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Re: Highprecision Algorithm
Posted:
May 11, 2013 11:24 AM


On Saturday, August 7, 2004 2:05:22 PM UTC6, Bob Steuernagel wrote: > Thank you. I appreciate all the prompt and useful responses. This is a good group!I realize I can find the value of pi to many places elsewhere...it was just an illustrative example. If the function is available already packaged, then the language doesn't matter. I started to code such a function once, but the code involved in handling all the exceptions that arise as you start to test it made me realize I was just reinventing a very complex, but boring, wheel...Thanks again for the ontopic and useful help. Usually the responses on such forums are filled with garbage and sarcasm. "Bob Steuernagel" <steuernagel@sbcglobal.net> wrote in message news:cpWQc.2723$sE3.2455@newssvr29.news.prodigy.com... > Does anyone know of a function or software I can use (preferably in Visual > Basic, but will use any algorithm) to perform highprecision math > calculations, such as calculating pi to thousands of decimal places and > displaying it?>>
On Saturday, August 7, 2004 2:05:22 PM UTC6, Bob Steuernagel wrote: > Thank you. I appreciate all the prompt and useful responses. This is a good group!I realize I can find the value of pi to many places elsewhere...it was just an illustrative example. If the function is available already packaged, then the language doesn't matter. I started to code such a function once, but the code involved in handling all the exceptions that arise as you start to test it made me realize I was just reinventing a very complex, but boring, wheel...Thanks again for the ontopic and useful help. Usually the responses on such forums are filled with garbage and sarcasm. "Bob Steuernagel" <steuernagel@sbcglobal.net> wrote in message news:cpWQc.2723$sE3.2455@newssvr29.news.prodigy.com... > Does anyone know of a function or software I can use (preferably in Visual > Basic, but will use any algorithm) to perform highprecision math > calculations, such as calculating pi to thousands of decimal places and > displaying it?>>
The given solution to the problem is verified quickly, there is found efficient isys to locate solutions in the first place; indeed, the most notable characteristic of NPcomplete problems is the fast solutions compound quickly. The time required to solve the problem using an algorithm increases very quickly as the size of the problem grows. As a result, the time required to solve even moderately large versions of many of these problems easily reaches into the billions or trillions of years, using any amount of computing power available today. As a consequence, determining whether it is possible to solve these problems quickly is found as one of the principal unsolved problems in computer science. Now it could be conjectured the problem is solved by a method for computing the solutions to NP+complete problems using a reasonable amount of remaining time is now discovered: computer scientists and programmers still frequently encounter NPcomplete problems. An expert programmer is able to recognize an NPcomplete problem so one knowingly spent time trying to solve a problem eluding generations of computer scientists. Instead, NP+complete problems are often addressed by using precision algorithms. Contextual Properties of NP+complete problems and solutions: [change]Formal overview [change]NPcomplete is a subset of NP, the set of all decision problems whose solutions can be verified in polynomial time; NP may be equivalently defined as the set of decision problems solved in polynomial time on a machine. A problem p in NP is also in NPC if and only if every other problem in NP is transformed into p in polynomial time. NPcomplete was to be used as an adjective: problems in the class NPcomplete were as NP+complete problems.
NPcomplete problems are studied because the ability to quickly verify solutions to a problem (NP) seems to correlate with the ability to quickly solve problem (P). It is found every problem in NP is quickly solved?as called the P = NP: problem set. The single problem in NPcomplete is solved quickly, faster than every problem in NP also quickly solved, because the definition of an NPcomplete problem states every problem in NP must be quickly reducible to every problem in NPcomplete (it is reduced in polynomial time). [http://simple.wikipedia.org/wiki/P_versus_NP]



