milindvdamle opened a new pull request #30533:
URL: https://github.com/apache/spark/pull/30533
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### What changes were proposed in this pull request?
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### Why are the changes needed?
The current example script (pi.py) produces an approximate value for pi
based on randomly-chosen points and is neither deterministic nor accurate. A
new example is needed to fix this issue.
https://en.wikipedia.org/wiki/Approximations_of_%CF%80
http://oeis.org/wiki/Pi#Decimal_expansion_of_.CF.80.E2.80.8A2
https://mathworld.wolfram.com/PiFormulas.html
This new example calculates pi using a partial sum of series that implements
the formula shown in the attached image.
### Does this PR introduce _any_ user-facing change?
Yes, it provides an additional example python script (series-pi.py) to
calculate pi.
### How was this patch tested?
The script accepts two optional command-line parameters. The first parameter
specifies the number of terms to use to approximate pi. The second parameter
specifies the number of Spark partitions to use to calculate the result.
The script was run multiple times with 10 million terms, 100 million terms,
500 million terms and 1 billion terms each as the value of the first parameter.
The resulting approximate value for pi was verified against the published/known
approximation (https://oeis.org/A000796).
Two things were noted and verified:
1. For the same number of terms provided, it was verified that each run of
the script produced a deterministic value for pi.
2. Increasing the number of terms (first parameter) produced a more accurate
approximation.
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