To a petaflop and beyond!

[Spectere]

So IBM recently pushed a supercomputer to the petaflop mark: http://en.wikipedia.org/wiki/IBM_Roadrunner

Holy. Shit.

[Sqthreer!]

Mind explaining a petaflop cause I really don't understand the Wikipedia article about it. I am an retarded :[

[vladgd]

english plox

[Zakamiro]

1,026,000,000,000 floating point operations per second. Like calculations/instructions per second, but done by measuring floating point operations. Scientific software has a heavy usage of this kind of operation (variables, more programming jargon continued), so that's why they use "FLOPS".

It's basically an incredible and ungodly computer setup that is worthy of incredible glamoring if you can understand how incredible it is.

[Bobbias]

Yeah.

WARNING: LONG POST AHEAD.

Spec: you can correct me if any of this is a bit off.

Floating point numbers (numbers with a decimal and such, like 3.1415926535) are the most difficult types of numbers to represent and work with in computers. Because they are a complex number, an operation with them is a lot slower and more cumbersome than an operation on a normal number. If you were adding 10 and 5 together (1010 and 0101 respectively) you'd get 16 (1111). I won't go into much more detail, other than to say that adding the 2 simple binary numbers is really easy to do. However, floating point numbers are much more complicated.

The IEEE-754 standard defines a floating point number like this:
It's 32 bits long.
It's made up of 3 sections.

It's basically like this: +/- mantissa * 2 ^ exponent. (that is: positive or negative identifier, mantissa times 2 to the power of exponent)

The Sign Bit: A single binary bit telling whether the number is positive or negative.

The Exponent: The exponent can range from -127 to +128. It doesn't have a sign bit. Since there are 256 possible numbers, to get that range to go from -127 to +128, we simply subtract 127 from whatever number is stored here. 2 is raised to this power and the mantissa is multiplied with it to get the real number we're representing with this.

The Mantissa: The mantissa is the bulk of the actual number. It's 23 bits long when stored. This number always has a 1 in front of it so it totals as 24 bits in reality.

Here's an example: we want to represent the number -12.5.
The binary representation is:

SEEEEEEE	EMMMMMMM	MMMMMMMM	MMMMMMMM
11000001	01001000	00000000	00000000

• S being the Sign Bit.
• E the exponent.
• And M being the mantissa.

Now, let's take the number apart:

• The Sign Bit is 1. That means it's negative.
• The exponent value is 10000010 binary or 130 decimal. Subtracting 127 from 130 leaves 3, which is the actual exponent. (remember, this means 2 to the power of 3)
• The mantissa appears as the following binary number:
  1001000 00000000 00000000
• This number always has a 1 added onto the left end of it, making it 24 bits, instead of 23, and gives this value:
  1.1001000 00000000 00000000
• Now we need to adjust the mantissa, according to the exponent. We move the point left for negative numbers, and right for positive. The result is this:
  1100.1000 00000000 00000000
• Everything to the left of the decimal represents a binary number by itself. 1100 is the number 12 (2³ + 2², which is 8 + 4).
• Everything to the right of it also represents another binary number. However, this one is a bit different. Instead of representing the positive powers of 2, this part represents negative powers of 2. For example, .1000 represents 1 x 2^-1 + 0 x 2^-2 + 0 x 2^-3 + 0 x 2^-4. 2^-1 = .5.
• If you add the 12 and the .5 sections together, and use the sign bit to realize it,s a negative number, you realize that we now have the number -12.5.

Now, if we were to add numbers like that, it'd be a pretty complex process, taking a lot longer than even simple addition.
You first make the numbers have the same exponent (in a computer, even this takes a couple steps), then add the 2 mantissas together, and then round off to the requisite number of digits (I think this would also have a number of steps to it).

[Zakamiro]

holy shit bobbias... I was trying not to get that detailed, but.. damn.

anyway, not only is performance important, but the reliability of the supercomputer. I forget where I read it... :[

But basically, with so many computer components running at once, something will fail in about 10-15 minutes, do to MTBF. (mean time between failures) So, while performance is also important, so is being able to quickly replace the failed unit as quickly as possible. In fact, different architectures of supercomputers can help severity of a mechanical failure.. But yeah, anyway.

[Spectere]

1,026,000,000,000 floating point operations per second.

You dropped a few zeroes -- that's "only" 1.026 teraflops.   1,026,000,000,000,000 is what you're looking for.

And looks like a pretty good explanation of IEEE floats above.

[Zakamiro]

"Thomas P. D'Agostino, the administrator of the National Nuclear Security Administration, said that if all six billion people on earth used hand calculators and performed calculations 24 hours a day and seven days a week, it would take them 46 years to do what the Roadrunner can in one day."

[Bobbias]

Yep. That is just plain fucking awesome.