You perhaps know that one of the reasons slashdot itself (one of the major tech sites on the internet) doesn't support unicode fully is not only due to the laziness of the developers. Gmail until recently also had difficulties. The DNS system as well has all sorts of troubles with the Russian 'a' and the ASCII 'a'. Just selecting through several pages of memory to draw the right symbol is not going to happen without some cost.

"Displaying text and pictures" is not so simple as it may sound. Do you remember the JPEG flaw that was used as an exploit in Internet Explorer?

I'm not against supporting all sorts of character sets, but we can't imagine that it doesn't come without a price and potentially with several possible dangers.

IF Wingdings fonts makes my computer run as slow as molasses and weakens its security, then it is simply a flaw and not a feature. If our beloved web browser programmers however spend more time on implementing emoj than web standards, we have a problem. If they can get it to work without destroying fundamental functionality, I don't really care.

Another reason browsers are way too bloated. This stuff does not come for free. Not to mention the possible security implications. What happens when a malformed emoj is put in the address field? What about in the preferences? What about as a http-header?

Seriously, some features should just not be implemented, just like kids should not be given everything they ask for. Not everything you want is good for you, nor good for the internet.

And get off my lawn.

If you using a lot of terminals, I would suggest using a tiled window manager like i3. New terminal is only a key press away and it is very efficient once you master it.

AKA Publicity Stunt. They are riding the coat-tails of the Sony hack and want everyone to talk about X Box.

The option "Find/Fix/End Relationship" is a bit like the old DOS prompt :

Data error reading Drive C:
Abort, Retry, Fail?

Funny thing is that none of the options ever worked in DOS either....

If you are using a SSH tunnel or similarly with a VPN, you are already doing 'everything' over SSH, that is to say the whole network connection. Even my X11 server is using it right now.

However HTTP/S, SMTP and the like are protocols, not transport mechanisms.

True, the table is a question of space/accuracy trade-off.

The process of correcting is in the interpolation, which is why I included the additional links in the same thread.

For instance in the simple manner of simple linear interpolation one can interpolate an arbitrary \epsilon between two table values. Repeating this brings us closer to a fixed point. The book that I linked to gives also many other ways of interpolation, as well as the article. It is this interpolation that is the manner of finding increased accuracy.

The article I linked to states that the method that he employs shows a noticeable gain over recalculating the value [though it is not the same function in discussion]. As in most algorithms it depends a lot on what is more important - space or time.

And a nice pdf paper illustrating this technique and its merits

Here is a nice book that we had in our school days illustrating these sorts of techniques

For pow(a,b), [a,b real numbers], you are essentially calculating:

  a^b = (e^log(a))^b) or pow(pow(e, log(a)), b) which is e^(b*log(a)) or pow(e, b*log(a)) where e is the base of the natural logarithm.

What you have in your table are the values for e^x and log(x), like any good book of logarithms of ancient times. Precision according to your needs. For quick lookup you can even index the mantissa in a b-tree if your table is huge.

Then it becomes very quick:

step 1: look up log (a) in the table, interpolate if needed.
step 2: calculate b * (value in last step).
step 3: lookup up e^x where x is the value at step 2 in your table, interpolate if needed.
step 4: profit! as you now have your result.

And as a bonus, you are sure the result is within the precision of your table immediately, within the error of your interpolation.

Note that interpolation for exp(x) is quite fast. There are some exotic methods out there as well for interpolating exp(x) and log(x), as per this abstract which are quite efficient if you need high precision. For 10 digit precision you could easily fit both your tables into 8k.

What is perhaps a bit of irony of history, even for humans a lookup table is faster and more precise than manually calculating it via formula. That is why they published books of logarithms. Using interpolation you can even stretch out the precision to several more digits. With a table of values in memory you can also narrow down the inputs to Newton's method and calculate any differentiable function very quickly to an arbitrary precision. With some functions the linear approximation is so close that you can reduce it in just a few cycles.

Even in most trigonometric functions there is a simple table upon which the angle addition formulas are used to get the other values[an old example].

Given the size of most operating systems, where 8k of ram is hardly noticed (most gifs are larger than this), I am actually quite surprised that the lookup table method is not more used. It would seem one of the first things to put in cache on your ALU.

Preach it brother! The whole world should be using BSD!

What is most disconcerting is the enormous amount of waste that Bitcoin produces. Just the amount of computing power wasted in 'mining' is such that the electricity used to run the machine no longer pays itself. When a currency costs more to produce than its worth, there is already an economic crisis and the currency is no viable. For instance, when a dime costs more than $.10 to produce, it will be more worthwhile to actually melt the coin down than actually use it. Bitcoin crossed this barrier quite awhile ago, making it actually more expensive to use than normal currency. When bitcoin cannot guarantee neither anonymity, nor any more security than cash, there is no real reason to use it.

Surely there must be some better way to make a cryptocurrency without the 'proof of work' concept. The original idea of 'proof of work' on which bitcoin is based was actually to prevent spam by making each email cost a few cpu cycles. Now the whole world is just burning cpu/gpu cycles for no other reason than trying to get money for free. Certainly there must be a better way to make financial transactions secure.

Reminds me a bit of the Tulip Mania, but in this case completely separated from any physical good. People are investing in cryptographic hashes of all things, which only have value inasmuch as some people think they do. There is no army paying its soldiers in bitcoin.

Thanks for the information. Volcanoes are amazing things. I remember when Mt. St. Helens erupted. It caused enormous damage and yet not too many things are extinct because of it. To have so many extinctions linked to one timespan seems to indicate something much more than just a series of volcanoes. Of course any life suffering from a cataclysmic event would not be helped by a long series of eruptions.

That should be km^3 of course, silly.