li> |
| <li><a href="#crc_ex">Pre-Defined CRC Samples</a></li> |
| <li><a href="#references">References</a></li> |
| <li><a href="#credits">Credits</a> |
| <ul> |
| <li><a href="#contributors">Contributors</a></li> |
| <li><a href="#acknowledgements">Acknowledgements</a></li> |
| <li><a href="#history">History</a></li> |
| </ul></li> |
| </ol> |
| |
| <h2><a name="header">Header Synopsis</a></h2> |
| |
| <blockquote><pre>#include <boost/integer.hpp> <i>// for boost::uint_t</i> |
| #include <cstddef> <i>// for std::size_t</i> |
| |
| namespace boost |
| { |
| |
| template < std::size_t Bits > |
| class crc_basic; |
| |
| template < std::size_t Bits, <em>impl_def</em> TruncPoly = 0u, |
| <em>impl_def</em> InitRem = 0u, |
| <em>impl_def</em> FinalXor = 0u, bool ReflectIn = false, |
| bool ReflectRem = false > |
| class crc_optimal; |
| |
| template < std::size_t Bits, <em>impl_def</em> TruncPoly, |
| <em>impl_def</em> InitRem, <em>impl_def</em> FinalXor, |
| bool ReflectIn, bool ReflectRem > |
| typename uint_t<Bits>::fast crc( void const *buffer, |
| std::size_t byte_count ); |
| |
| template < std::size_t Bits, <em>impl_def</em> TruncPoly > |
| typename uint_t<Bits>::fast augmented_crc( void const *buffer, |
| std::size_t byte_count, |
| typename uint_t<Bits>::fast initial_remainder ); |
| |
| template < std::size_t Bits, <em>impl_def</em> TruncPoly > |
| typename uint_t<Bits>::fast augmented_crc( void const *buffer, |
| std::size_t byte_count ); |
| |
| typedef crc_optimal<16, 0x8005, 0, 0, true, true> crc_16_type; |
| typedef crc_optimal<16, 0x1021, 0xFFFF, 0, false, false> crc_ccitt_type; |
| typedef crc_optimal<16, 0x8408, 0, 0, true, true> crc_xmodem_type; |
| |
| typedef crc_optimal<32, 0x04C11DB7, 0xFFFFFFFF, 0xFFFFFFFF, true, true> |
| crc_32_type; |
| |
| } |
| </pre></blockquote> |
| |
| <p>The implementation-defined type <var>impl_def</var> stands for the |
| quickest-to-manipulate built-in unsigned integral type that can |
| represent at least <var>Bits</var> bits.</p> |
| |
| <h2><a name="rationale">Rationale</a></h2> |
| |
| <p>A common error detection technique, especially with electronic |
| communications, is an appended checksum. The transmitter sends its data |
| bits, followed by the bits of the checksum. The checksum is based on |
| operations done on the data bit stream. The receiver applies the same |
| operations on the bits it gets, and then gets the checksum. If the |
| computed checksum doesn't match the received checksum, then an error |
| ocurred in the transmission. There is the slight chance that the error |
| is only in the checksum, and an actually-correct data stream is |
| rejected. There is also the chance of an error occurring that does not |
| change the checksum, making that error invisible. CRC is a common |
| checksum type, used for error detection for hardware interfaces and |
| encoding formats.</p> |
| |
| <h2><a name="background">Background</a></h2> |
| |
| <p>CRCs work by computing the remainder of a modulo-2 polynominal |
| division. The message is treated as the (binary) coefficents of a long |
| polynominal for the dividend, with the earlier bits of the message fed |
| first as the polynominal's highest coefficents. A particular CRC |
| algorithm has another polynominal associated with it to be used as the |
| divisor. The quotient is ignored. The remainder of the division |
| considered the checksum. However, the division uses modulo-2 rules (no |
| carries) for the coefficents.</p> |
| |
| <p>See <cite><a href="http://www.ross.net/crc/crcpaper.html">A |
| Painless Guide to CRC Error Detection Algorithms</a></cite> for complete |
| information. A clearer guide is at the <a |
| href="http://www.netrino.com/Connecting/2000-01/">Easier Said Than |
| Done</a> web page.</p> |
| |
| <h3><a name="parameters">CRC Parameters</a></h3> |
| |
| <dl> |
| <dt>Truncated polynominal |
| <dd>The divisor polynominal has a degree one bit larger than the |
| checksum (remainder) size. That highest bit is always one, so |
| it is ignored when describing a particular CRC type. Excluding |
| this bit makes the divisor fit in the same data type as the |
| checksum. |
| |
| <dt>Initial remainder |
| <dd>The interim CRC remainder changes as each bit is processed. |
| Usually, the interim remainder starts at zero, but some CRCs use |
| a different initial value to avoid "blind spots." A |
| blind spot is when a common sequence of message bits does not |
| change certain interim remainder values. |
| |
| <dt>Final XOR value |
| <dd>A CRC remainder can be combined with a defined value, <i>via</i> |
| a bitwise exclusive-or operation, before being returned to the |
| user. The value is usually zero, meaning the interim remainder |
| is returned unchanged. The other common value is an all-ones |
| value, meaning that the bitwise complement of the interim |
| remainder is returned. |
| |
| <dt>Reflected input |
| <dd>A message's bits are usually fed a byte at a time, with the |
| highest bits of the byte treated as the higher bits of the |
| dividend polynominal. Some CRCs reflect the bits (about the |
| byte's center, so the first and last bits are switched, |
| <i>etc.</i>) before feeding. |
| |
| <dt>Reflected (remainder) output |
| <dd>Some CRCs return the reflection of the interim remainder (taking |
| place <em>before</em> the final XOR value stage). |
| </dl> |
| |
| <h2><a name="crc_basic">Theoretical CRC Computer</a></h2> |
| |
| <blockquote><pre>template < std::size_t Bits > |
| class boost::crc_basic |
| { |
| public: |
| // Type |
| typedef <em>implementation_defined</em> value_type; |
| |
| // Constant reflecting template parameter |
| static std::size_t const bit_count = Bits; |
| |
| // Constructor |
| explicit crc_basic( value_type truncated_polynominal, |
| value_type initial_remainder = 0, value_type final_xor_value = 0, |
| bool reflect_input = false, bool reflect_remainder = false ); |
| |
| // Internal Operations |
| value_type get_truncated_polynominal() const; |
| value_type get_initial_remainder() const; |
| value_type get_final_xor_value() const; |
| bool get_reflect_input() const; |
| bool get_reflect_remainder() const; |
| |
| value_type get_interim_remainder() const; |
| void reset( value_type new_rem ); |
| void reset(); |
| |
| // External Operations |
| void process_bit( bool bit ); |
| void process_bits( unsigned char bits, std::size_t bit_count ); |
| void process_byte( unsigned char byte ); |
| void process_block( void const *bytes_begin, void const *bytes_end ); |
| void process_bytes( void const *buffer, std::size_t byte_count ); |
| |
| value_type checksum() const; |
| |
| }; |
| </pre></blockquote> |
| |
| <p>The <code>value_type</code> is the smallest built-in type that can |
| hold the specified (by <code>Bits</code>) number of bits. This should |
| be <code>boost::uint_t<Bits>::least</code>, see the <a |
| href="../integer/doc/html/boost_integer/integer.html">documentation for integer type |
| selection</a> for details.</p> |
| |
| <p>This implementation is slow since it computes its CRC the same way as |
| in theory, bit by bit. No optimizations are performed. It wastes space |
| since most of the CRC parameters are specified at run-time as |
| constructor parameters.</p> |
| |
| <h2><a name="crc_optimal">Optimized CRC Computer</a></h2> |
| |
| <blockquote><pre>template < std::size_t Bits, <em>impl_def</em> TruncPoly, |
| <em>impl_def</em> InitRem, <em>impl_def</em> FinalXor, |
| bool ReflectIn, bool ReflectRem > |
| class boost::crc_optimal |
| { |
| public: |
| // Type |
| typedef <em>implementation_defined</em> value_type; |
| |
| // Constants reflecting template parameters |
| static std::size_t const bit_count = Bits; |
| static value_type const truncated_polynominal = TruncPoly; |
| static value_type const initial_remainder = InitRem; |
| static value_type const final_xor_value = FinalXor; |
| static bool const reflect_input = ReflectIn; |
| static bool const reflect_remainder = ReflectRem; |
| |
| // Constructor |
| explicit crc_optimal( value_type init_rem = InitRem ); |
| |
| // Internal Operations |
| value_type get_truncated_polynominal() const; |
| value_type get_initial_remainder() const; |
| value_type get_final_xor_value() const; |
| bool get_reflect_input() const; |
| bool get_reflect_remainder() const; |
| |
| value_type get_interim_remainder() const; |
| void reset( value_type new_rem = InitRem ); |
| |
| // External Operations |
| void process_byte( unsigned char byte ); |
| void process_block( void const *bytes_begin, void const *bytes_end ); |
| void process_bytes( void const *buffer, std::size_t byte_count ); |
| |
| value_type checksum() const; |
| |
| // Operators |
| void operator ()( unsigned char byte ); |
| value_type operator ()() const; |
| |
| }; |
| </pre></blockquote> |
| |
| <p>The <code>value_type</code> is the quickest-to-manipulate built-in |
| type that can hold at least the specified (by <code>Bits</code>) number |
| of bits. This should be <code>boost::uint_t<Bits>::fast</code>. |
| See the <a href="../integer/doc/html/boost_integer/integer.html">integer type selection |
| documentation</a> for details. The <code>TruncPoly</code>, |
| <code>InitRem</code>, and <code>FinalXor</code> template parameters also |
| are of this type.</p> |
| |
| <p>This implementation is fast since it uses as many optimizations as |
| practical. All of the CRC parameters are specified at compile-time as |
| template parameters. No individual bits are considered; only whole |
| bytes are passed. A table of interim CRC values versus byte values is |
| pre-computed when the first object using a particular bit size, |
| truncated polynominal, and input reflection state is processed.</p> |
| |
| <h2><a name="usage">Computer Usage</a></h2> |
| |
| <p>The two class templates have different policies on where the CRC's |
| parameters go. Both class templates use the number of bits in the CRC |
| as the first template parameter. The theoretical computer class |
| template has the bit count as its only template parameter, all the other |
| CRC parameters are entered through the constructor. The optimized |
| computer class template obtains all its CRC parameters as template |
| parameters, and instantiated objects are usually |
| default-constructed.</p> |
| |
| <p>The CRC parameters can be inspected at run-time with the following |
| member functions: <code>get_truncated_polynominal</code>, |
| <code>get_initial_remainder</code>, <code>get_final_xor_value</code>, |
| <code>get_reflect_input</code>, and <code>get_reflect_remainder</code>. |
| The fast computer also provides compile-time constants for its CRC |
| parameters.</p> |
| |
| <p>The <code>get_interim_remainder</code> member function returns the |
| internal state of the CRC remainder. It represents the unreflected |
| remainder of the last division. Saving an interim remainder allows the |
| freezing of CRC processing, as long as the other CRC parameters and the |
| current position of the bit stream are saved. Restarting a frozen |
| stream involves constructing a new computer with the most of the old |
| computer's parameters. The only change is to use the frozen remainder |
| as the new computer's initial remainder. Then the interrupted bit |
| stream can be fed as if nothing happened. The fast CRC computer has a |
| special constructor that takes one argument, an interim remainder, for |
| this purpose (overriding the initial remainder CRC parameter).</p> |
| |
| <p>The <code>reset</code> member functions reset the internal state of |
| the CRC remainder to the given value. If no value is given, then the |
| internal remainder is set to the initial remainder value when the object |
| was created. The remainder must be unreflected. When a CRC calculation |
| is finished, calling <code>reset</code> lets the object be reused for a |
| new session.</p> |
| |
| <p>After any construction, both CRC computers work the same way. |
| Feeding new data to a computer is in a seperate operation(s) from |
| extracting the current CRC value from the computer. The following table |
| lists the feeding and extracting operations.</p> |
| |
| <table cellpadding="5" border="1"> |
| <caption>Regular CRC Operations</caption> |
| <tr> |
| <th>Operation</th> |
| <th>Description</th> |
| </tr> |
| <tr> |
| <td><code>void process_bit( bool bit );</code></td> |
| <td>Feeds the single <var>bit</var> to the computer, updating |
| the interim CRC. It is only defined for the slow CRC |
| computer.</td> |
| </tr> |
| <tr> |
| <td><code>void process_bits( unsigned char bits, std::size_t |
| bit_count );</code></td> |
| <td>Acts as applying <code>process_bit</code> to the lowest |
| <var>bit_count</var> bits given in <var>bits</var>, most |
| significant relevant bit first. The results are undefined |
| if <var>bit_count</var> exceeds the number of bits per byte. |
| It is only defined for the slow CRC computer.</td> |
| </tr> |
| <tr> |
| <td><code>void process_byte( unsigned char byte );</code></td> |
| <td>Acts as applying <code>process_bit</code> to the all the |
| bits in <var>byte</var>. If reflection is not desired, the |
| bits are fed from the most to least significant. The bits |
| are fed in the opposite order if reflection is desired.</td> |
| </tr> |
| <tr> |
| <td><code>void process_block( void const *bytes_begin, void |
| const *bytes_end );</code></td> |
| <td>Acts as applying <code>process_byte</code> to each byte in |
| the given memory block. This memory block starts at |
| <var>bytes_begin</var> and finishes before |
| <var>bytes_end</var>. The bytes are processed in that |
| order.</td> |
| </tr> |
| <tr> |
| <td><code>void process_bytes( void const *buffer, std::size_t |
| byte_count );</code></td> |
| <td>Acts as applying <code>process_byte</code> to each byte in |
| the given memory block. This memory block starts at |
| <var>buffer</var> and lasts for <var>byte_count</var> bytes. |
| The bytes are processed in ascending order.</td> |
| </tr> |
| <tr> |
| <td><code>value_type checksum() const;</code></td> |
| <td>Returns the CRC checksum of the data passed in so far, |
| possibly after applying the remainder-reflection and |
| exclusive-or operations.</td> |
| </tr> |
| <tr> |
| <td><code>void operator ()( unsigned char byte );</code></td> |
| <td>Calls <code>process_byte</code>. This member function lets |
| its object act as a (stateful) function object. It is only |
| defined for the fast CRC computer.</td> |
| </tr> |
| <tr> |
| <td><code>value_type operator ()() const;</code></td> |
| <td>Calls <code>checksum</code>. This member function lets |
| its object act as a generator function object. It is only |
| defined for the fast CRC computer.</td> |
| </tr> |
| </table> |
| |
| <p>You can use them like this:</p> |
| |
| <blockquote><pre>#include <boost/crc.hpp> <i>// for boost::crc_basic, boost::crc_optimal</i> |
| #include <boost/cstdint.hpp> <i>// for boost::uint16_t</i> |
| |
| #include <algorithm> <i>// for std::for_each</i> |
| #include <cassert> <i>// for assert</i> |
| #include <cstddef> <i>// for std::size_t</i> |
| #include <iostream> <i>// for std::cout</i> |
| #include <ostream> <i>// for std::endl</i> |
| |
| |
| // Main function |
| int |
| main () |
| { |
| // This is "123456789" in ASCII |
| unsigned char const data[] = { 0x31, 0x32, 0x33, 0x34, 0x35, 0x36, 0x37, |
| 0x38, 0x39 }; |
| std::size_t const data_len = sizeof( data ) / sizeof( data[0] ); |
| |
| // The expected CRC for the given data |
| boost::uint16_t const expected = 0x29B1; |
| |
| // Simulate CRC-CCITT |
| boost::crc_basic<16> crc_ccitt1( 0x1021, 0xFFFF, 0, false, false ); |
| crc_ccitt1.process_bytes( data, data_len ); |
| assert( crc_ccitt1.checksum() == expected ); |
| |
| // Repeat with the optimal version (assuming a 16-bit type exists) |
| boost::crc_optimal<16, 0x1021, 0xFFFF, 0, false, false> crc_ccitt2; |
| crc_ccitt2 = std::for_each( data, data + data_len, crc_ccitt2 ); |
| assert( crc_ccitt2() == expected ); |
| |
| std::cout << "All tests passed." << std::endl; |
| return 0; |
| } |
| </pre></blockquote> |
| |
| <h2><a name="crc_func">CRC Function</a></h2> |
| |
| <blockquote><pre>template < std::size_t Bits, <em>impl_def</em> TruncPoly, |
| <em>impl_def</em> InitRem, <em>impl_def</em> FinalXor, |
| bool ReflectIn, bool ReflectRem > |
| typename boost::uint_t<Bits>::fast |
| boost::crc( void const *buffer, std::size_t byte_count ); |
| </pre></blockquote> |
| |
| <p>The <code>boost::crc</code> function template computes the CRC of a |
| given data block. The data block starts at the address given by |
| <var>buffer</var> and lasts for <var>byte_count</var> bytes. The CRC |
| parameters are passed through template arguments, identical to the |
| optimized CRC computer (<a href="#crc_optimal">see above</a>). In fact, |
| such a computer is used to implement this function.</p> |
| |
| <h2><a name="a_crc_func">Augmented-CRC Functions</a></h2> |
| |
| <blockquote><pre>template < std::size_t Bits, <em>impl_def</em> TruncPoly > |
| typename boost::uint_t<Bits>::fast |
| boost::augmented_crc( void const *buffer, std::size_t byte_count, |
| typename boost::uint_t<Bits>::fast initial_remainder ); |
| |
| template < std::size_t Bits, <em>impl_def</em> TruncPoly > |
| typename boost::uint_t<Bits>::fast |
| boost::augmented_crc( void const *buffer, std::size_t byte_count ); |
| </pre></blockquote> |
| |
| <p>All the other CRC-computing function or class templates work assuming |
| that the division steps start immediately on the first message bits. |
| The two <code>boost::augmented_crc</code> function templates have a |
| different division order. Instead of combining (<i>via</i> bitwise |
| exclusive-or) the current message bit with the highest bit of a separate |
| remainder, these templates shift a new message bit into the low bit of a |
| remainder register as the highest bit is shifted out. The new method |
| means that the bits in the inital remainder value are processed before |
| any of the actual message bits are processed. To compensate, the real |
| CRC can only be extracted after feeding enough zero bits (the same count |
| as the register size) after the message bits.</p> |
| |
| <p>The template parameters of both versions of the function template are |
| the CRC's bit size (<code>Bits</code>) and the truncated polynominal |
| (<code>TruncPoly</code>). The version of the function template that |
| takes two arguments calls the three-argument version with the |
| <var>initial_remainder</var> parameter filled as zero. Both versions |
| work on the data block starting at the address <var>buffer</var> for |
| <var>byte_count</var> bytes.</p> |
| |
| <p>These function templates are useful if the bytes of the CRC directly |
| follow the message's bytes. First, set the bytes of where the CRC will |
| go to zero. Then use <code>augmented_crc</code> over the augmented |
| message, <i>i.e.</i> the message bytes and the appended CRC bytes. Then |
| assign the result to the CRC. To later check a received message, either |
| use <code>augmented_crc</code> (with the same parameters as |
| transmission, of course) on the received <em>unaugmented</em> message |
| and check if the result equals the CRC, or use |
| <code>augmented_crc</code> on the received <em>augmented</em> message |
| and check if the result equals zero. Note that the CRC has to be stored |
| with the more-significant bytes first (big-endian).</p> |
| |
| <p>Interruptions in the CRC data can be handled by feeding the result of |
| <code>augmented_crc</code> of the previous data block as the |
| <var>initial_remainder</var> when calling <code>augmented_crc</code> on |
| the next data block. Remember that the actual CRC can only be |
| determined after feeding the augmented bytes. Since this method uses |
| modulo-2 polynominal division at its most raw, neither final XOR values |
| nor reflection can be used.</p> |
| |
| <p>Note that for the same CRC system, the initial remainder for |
| augmented message method will be different than for the unaugmented |
| message method. The main exception is zero; if the augmented-CRC |
| algorithm uses a zero initial remainder, the equivalent unaugmented-CRC |
| algorithm will also use a zero initial remainder. Given an initial |
| remainder for a augmented-CRC algorithm, the result from processing just |
| zero-valued CRC bytes without any message bytes is the equivalent inital |
| remainder for the unaugmented-CRC algorithm. An example follows:</p> |
| |
| <blockquote><pre>#include <boost/crc.hpp> <i>// for boost::crc_basic, boost::augmented_crc</i> |
| #include <boost/cstdint.hpp> <i>// for boost::uint16_t</i> |
| |
| #include <cassert> <i>// for assert</i> |
| #include <iostream> <i>// for std::cout</i> |
| #include <ostream> <i>// for std::endl</i> |
| |
| |
| // Main function |
| int |
| main () |
| { |
| using boost::uint16_t; |
| using boost::augmented_crc; |
| |
| uint16_t data[6] = { 2, 4, 31, 67, 98, 0 }; |
| uint16_t const init_rem = 0x123; |
| |
| uint16_t crc1 = augmented_crc<16, 0x8005>( data, sizeof(data), init_rem ); |
| |
| uint16_t const zero = 0; |
| uint16_t const new_init_rem = augmented_crc<16, 0x8005>( &zero, sizeof(zero) ); |
| |
| boost::crc_basic<16> crc2( 0x8005, new_init_rem ); |
| crc2.process_block( data, &data[5] ); // don't include CRC |
| assert( crc2.checksum() == crc1 ); |
| |
| std::cout << "All tests passed." << std::endl; |
| return 0; |
| } |
| </pre></blockquote> |
| |
| <h2><a name="crc_ex">Pre-Defined CRC Samples</a></h2> |
| |
| <p>Four sample CRC types are given, representing several common CRC |
| algorithms. For example, computations from <code>boost::crc_32_type</code> |
| can be used for implementing the PKZip standard. Note that, in general, this |
| library is concerned with CRC implementation, and not with determining |
| "good" sets of CRC parameters.</p> |
| |
| <table cellpadding="5" border="1"> |
| <caption>Common CRCs</caption> |
| <tr> |
| <th>Algorithm</th> |
| <th>Example Protocols</th> |
| </tr> |
| <tr> |
| <td><code>crc_16_type</code></td> |
| <td>BISYNCH, ARC</td> |
| </tr> |
| <tr> |
| <td><code>crc_ccitt_type</code></td> |
| <td>designated by CCITT (Comité Consultatif International |
| Télégraphique et Téléphonique)</td> |
| </tr> |
| <tr> |
| <td><code>crc_xmodem_type</code></td> |
| <td>XMODEM</td> |
| </tr> |
| <tr> |
| <td><code>crc_32_type</code></td> |
| <td>PKZip, AUTODIN II, Ethernet, FDDI</td> |
| </tr> |
| </table> |
| |
| <hr> |
| |
| <h2><a name="references">References</a></h2> |
| |
| <ul> |
| <li>The CRC header itself: <cite><a href="../../boost/crc.hpp">crc.hpp</a></cite> |
| <li>Some test code: <cite><a href="test/crc_test.cpp">crc_test.cpp</a></cite> |
| <li>Some example code: <cite><a href="crc_example.cpp">crc_example.cpp</a></cite> |
| </ul> |
| |
| <h2><a name="credits">Credits</a></h2> |
| |
| <h3><a name="contributors">Contributors</a></h3> |
| |
| <dl> |
| <dt>Michael Barr (<a |
| href="mailto:mbarr@netrino.com">mbarr@netrino.com</a>) |
| <dd>Wrote <a |
| href="http://www.netrino.com/Connecting/2000-01/">Easier Said |
| Than Done</a>, a less-confusing guide to implementing CRC |
| algorithms. (Originally published as "Slow and Steady |
| Never Lost the Race" in the January 2000 issue of <cite><a |
| href="http://www.embedded.com/">Embedded Systems |
| Programming</a></cite>, pages 37–46.) |
| |
| <dt>Daryle Walker |
| <dd>Started the library and contributed the theoretical and optimal |
| CRC computation class templates and the CRC computing function |
| template. Contributed <cite><a |
| href="test/crc_test.cpp">crc_test.cpp</a></cite> and <cite><a |
| href="crc_example.cpp">crc_example.cpp</a></cite>. |
| |
| <dt>Ross N. Williams |
| <dd>Wrote <cite><a href="http://www.ross.net/crc/crcpaper.html">A |
| Painless Guide to CRC Error Detection Algorithms</a></cite>, a |
| definitive source of CRC information. |
| </dl> |
| |
| <h3><a name="acknowledgements">Acknowledgements</a></h3> |
| |
| <p>For giving advice on compiler/C++ compliance, implementation, |
| interface, algorithms, and bug reports:</p> |
| |
| <ul> |
| <li>Darin Adler</li> |
| <li>Beman Dawes</li> |
| <li>Doug Gregor</li> |
| <li>John Maddock</li> |
| <li>Joe Mariadassou</li> |
| <li>Jens Maurer</li> |
| <li>Vladimir Prus</li> |
| <li>Joel Young</li> |
| </ul> |
| |
| <h3><a name="history">History</a></h3> |
| |
| <dl> |
| <dt>15 Jun 2003, Daryle Walker |
| <dd>Added example program. |
| |
| <dt>14 May 2001, Daryle Walker |
| <dd>Initial version. |
| </dl> |
| |
| <hr> |
| |
| <p>Revised: 15 June 2003</p> |
| |
| <p>Copyright 2001, 2003 Daryle Walker. Use, modification, and distribution |
| are subject to the Boost Software License, Version 1.0. (See accompanying |
| file <a href="../../LICENSE_1_0.txt">LICENSE_1_0.txt</a> or a copy at |
| <<a href="http://www.boost.org/LICENSE_1_0.txt">http://www.boost.org/LICENSE_1_0.txt</a>>.)</p> |
| |
| </body> |
| </html> |