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@@ -23,7 +23,7 @@
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for large n, say n > 100,000,000.
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For computing the lower bits of π, consider using <i>bbp</i>.
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- <h3>The distbbp Program</h3>
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+ <h2>The distbbp Program</h2>
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The main class is DistBbp
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and the actually computation is done by DistSum jobs.
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The steps for launching the jobs are:
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@@ -39,8 +39,10 @@
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<li>Combine the job outputs and print the π bits.</li>
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</ol>
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-<table summary="The Bits of Pi"><tr valign=top><td width=420>
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- <h3>The Bits of π</h3>
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+<table>
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+<caption>"The Bits of Pi"</caption>
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+<tr><td>
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+ <h2>The Bits of π</h2>
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<p>
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The table on the right are the results computed by distbbp.
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</p>
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@@ -56,7 +58,7 @@ The table on the right are the results computed by distbbp.
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<li>The computations in Row 13 and Row 14 were completed on May 20, 2009.
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It seems that the corresponding bits were never computed before.</li>
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</ul></li>
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-<li>The first part of Row 15 (<tt>6216B06</tt>)
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+<li>The first part of Row 15 (<code>6216B06</code>)
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<ul><li>The first 30% of the computation was done in idle cycles of some
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clusters spread over 20 days.</li>
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@@ -69,7 +71,7 @@ The table on the right are the results computed by distbbp.
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<a href="http://yahoohadoop.tumblr.com/post/98338598026/hadoop-computes-the-10-15-1st-bit-of-%CF%80">this YDN blog</a>.</li>
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</ul></li>
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-<li>The second part of Row 15 (<tt>D3611</tt>)
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+<li>The second part of Row 15 (<code>D3611</code>)
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<ul><li>The starting position is 1,000,000,000,000,053, totally 20 bits.</li>
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<li>Two computations, at positions <i>n</i> and <i>n</i>+4, were performed.
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<li>A single computation was divided into 14,000 jobs
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@@ -85,42 +87,42 @@ The table on the right are the results computed by distbbp.
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computed ever in the history.</li>
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</ul></li>
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</ul>
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-</td><td width=20></td><td>
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-<table border=1 width=400 cellpadding=5 summary="Pi in hex">
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-<tr><th width=30></th><th>Position <i>n</i></th><th>π bits (in hex) starting at <i>n</i></th></tr>
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-
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-<tr><td align=right>0</td><td align=right>1</td><td><tt>243F6A8885A3</tt><sup>*</sup></td></tr>
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-<tr><td align=right>1</td><td align=right>11</td><td><tt>FDAA22168C23</tt></td></tr>
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-<tr><td align=right>2</td><td align=right>101</td><td><tt>3707344A409</tt></td></tr>
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-<tr><td align=right>3</td><td align=right>1,001</td><td><tt>574E69A458F</tt></td></tr>
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-
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-<tr><td align=right>4</td><td align=right>10,001</td><td><tt>44EC5716F2B</tt></td></tr>
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-<tr><td align=right>5</td><td align=right>100,001</td><td><tt>944F7A204</tt></td></tr>
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-<tr><td align=right>6</td><td align=right>1,000,001</td><td><tt>6FFFA4103</tt></td></tr>
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-<tr><td align=right>7</td><td align=right>10,000,001</td><td><tt>6CFDD54E3</tt></td></tr>
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-<tr><td align=right>8</td><td align=right>100,000,001</td><td><tt>A306CFA7</tt></td></tr>
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-
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-<tr><td align=right>9</td><td align=right>1,000,000,001</td><td><tt>3E08FF2B</tt></td></tr>
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-<tr><td align=right>10</td><td align=right>10,000,000,001</td><td><tt>0A8BD8C0</tt></td></tr>
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-<tr><td align=right>11</td><td align=right>100,000,000,001</td><td><tt>B2238C1</tt></td></tr>
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-<tr><td align=right>12</td><td align=right>1,000,000,000,001</td><td><tt>0FEE563</tt></td></tr>
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-<tr><td align=right>13</td><td align=right>10,000,000,000,001</td><td><tt>896DC3</tt></td></tr>
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-
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-<tr><td align=right>14</td><td align=right>100,000,000,000,001</td><td><tt>C216EC</tt></td></tr>
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-<tr><td align=right>15</td><td align=right>1,000,000,000,000,001</td><td><tt>6216B06</tt> ... <tt>D3611</tt></td></tr>
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+</td><td></td><td>
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+<table border=1><caption>"Pi in hex"</caption>
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+<tr><th></th><th>Position <i>n</i></th><th>π bits (in hex) starting at <i>n</i></th></tr>
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+
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+<tr><td>0</td><td>1</td><td><code>243F6A8885A3</code><sup>*</sup></td></tr>
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+<tr><td>1</td><td>11</td><td><code>FDAA22168C23</code></td></tr>
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+<tr><td>2</td><td>101</td><td><code>3707344A409</code></td></tr>
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+<tr><td>3</td><td>1,001</td><td><code>574E69A458F</code></td></tr>
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+
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+<tr><td>4</td><td>10,001</td><td><code>44EC5716F2B</code></td></tr>
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+<tr><td>5</td><td>100,001</td><td><code>944F7A204</code></td></tr>
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+<tr><td>6</td><td>1,000,001</td><td><code>6FFFA4103</code></td></tr>
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+<tr><td>7</td><td>10,000,001</td><td><code>6CFDD54E3</code></td></tr>
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+<tr><td>8</td><td>100,000,001</td><td><code>A306CFA7</code></td></tr>
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+
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+<tr><td>9</td><td>1,000,000,001</td><td><code>3E08FF2B</code></td></tr>
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+<tr><td>10</td><td>10,000,000,001</td><td><code>0A8BD8C0</code></td></tr>
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+<tr><td>11</td><td>100,000,000,001</td><td><code>B2238C1</code></td></tr>
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+<tr><td>12</td><td>1,000,000,000,001</td><td><code>0FEE563</code></td></tr>
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+<tr><td>13</td><td>10,000,000,000,001</td><td><code>896DC3</code></td></tr>
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+
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+<tr><td>14</td><td>100,000,000,000,001</td><td><code>C216EC</code></td></tr>
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+<tr><td>15</td><td>1,000,000,000,000,001</td><td><code>6216B06</code> ... <code>D3611</code></td></tr>
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</table>
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<sup>*</sup>
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By representing π in decimal, hexadecimal and binary, we have
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-<table summary="Pi in various formats"><tr>
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- <td>π</td><td>=</td><td><tt>3.1415926535 8979323846 2643383279</tt> ...</td>
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+<table><caption>"Pi in various formats"</caption><tr>
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+ <td>π</td><td>=</td><td><code>3.1415926535 8979323846 2643383279</code> ...</td>
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</tr><tr>
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- <td></td><td>=</td><td><tt>3.243F6A8885 A308D31319 8A2E037073</tt> ...</td>
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+ <td></td><td>=</td><td><code>3.243F6A8885 A308D31319 8A2E037073</code> ...</td>
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</tr><tr>
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- <td></td><td>=</td><td><tt>11.0010010000 1111110110 1010100010</tt> ...</td>
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+ <td></td><td>=</td><td><code>11.0010010000 1111110110 1010100010</code> ...</td>
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</tr></table>
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-The first ten bits of π are <tt>0010010000</tt>.
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+The first ten bits of π are <code>0010010000</code>.
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</td></tr></table>
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@@ -130,7 +132,8 @@ The first ten bits of π are <tt>0010010000</tt>.
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$ hadoop org.apache.hadoop.examples.pi.DistBbp \
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<b> <nThreads> <nJobs> <type> <nPart> <remoteDir> <localDir></pre>
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And the parameters are:
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- <table summary="command line option">
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+ <table>
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+ <caption>"command line option"</caption>
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<tr>
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<td><b></td>
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<td>The number of bits to skip, i.e. compute the (b+1)th position.</td>
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