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<div id="projectbrief">Aaru Data Preservation Suite - Format Library</div>
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<p>Reed-Solomon erasure codec over GF(2^8).
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;stdlib.h&gt;</code><br />
<code>#include &lt;string.h&gt;</code><br />
<code>#include &quot;<a class="el" href="reed__solomon_8h_source.html">reed_solomon.h</a>&quot;</code><br />
<code>#include &quot;<a class="el" href="gf256_8h_source.html">gf256.h</a>&quot;</code><br />
</div>
<p><a href="reed__solomon_8c_source.html">Go to the source code of this file.</a></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 id="header-nested-classes" class="groupheader"><a id="nested-classes" name="nested-classes"></a>
Data Structures</h2></td></tr>
<tr class="memitem:rs_5Fcontext" id="r_rs_5Fcontext"><td class="memItemLeft">struct &#160;</td><td class="memItemRight"><a class="el" href="structrs__context.html">rs_context</a></td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 id="header-func-members" class="groupheader"><a id="func-members" name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:acc87b5f3503d2dad1f8825de7f70cfb4" id="r_acc87b5f3503d2dad1f8825de7f70cfb4"><td class="memItemLeft">static uint8_t *&#160;</td><td class="memItemRight"><a class="el" href="#acc87b5f3503d2dad1f8825de7f70cfb4">build_vandermonde</a> (uint16_t <a class="el" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>, uint16_t M)</td></tr>
<tr class="memdesc:acc87b5f3503d2dad1f8825de7f70cfb4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Build a Vandermonde matrix (K+M) x K in GF(2^8). <br /></td></tr>
<tr class="memitem:a2796c2f5ddbc2396aaeca8bda5590b88" id="r_a2796c2f5ddbc2396aaeca8bda5590b88"><td class="memItemLeft">static int&#160;</td><td class="memItemRight"><a class="el" href="#a2796c2f5ddbc2396aaeca8bda5590b88">invert_matrix</a> (const uint8_t *mat, uint8_t *inv, uint16_t <a class="el" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>)</td></tr>
<tr class="memdesc:a2796c2f5ddbc2396aaeca8bda5590b88"><td class="mdescLeft">&#160;</td><td class="mdescRight">Invert a K x K matrix in-place using Gaussian elimination over GF(2^8). <br /></td></tr>
<tr class="memitem:a68a7b13ef6443640abc2818a3bd7d5bf" id="r_a68a7b13ef6443640abc2818a3bd7d5bf"><td class="memItemLeft"><a class="el" href="structrs__context.html">rs_context</a> *&#160;</td><td class="memItemRight"><a class="el" href="#a68a7b13ef6443640abc2818a3bd7d5bf">rs_create</a> (uint16_t <a class="el" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>, uint16_t M)</td></tr>
<tr class="memdesc:a68a7b13ef6443640abc2818a3bd7d5bf"><td class="mdescLeft">&#160;</td><td class="mdescRight">Create a Reed-Solomon codec for RS(K, M) over GF(2^8). <br /></td></tr>
<tr class="memitem:a5eed1476ef3e8666f011b529337b8518" id="r_a5eed1476ef3e8666f011b529337b8518"><td class="memItemLeft">void&#160;</td><td class="memItemRight"><a class="el" href="#a5eed1476ef3e8666f011b529337b8518">rs_free</a> (<a class="el" href="structrs__context.html">rs_context</a> *ctx)</td></tr>
<tr class="memdesc:a5eed1476ef3e8666f011b529337b8518"><td class="mdescLeft">&#160;</td><td class="mdescRight">Free a Reed-Solomon codec context. <br /></td></tr>
<tr class="memitem:ada549b6a6028807b96d975bba70bea2d" id="r_ada549b6a6028807b96d975bba70bea2d"><td class="memItemLeft">uint8_t&#160;</td><td class="memItemRight"><a class="el" href="#ada549b6a6028807b96d975bba70bea2d">rs_get_coefficient</a> (const <a class="el" href="structrs__context.html">rs_context</a> *ctx, uint16_t m, uint16_t k)</td></tr>
<tr class="memdesc:ada549b6a6028807b96d975bba70bea2d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get the generator matrix coefficient for parity shard m, data shard k. <br /></td></tr>
<tr class="memitem:ab02dd67e8f4b96de007048f30649adb1" id="r_ab02dd67e8f4b96de007048f30649adb1"><td class="memItemLeft">void&#160;</td><td class="memItemRight"><a class="el" href="#ab02dd67e8f4b96de007048f30649adb1">rs_encode_incremental</a> (uint8_t coeff, const uint8_t *data, uint8_t *parity, size_t shard_size)</td></tr>
<tr class="memdesc:ab02dd67e8f4b96de007048f30649adb1"><td class="mdescLeft">&#160;</td><td class="mdescRight">Incrementally accumulate one data shard's contribution to one parity shard. <br /></td></tr>
<tr class="memitem:aea0122b72cfa6f77a4751d5466e73024" id="r_aea0122b72cfa6f77a4751d5466e73024"><td class="memItemLeft">int&#160;</td><td class="memItemRight"><a class="el" href="#aea0122b72cfa6f77a4751d5466e73024">rs_decode</a> (const <a class="el" href="structrs__context.html">rs_context</a> *ctx, uint8_t **shards, const uint8_t *present, size_t shard_size)</td></tr>
<tr class="memdesc:aea0122b72cfa6f77a4751d5466e73024"><td class="mdescLeft">&#160;</td><td class="mdescRight">Decode (reconstruct) erased shards. <br /></td></tr>
</table>
<a name="details" id="details"></a><h2 id="header-details" class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Reed-Solomon erasure codec over GF(2^8). </p>
<p>Implements RS(K, M) encoding and decoding using a Vandermonde-derived generator matrix. Encoding is incremental (one data shard at a time). Decoding uses Gaussian elimination to reconstruct erased shards.</p>
<p>The coding matrix is (K+M) x K where:</p><ul>
<li>Top K rows form an identity matrix (data shards pass through unchanged)</li>
<li>Bottom M rows are the generator matrix (parity = G * data)</li>
</ul>
<p>Generator matrix construction: Start with a (K+M) x K Vandermonde matrix V where V[i][j] = i^j in GF(2^8). Invert the top K x K submatrix and multiply the entire matrix by the inverse so that the top K rows become identity. The bottom M rows are the generator. </p>
<p class="definition">Definition in file <a class="el" href="reed__solomon_8c_source.html">reed_solomon.c</a>.</p>
</div><a name="doc-func-members" id="doc-func-members"></a><h2 id="header-doc-func-members" class="groupheader">Function Documentation</h2>
<a id="acc87b5f3503d2dad1f8825de7f70cfb4" name="acc87b5f3503d2dad1f8825de7f70cfb4"></a>
<h2 class="memtitle"><span class="permalink"><a href="#acc87b5f3503d2dad1f8825de7f70cfb4">&#9670;&#160;</a></span>build_vandermonde()</h2>
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<td class="memname">uint8_t * build_vandermonde </td>
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<td class="paramtype">uint16_t</td> <td class="paramname"><span class="paramname"><em>K</em></span>, </td>
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<td class="paramkey"></td>
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<td class="paramtype">uint16_t</td> <td class="paramname"><span class="paramname"><em>M</em></span>&#160;)</td>
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<p>Build a Vandermonde matrix (K+M) x K in GF(2^8). </p>
<p>V[i][j] = i^j in GF(2^8), where i is the row index and j is the column index. Row 0 is all zeros except column 0 (since 0^0 = 1 by convention, 0^j = 0 for j&gt;0). We use row indices 0..K+M-1. </p>
<p class="definition">Definition at line <a class="el" href="reed__solomon_8c_source.html#l00058">58</a> of file <a class="el" href="reed__solomon_8c_source.html">reed_solomon.c</a>.</p>
<p class="reference">References <a class="el" href="gf256_8c_source.html#l00077">gf256_mul()</a>, and <a class="el" href="sha256_8c_source.html#l00031">K</a>.</p>
<p class="reference">Referenced by <a class="el" href="reed__solomon_8c_source.html#l00150">rs_create()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a2796c2f5ddbc2396aaeca8bda5590b88">&#9670;&#160;</a></span>invert_matrix()</h2>
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<td class="memname">int invert_matrix </td>
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<td class="paramtype">const uint8_t *</td> <td class="paramname"><span class="paramname"><em>mat</em></span>, </td>
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<td class="paramtype">uint8_t *</td> <td class="paramname"><span class="paramname"><em>inv</em></span>, </td>
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<td class="paramtype">uint16_t</td> <td class="paramname"><span class="paramname"><em>K</em></span>&#160;)</td>
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<p>Invert a K x K matrix in-place using Gaussian elimination over GF(2^8). </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">mat</td><td>The matrix to invert, stored row-major in K*K bytes. </td></tr>
<tr><td class="paramname">inv</td><td>Output inverse matrix (must be pre-initialized to identity). </td></tr>
<tr><td class="paramname"><a class="el" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a></td><td>Matrix dimension. </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>0 on success, -1 if singular. </dd></dl>
<p class="definition">Definition at line <a class="el" href="reed__solomon_8c_source.html#l00084">84</a> of file <a class="el" href="reed__solomon_8c_source.html">reed_solomon.c</a>.</p>
<p class="reference">References <a class="el" href="gf256_8c_source.html#l00092">gf256_inv()</a>, <a class="el" href="gf256_8c_source.html#l00077">gf256_mul()</a>, and <a class="el" href="sha256_8c_source.html#l00031">K</a>.</p>
<p class="reference">Referenced by <a class="el" href="reed__solomon_8c_source.html#l00150">rs_create()</a>, and <a class="el" href="reed__solomon_8c_source.html#l00218">rs_decode()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a68a7b13ef6443640abc2818a3bd7d5bf">&#9670;&#160;</a></span>rs_create()</h2>
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<td class="memname"><a class="el" href="structrs__context.html">rs_context</a> * rs_create </td>
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<td class="paramtype">uint16_t</td> <td class="paramname"><span class="paramname"><em>K</em></span>, </td>
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<td class="paramkey"></td>
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<p>Create a Reed-Solomon codec for RS(K, M) over GF(2^8). </p>
<p>K = number of data shards, M = number of parity shards. K + M must be &lt;= 255 (GF(2^8) field size minus 1).</p>
<p>The codec precomputes the Vandermonde-derived generator matrix (M rows x K columns) used for encoding.</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname"><a class="el" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a></td><td>Number of data shards (&gt;= 1). </td></tr>
<tr><td class="paramname">M</td><td>Number of parity shards (&gt;= 1). </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>Codec context, or NULL on error. </dd></dl>
<p class="definition">Definition at line <a class="el" href="reed__solomon_8c_source.html#l00150">150</a> of file <a class="el" href="reed__solomon_8c_source.html">reed_solomon.c</a>.</p>
<p class="reference">References <a class="el" href="reed__solomon_8c_source.html#l00058">build_vandermonde()</a>, <a class="el" href="reed__solomon_8c_source.html#l00048">rs_context::coding</a>, <a class="el" href="reed__solomon_8c_source.html#l00047">rs_context::gen</a>, <a class="el" href="gf256_8c_source.html#l00077">gf256_mul()</a>, <a class="el" href="reed__solomon_8c_source.html#l00084">invert_matrix()</a>, <a class="el" href="sha256_8c_source.html#l00031">K</a>, <a class="el" href="reed__solomon_8c_source.html#l00045">rs_context::K</a>, and <a class="el" href="reed__solomon_8c_source.html#l00046">rs_context::M</a>.</p>
<p class="reference">Referenced by <a class="el" href="erasure_8c_source.html#l00082">aaruf_set_erasure_coding()</a>, <a class="el" href="erasure_8c_source.html#l00941">ec_load_ecmb()</a>, and <a class="el" href="erasure_8c_source.html#l00495">ec_write_batch_parity()</a>.</p>
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<a id="aea0122b72cfa6f77a4751d5466e73024" name="aea0122b72cfa6f77a4751d5466e73024"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aea0122b72cfa6f77a4751d5466e73024">&#9670;&#160;</a></span>rs_decode()</h2>
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<td class="memname">int rs_decode </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="structrs__context.html">rs_context</a> *</td> <td class="paramname"><span class="paramname"><em>ctx</em></span>, </td>
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<td class="paramtype">size_t</td> <td class="paramname"><span class="paramname"><em>shard_size</em></span>&#160;)</td>
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<p>Decode (reconstruct) erased shards. </p>
<p>Given K+M shards where some are erased, reconstruct the erased ones using Gaussian elimination over GF(2^8).</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">ctx</td><td>Codec context. </td></tr>
<tr><td class="paramname">shards</td><td>Array of K+M shard pointers (each shard_size bytes). Erased shards must point to allocated buffers of shard_size bytes (content will be overwritten). </td></tr>
<tr><td class="paramname">present</td><td>Boolean array of K+M entries: 1 = shard is valid, 0 = shard is erased. </td></tr>
<tr><td class="paramname">shard_size</td><td>Number of bytes per shard. </td></tr>
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</dd>
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<dl class="section return"><dt>Returns</dt><dd>0 on success, -1 if too many erasures (&gt; M), -2 on allocation failure. </dd></dl>
<p class="definition">Definition at line <a class="el" href="reed__solomon_8c_source.html#l00218">218</a> of file <a class="el" href="reed__solomon_8c_source.html">reed_solomon.c</a>.</p>
<p class="reference">References <a class="el" href="reed__solomon_8c_source.html#l00048">rs_context::coding</a>, <a class="el" href="gf256_8c_source.html#l00077">gf256_mul()</a>, <a class="el" href="gf256_8c_source.html#l00324">gf256_mul_region()</a>, <a class="el" href="reed__solomon_8c_source.html#l00084">invert_matrix()</a>, <a class="el" href="sha256_8c_source.html#l00031">K</a>, <a class="el" href="reed__solomon_8c_source.html#l00045">rs_context::K</a>, and <a class="el" href="reed__solomon_8c_source.html#l00046">rs_context::M</a>.</p>
<p class="reference">Referenced by <a class="el" href="erasure_8c_source.html#l01145">ec_recover_data_block()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#ab02dd67e8f4b96de007048f30649adb1">&#9670;&#160;</a></span>rs_encode_incremental()</h2>
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<td class="memname">void rs_encode_incremental </td>
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<td class="paramtype">uint8_t</td> <td class="paramname"><span class="paramname"><em>coeff</em></span>, </td>
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<td class="paramtype">size_t</td> <td class="paramname"><span class="paramname"><em>shard_size</em></span>&#160;)</td>
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<p>Incrementally accumulate one data shard's contribution to one parity shard. </p>
<p>Computes: parity[i] ^= GF_mul(data[i], coeff) for all i in [0, shard_size).</p>
<p>This is the core primitive for streaming write: for each data block written, call this M times (once per parity shard) with the appropriate coefficient.</p>
<p>For M=1 (XOR-only), coeff is always 1, and this reduces to XOR.</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">coeff</td><td>GF(2^8) coefficient from <a class="el" href="reed__solomon_8h.html#ada549b6a6028807b96d975bba70bea2d" title="Get the generator matrix coefficient for parity shard m, data shard k.">rs_get_coefficient()</a>. </td></tr>
<tr><td class="paramname">data</td><td>Data shard bytes (read-only, shard_size bytes). </td></tr>
<tr><td class="paramname">parity</td><td>Parity shard accumulator (read-write, shard_size bytes, must be zeroed before first call). </td></tr>
<tr><td class="paramname">shard_size</td><td>Number of bytes per shard. </td></tr>
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<p class="definition">Definition at line <a class="el" href="reed__solomon_8c_source.html#l00213">213</a> of file <a class="el" href="reed__solomon_8c_source.html">reed_solomon.c</a>.</p>
<p class="reference">References <a class="el" href="gf256_8c_source.html#l00324">gf256_mul_region()</a>.</p>
<p class="reference">Referenced by <a class="el" href="erasure_8c_source.html#l00228">ec_accumulate_data_block()</a>, and <a class="el" href="erasure_8c_source.html#l00495">ec_write_batch_parity()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a5eed1476ef3e8666f011b529337b8518">&#9670;&#160;</a></span>rs_free()</h2>
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<td class="memname">void rs_free </td>
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<td class="paramtype"><a class="el" href="structrs__context.html">rs_context</a> *</td> <td class="paramname"><span class="paramname"><em>ctx</em></span></td><td>)</td>
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<p>Free a Reed-Solomon codec context. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">ctx</td><td>Context returned by <a class="el" href="reed__solomon_8h.html#a68a7b13ef6443640abc2818a3bd7d5bf" title="Create a Reed-Solomon codec for RS(K, M) over GF(2^8).">rs_create()</a>. </td></tr>
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<p class="definition">Definition at line <a class="el" href="reed__solomon_8c_source.html#l00201">201</a> of file <a class="el" href="reed__solomon_8c_source.html">reed_solomon.c</a>.</p>
<p class="reference">References <a class="el" href="reed__solomon_8c_source.html#l00048">rs_context::coding</a>.</p>
<p class="reference">Referenced by <a class="el" href="erasure_8c_source.html#l00082">aaruf_set_erasure_coding()</a>, <a class="el" href="erasure_8c_source.html#l00876">ec_free()</a>, and <a class="el" href="erasure_8c_source.html#l00495">ec_write_batch_parity()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#ada549b6a6028807b96d975bba70bea2d">&#9670;&#160;</a></span>rs_get_coefficient()</h2>
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<td class="memname">uint8_t rs_get_coefficient </td>
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<td class="paramtype">const <a class="el" href="structrs__context.html">rs_context</a> *</td> <td class="paramname"><span class="paramname"><em>ctx</em></span>, </td>
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<td class="paramtype">uint16_t</td> <td class="paramname"><span class="paramname"><em>m</em></span>, </td>
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<td class="paramtype">uint16_t</td> <td class="paramname"><span class="paramname"><em>k</em></span>&#160;)</td>
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<p>Get the generator matrix coefficient for parity shard m, data shard k. </p>
<p>During incremental encoding, call this to get the coefficient, then call <a class="el" href="reed__solomon_8h.html#ab02dd67e8f4b96de007048f30649adb1" title="Incrementally accumulate one data shard&#39;s contribution to one parity shard.">rs_encode_incremental()</a> with it.</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">ctx</td><td>Codec context. </td></tr>
<tr><td class="paramname">m</td><td>Parity shard index (0 .. M-1). </td></tr>
<tr><td class="paramname">k</td><td>Data shard index (0 .. K-1). </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>GF(2^8) coefficient. </dd></dl>
<p class="definition">Definition at line <a class="el" href="reed__solomon_8c_source.html#l00208">208</a> of file <a class="el" href="reed__solomon_8c_source.html">reed_solomon.c</a>.</p>
<p class="reference">References <a class="el" href="reed__solomon_8c_source.html#l00047">rs_context::gen</a>, and <a class="el" href="reed__solomon_8c_source.html#l00045">rs_context::K</a>.</p>
<p class="reference">Referenced by <a class="el" href="erasure_8c_source.html#l00228">ec_accumulate_data_block()</a>, and <a class="el" href="erasure_8c_source.html#l00495">ec_write_batch_parity()</a>.</p>
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