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Reduce XML validation errors caused by inappropriate usage of ( and )
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xml/issue4212.xml

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@@ -26,9 +26,9 @@ This allows us to state the result precisely, and makes it clear how each round
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values of the previous rounds.
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<p/>
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It seems convenient to change the round counter <math><mi>q</mi></math> to be 1-based (and
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<math><msup><mi>X</mi><mrow>(<mn>0</mn>)</mrow></msup></math>
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<math><msup><mi>X</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></msup></math>
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is an alias for the initial value, <math><mi>X</mi></math>), so that the final result is
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<math><msup><mi>X</mi><mrow>(<mi>r</mi>)</mrow></msup></math>.
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<math><msup><mi>X</mi><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow></msup></math>.
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</p>
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</discussion>
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@@ -60,20 +60,20 @@ the <math><mi>i</mi></math>th element of <math><mi>Y</mi></math> after applying
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and the length-<math><mi>n</mi></math> sequence <math><mi>X</mi></math> into a length-<math><mi>n</mi></math> output
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sequence <math><mi>Y</mi></math>. Philox applies an <math><mi>r</mi></math>-round substitution-permutation network to
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the values in <math><mi>X</mi></math>. <del>A single round of the generation algorithm performs the following steps:</del>
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<ins>That is, there are intermediate values <math><msup><mi>X</mi><mrow>(<mn>0</mn>)</mrow></msup></math>,
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<math><msup><mi>X</mi><mrow>(<mn>1</mn>)</mrow></msup></math>, &hellip;,
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<math><msup><mi>X</mi><mrow>(<mi>r</mi>)</mrow></msup></math>, where
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<math><msup><mi>X</mi><mrow>(<mn>0</mn>)</mrow></msup><mo>:=</mo><mi>X</mi></math>, and for each round
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<math><mi>q</mi></math> (with <math><mi>q</mi><mo>=</mo><mn>1</mn>, &hellip;, <mi>r</mi></math>),
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<math><msup><mi>X</mi><mrow>(<mi>q</mi>)</mrow></msup></math> is computed from
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<math><msup><mi>X</mi><mrow>(<mi>q</mi><mo>-</mo><mn>1</mn>)</mrow></msup></math> as follows. The output sequence
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is <math><msup><mi>X</mi><mrow>(<mi>r</mi>)</mrow></msup></math>.</ins>
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<ins>That is, there are intermediate values <math><msup><mi>X</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></msup></math>,
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<math><msup><mi>X</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msup></math>, &hellip;,
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<math><msup><mi>X</mi><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow></msup></math>, where
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<math><msup><mi>X</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></msup><mo>:=</mo><mi>X</mi></math>, and for each round
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<math><mi>q</mi></math> (with <math><mi>q</mi><mo>=</mo><mn>1</mn>,<mo>&hellip;</mo>, <mi>r</mi></math>),
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<math><msup><mi>X</mi><mrow><mo>(</mo><mi>q</mi><mo>)</mo></mrow></msup></math> is computed from
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<math><msup><mi>X</mi><mrow><mo>(</mo><mi>q</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></msup></math> as follows. The output sequence
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is <math><msup><mi>X</mi><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow></msup></math>.</ins>
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</p>
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<ol style="list-style-type: none">
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<li><p>(4.1) &mdash; <del>The output sequence <math><mi>X</mi><mi>'</mi></math> of the previous round (<math><mi>X</mi></math>
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in case of the first round) is permuted to obtain the intermediate state <math><mi>V</mi></math>:</del></p>
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<blockquote><pre>
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<del><math><msub><mi>V</mi><mrow><mi>j</mi></mrow></msub><mo>=</mo><msub><mi>X</mi>'<mrow><msub><mi>f</mi><mrow><mi>n</mi></mrow></msub>(<mi>j</mi>)</mrow></msub></math></del>
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<del><math><msub><mi>V</mi><mrow><mi>j</mi></mrow></msub><mo>=</mo><msub><mi>X</mi>'<mrow><msub><mi>f</mi><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>j</mi><mo>)</mo></mrow></msub></math></del>
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</pre></blockquote>
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<p>
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<ins>An intermediate state <math><msup><mi>V</mi><mrow>(<mi>q</mi>)</mrow></msup></math> is obtained

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