PI to 2.7 trillion places on a desktop(bellard.org)
bellard.org
PI to 2.7 trillion places on a desktop
http://bellard.org/pi/pi2700e9/
16 comments
In case you didn't know, this is the guy who started ffmpeg which does the heavy lifting in projects like VLC, etc.
He's also behind QEMU (cross-platform, multi-architecture CPU emulator/dynamic recompiler/virtualizer), TCC (the Tiny C Compiler) and various other projects.
see http://bellard.org/
see http://bellard.org/
QEMU also provides components used by Xen HVM mode and the KVM virtualization systems.
Apart from the interestingness angle, can somebody explain to me how the value of π to 2.7 trillion decimal places is useful?
From the FAQ:
== Why did you do this ?
I am not especially interested in the digits of Pi, but in the various algorithms involved to do arbitrary-precision arithmetic. Optimizing these algorithms to get good performance is a difficult programming challenge. Arbitrary-precision arithmetic with huge numbers has little practical use, but some of the involved algorithms are interesting to do other things. In particular:
- The Discrete Fourier Transform. This transform is widely used in many algorithms and most modern electronic appliances (such as digital televisions, cell phones and music players) include at least one instance of it.
- The reliable managing of a very large amount of disk storage, at least for a single computer. Specific methods were developed to ensure high reliability and high disk I/O bandwidth. The same ideas can be applied to other fields such as video streaming or data base access.
- The whole computation is an extensive test for a computer including its CPU, RAM, disk storage and cooling system. A single bit error during the computation gives a bad result. A bad cooling results in a hardware failure.
== Why did you do this ?
I am not especially interested in the digits of Pi, but in the various algorithms involved to do arbitrary-precision arithmetic. Optimizing these algorithms to get good performance is a difficult programming challenge. Arbitrary-precision arithmetic with huge numbers has little practical use, but some of the involved algorithms are interesting to do other things. In particular:
- The Discrete Fourier Transform. This transform is widely used in many algorithms and most modern electronic appliances (such as digital televisions, cell phones and music players) include at least one instance of it.
- The reliable managing of a very large amount of disk storage, at least for a single computer. Specific methods were developed to ensure high reliability and high disk I/O bandwidth. The same ideas can be applied to other fields such as video streaming or data base access.
- The whole computation is an extensive test for a computer including its CPU, RAM, disk storage and cooling system. A single bit error during the computation gives a bad result. A bad cooling results in a hardware failure.
Useful? Let's put it this way: if you wanted to build a disc the size of the universe, to a precision of one atom, 50 digits of pi would be more than sufficient.
But, as Benjamin Franklin was wont to ask, what's the use of a newborn baby?
But, as Benjamin Franklin was wont to ask, what's the use of a newborn baby?
Just a few off the top of my head ...
It's still not known if pi is "normal" - has an equal distribution of digits. This can be used to test the hypothesis.
The digits of pi are apparently random, so different calculations on different machines can be compared to see if either is behaving oddly.
Computing pi is sometimes used as a benchmark for a machine's speed.
Some people are unreasonably obsessed.
The digits of pi can be used as "concrete random" numbers.
It's still not known if pi is "normal" - has an equal distribution of digits. This can be used to test the hypothesis.
The digits of pi are apparently random, so different calculations on different machines can be compared to see if either is behaving oddly.
Computing pi is sometimes used as a benchmark for a machine's speed.
Some people are unreasonably obsessed.
The digits of pi can be used as "concrete random" numbers.
>The digits of pi are apparently random, so different calculations on different machines can be compared to see if either is behaving oddly.
Can you please explain what do you mean by this? Digits of pi must be same no matter which machine is used to calculate.
Can you please explain what do you mean by this? Digits of pi must be same no matter which machine is used to calculate.
Your use of the word "must" is the key. The digits of pi are supposed to be the same, but if a cosmic ray flip a bit, or if the machine becomes unstable because it runs hot, or if there's a bug in the FPU (such as happened to Intel) then results can differ, even when they shouldn't. Computing pi to very large numbers of digits is a standard warmup to make sure that new hardware is working correctly. It's only one of many tests, but it has found hardware bugs.
I remember using a machine that started to give incorrect answers when it ran too hot, and it ran hot when it was working full speed. We had to tweak the compiler to add extra NOPs into the instruction path becuase the micro-code used less power in a NOP, thus generated less heat.
EDIT: I've realised this is another example of the sofware fixed the hardware: http://news.ycombinator.com/item?id=1031384
I remember using a machine that started to give incorrect answers when it ran too hot, and it ran hot when it was working full speed. We had to tweak the compiler to add extra NOPs into the instruction path becuase the micro-code used less power in a NOP, thus generated less heat.
EDIT: I've realised this is another example of the sofware fixed the hardware: http://news.ycombinator.com/item?id=1031384
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Simply put, digits of pi must be same no matter which machine is used to calculate.
You can ask that of a lot of math as well. A lot of stuff has only become useful recently though. E.g. abstract algebra is used in material science.
From here: http://en.wikipedia.org/wiki/Group_theory
"An understanding of group theory is also important in physics and chemistry and material science."
In short, any time we break a new barrier we open ourselves up to something potentially useful for the future.
From here: http://en.wikipedia.org/wiki/Group_theory
"An understanding of group theory is also important in physics and chemistry and material science."
In short, any time we break a new barrier we open ourselves up to something potentially useful for the future.
In addition to my previous reply, ask yourself this:
How would you do it?
There are some serious technical challenges, and the FAQ and accompanying paper mention some. It's not easy, so "just for the challenge" might be an answer. "To learn stuff" is another.
In short, the value isn't always in the destination, it's sometimes in the journey.
How would you do it?
There are some serious technical challenges, and the FAQ and accompanying paper mention some. It's not easy, so "just for the challenge" might be an answer. "To learn stuff" is another.
In short, the value isn't always in the destination, it's sometimes in the journey.
If you're a romantic, this: http://www.xkcd.com/10/
Also, in Contact (the novel) a hidden message in Pi is a key component in a debate about the existence of god.
In reality, because he can.
Also, in Contact (the novel) a hidden message in Pi is a key component in a debate about the existence of god.
In reality, because he can.
How is climbing Mount Everest useful?
We do it because it's there.
We do it because it's there.
You can get a job working for the government? http://pi.nersc.gov/