Re: Randomness of digits within pi

On 11 Nov, 13:48, David Bernier <david...@xxxxxxxxxxxx> wrote:
David Bernier wrote:
jonas.thornv...@xxxxxxxxxxx wrote:
On 9 Nov, 17:58, gr...@xxxxxxxxxxxxxxxxx (Daniel Grubb) wrote:
[...]
Here's a program that can calculate pi to 33 million places fairly
quickly
on most modern machines.

http://www.geocities.com/hjsmithh/Pi/Super_Pi.html

Ok i admit i am being lazy anyone who can distribute it as file on
bittorent?
Someone must have run the program and burned it down?

You might want to send an e-mail to Xavier Gourdon, the author
of the program Pifast ...

I used Xavier Gourdon's PiFast43.exe program to compute
pi to 1 billion decimals. It took about 12 to 25 hours on a PC
with an Athlon XP 2200 32-bit processor and 1 GB of RAM.

The resulting file, at 1.28 GB, can be opened with Notepad
to see the first 50 or 100 lines or so, but it is so large that
it takes minutes to go down 2 pages.

I believe it would it would be easy to access the file
using C or C++ with fopen(), fscanf(), fclose().

I seem to remember that the file has line numbers,
line feeds/CR (the Windows CR+LF line breaks) and
some information about the start and finish of the
computation at the beginning of the file.

Cf.:
<http://numbers.computation.free.fr/Constants/PiProgram/pifast.html>

I wrote a program in C to read the 1.28 GB file, so as to ignore all
characters that are spaces, line feeds,
carriage returns, whitespace, text, "3." and the line numbers (each line
had 50 digits).

Up to 800 million decimals after the point, I got a distribution of:
0s: 79991897
1s: 79997003
2s: 80003316
3s: 79989651
4s: 80016073
5s: 79996120
6s: 80004148
7s: 79995109
8s: 80002933
9s: 80003750

This agrees with Yasumasa Kanada's data here:
<ftp://pi.super-computing.org/pub/pi/pi.all.freq.3b>

But i hope you people *of any should understand* that counting
standalone decimal digits will tell you nothing about any pattern in
the string?

It only tell you that each standalone decimal digit is uniform
distributed, and that really say nothing.
I know about diehard, and statistic tests, but if you really looking
for pinning down an anomaly to show that a expanding function do not
output uniform distribution of output you should look for anomalies of
longer digit lengths i understand that only around 350 billions or was
it 3,5 billions values of pi is known.

I would pick a value of say one 100 000 to 10 millions to look for in
the data and try to find anomalies, because if you find an anomaly of
that size it would certainly say something about the function itself.

So why can't you make a search for 111111,222222,... to 999999 and
1111111,2222222,7777777... to 9999999 if you already programmed a
short snippet.

I do not remember much about standard deviation and how large that
would be normal in using a number of size xxxxxx or xxxxxxx within 1,2
billion.

Maybe someone could inform me what would be considered normal standard
deviation and how many of size xxxxxx and xxxxxxx one would presume to
find within 1,2 billion, i do not have the formula.

But i would guess 1200 and 120 of xxxxxx sized number and xxxxxxx
sized?






At 1000 million decimals, my counts were off by about 0 to 10.

Comparing with "Billion Digit Pi" at:
<http://web.ukonline.co.uk/home52365/pi.htm> ,
out of the last 300 digits, roughly the first 220 to 225 agree (when
asking for last 1000 of the billion digits).

So it seems likely the first 999,999,900 decimals in my file are right.

I went looking for MD5 hash values and didn't have much success. By
writing the first
1 million decimals to a file (and no other characters), I get an MD5 hash of
e668904c195521a2a2dfef948ac54c8e .

"The Starman" gets an MD5 hash of e668904c195521a2a2dfef948ac54c8e for
the same file (or file description ... ) here:
<http://www.geocities.com/tsrmath/pi/picalcs.htm#PMD5> .

Quite interesting is his "PI Error at UCLA" page:
<http://www.geocities.com/tsrmath/pi/UCLApiError.html>

David Bernier- Dölj citerad text -

- Visa citerad text -


.

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