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From "Tsz Wo (Nicholas), SZE (JIRA)" <j...@apache.org>
Subject [jira] Commented: (MAPREDUCE-1923) Support arbitrary precision in the distbbp example
Date Sat, 24 Jul 2010 20:43:50 GMT

    [ https://issues.apache.org/jira/browse/MAPREDUCE-1923?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=12892027#action_12892027
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Tsz Wo (Nicholas), SZE commented on MAPREDUCE-1923:
---------------------------------------------------

I used it to compute the first 1 billion bits of pi as shown below.
|| Starting Position || Precision (in bits) || Time Used || CPU Time || Date Completed ||
|          1 | 800,001,000 | 10 days | 19 years | June 23, 2010 |
| 800,000,001 | 200,001,000 | 3 days | 8 years | June 22, 2010 |

Note that
- There jobs were run on the idle slices.  Therefore, Time Used != Cluster Time.
- The cluster has 1000 nodes. Each node had 2 quad-core CPUs with clock speed ranging from
2.0 GHz to 2.5 GHz.

> Support arbitrary precision in the distbbp example
> --------------------------------------------------
>
>                 Key: MAPREDUCE-1923
>                 URL: https://issues.apache.org/jira/browse/MAPREDUCE-1923
>             Project: Hadoop Map/Reduce
>          Issue Type: Improvement
>          Components: examples
>            Reporter: Tsz Wo (Nicholas), SZE
>            Assignee: Tsz Wo (Nicholas), SZE
>            Priority: Minor
>         Attachments: Mod1Fraction_IntArray.java
>
>
> The precision obtained by _distbbp_ is limited by Java {{double}} (IEEE 754 64-bit),
which has machine epsilon e=2^(-53).  When it is used to compute the 10^15 th bit of π, only
26-bit precision with 99.9999998% confident is obtained.  (Will provide the error analysis
later.)   It would be great if it supports arbitrary precision arithmetics.

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