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<div id="projectbrief">Aaru Data Preservation Suite - Format Library</div>
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<div class="headertitle"><div class="title">reed_solomon.c</div></div>
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<a href="reed__solomon_8c.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">/*</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment"> * This file is part of the Aaru Data Preservation Suite.</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment"> * Copyright (c) 2019-2026 Natalia Portillo.</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment"> *</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment"> * This library is free software; you can redistribute it and/or modify</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment"> * it under the terms of the GNU Lesser General Public License as</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment"> * published by the Free Software Foundation; either version 2.1 of the</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment"> * License, or (at your option) any later version.</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment"> *</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment"> * This library is distributed in the hope that it will be useful, but</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment"> * WITHOUT ANY WARRANTY; without even the implied warranty of</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment"> * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="comment"> * Lesser General Public License for more details.</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="comment"> *</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="comment"> * You should have received a copy of the GNU Lesser General Public</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="comment"> * License along with this library; if not, see &lt;http://www.gnu.org/licenses/&gt;.</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="comment"> */</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span></div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> </div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span><span class="preprocessor">#include &lt;stdlib.h&gt;</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="preprocessor">#include &lt;string.h&gt;</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> </div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="preprocessor">#include &quot;<a class="code" href="reed__solomon_8h.html">reed_solomon.h</a>&quot;</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="preprocessor">#include &quot;<a class="code" href="gf256_8h.html">gf256.h</a>&quot;</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> </div>
<div class="foldopen" id="foldopen00043" data-start="{" data-end="};">
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"><a class="line" href="structrs__context.html"> 43</a></span><span class="keyword">struct </span><a class="code hl_struct" href="structrs__context.html">rs_context</a></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span>{</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"><a class="line" href="structrs__context.html#a0556d83b00b3af8a2910a7c7590dedb9"> 45</a></span> uint16_t <a class="code hl_variable" href="structrs__context.html#a0556d83b00b3af8a2910a7c7590dedb9">K</a>; </div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"><a class="line" href="structrs__context.html#a99a1308586c359eb0a9e01013f747ce0"> 46</a></span> uint16_t <a class="code hl_variable" href="structrs__context.html#a99a1308586c359eb0a9e01013f747ce0">M</a>; </div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"><a class="line" href="structrs__context.html#a259f50a8bdf8eba3428b248d4cc0508f"> 47</a></span> uint8_t *<a class="code hl_variable" href="structrs__context.html#a259f50a8bdf8eba3428b248d4cc0508f">gen</a>; </div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"><a class="line" href="structrs__context.html#aec019cf5f92ed400ad684fc2f04d668f"> 48</a></span> uint8_t *<a class="code hl_variable" href="structrs__context.html#aec019cf5f92ed400ad684fc2f04d668f">coding</a>; </div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span>};</div>
</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span></div>
<div class="foldopen" id="foldopen00058" data-start="{" data-end="}">
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"><a class="line" href="reed__solomon_8c.html#acc87b5f3503d2dad1f8825de7f70cfb4"> 58</a></span><span class="keyword">static</span> uint8_t *<a class="code hl_function" href="reed__solomon_8c.html#acc87b5f3503d2dad1f8825de7f70cfb4">build_vandermonde</a>(uint16_t <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>, uint16_t M)</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span>{</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keyword">const</span> uint16_t N = <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> + M;</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> uint8_t *V = calloc((<span class="keywordtype">size_t</span>)N * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>, <span class="keyword">sizeof</span>(uint8_t));</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="keywordflow">if</span>(!V) <span class="keywordflow">return</span> NULL;</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> </div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="keywordflow">for</span>(uint16_t i = 0; i &lt; N; i++)</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> {</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> uint8_t val = 1; <span class="comment">/* i^0 = 1 */</span></div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="keywordflow">for</span>(uint16_t j = 0; j &lt; <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>; j++)</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> {</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> V[(size_t)i * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> + j] = val;</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> val = <a class="code hl_function" href="gf256_8c.html#af1afff8141cfc915bb37fc01dab39995">gf256_mul</a>(val, (uint8_t)i);</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> }</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> }</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="keywordflow">return</span> V;</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span>}</div>
</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span></div>
<div class="foldopen" id="foldopen00084" data-start="{" data-end="}">
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"><a class="line" href="reed__solomon_8c.html#a2796c2f5ddbc2396aaeca8bda5590b88"> 84</a></span><span class="keyword">static</span> <span class="keywordtype">int</span> <a class="code hl_function" href="reed__solomon_8c.html#a2796c2f5ddbc2396aaeca8bda5590b88">invert_matrix</a>(<span class="keyword">const</span> uint8_t *mat, uint8_t *inv, uint16_t <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>)</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span>{</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="comment">/* Work on a copy to avoid modifying input */</span></div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> uint8_t *work = malloc((<span class="keywordtype">size_t</span>)<a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>);</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <span class="keywordflow">if</span>(!work) <span class="keywordflow">return</span> -1;</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> memcpy(work, mat, (<span class="keywordtype">size_t</span>)<a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>);</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> </div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="comment">/* Initialize inv to identity */</span></div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> memset(inv, 0, (<span class="keywordtype">size_t</span>)<a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>);</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="keywordflow">for</span>(uint16_t i = 0; i &lt; <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>; i++)</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> inv[(<span class="keywordtype">size_t</span>)i * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> + i] = 1;</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> </div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="comment">/* Forward elimination */</span></div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="keywordflow">for</span>(uint16_t col = 0; col &lt; <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>; col++)</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> {</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <span class="comment">/* Find pivot */</span></div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> uint16_t pivot = col;</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="keywordflow">while</span>(pivot &lt; <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> &amp;&amp; work[(<span class="keywordtype">size_t</span>)pivot * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> + col] == 0)</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> pivot++;</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="keywordflow">if</span>(pivot == <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>) { free(work); <span class="keywordflow">return</span> -1; } <span class="comment">/* Singular */</span></div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> </div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <span class="comment">/* Swap rows if needed */</span></div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> <span class="keywordflow">if</span>(pivot != col)</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> {</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> <span class="keywordflow">for</span>(uint16_t j = 0; j &lt; <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>; j++)</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> {</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> uint8_t tmp = work[(size_t)col * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> + j];</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> work[(size_t)col * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> + j] = work[(<span class="keywordtype">size_t</span>)pivot * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> + j];</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> work[(size_t)pivot * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> + j] = tmp;</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> </div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> tmp = inv[(size_t)col * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> + j];</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> inv[(size_t)col * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> + j] = inv[(<span class="keywordtype">size_t</span>)pivot * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> + j];</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> inv[(size_t)pivot * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> + j] = tmp;</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> }</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> }</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> </div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <span class="comment">/* Scale pivot row to make diagonal element 1 */</span></div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> uint8_t diag = work[(size_t)col * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> + col];</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <span class="keywordflow">if</span>(diag != 1)</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> {</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> uint8_t inv_diag = <a class="code hl_function" href="gf256_8c.html#a43b3c7a9e2c10d25670fd961ae2916ca">gf256_inv</a>(diag);</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> <span class="keywordflow">for</span>(uint16_t j = 0; j &lt; <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>; j++)</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> {</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> work[(size_t)col * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> + j] = <a class="code hl_function" href="gf256_8c.html#af1afff8141cfc915bb37fc01dab39995">gf256_mul</a>(work[(<span class="keywordtype">size_t</span>)col * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> + j], inv_diag);</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> inv[(size_t)col * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> + j] = <a class="code hl_function" href="gf256_8c.html#af1afff8141cfc915bb37fc01dab39995">gf256_mul</a>(inv[(<span class="keywordtype">size_t</span>)col * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> + j], inv_diag);</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> }</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> }</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> </div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> <span class="comment">/* Eliminate column in all other rows */</span></div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> <span class="keywordflow">for</span>(uint16_t row = 0; row &lt; <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>; row++)</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> {</div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> <span class="keywordflow">if</span>(row == col) <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> uint8_t factor = work[(size_t)row * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> + col];</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> <span class="keywordflow">if</span>(factor == 0) <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> <span class="keywordflow">for</span>(uint16_t j = 0; j &lt; <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>; j++)</div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> {</div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> work[(size_t)row * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> + j] ^= <a class="code hl_function" href="gf256_8c.html#af1afff8141cfc915bb37fc01dab39995">gf256_mul</a>(factor, work[(<span class="keywordtype">size_t</span>)col * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> + j]);</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> inv[(size_t)row * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> + j] ^= <a class="code hl_function" href="gf256_8c.html#af1afff8141cfc915bb37fc01dab39995">gf256_mul</a>(factor, inv[(<span class="keywordtype">size_t</span>)col * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> + j]);</div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> }</div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> }</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> }</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> </div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> free(work);</div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span>}</div>
</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> </div>
<div class="foldopen" id="foldopen00150" data-start="{" data-end="}">
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"><a class="line" href="reed__solomon_8c.html#a68a7b13ef6443640abc2818a3bd7d5bf"> 150</a></span><a class="code hl_struct" href="structrs__context.html">rs_context</a> *<a class="code hl_function" href="reed__solomon_8c.html#a68a7b13ef6443640abc2818a3bd7d5bf">rs_create</a>(uint16_t <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>, uint16_t M)</div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span>{</div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> <span class="keywordflow">if</span>(<a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> == 0 || M == 0 || (uint32_t)<a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> + M &gt; 255) <span class="keywordflow">return</span> NULL;</div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> </div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> <a class="code hl_struct" href="structrs__context.html">rs_context</a> *ctx = calloc(1, <span class="keyword">sizeof</span>(<a class="code hl_struct" href="structrs__context.html">rs_context</a>));</div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> <span class="keywordflow">if</span>(!ctx) <span class="keywordflow">return</span> NULL;</div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> ctx-&gt;<a class="code hl_variable" href="structrs__context.html#a0556d83b00b3af8a2910a7c7590dedb9">K</a> = <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>;</div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> ctx-&gt;<a class="code hl_variable" href="structrs__context.html#a99a1308586c359eb0a9e01013f747ce0">M</a> = M;</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> </div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> <span class="keyword">const</span> uint16_t N = <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> + M;</div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> </div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> <span class="comment">/* Build Vandermonde matrix */</span></div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> uint8_t *V = <a class="code hl_function" href="reed__solomon_8c.html#acc87b5f3503d2dad1f8825de7f70cfb4">build_vandermonde</a>(<a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>, M);</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> <span class="keywordflow">if</span>(!V) { free(ctx); <span class="keywordflow">return</span> NULL; }</div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> </div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> <span class="comment">/* Invert top K x K submatrix */</span></div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> uint8_t *top_inv = malloc((<span class="keywordtype">size_t</span>)<a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>);</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> <span class="keywordflow">if</span>(!top_inv) { free(V); free(ctx); <span class="keywordflow">return</span> NULL; }</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> </div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> <span class="keywordflow">if</span>(<a class="code hl_function" href="reed__solomon_8c.html#a2796c2f5ddbc2396aaeca8bda5590b88">invert_matrix</a>(V, top_inv, <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>) != 0)</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> {</div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> free(top_inv);</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> free(V);</div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> free(ctx);</div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> <span class="keywordflow">return</span> NULL;</div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> }</div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> </div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> <span class="comment">/* Compute coding matrix = V * top_inv^(-1) so top K rows become identity */</span></div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> ctx-&gt;<a class="code hl_variable" href="structrs__context.html#aec019cf5f92ed400ad684fc2f04d668f">coding</a> = calloc((<span class="keywordtype">size_t</span>)N * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>, <span class="keyword">sizeof</span>(uint8_t));</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> <span class="keywordflow">if</span>(!ctx-&gt;<a class="code hl_variable" href="structrs__context.html#aec019cf5f92ed400ad684fc2f04d668f">coding</a>) { free(top_inv); free(V); free(ctx); <span class="keywordflow">return</span> NULL; }</div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> </div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> <span class="keywordflow">for</span>(uint16_t i = 0; i &lt; N; i++)</div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> {</div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> <span class="keywordflow">for</span>(uint16_t j = 0; j &lt; <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>; j++)</div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> {</div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> uint8_t val = 0;</div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> <span class="keywordflow">for</span>(uint16_t m = 0; m &lt; <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>; m++)</div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> val ^= <a class="code hl_function" href="gf256_8c.html#af1afff8141cfc915bb37fc01dab39995">gf256_mul</a>(V[(<span class="keywordtype">size_t</span>)i * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> + m], top_inv[(<span class="keywordtype">size_t</span>)m * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> + j]);</div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> ctx-&gt;<a class="code hl_variable" href="structrs__context.html#aec019cf5f92ed400ad684fc2f04d668f">coding</a>[(size_t)i * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> + j] = val;</div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> }</div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> }</div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> </div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> free(top_inv);</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> free(V);</div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> </div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> <span class="comment">/* Generator matrix = bottom M rows of the coding matrix */</span></div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> ctx-&gt;<a class="code hl_variable" href="structrs__context.html#a259f50a8bdf8eba3428b248d4cc0508f">gen</a> = ctx-&gt;<a class="code hl_variable" href="structrs__context.html#aec019cf5f92ed400ad684fc2f04d668f">coding</a> + (size_t)<a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>;</div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> </div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> <span class="keywordflow">return</span> ctx;</div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span>}</div>
</div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> </div>
<div class="foldopen" id="foldopen00201" data-start="{" data-end="}">
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"><a class="line" href="reed__solomon_8c.html#a5eed1476ef3e8666f011b529337b8518"> 201</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="reed__solomon_8c.html#a5eed1476ef3e8666f011b529337b8518">rs_free</a>(<a class="code hl_struct" href="structrs__context.html">rs_context</a> *ctx)</div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span>{</div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> <span class="keywordflow">if</span>(!ctx) <span class="keywordflow">return</span>;</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> free(ctx-&gt;<a class="code hl_variable" href="structrs__context.html#aec019cf5f92ed400ad684fc2f04d668f">coding</a>); <span class="comment">/* gen points inside coding, don&#39;t free separately */</span></div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> free(ctx);</div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span>}</div>
</div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> </div>
<div class="foldopen" id="foldopen00208" data-start="{" data-end="}">
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"><a class="line" href="reed__solomon_8c.html#ada549b6a6028807b96d975bba70bea2d"> 208</a></span>uint8_t <a class="code hl_function" href="reed__solomon_8c.html#ada549b6a6028807b96d975bba70bea2d">rs_get_coefficient</a>(<span class="keyword">const</span> <a class="code hl_struct" href="structrs__context.html">rs_context</a> *ctx, uint16_t m, uint16_t k)</div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span>{</div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> <span class="keywordflow">return</span> ctx-&gt;<a class="code hl_variable" href="structrs__context.html#a259f50a8bdf8eba3428b248d4cc0508f">gen</a>[(size_t)m * ctx-&gt;<a class="code hl_variable" href="structrs__context.html#a0556d83b00b3af8a2910a7c7590dedb9">K</a> + k];</div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span>}</div>
</div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> </div>
<div class="foldopen" id="foldopen00213" data-start="{" data-end="}">
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"><a class="line" href="reed__solomon_8c.html#ab02dd67e8f4b96de007048f30649adb1"> 213</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="reed__solomon_8c.html#ab02dd67e8f4b96de007048f30649adb1">rs_encode_incremental</a>(uint8_t coeff, <span class="keyword">const</span> uint8_t *data, uint8_t *parity, <span class="keywordtype">size_t</span> shard_size)</div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span>{</div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> <a class="code hl_function" href="gf256_8c.html#ad9ea1dd38b7a45e2c9f967c26d7b05df">gf256_mul_region</a>(parity, data, coeff, shard_size);</div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span>}</div>
</div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> </div>
<div class="foldopen" id="foldopen00218" data-start="{" data-end="}">
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"><a class="line" href="reed__solomon_8c.html#aea0122b72cfa6f77a4751d5466e73024"> 218</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="reed__solomon_8c.html#aea0122b72cfa6f77a4751d5466e73024">rs_decode</a>(<span class="keyword">const</span> <a class="code hl_struct" href="structrs__context.html">rs_context</a> *ctx, uint8_t **shards, <span class="keyword">const</span> uint8_t *present, <span class="keywordtype">size_t</span> shard_size)</div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span>{</div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> <span class="keyword">const</span> uint16_t <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> = ctx-&gt;<a class="code hl_variable" href="structrs__context.html#a0556d83b00b3af8a2910a7c7590dedb9">K</a>;</div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> <span class="keyword">const</span> uint16_t M = ctx-&gt;<a class="code hl_variable" href="structrs__context.html#a99a1308586c359eb0a9e01013f747ce0">M</a>;</div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> <span class="keyword">const</span> uint16_t N = <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> + M;</div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span> </div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> <span class="comment">/* Count erasures */</span></div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> uint16_t num_erased = 0;</div>
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> <span class="keywordflow">for</span>(uint16_t i = 0; i &lt; N; i++)</div>
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span> <span class="keywordflow">if</span>(!present[i]) num_erased++;</div>
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span> </div>
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> <span class="keywordflow">if</span>(num_erased == 0) <span class="keywordflow">return</span> 0; <span class="comment">/* Nothing to do */</span></div>
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> <span class="keywordflow">if</span>(num_erased &gt; M) <span class="keywordflow">return</span> -1; <span class="comment">/* Too many erasures */</span></div>
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> </div>
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> <span class="comment">/* Build the submatrix from rows of the coding matrix corresponding to</span></div>
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span><span class="comment"> * the K surviving shards. We need exactly K surviving shards to form</span></div>
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span><span class="comment"> * a K x K system. */</span></div>
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> </div>
<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> <span class="comment">/* Collect indices of surviving shards (pick first K) */</span></div>
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span> uint16_t *surviving = malloc((<span class="keywordtype">size_t</span>)<a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> * <span class="keyword">sizeof</span>(uint16_t));</div>
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span> <span class="keywordflow">if</span>(!surviving) <span class="keywordflow">return</span> -2;</div>
<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> </div>
<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span> uint16_t s = 0;</div>
<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> <span class="keywordflow">for</span>(uint16_t i = 0; i &lt; N &amp;&amp; s &lt; <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>; i++)</div>
<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span> {</div>
<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span> <span class="keywordflow">if</span>(present[i]) surviving[s++] = i;</div>
<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span> }</div>
<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> </div>
<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> <span class="keywordflow">if</span>(s &lt; <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>) { free(surviving); <span class="keywordflow">return</span> -1; } <span class="comment">/* Not enough surviving shards */</span></div>
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> </div>
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> <span class="comment">/* Build K x K submatrix from surviving rows of the coding matrix */</span></div>
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> uint8_t *submat = malloc((<span class="keywordtype">size_t</span>)<a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>);</div>
<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> <span class="keywordflow">if</span>(!submat) { free(surviving); <span class="keywordflow">return</span> -2; }</div>
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> </div>
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> <span class="keywordflow">for</span>(uint16_t i = 0; i &lt; <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>; i++)</div>
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> memcpy(submat + (<span class="keywordtype">size_t</span>)i * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>, ctx-&gt;<a class="code hl_variable" href="structrs__context.html#aec019cf5f92ed400ad684fc2f04d668f">coding</a> + (<span class="keywordtype">size_t</span>)surviving[i] * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>, <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>);</div>
<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> </div>
<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> <span class="comment">/* Invert the submatrix */</span></div>
<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> uint8_t *submat_inv = malloc((<span class="keywordtype">size_t</span>)<a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>);</div>
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> <span class="keywordflow">if</span>(!submat_inv) { free(submat); free(surviving); <span class="keywordflow">return</span> -2; }</div>
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> </div>
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> <span class="keywordflow">if</span>(<a class="code hl_function" href="reed__solomon_8c.html#a2796c2f5ddbc2396aaeca8bda5590b88">invert_matrix</a>(submat, submat_inv, <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>) != 0)</div>
<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span> {</div>
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> free(submat_inv);</div>
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> free(submat);</div>
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> free(surviving);</div>
<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span> <span class="keywordflow">return</span> -1; <span class="comment">/* Should not happen if coding matrix is MDS */</span></div>
<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span> }</div>
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span> </div>
<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span> <span class="comment">/* Reconstruct erased shards:</span></div>
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span><span class="comment"> * For each erased shard e, compute:</span></div>
<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span><span class="comment"> * shard[e] = sum over j=0..K-1 of (coding[e][j] * decoded_data[j])</span></div>
<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span><span class="comment"> *</span></div>
<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span><span class="comment"> * But decoded_data = submat_inv * surviving_shards</span></div>
<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span><span class="comment"> * So: shard[e] = sum_j coding[e][j] * (sum_k submat_inv[j][k] * surviving_shards[k])</span></div>
<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span><span class="comment"> *</span></div>
<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span><span class="comment"> * Reorder: shard[e] = sum_k (sum_j coding[e][j] * submat_inv[j][k]) * surviving_shards[k]</span></div>
<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span><span class="comment"> * Let repair_row[e][k] = sum_j coding[e][j] * submat_inv[j][k]</span></div>
<div class="line"><a id="l00276" name="l00276"></a><span class="lineno"> 276</span><span class="comment"> */</span></div>
<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span> <span class="keywordflow">for</span>(uint16_t e = 0; e &lt; N; e++)</div>
<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span> {</div>
<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"> 279</span> <span class="keywordflow">if</span>(present[e]) <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"> 280</span> </div>
<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</span> <span class="comment">/* Compute repair coefficients for this erased shard */</span></div>
<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span> memset(shards[e], 0, shard_size);</div>
<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span> </div>
<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span> <span class="keywordflow">for</span>(uint16_t k = 0; k &lt; <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>; k++)</div>
<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span> {</div>
<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</span> <span class="comment">/* Compute combined coefficient: sum_j coding[e][j] * submat_inv[j][k] */</span></div>
<div class="line"><a id="l00287" name="l00287"></a><span class="lineno"> 287</span> uint8_t coeff = 0;</div>
<div class="line"><a id="l00288" name="l00288"></a><span class="lineno"> 288</span> <span class="keywordflow">for</span>(uint16_t j = 0; j &lt; <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a>; j++)</div>
<div class="line"><a id="l00289" name="l00289"></a><span class="lineno"> 289</span> coeff ^= <a class="code hl_function" href="gf256_8c.html#af1afff8141cfc915bb37fc01dab39995">gf256_mul</a>(ctx-&gt;<a class="code hl_variable" href="structrs__context.html#aec019cf5f92ed400ad684fc2f04d668f">coding</a>[(<span class="keywordtype">size_t</span>)e * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> + j], submat_inv[(<span class="keywordtype">size_t</span>)j * <a class="code hl_variable" href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a> + k]);</div>
<div class="line"><a id="l00290" name="l00290"></a><span class="lineno"> 290</span> </div>
<div class="line"><a id="l00291" name="l00291"></a><span class="lineno"> 291</span> <span class="keywordflow">if</span>(coeff != 0)</div>
<div class="line"><a id="l00292" name="l00292"></a><span class="lineno"> 292</span> <a class="code hl_function" href="gf256_8c.html#ad9ea1dd38b7a45e2c9f967c26d7b05df">gf256_mul_region</a>(shards[e], shards[surviving[k]], coeff, shard_size);</div>
<div class="line"><a id="l00293" name="l00293"></a><span class="lineno"> 293</span> }</div>
<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span> }</div>
<div class="line"><a id="l00295" name="l00295"></a><span class="lineno"> 295</span> </div>
<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span> free(submat_inv);</div>
<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span> free(submat);</div>
<div class="line"><a id="l00298" name="l00298"></a><span class="lineno"> 298</span> free(surviving);</div>
<div class="line"><a id="l00299" name="l00299"></a><span class="lineno"> 299</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00300" name="l00300"></a><span class="lineno"> 300</span>}</div>
</div>
<div class="ttc" id="agf256_8c_html_a43b3c7a9e2c10d25670fd961ae2916ca"><div class="ttname"><a href="gf256_8c.html#a43b3c7a9e2c10d25670fd961ae2916ca">gf256_inv</a></div><div class="ttdeci">uint8_t gf256_inv(uint8_t a)</div><div class="ttdoc">Compute multiplicative inverse in GF(2^8).</div><div class="ttdef"><b>Definition</b> <a href="gf256_8c_source.html#l00092">gf256.c:92</a></div></div>
<div class="ttc" id="agf256_8c_html_ad9ea1dd38b7a45e2c9f967c26d7b05df"><div class="ttname"><a href="gf256_8c.html#ad9ea1dd38b7a45e2c9f967c26d7b05df">gf256_mul_region</a></div><div class="ttdeci">void gf256_mul_region(uint8_t *dst, const uint8_t *src, uint8_t coeff, size_t len)</div><div class="ttdoc">Multiply-accumulate a region: dst[i] ^= GF_mul(src[i], coeff) for all i.</div><div class="ttdef"><b>Definition</b> <a href="gf256_8c_source.html#l00324">gf256.c:324</a></div></div>
<div class="ttc" id="agf256_8c_html_af1afff8141cfc915bb37fc01dab39995"><div class="ttname"><a href="gf256_8c.html#af1afff8141cfc915bb37fc01dab39995">gf256_mul</a></div><div class="ttdeci">uint8_t gf256_mul(uint8_t a, uint8_t b)</div><div class="ttdoc">Multiply two elements in GF(2^8) with polynomial 0x11D.</div><div class="ttdef"><b>Definition</b> <a href="gf256_8c_source.html#l00077">gf256.c:77</a></div></div>
<div class="ttc" id="agf256_8h_html"><div class="ttname"><a href="gf256_8h.html">gf256.h</a></div></div>
<div class="ttc" id="areed__solomon_8c_html_a2796c2f5ddbc2396aaeca8bda5590b88"><div class="ttname"><a href="reed__solomon_8c.html#a2796c2f5ddbc2396aaeca8bda5590b88">invert_matrix</a></div><div class="ttdeci">static int invert_matrix(const uint8_t *mat, uint8_t *inv, uint16_t K)</div><div class="ttdoc">Invert a K x K matrix in-place using Gaussian elimination over GF(2^8).</div><div class="ttdef"><b>Definition</b> <a href="#l00084">reed_solomon.c:84</a></div></div>
<div class="ttc" id="areed__solomon_8c_html_a5eed1476ef3e8666f011b529337b8518"><div class="ttname"><a href="reed__solomon_8c.html#a5eed1476ef3e8666f011b529337b8518">rs_free</a></div><div class="ttdeci">void rs_free(rs_context *ctx)</div><div class="ttdoc">Free a Reed-Solomon codec context.</div><div class="ttdef"><b>Definition</b> <a href="#l00201">reed_solomon.c:201</a></div></div>
<div class="ttc" id="areed__solomon_8c_html_a68a7b13ef6443640abc2818a3bd7d5bf"><div class="ttname"><a href="reed__solomon_8c.html#a68a7b13ef6443640abc2818a3bd7d5bf">rs_create</a></div><div class="ttdeci">rs_context * rs_create(uint16_t K, uint16_t M)</div><div class="ttdoc">Create a Reed-Solomon codec for RS(K, M) over GF(2^8).</div><div class="ttdef"><b>Definition</b> <a href="#l00150">reed_solomon.c:150</a></div></div>
<div class="ttc" id="areed__solomon_8c_html_ab02dd67e8f4b96de007048f30649adb1"><div class="ttname"><a href="reed__solomon_8c.html#ab02dd67e8f4b96de007048f30649adb1">rs_encode_incremental</a></div><div class="ttdeci">void rs_encode_incremental(uint8_t coeff, const uint8_t *data, uint8_t *parity, size_t shard_size)</div><div class="ttdoc">Incrementally accumulate one data shard&#39;s contribution to one parity shard.</div><div class="ttdef"><b>Definition</b> <a href="#l00213">reed_solomon.c:213</a></div></div>
<div class="ttc" id="areed__solomon_8c_html_acc87b5f3503d2dad1f8825de7f70cfb4"><div class="ttname"><a href="reed__solomon_8c.html#acc87b5f3503d2dad1f8825de7f70cfb4">build_vandermonde</a></div><div class="ttdeci">static uint8_t * build_vandermonde(uint16_t K, uint16_t M)</div><div class="ttdoc">Build a Vandermonde matrix (K+M) x K in GF(2^8).</div><div class="ttdef"><b>Definition</b> <a href="#l00058">reed_solomon.c:58</a></div></div>
<div class="ttc" id="areed__solomon_8c_html_ada549b6a6028807b96d975bba70bea2d"><div class="ttname"><a href="reed__solomon_8c.html#ada549b6a6028807b96d975bba70bea2d">rs_get_coefficient</a></div><div class="ttdeci">uint8_t rs_get_coefficient(const rs_context *ctx, uint16_t m, uint16_t k)</div><div class="ttdoc">Get the generator matrix coefficient for parity shard m, data shard k.</div><div class="ttdef"><b>Definition</b> <a href="#l00208">reed_solomon.c:208</a></div></div>
<div class="ttc" id="areed__solomon_8c_html_aea0122b72cfa6f77a4751d5466e73024"><div class="ttname"><a href="reed__solomon_8c.html#aea0122b72cfa6f77a4751d5466e73024">rs_decode</a></div><div class="ttdeci">int rs_decode(const rs_context *ctx, uint8_t **shards, const uint8_t *present, size_t shard_size)</div><div class="ttdoc">Decode (reconstruct) erased shards.</div><div class="ttdef"><b>Definition</b> <a href="#l00218">reed_solomon.c:218</a></div></div>
<div class="ttc" id="areed__solomon_8h_html"><div class="ttname"><a href="reed__solomon_8h.html">reed_solomon.h</a></div></div>
<div class="ttc" id="asha256_8c_html_a22c6551e88df4c5c42fce3d0641adb64"><div class="ttname"><a href="sha256_8c.html#a22c6551e88df4c5c42fce3d0641adb64">K</a></div><div class="ttdeci">static const uint32_t K[64]</div><div class="ttdef"><b>Definition</b> <a href="sha256_8c_source.html#l00031">sha256.c:31</a></div></div>
<div class="ttc" id="astructrs__context_html"><div class="ttname"><a href="structrs__context.html">rs_context</a></div><div class="ttdef"><b>Definition</b> <a href="#l00043">reed_solomon.c:44</a></div></div>
<div class="ttc" id="astructrs__context_html_a0556d83b00b3af8a2910a7c7590dedb9"><div class="ttname"><a href="structrs__context.html#a0556d83b00b3af8a2910a7c7590dedb9">rs_context::K</a></div><div class="ttdeci">uint16_t K</div><div class="ttdoc">Number of data shards.</div><div class="ttdef"><b>Definition</b> <a href="#l00045">reed_solomon.c:45</a></div></div>
<div class="ttc" id="astructrs__context_html_a259f50a8bdf8eba3428b248d4cc0508f"><div class="ttname"><a href="structrs__context.html#a259f50a8bdf8eba3428b248d4cc0508f">rs_context::gen</a></div><div class="ttdeci">uint8_t * gen</div><div class="ttdoc">Generator matrix: M rows x K columns (row-major).</div><div class="ttdef"><b>Definition</b> <a href="#l00047">reed_solomon.c:47</a></div></div>
<div class="ttc" id="astructrs__context_html_a99a1308586c359eb0a9e01013f747ce0"><div class="ttname"><a href="structrs__context.html#a99a1308586c359eb0a9e01013f747ce0">rs_context::M</a></div><div class="ttdeci">uint16_t M</div><div class="ttdoc">Number of parity shards.</div><div class="ttdef"><b>Definition</b> <a href="#l00046">reed_solomon.c:46</a></div></div>
<div class="ttc" id="astructrs__context_html_aec019cf5f92ed400ad684fc2f04d668f"><div class="ttname"><a href="structrs__context.html#aec019cf5f92ed400ad684fc2f04d668f">rs_context::coding</a></div><div class="ttdeci">uint8_t * coding</div><div class="ttdoc">Full coding matrix: (K+M) rows x K columns.</div><div class="ttdef"><b>Definition</b> <a href="#l00048">reed_solomon.c:48</a></div></div>
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