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 flat assembler > Heap > Message embedded in the digits of pi
Author
neville

Joined: 13 Jul 2008
Posts: 507
Location: New Zealand
EDIT: I was a bit hasty and should've done more checking The data I used was incorrect so this "message" isn't what I thought it was! See my next post below.

If you have some spare time get pi accurate to about 500000 base29 digits using the standard digit definitions 0-9,A-S so S is the MSD.

This message starts at the 321767th, 405982nd and 491416th digits.

Digits are numbered from after the integer 3 i.e. the fractional digits.

The first 20 base29 fractional digits of pi are:
Code:
`4328N0CJQMJQCB9I47BE    `

What is the message?

I hope I got it right

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FAMOS - the first memory operating system

Last edited by neville on 12 Jan 2017, 19:40; edited 1 time in total
12 Jan 2017, 02:50
sleepsleep

Joined: 05 Oct 2006
Posts: 8217
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care to explain, sorry for my dumb processor
12 Jan 2017, 09:54
neville

Joined: 13 Jul 2008
Posts: 507
Location: New Zealand
If you have some spare time get pi accurate to about 300000 base36 digits using the standard digit definitions 0-9,A-Z so Z is the MSD.

This message starts at the 186842nd, 186963rd and 234322nd digits.

Digits are numbered from after the integer 3 i.e. the fractional digits.

The first 20 base36 fractional digits of pi are:
Code:
`53I5AB8P5FSA5JHK72I8    `

What is the message?

I hope I got it right this time!

@sleepsleep
I was playing around with some algorithms to generate pi using memory buffers in flat real mode. I was hoping to generate millions of digits using large amounts of memory but my algorithms are still a bit slow. So I started generating pi in different bases instead...

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FAMOS - the first memory operating system
12 Jan 2017, 19:57
sleepsleep

Joined: 05 Oct 2006
Posts: 8217
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i don't know much about pi,
not sure how people came up with those infinite decimal of pi,
12 Jan 2017, 21:10
neville

Joined: 13 Jul 2008
Posts: 507
Location: New Zealand
Yes there are lots of clever algorithms to calculate pi. Some implementations are very small too - less than 100 bytes of code. Memory is used as virtual arbitrary-width registers, and integer arithmetic is used by multiplying by suitably large constants. So if you have say 3GB of memory available, and you need 3 "registers" for holding intermediate results etc you can do 1GB = 8Gbit arithmetic, calculating pi accurate to about 8 billion bits. In decimal, thats equivalent to about 2.4 billion digits.

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FAMOS - the first memory operating system
12 Jan 2017, 23:30
idle

Joined: 06 Jan 2011
Posts: 359
Location: ukraina
Have you tried PI-numeric system, when pi is the basis?
15 Feb 2017, 08:48
Enko

Joined: 03 Apr 2007
Posts: 678
Location: Mar del Plata
What about base 16 aka Hex?

https://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula

With that algorithm you could generate any digit of pie in any position.
Quote:
The formula can directly calculate the value of any given digit of π without calculating the preceding digits
15 Feb 2017, 13:36
neville

Joined: 13 Jul 2008
Posts: 507
Location: New Zealand
idle wrote:
Have you tried PI-numeric system, when pi is the basis?
Well then there would be no fractional expansion of pi because, in base pi, pi would be exactly equal to 10 .So not much scope for embedded messages in long digit sequences any more

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FAMOS - the first memory operating system
15 Feb 2017, 22:41
bitRAKE

Joined: 21 Jul 2003
Posts: 2776
Location: dank orb
The BBP algorithm allows for the full use of the memory - no long integers. Just the conversion to another base is needed. It's also possible to convert in batches (for example, cache size).

https://board.flatassembler.net/topic.php?t=7816
16 Feb 2017, 05:42
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