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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 21:03:50 GMT

    [ https://issues.apache.org/jira/browse/MAPREDUCE-1923?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=12892030#action_12892030
] 

Tsz Wo (Nicholas), SZE commented on MAPREDUCE-1923:
---------------------------------------------------

I also have re-computed the bits at the 10^15 th position and obtained a longer bit sequence.
{noformat}
Starting position: 1,000,000,000,000,001
Number of bits   : 228 bits
Bit in Hex       :

  6216B069 CB6C1D36 117099E4 3646A6D4 48D887CC D95CC79A C84E60D2 3
{noformat}
The results agree with the ones posted in [MAPREDUCE-637|https://issues.apache.org/jira/browse/MAPREDUCE-637?focusedCommentId=12725883&page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel#action_12725883]
and [PiHex|http://oldweb.cecm.sfu.ca/projects/pihex/announce1q.html].

As usual, two computations were preformed as shown below.
|| Starting Position || Precision (in bits) || Time Used || CPU Time || Date Completed ||
| 999,999,999,999,993 | 288 | 13 days | 248 years | July 2, 2010 |
| 1,000,000,000,000,001 | 256 | 25 days | 283 years | July 6, 2010 |
See also [the note|https://issues.apache.org/jira/browse/MAPREDUCE-1923?focusedCommentId=12892027&page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel#action_12892027]
in the previous comment.

> 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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