64-bit ARM coming

[kevinsbane]

Would it take more computing power to push 64 bit instructions as opposed to pure 32 bit instructions?

I was reading your post and other people post with my gf (she's an engineer) and we had a pretty bad laugh.

there's no need to take in account logarithms here.

the scientific notation of 2.0 is 2.0*10^0

the scientific notation of 9.0 is 9.0*10^0


the scientific notation of 10 is 1.0*10^1

So 10 is one order of magnitude greater than 9 or 2.

Order of magnitudes are integer numbers.




and that someone is not you as you are confusing the logarithmic scale with order of magnitude.

Your girlfriend is an engineer! Congratulations. So am I. The logarithms were brought in because they are necessary to show why 2 is NOT an order of magnitude smaller than 10. In fact, logarithms are required to compute any difference when thinking in terms of orders of magnitude.

I think you're confusing the order of magnitude of any given number, and then comparing that to the order of magnitude of any other given number. This is incorrect. 2 -> 10 is debatable and like others, I'd be inclined to let it slide... but 9.9 -> 10? It's true that the order of magnitude of 9.9 is 0, and the order of magnitude of 10 is 1, but that does not mean 10 is an order of magnitude larger than 9.9. As I calculated in my previous post, it would be 0.054.... if orders of magnitude could be shown that way. Since, as you said, they must be integers, the correct conclusion would be to say that 10 is 0 orders of magnitude larger than 9.9.

 

[ncalipari]

Does this really matter? http://en.wikipedia.org/wiki/Argument_from_authority This is a common logical fallacy. Even if you are published, it doesn't make you any less wrong here.

so when you need to have hearth surgery you don't check that the doctor is actually a trained physician?

 

[Ferzerp]

so when you need to have hearth surgery you don't check that the doctor is actually a trained physician?

I think I'd rather have a bricklayer do my hearth surgery.

 

[ncalipari]

Truth be told, I don't see too much of an issue with saying that 10 is an order of magnitude different from 2... It is stretching a little, but not TOO far off. I do, however, have a problem with saying 9.9 is an order of magnitude different from 10. That is just plain wrong.

9.9 is not an order of magnitude greater than 10. 9.90 instead is.

Scientific Notation 101

 

[ncalipari]

I think you're confusing the order of magnitude of any given number, and then comparing that to the order of magnitude of any other given number. This is incorrect.

I'm sorry to announce you that that is how the measure theory handles numbers.

 

[GammaLaser]

Once Romley hits theyll again start at the middle, til SandyBridgeEX and IvyBridge EX Xeon's hit the market - in dense quaters im quite sure they'll start to really chip a nasty tooth in Sparc/Power7.

There will not be a Sandy EX --

Sandy Bridge-EP is designed to be fairly configurable to target different markets. There are two sockets, the high-end socket R (LGA2011) and the more cost optimized socket B2 (LGA1356). Compared to the desktop Sandy Bridge (LGA1155), there are additional pins for I/O and power and ground. Unlike previous generations, there will be no separate EX version of Sandy Bridge – that will wait until the 22nm Ivy Bridge. The TDP was not disclosed, but is probably as high as 150W given past server products and the newly integrated I/O.

http://realworldtech.com/page.cfm?ArticleID=RWT072811020122

 

[ncalipari]

Anyhow guys honestly I'm not paid to indulge in online flamewars.

Anyhow I invite you to make yourself a question, before talking again of error measure, make yourself a question:

If I were to compute the value of:

for X in a Neighbourhood of 0, how much would it be?























If your answer is 1, then it's better that you spend some more time on books to learn what scientific notation is, and how computers handles floats.

 

[Cogman]

so when you need to have hearth surgery you don't check that the doctor is actually a trained physician?

Now your are hitting the strawman. Want to do more logical fallacies? My position is, just because you have a math degree doesn't mean that you are right in this particular instance. You could have a degree in orders of magnitude and that still wouldn't make you right about this. I said nothing about the actions people should take in regards to receiving advice on a subject they have no training in.

It just so happens, that I'm an Engineer by trade... Orders of Magnitude are like Engineering 101. That being said, I could easily have no degree and that STILL wouldn't make your argument solid.

Would you argue that just because you are a Math major, the act of you saying 1=2 would be a true statement? I think not (I hope not). That is what is happening here. You are taking a false statement, declaring that it is true, and then when people call you out on it, you are declaring "The statement is true because I'm a math major!".

 

[MisterMac]

There will not be a Sandy EX --



http://realworldtech.com/page.cfm?ArticleID=RWT072811020122

http://regmedia.co.uk/2011/05/29/intel_sandy_bridge_platform_1.jpg

They're own roadmap suggested it earlier.


Maybe maybe not, but by the time these chips hit, so will IVY, so it makes sense.

Serverworld got sacrificed abit and the consumers got spoiled with SandyBridge.

they're moving to fast for their own good now

 

[Cogman]

9.9 is not an order of magnitude greater than 10. 9.90 instead is.

Scientific Notation 101

lol, that is the dumbest argument you've yet come up with. For the record, this is NOT scientific notation. Scientific notation is number x 10^power. In other words, 9.9 * 10 ^ 0 is scientific notation. 9.90 is not.

Go learn what scientific notation actually is and why it has no relevance to orders of magnitude. It is a way to represent numbers, nothing more. Trying to make it out as the definitive guide to logarithmic scales is silly and pathetic.

 

[Cogman]

Anyhow guys honestly I'm not paid to indulge in online flamewars.

Anyhow I invite you to make yourself a question, before talking again of error measure, make yourself a question:

If I were to compute the value of:

for X in a Neighbourhood of 0, how much would it be?

If your answer is 1, then it's better that you spend some more time on books to learn what scientific notation is, and how computers handles floats.

This has even less to do with orders of magnitude than your previous posts did... Floating point numbers have NOTHING to do with orders of magnitude... (other than, MAYBE, part of the number is to indicate the power of the mantissa.)

 

[ncalipari]

lol, that is the dumbest argument you've yet come up with. For the record, this is NOT scientific notation. Scientific notation is number x 10^power. In other words, 9.9 * 10 ^ 0 is scientific notation. 9.90 is not.

never said that that was written in SN

This has even less to do with orders of magnitude than your previous posts did... Floating point numbers have NOTHING to do with orders of magnitude... (other than, MAYBE, part of the number is to indicate the power of the mantissa.)

Numbers are, in general, represented approximately to a fixed number of significant digits and scaled using an exponent.

http://en.wikipedia.org/wiki/Floating_point

 

[Cogman]

never said that that was written in SN

Then why are you siting SN as the reason for the big difference? You take two numbers, not written in SN, then you proclaim 9.9 is not an order of magnitude difference but 9.90 is an order of magnitude difference because of SN!

Tell me, how is SN relevant when you admit that you aren't even USING SN to prove relevance?

http://en.wikipedia.org/wiki/Floating_point

Again, what does this have to do with orders of magnitude?

Here are a few links for you.

http://en.wikipedia.org/wiki/Order_of_magnitude

An order-of-magnitude difference between two values is a factor of 10. For example, the mass of the planet Saturn is 95 times than of Earth, so Saturn is two orders of magnitude more massive than Earth. Order-of-magnitude differences are called decades when measured on a logarithmic scale.

http://simple.wikipedia.org/wiki/Order_of_magnitude

Orders of magnitude are generally used to make very approximate comparisons. If two numbers differ by one order of magnitude, one is about ten times larger than the other. If they differ by two orders of magnitude, they differ by a factor of about 100. Two numbers of the same order of magnitude have roughly the same scale: the larger value is less than ten times the smaller value.

http://www2.pvc.maricopa.edu/tutor/chem/chem151/metric/magnitude.html

A number rounded to the nearest power of 10 is called an order of magnitude

http://www.vendian.org/envelope/TemporaryURL/what_is_oom.html

If a number is in scientific notation, is the 10x the oom?

Only sometimes.

99 is written in scinote as 9.9 × 101.
So is it's order of magnitude 101? Just 10 ?
100, 102, is much closer.

So, in scientific notation A × 10x,
the 10x is only the nearest power of ten if the A is < sqrt(10). That's 3.162... .
Otherwise, it is only the 2nd nearest.

Thus just taking the 10x has a worst case error of &#215;10, rather than only &#215;sqrt(10).
(And introduces a systematic error - numbers are always made smaller.)

This is analogous to using truncation ("floor") rather than rounding when converting Real numbers (floats) to Integers.

But sometimes this is good enough.
And it is sometimes called "order of magnitude" - oh well.

 

[Voo]

This has even less to do with orders of magnitude than your previous posts did... Floating point numbers have NOTHING to do with orders of magnitude... (other than, MAYBE, part of the number is to indicate the power of the mantissa.)

He's now mixing scientific notation with finite fp representations (whatever those two have to do with each other), you have to admit his "argument" is getting more and more funny

And then his formula is great - because let's see what my computer is producing for it:

In[1]:= Limit[(1 - (1 - x))/x, x -> 0]

Out[1]= 1

Not relevant? I completely agree but then I'm not sure there's actually a point he's trying to make. Though isn't it nice that we don't have to represent everything as IEEE 754 on computers just because those may be floats?

 

[Schmide]

But there's no many to one mapping for base -2. Warren has a proof in his book where he shows that the 2^n bit patterns in a n-bit word uniquely represent all integers in a range. That's not necessarily true for rationals, but that shouldn't matter there. The question is how you'd intelligently define an order of magnitude there though.

Yeah you're right I was thinking rational exponents 0 to < 1 rather than the integer magnitude this discussion is about. Guess I'll ask for my college money back.

 

[ncalipari]

Not relevant? I completely agree but then I'm not sure there's actually a point he's trying to make.

That most of the people here lacks any clue of numeric algebra.

Anyhow I didn't ask the value of the limit, but just a value in the neighborhood of 0.

 

[Voo]

That most of the people here lacks any clue of numeric algebra.

Anyhow I didn't ask the value of the limit, but just a value in the neighborhood of 0.

And clearly to show your vast understanding of numeric algebra.. we go to finite fp representations, because that makes really sense

And don't you worry, we can do the same for let's say 10^-10? Should be in the neighborhood of 0 good enough:

In[3]:= f[x_] := (1 - (1 - x))/x
f[10^-10]

Out[4]= 1

Maybe we try with something smaller?
In[5]:= f[10^-100]

Out[5]= 1

What point were you making? That you can't get arbitrary precision out of your average ieeee 754 floats? Whatever that has to do with scientific notation..

 

[ncalipari]

What point were you making? That you can't get arbitrary precision out of your average ieeee 754 floats? Whatever that has to do with scientific notation..

You should understand why the result is 1, and what result should come out without algebraic substitution.

The python shell doesn't implement algebraic substitution and gives a result closer to reality.

Matlab gives you the true result (plot it)

 

[Cogman]

You should understand why the result is 1, and what result should come out without algebraic substitution.

The python shell doesn't implement algebraic substitution and gives a result closer to reality.

Matlab gives you the true result (plot it)

WolframAlpha says it is 1 and plots it as 1...
http://www.wolframalpha.com/input/?i=plot+&#37;281-(1-x))/x
http://www.wolframalpha.com/input/?i=lim+x->0+(1-(1-x))/x

I'm now seriously doubt that
a. You have a degree in math
b. You have a girlfriend engineer that agrees with you.

This is calc 101 stuff.

 

[kevinsbane]

9.9 is not an order of magnitude greater than 10. 9.90 instead is.

Scientific Notation 101

Wait.

9.90 is an order of magnitude greater than 10? Can I quote you on that?

Perhaps you are thinking of significant digits then. Because Order of Magnitude != scientific notation != significant digits.

9.90 = 2 significant digits; 1 more than 99.0.
99 is an order of magnitude (10^1) greater than 9.90.

10 is one order of magnitude greater than 1. 10.00000000000000000000000000 is still only 1 order of magnitude greater than 1.

I fail to see how order of magnitude has anything to do with computers. Hm. That's ironic. I'll stop now.

 

[ncalipari]

WolframAlpha says it is 1 and plots it as 1...
http://www.wolframalpha.com/input/?i=plot+(1-(1-x))/x
http://www.wolframalpha.com/input/?i=lim+x->0+(1-(1-x))/x

I'm now seriously doubt that
a. You have a degree in math
b. You have a girlfriend engineer that agrees with you.

This is calc 101 stuff.

still using algebraic substitution.... you are missing the point...

 

[ncalipari]

Wait.

9.90 is an order of magnitude greater than 10.0? Can I quote you on that?

absolutely

Perhaps you are thinking of significant digits then. Because Order of Magnitude != scientific notation != significant digits.

9.90 = 2 significant digits; 1 more than 99.0.
99 is an order of magnitude (10^1) greater than 9.90.

10 is one order of magnitude larger than 1. 10.00000000000000000000000000 is still only 1 order of magnitude larger than 1.

So when you store a result of one of your experiment in scientific notation you don't take account of significant digit? Or You just store all the digits?

If I decide that I drop the last digit, then:

if my scale return me 9.9, I store it as 1.0E01

If My scale return me 9.90 I store it as 9.9E00

If My scale return me 10.0 I store it as 1.0E01

The First and the third result are one order of magnitude greater than the second result.

Order of magnitudes confront exponents, not digits, of numebrs stored in scientific notation.


There is no need to use logarithms (LOL), or fractional magnitudes (LOLOL).

Even though this increase the absolute error, it minimize the relative error. Which why it is used in scientific computation.

If you think otherwise, you should follow again physics 101.

I fail to see how order of magnitude has anything to do with computers. Hm. That's ironic. I'll stop now.

Maybe you should learn why people decided to handle floats the way they handles them.

 

[Cogman]

still using algebraic substitution.... you are missing the point...

You have a point?


Welp, that's it, I'm done here. If you really do have the math degrees you claim, then I weep for the institutes of higher education that allowed this level of incompetence through their system. It would truly speak to how poor education is in general.

 

[ncalipari]

You have a point?


Welp, that's it, I'm done here. If you really do have the math degrees you claim, then I weep for the institutes of higher education that allowed this level of incompetence through their system. It would truly speak to how poor education is in general.

I guess you tried via Python shell but couldn't understand the result, so you are dropping the argument. Nice way out

 

[Voo]

I guess you tried via Python shell but couldn't understand the result, so you are dropping the argument. Nice way out

	public static BigDecimal compute(String x) {
		BigDecimal val = new BigDecimal(x);
		BigDecimal divisor = BigDecimal.ONE.subtract(BigDecimal.ONE.subtract(val));
		BigDecimal dividend = val;
		return divisor.divide(dividend);
	}
	System.out.println(compute("0.000000001")); // "1"

Guess what the result is - and no, obviously no arithmetic substitution here. You're just confusing one particular popular fp representation with.. well no idea what this even has to do with the whole topic. There are dozens of different ways to represent floats.

So it was fun to guess what you come up next with, but time for me to get some sleep. Although I really enjoy seeing how you can throw completely unrelated and different topics (fp precision, significant digits,..) into one topic!