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<div id="projectname">libaaruformat<span id="projectnumber"> 1.0</span>
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<div id="projectbrief">Aaru Data Preservation Suite - Format Library</div>
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<div class="headertitle"><div class="title">gf256.c File Reference</div></div>
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<p>GF(2^8) arithmetic with SIMD-accelerated region multiply.
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<a href="#details">More...</a></p>
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<div class="textblock"><code>#include <stddef.h></code><br />
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<code>#include <stdint.h></code><br />
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<code>#include <string.h></code><br />
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<code>#include "<a class="el" href="gf256_8h_source.html">gf256.h</a>"</code><br />
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<code>#include "<a class="el" href="simd_8h_source.html">aaruformat/simd.h</a>"</code><br />
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</div>
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<p><a href="gf256_8c_source.html">Go to the source code of this file.</a></p>
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<table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 id="header-func-members" class="groupheader"><a id="func-members" name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:ab20c63e8967dbedeb2a0fb212e5aa8f8" id="r_ab20c63e8967dbedeb2a0fb212e5aa8f8"><td class="memItemLeft">static void </td><td class="memItemRight"><a class="el" href="#ab20c63e8967dbedeb2a0fb212e5aa8f8">gf256_init_tables</a> (void)</td></tr>
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<tr class="memdesc:ab20c63e8967dbedeb2a0fb212e5aa8f8"><td class="mdescLeft"> </td><td class="mdescRight">Initialize log/antilog tables for GF(2^8) with polynomial 0x11D. <br /></td></tr>
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<tr class="memitem:af1afff8141cfc915bb37fc01dab39995" id="r_af1afff8141cfc915bb37fc01dab39995"><td class="memItemLeft">uint8_t </td><td class="memItemRight"><a class="el" href="#af1afff8141cfc915bb37fc01dab39995">gf256_mul</a> (uint8_t a, uint8_t b)</td></tr>
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<tr class="memdesc:af1afff8141cfc915bb37fc01dab39995"><td class="mdescLeft"> </td><td class="mdescRight">Multiply two elements in GF(2^8) with polynomial 0x11D. <br /></td></tr>
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<tr class="memitem:a1f0071a2ea261bdd2a59cc757a3ce13c" id="r_a1f0071a2ea261bdd2a59cc757a3ce13c"><td class="memItemLeft">uint8_t </td><td class="memItemRight"><a class="el" href="#a1f0071a2ea261bdd2a59cc757a3ce13c">gf256_div</a> (uint8_t a, uint8_t b)</td></tr>
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<tr class="memdesc:a1f0071a2ea261bdd2a59cc757a3ce13c"><td class="mdescLeft"> </td><td class="mdescRight">Divide two elements in GF(2^8). <br /></td></tr>
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<tr class="memitem:a43b3c7a9e2c10d25670fd961ae2916ca" id="r_a43b3c7a9e2c10d25670fd961ae2916ca"><td class="memItemLeft">uint8_t </td><td class="memItemRight"><a class="el" href="#a43b3c7a9e2c10d25670fd961ae2916ca">gf256_inv</a> (uint8_t a)</td></tr>
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<tr class="memdesc:a43b3c7a9e2c10d25670fd961ae2916ca"><td class="mdescLeft"> </td><td class="mdescRight">Compute multiplicative inverse in GF(2^8). <br /></td></tr>
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<tr class="memitem:adbf1ecc4540ea968b5503c40e9a95c61" id="r_adbf1ecc4540ea968b5503c40e9a95c61"><td class="memItemLeft">static void </td><td class="memItemRight"><a class="el" href="#adbf1ecc4540ea968b5503c40e9a95c61">gf256_build_mul_tables</a> (uint8_t coeff, uint8_t low_tbl[16], uint8_t hi_tbl[16])</td></tr>
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<tr class="memdesc:adbf1ecc4540ea968b5503c40e9a95c61"><td class="mdescLeft"> </td><td class="mdescRight">Build the two 16-byte nibble lookup tables for a given coefficient. <br /></td></tr>
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<tr class="memitem:ab25d615b33a0d7af9b9313494ac30f91" id="r_ab25d615b33a0d7af9b9313494ac30f91"><td class="memItemLeft">static void </td><td class="memItemRight"><a class="el" href="#ab25d615b33a0d7af9b9313494ac30f91">gf256_mul_region_scalar</a> (uint8_t *dst, const uint8_t *src, uint8_t coeff, size_t len)</td></tr>
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<tr class="memitem:ad1a9a733d8545bb5b217b49aea7aa43a" id="r_ad1a9a733d8545bb5b217b49aea7aa43a"><td class="memItemLeft">static void </td><td class="memItemRight"><a class="el" href="#ad1a9a733d8545bb5b217b49aea7aa43a">gf256_xor_region_scalar</a> (uint8_t *dst, const uint8_t *src, size_t len)</td></tr>
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<tr class="memitem:ad9ea1dd38b7a45e2c9f967c26d7b05df" id="r_ad9ea1dd38b7a45e2c9f967c26d7b05df"><td class="memItemLeft">void </td><td class="memItemRight"><a class="el" href="#ad9ea1dd38b7a45e2c9f967c26d7b05df">gf256_mul_region</a> (uint8_t *dst, const uint8_t *src, uint8_t coeff, size_t len)</td></tr>
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<tr class="memdesc:ad9ea1dd38b7a45e2c9f967c26d7b05df"><td class="mdescLeft"> </td><td class="mdescRight">Multiply-accumulate a region: dst[i] ^= GF_mul(src[i], coeff) for all i. <br /></td></tr>
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<tr class="memitem:a2e7b136d97e3214ff718f46542e276da" id="r_a2e7b136d97e3214ff718f46542e276da"><td class="memItemLeft">void </td><td class="memItemRight"><a class="el" href="#a2e7b136d97e3214ff718f46542e276da">gf256_xor_region</a> (uint8_t *dst, const uint8_t *src, size_t len)</td></tr>
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<tr class="memdesc:a2e7b136d97e3214ff718f46542e276da"><td class="mdescLeft"> </td><td class="mdescRight">XOR a region: dst[i] ^= src[i] for all i. <br /></td></tr>
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</table><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 id="header-var-members" class="groupheader"><a id="var-members" name="var-members"></a>
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Variables</h2></td></tr>
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<tr class="memitem:a49a3de03e67667af04f5c8014fdbe293" id="r_a49a3de03e67667af04f5c8014fdbe293"><td class="memItemLeft">static uint8_t </td><td class="memItemRight"><a class="el" href="#a49a3de03e67667af04f5c8014fdbe293">gf256_log_table</a> [256]</td></tr>
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<tr class="memdesc:a49a3de03e67667af04f5c8014fdbe293"><td class="mdescLeft"> </td><td class="mdescRight">Log table: gf256_log[x] = discrete log base 2 of x in GF(2^8). <br /></td></tr>
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<tr class="memitem:ad692be2f1e47066d0a53e97a3a38eb21" id="r_ad692be2f1e47066d0a53e97a3a38eb21"><td class="memItemLeft">static uint8_t </td><td class="memItemRight"><a class="el" href="#ad692be2f1e47066d0a53e97a3a38eb21">gf256_exp_table</a> [512]</td></tr>
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<tr class="memdesc:ad692be2f1e47066d0a53e97a3a38eb21"><td class="mdescLeft"> </td><td class="mdescRight">Anti-log (exp) table: gf256_exp[i] = 2^i mod P. <br /></td></tr>
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<tr class="memitem:aa3d36bc7f91e5c5fe01b56acd8ebbbd9" id="r_aa3d36bc7f91e5c5fe01b56acd8ebbbd9"><td class="memItemLeft">static int </td><td class="memItemRight"><a class="el" href="#aa3d36bc7f91e5c5fe01b56acd8ebbbd9">gf256_tables_initialized</a> = 0</td></tr>
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<tr class="memdesc:aa3d36bc7f91e5c5fe01b56acd8ebbbd9"><td class="mdescLeft"> </td><td class="mdescRight">Flag to ensure tables are initialized exactly once. <br /></td></tr>
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</table>
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<a name="details" id="details"></a><h2 id="header-details" class="groupheader">Detailed Description</h2>
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<div class="textblock"><p>GF(2^8) arithmetic with SIMD-accelerated region multiply. </p>
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<p>Galois Field GF(2^8) with irreducible polynomial x^8 + x^4 + x^3 + x^2 + 1 (0x11D). Uses log/antilog tables for scalar operations and 4-bit nibble split tables with SIMD shuffle for vectorized region multiply-accumulate. </p>
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<p class="definition">Definition in file <a class="el" href="gf256_8c_source.html">gf256.c</a>.</p>
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</div><a name="doc-func-members" id="doc-func-members"></a><h2 id="header-doc-func-members" class="groupheader">Function Documentation</h2>
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<a id="adbf1ecc4540ea968b5503c40e9a95c61" name="adbf1ecc4540ea968b5503c40e9a95c61"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#adbf1ecc4540ea968b5503c40e9a95c61">◆ </a></span>gf256_build_mul_tables()</h2>
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<td class="memname">void gf256_build_mul_tables </td>
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<td>(</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="paramkey"></td>
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<td class="paramtype">uint8_t</td> <td class="paramname"><span class="paramname"><em>low_tbl</em></span>[16], </td>
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<td class="paramtype">uint8_t</td> <td class="paramname"><span class="paramname"><em>hi_tbl</em></span>[16] )</td>
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<span class="mlabels"><span class="mlabel static">static</span></span> </td>
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<p>Build the two 16-byte nibble lookup tables for a given coefficient. </p>
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<p class="definition">Definition at line <a class="el" href="gf256_8c_source.html#l00114">114</a> of file <a class="el" href="gf256_8c_source.html">gf256.c</a>.</p>
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<p class="reference">References <a class="el" href="gf256_8c_source.html#l00051">gf256_init_tables()</a>, and <a class="el" href="gf256_8c_source.html#l00077">gf256_mul()</a>.</p>
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<p class="reference">Referenced by <a class="el" href="gf256_8c_source.html#l00126">gf256_mul_region_scalar()</a>.</p>
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</div>
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</div>
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<a id="a1f0071a2ea261bdd2a59cc757a3ce13c" name="a1f0071a2ea261bdd2a59cc757a3ce13c"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a1f0071a2ea261bdd2a59cc757a3ce13c">◆ </a></span>gf256_div()</h2>
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<td class="memname">uint8_t gf256_div </td>
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<td>(</td>
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<td class="paramtype">uint8_t</td> <td class="paramname"><span class="paramname"><em>a</em></span>, </td>
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<td class="paramtype">uint8_t</td> <td class="paramname"><span class="paramname"><em>b</em></span> )</td>
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<p>Divide two elements in GF(2^8). </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">a</td><td>Dividend. </td></tr>
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<tr><td class="paramname">b</td><td>Divisor (must be non-zero). </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>Quotient a/b in GF(2^8). </dd></dl>
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<p class="definition">Definition at line <a class="el" href="gf256_8c_source.html#l00084">84</a> of file <a class="el" href="gf256_8c_source.html">gf256.c</a>.</p>
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<p class="reference">References <a class="el" href="gf256_8c_source.html#l00043">gf256_exp_table</a>, <a class="el" href="gf256_8c_source.html#l00051">gf256_init_tables()</a>, and <a class="el" href="gf256_8c_source.html#l00041">gf256_log_table</a>.</p>
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<a id="ab20c63e8967dbedeb2a0fb212e5aa8f8" name="ab20c63e8967dbedeb2a0fb212e5aa8f8"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ab20c63e8967dbedeb2a0fb212e5aa8f8">◆ </a></span>gf256_init_tables()</h2>
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<td class="memname">void gf256_init_tables </td>
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<td>(</td>
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<td class="paramtype">void</td> <td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
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<span class="mlabels"><span class="mlabel static">static</span></span> </td>
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<p>Initialize log/antilog tables for GF(2^8) with polynomial 0x11D. </p>
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<p class="definition">Definition at line <a class="el" href="gf256_8c_source.html#l00051">51</a> of file <a class="el" href="gf256_8c_source.html">gf256.c</a>.</p>
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<p class="reference">References <a class="el" href="gf256_8c_source.html#l00043">gf256_exp_table</a>, <a class="el" href="gf256_8c_source.html#l00041">gf256_log_table</a>, and <a class="el" href="gf256_8c_source.html#l00046">gf256_tables_initialized</a>.</p>
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<p class="reference">Referenced by <a class="el" href="gf256_8c_source.html#l00114">gf256_build_mul_tables()</a>, <a class="el" href="gf256_8c_source.html#l00084">gf256_div()</a>, <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="gf256_8c_source.html#l00324">gf256_mul_region()</a>.</p>
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<a id="a43b3c7a9e2c10d25670fd961ae2916ca" name="a43b3c7a9e2c10d25670fd961ae2916ca"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a43b3c7a9e2c10d25670fd961ae2916ca">◆ </a></span>gf256_inv()</h2>
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<td class="memname">uint8_t gf256_inv </td>
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<td>(</td>
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<td class="paramtype">uint8_t</td> <td class="paramname"><span class="paramname"><em>a</em></span></td><td>)</td>
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<p>Compute multiplicative inverse in GF(2^8). </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">a</td><td>Element (must be non-zero). </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>Inverse a^(-1) in GF(2^8). </dd></dl>
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<p class="definition">Definition at line <a class="el" href="gf256_8c_source.html#l00092">92</a> of file <a class="el" href="gf256_8c_source.html">gf256.c</a>.</p>
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<p class="reference">References <a class="el" href="gf256_8c_source.html#l00043">gf256_exp_table</a>, <a class="el" href="gf256_8c_source.html#l00051">gf256_init_tables()</a>, and <a class="el" href="gf256_8c_source.html#l00041">gf256_log_table</a>.</p>
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<p class="reference">Referenced by <a class="el" href="reed__solomon_8c_source.html#l00084">invert_matrix()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#af1afff8141cfc915bb37fc01dab39995">◆ </a></span>gf256_mul()</h2>
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<td class="memname">uint8_t gf256_mul </td>
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<td>(</td>
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<td class="paramtype">uint8_t</td> <td class="paramname"><span class="paramname"><em>a</em></span>, </td>
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<p>Multiply two elements in GF(2^8) with polynomial 0x11D. </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">a</td><td>First operand. </td></tr>
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<tr><td class="paramname">b</td><td>Second operand. </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>Product a*b in GF(2^8). </dd></dl>
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<p class="definition">Definition at line <a class="el" href="gf256_8c_source.html#l00077">77</a> of file <a class="el" href="gf256_8c_source.html">gf256.c</a>.</p>
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<p class="reference">References <a class="el" href="gf256_8c_source.html#l00043">gf256_exp_table</a>, <a class="el" href="gf256_8c_source.html#l00051">gf256_init_tables()</a>, and <a class="el" href="gf256_8c_source.html#l00041">gf256_log_table</a>.</p>
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<p class="reference">Referenced by <a class="el" href="reed__solomon_8c_source.html#l00058">build_vandermonde()</a>, <a class="el" href="gf256_8c_source.html#l00114">gf256_build_mul_tables()</a>, <a class="el" href="reed__solomon_8c_source.html#l00084">invert_matrix()</a>, <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="#ad9ea1dd38b7a45e2c9f967c26d7b05df">◆ </a></span>gf256_mul_region()</h2>
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<td class="memname">void gf256_mul_region </td>
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<td>(</td>
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<td class="paramtype">uint8_t *</td> <td class="paramname"><span class="paramname"><em>dst</em></span>, </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>len</em></span> )</td>
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<p>Multiply-accumulate a region: dst[i] ^= GF_mul(src[i], coeff) for all i. </p>
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<p>Uses SIMD acceleration when available (AVX2 > SSSE3 > NEON > scalar). If coeff is 0, this is a no-op. If coeff is 1, this is XOR.</p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">dst</td><td>Destination buffer (read-modify-write). </td></tr>
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<tr><td class="paramname">src</td><td>Source buffer (read-only). </td></tr>
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<tr><td class="paramname">coeff</td><td>GF(2^8) coefficient. </td></tr>
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<tr><td class="paramname">len</td><td>Number of bytes to process. </td></tr>
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<p class="definition">Definition at line <a class="el" href="gf256_8c_source.html#l00324">324</a> of file <a class="el" href="gf256_8c_source.html">gf256.c</a>.</p>
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<p class="reference">References <a class="el" href="gf256_8c_source.html#l00051">gf256_init_tables()</a>, <a class="el" href="gf256_8c_source.html#l00126">gf256_mul_region_scalar()</a>, and <a class="el" href="gf256_8c_source.html#l00344">gf256_xor_region()</a>.</p>
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<p class="reference">Referenced by <a class="el" href="reed__solomon_8c_source.html#l00218">rs_decode()</a>, and <a class="el" href="reed__solomon_8c_source.html#l00213">rs_encode_incremental()</a>.</p>
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<a id="ab25d615b33a0d7af9b9313494ac30f91" name="ab25d615b33a0d7af9b9313494ac30f91"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ab25d615b33a0d7af9b9313494ac30f91">◆ </a></span>gf256_mul_region_scalar()</h2>
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<td class="memname">void gf256_mul_region_scalar </td>
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<td>(</td>
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<td class="paramtype">uint8_t *</td> <td class="paramname"><span class="paramname"><em>dst</em></span>, </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>len</em></span> )</td>
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<span class="mlabels"><span class="mlabel static">static</span></span> </td>
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<p class="definition">Definition at line <a class="el" href="gf256_8c_source.html#l00126">126</a> of file <a class="el" href="gf256_8c_source.html">gf256.c</a>.</p>
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<p class="reference">References <a class="el" href="gf256_8c_source.html#l00114">gf256_build_mul_tables()</a>.</p>
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<p class="reference">Referenced by <a class="el" href="gf256_8c_source.html#l00324">gf256_mul_region()</a>.</p>
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<a id="a2e7b136d97e3214ff718f46542e276da" name="a2e7b136d97e3214ff718f46542e276da"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a2e7b136d97e3214ff718f46542e276da">◆ </a></span>gf256_xor_region()</h2>
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<td class="memname">void gf256_xor_region </td>
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<td>(</td>
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<td class="paramtype">uint8_t *</td> <td class="paramname"><span class="paramname"><em>dst</em></span>, </td>
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<td class="paramkey"></td>
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<td class="paramtype">const uint8_t *</td> <td class="paramname"><span class="paramname"><em>src</em></span>, </td>
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<td class="paramtype">size_t</td> <td class="paramname"><span class="paramname"><em>len</em></span> )</td>
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<p>XOR a region: dst[i] ^= src[i] for all i. </p>
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<p>Uses SIMD acceleration when available.</p>
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<dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">dst</td><td>Destination buffer (read-modify-write). </td></tr>
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<tr><td class="paramname">src</td><td>Source buffer (read-only). </td></tr>
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<tr><td class="paramname">len</td><td>Number of bytes to process. </td></tr>
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<p class="definition">Definition at line <a class="el" href="gf256_8c_source.html#l00344">344</a> of file <a class="el" href="gf256_8c_source.html">gf256.c</a>.</p>
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<p class="reference">References <a class="el" href="gf256_8c_source.html#l00135">gf256_xor_region_scalar()</a>.</p>
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<p class="reference">Referenced by <a class="el" href="gf256_8c_source.html#l00324">gf256_mul_region()</a>.</p>
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<a id="ad1a9a733d8545bb5b217b49aea7aa43a" name="ad1a9a733d8545bb5b217b49aea7aa43a"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ad1a9a733d8545bb5b217b49aea7aa43a">◆ </a></span>gf256_xor_region_scalar()</h2>
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<td>(</td>
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<td class="paramtype">uint8_t *</td> <td class="paramname"><span class="paramname"><em>dst</em></span>, </td>
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<td class="paramtype">size_t</td> <td class="paramname"><span class="paramname"><em>len</em></span> )</td>
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<p class="definition">Definition at line <a class="el" href="gf256_8c_source.html#l00135">135</a> of file <a class="el" href="gf256_8c_source.html">gf256.c</a>.</p>
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<p class="reference">Referenced by <a class="el" href="gf256_8c_source.html#l00344">gf256_xor_region()</a>.</p>
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<a name="doc-var-members" id="doc-var-members"></a><h2 id="header-doc-var-members" class="groupheader">Variable Documentation</h2>
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<a id="ad692be2f1e47066d0a53e97a3a38eb21" name="ad692be2f1e47066d0a53e97a3a38eb21"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ad692be2f1e47066d0a53e97a3a38eb21">◆ </a></span>gf256_exp_table</h2>
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<p>Anti-log (exp) table: gf256_exp[i] = 2^i mod P. </p>
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<p>Extended to 512 entries to avoid modular reduction. </p>
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<p class="definition">Definition at line <a class="el" href="gf256_8c_source.html#l00043">43</a> of file <a class="el" href="gf256_8c_source.html">gf256.c</a>.</p>
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<p class="reference">Referenced by <a class="el" href="gf256_8c_source.html#l00084">gf256_div()</a>, <a class="el" href="gf256_8c_source.html#l00051">gf256_init_tables()</a>, <a class="el" href="gf256_8c_source.html#l00092">gf256_inv()</a>, and <a class="el" href="gf256_8c_source.html#l00077">gf256_mul()</a>.</p>
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<a id="a49a3de03e67667af04f5c8014fdbe293" name="a49a3de03e67667af04f5c8014fdbe293"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a49a3de03e67667af04f5c8014fdbe293">◆ </a></span>gf256_log_table</h2>
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<p>Log table: gf256_log[x] = discrete log base 2 of x in GF(2^8). </p>
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<p>gf256_log[0] is undefined. </p>
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<p class="definition">Definition at line <a class="el" href="gf256_8c_source.html#l00041">41</a> of file <a class="el" href="gf256_8c_source.html">gf256.c</a>.</p>
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<p class="reference">Referenced by <a class="el" href="gf256_8c_source.html#l00084">gf256_div()</a>, <a class="el" href="gf256_8c_source.html#l00051">gf256_init_tables()</a>, <a class="el" href="gf256_8c_source.html#l00092">gf256_inv()</a>, and <a class="el" href="gf256_8c_source.html#l00077">gf256_mul()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#aa3d36bc7f91e5c5fe01b56acd8ebbbd9">◆ </a></span>gf256_tables_initialized</h2>
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<p>Flag to ensure tables are initialized exactly once. </p>
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<p class="definition">Definition at line <a class="el" href="gf256_8c_source.html#l00046">46</a> of file <a class="el" href="gf256_8c_source.html">gf256.c</a>.</p>
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<p class="reference">Referenced by <a class="el" href="gf256_8c_source.html#l00051">gf256_init_tables()</a>.</p>
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