Cointerpretability - Revision history

en>PWilkinson: Link disambiguation

2014-06-08T17:38:56Z

Link disambiguation

← Older revision		Revision as of 19:38, 8 June 2014
Line 1:		Line 1:
	~~{{Use dmy dates\|date=July 2012}}~~		I'm Stormy and I live in Rockwell. <br>I'm interested in Engineering, Leaf collecting and pressing and Korean art. I like to travel and reading fantasy.<br><br>my blog post; [http://drive.ilovetheory.com/content/saving-money-bookbyte-promo-code-what-know-you-clip Bookbyte promo code january 2014]
	[[Image:Randu.png\|thumb\|right\|[[Three-dimensional space\|Three-dimensional plot]] of 100,000 values generated with RANDU. Each point represents 3 consecutive pseudorandom values. It is clearly seen that the points fall in ~~15 [[2D geometric model\|two-dimensional]] [[Plane (mathematics)\|plane]]s~~.]]

	~~'''RANDU'''~~<~~ref~~>~~IBM,~~ ''System/360 Scientific Subroutine Package Version II Programmer's Manual,'' H20-0205-1, 1967, p. 54.</ref> is a [[linear congruential generator\|linear congruential]] [[pseudorandom number generator]] of the [[Park–Miller random number generator\|Park–Miller type]], which has been used since the 1960s.<ref name="Entacher-2000">
	~~{{cite web~~
	~~\| last = Entacher~~
	~~\| first = Karl~~
	~~\| title = A collection of classical pseudorandom number generators with linear structures - advanced version~~
	~~\| date = June 2000~~
	~~\| work =~~
	~~\| url=http://random.mat.sbg.ac.at/results/karl/server/server.html~~
	~~\| accessdate = 8 August 2013~~
	~~}}</ref> It is defined by the [[Recursion\|recurrence]]:~~

	~~:<math>V_{j+1} = 65539\cdot V_j\, \bmod\, 2^{31}\,</math>~~

	~~with the initial seed number~~, ~~<math>\scriptstyle V_0</math> as an [[even~~ and odd numbers\|odd number]]. It generates pseudorandom [[integer number\|integers]] <math>\scriptstyle V_j</math> which are [[uniform distribution (discrete)\|uniformly distributed]] in the interval {{nowrap\|[1, 2<sup>31</sup> − 1]}}, but in practical applications are often mapped into pseudorandom [[rational number\|rationals]] <math>\scriptstyle X_j</math> in the interval {{nowrap\|(0, 1)}}, by the formula:
	~~:<math>X_j = \frac{V_{j}}{2^{31}}</math>.~~

	~~It is widely considered to be one of the most ill-conceived random number generators ever designed. Notably, it fails the [[spectral test]] badly for dimensions greater than 2,~~ and ~~every integer result is odd~~. ~~(However, at least eight low-order bits are dropped when converted~~ to ~~single-precision floating-point).~~

	~~The reason for choosing these particular values is that with a 32-bit-integer word size, the arithmetic of mod 2<sup>31</sup>~~ and ~~<math>65539 (2^{16} + 3)</math> calculations could be done quickly, using special features of some computer hardware~~.

	~~== Problems with multiplier and modulus ==~~
	~~To show the problem with these values, of multiplier 65539 and modulus 2<sup>31~~<~~/sup~~>~~, consider the following calculation where every term should be taken mod 2~~<~~sup~~>~~31</sup>. Start by writing the recursive relation as:~~

	~~:<math>x_{k+2}=(2^{16}+3) x_{k+1}=(2^{16}+3 )^2 x_{k}\,</math>~~

	~~which becomes, after expanding the quadratic factor:~~

	~~:<math>x_{k+2}=(2^{32}+6 \cdot2^{16} +9 )x_{k}=~~[~~6 \cdot (2^{16}+3)-9]x_{k}\,</math>~~

	~~:because {{nowrap\|2<sup>32</sup> mod 2<sup>31</sup> {{=}} 0}}~~

	~~and allows us to show the correlation between three points as:~~

	~~:<math>x_{k+2}=6x_{k+1}-9x_{k}\,</math>~~

	As a result of this correlation, the points in three dimensional space (mod 2<sup>31</sup>) fall in a comparatively small number of planes, 15 to be exact.<ref>{{cite journal \|author=Marsaglia, George \|year=1968 \|title=Random Numbers Fall Mainly in the Planes \|journal=Proc. Natl. Acad. Sci. U.S.A. \|volume=61 \|issue=1 \|pages=25–28 \|url=http://~~www~~.~~pnas~~.~~org~~/content/61/1/25.citation \|doi=10.1073/pnas.61.1.25}}</ref> As a result of the wide use of RANDU in the early 1970s, many results from that time are seen as suspicious.<ref name="press92">{{cite book \|author=Press, William H., et al. \|year=1992 \|title=[[Numerical Recipes]] in Fortran 77: The Art of Scientific Computing \|edition=2nd \|isbn=0-~~521~~-~~43064~~-~~X}}</ref>~~

	~~This misbehavior was already detected in 1963<ref>ref. 7 of http://portal.acm.org/citation.cfm?id=363827</ref> on a 36~~-~~bit computer, and carefully reimplemented on the 32~~-~~bit IBM System/360.~~

	~~==Sample output==~~

	~~The start and end of the RANDU’s output period for the initial seed <math>\scriptstyle V_0 = 1</math> is:~~
	~~: 1, 65539, 393225, 1769499, 7077969, 26542323, …, 2141591611, 388843697, 238606867, 79531577, 477211307, 1 {{OEIS\|A096555}}~~

	~~==Quotations==~~

	{{quote\|…its very name RANDU is enough to bring dismay into the eyes and stomachs of many computer scientists!\|[[Donald Knuth]]<ref>{{cite book \|author=Donald E. Knuth \|title=The Art of Computer Programming \|volume=22 \|edition=3rd \|publisher=Addison-~~Wesley \|place=Boston \|year=1998}}</ref>}}~~

	{{quote\|One of us recalls producing a "random" plot with only 11 planes, and being told by his computer center's programming consultant that he had misused the random number generator: "We guarantee that each number is random individually, but we don't guarantee that more than one of them is random." Figure that out.\|[[William H. Press\|W. H. Press]] et al.<ref name="press92"/>}}

	~~==References==~~
	~~{{Reflist\|30em}}~~

	~~[[Category:Pseudorandom number generators]~~]

en>David Eppstein: /* References */ authorlink Dick de Jongh and Giorgi Japaridze

2013-01-06T20:32:11Z

References: authorlink Dick de Jongh and Giorgi Japaridze

← Older revision		Revision as of 22:32, 6 January 2013
Line 1:		Line 1:
			{{Use dmy dates\|date=July 2012}}
			[[Image:Randu.png\|thumb\|right\|[[Three-dimensional space\|Three-dimensional plot]] of 100,000 values generated with RANDU. Each point represents 3 consecutive pseudorandom values. It is clearly seen that the points fall in 15 [[2D geometric model\|two-dimensional]] [[Plane (mathematics)\|plane]]s.]]

			'''RANDU'''<ref>IBM, ''System/360 Scientific Subroutine Package Version II Programmer's Manual,'' H20-0205-1, 1967, p. 54.</ref> is a [[linear congruential generator\|linear congruential]] [[pseudorandom number generator]] of the [[Park–Miller random number generator\|Park–Miller type]], which has been used since the 1960s.<ref name="Entacher-2000">
			{{cite web
			\| last = Entacher
			\| first = Karl
			\| title = A collection of classical pseudorandom number generators with linear structures - advanced version
			\| date = June 2000
			\| work =
			\| url=http://random.mat.sbg.ac.at/results/karl/server/server.html
			\| accessdate = 8 August 2013
			}}</ref> It is defined by the [[Recursion\|recurrence]]:

	~~Within your desired~~ number ~~amongst gems~~, ~~you can give yourself prepared intelligently to give protection to myself against any factor you like. This particular really is exciting since it allows you to enjoy like a veteran~~ and ~~you can concern just about anyone healthy playing skills are robust~~.<br><br>~~In view that explained~~ in the ~~last Clash of Clans' Kin Wars overview~~, ~~anniversary alliance war is breach up~~ into ~~a couple phases: Alertness Day and Pursuit Day.~~ [~~http:~~/~~/Dict.leo.org/?search=Anniversary Anniversary]~~ the ~~look lasts 24 hours and means that you has~~ the ~~potential to accomplish altered things.~~<br><br>~~At hand~~ is ~~a patch game title button that you must click after entering~~ the ~~type of desired values~~. ~~When you check back concerning~~ the ~~game after thirty seconds to a minute~~, ~~you will already hold the items~~. ~~On that~~ point ~~is nothing wrong making use of secrets~~. ~~To hack~~ is ~~truly~~ the ~~best way in enjoy clash~~ of ~~clans cheats~~. ~~Make use of an Resources that you have,~~ and ~~take advantage of this 2013 Clash amongst Clans download! The actual reason why pay for coins or gems when you has~~ the ~~potential to get the needed foods~~ with ~~this tool! Hurry~~ and ~~get one's own very own Clash of Clans hack tool right now. The needed portions are just a brief number of clicks away.~~<br><br>~~In case you are searching in order for a particular game to buy but want regarding purchase it at the best price possible~~, consider the ~~"shopping" tab readily available on many search sites~~. ~~This will allow you to immediately analyze~~ the ~~prices of currently~~ the ~~game at all their major retailers online. Here's more information regarding~~ [~~http~~://~~prometeu.net clash of clans unlimited gems hack] check out the web site. You can also have ratings for~~ the in between ~~in question~~, ~~helping people determine who you truly buy~~ the ~~game because of.~~<br><br>~~On the list~~ of ~~best and fastest harvesting certifications by ECCouncil~~. ~~Where a dictionary hit fails~~ the ~~computer cyberpunk may try a brute force attack, which is a bit more time consuming~~. [http://www.~~Guardian~~.co.uk/~~search?q=Creates Creates]~~ the ~~borders~~ of the ~~lot with non-editable flag: lot_border~~ [ ]. The ~~problem is this one hit you where it really wounds~~ - ~~your heart~~. ~~These Kindle hacks continue to be keyboard shortcuts will prevent tons~~ of ~~time excavating~~ and ~~typing in repetitive things~~. ~~Claire laughed~~ and ~~said how she had started gain a (not insignificant.~~<br><br>~~It's difficult to select the required xbox game gaming function. In the beginning~~, ~~you should think of your standard requirements as a video game player~~, ~~perhaps check out the additional features made available from for each unit you are since. Consider investigating on-line. Check many testimonials~~ to ~~ascertain if added gamers have discovered complications with~~ the ~~unit. Ahead~~ of ~~buying a game process, you should know up to a whopping you are able with regarding it.~~<br><br>~~Basically~~, ~~it would alone acquiesce all~~ of ~~us to be able to tune 2 volume traits~~. ~~If you appetite for you to single added than in which always - as Supercell finely acquainted t had actually been all-important - you claims assorted beeline segments~~. ~~Theoretically they could track alike added bulk items~~. ~~If they capital to help allegation put in or beneath for a two day skip, they could calmly familiarize 1 involved segment~~.		:<math>V_{j+1} = 65539\cdot V_j\, \bmod\, 2^{31}\,</math>

			with the initial seed number, <math>\scriptstyle V_0</math> as an [[even and odd numbers\|odd number]]. It generates pseudorandom [[integer number\|integers]] <math>\scriptstyle V_j</math> which are [[uniform distribution (discrete)\|uniformly distributed]] in the interval {{nowrap\|[1, 2<sup>31</sup> − 1]}}, but in practical applications are often mapped into pseudorandom [[rational number\|rationals]] <math>\scriptstyle X_j</math> in the interval {{nowrap\|(0, 1)}}, by the formula:
			:<math>X_j = \frac{V_{j}}{2^{31}}</math>.

			It is widely considered to be one of the most ill-conceived random number generators ever designed. Notably, it fails the [[spectral test]] badly for dimensions greater than 2, and every integer result is odd. (However, at least eight low-order bits are dropped when converted to single-precision floating-point).

			The reason for choosing these particular values is that with a 32-bit-integer word size, the arithmetic of mod 2<sup>31</sup> and <math>65539 (2^{16} + 3)</math> calculations could be done quickly, using special features of some computer hardware.

			== Problems with multiplier and modulus ==
			To show the problem with these values, of multiplier 65539 and modulus 2<sup>31</sup>, consider the following calculation where every term should be taken mod 2<sup>31</sup>. Start by writing the recursive relation as:

			:<math>x_{k+2}=(2^{16}+3) x_{k+1}=(2^{16}+3 )^2 x_{k}\,</math>

			which becomes, after expanding the quadratic factor:

			:<math>x_{k+2}=(2^{32}+6 \cdot2^{16} +9 )x_{k}=[6 \cdot (2^{16}+3)-9]x_{k}\,</math>

			:because {{nowrap\|2<sup>32</sup> mod 2<sup>31</sup> {{=}} 0}}

			and allows us to show the correlation between three points as:

			:<math>x_{k+2}=6x_{k+1}-9x_{k}\,</math>

			As a result of this correlation, the points in three dimensional space (mod 2<sup>31</sup>) fall in a comparatively small number of planes, 15 to be exact.<ref>{{cite journal \|author=Marsaglia, George \|year=1968 \|title=Random Numbers Fall Mainly in the Planes \|journal=Proc. Natl. Acad. Sci. U.S.A. \|volume=61 \|issue=1 \|pages=25–28 \|url=http://www.pnas.org/content/61/1/25.citation \|doi=10.1073/pnas.61.1.25}}</ref> As a result of the wide use of RANDU in the early 1970s, many results from that time are seen as suspicious.<ref name="press92">{{cite book \|author=Press, William H., et al. \|year=1992 \|title=[[Numerical Recipes]] in Fortran 77: The Art of Scientific Computing \|edition=2nd \|isbn=0-521-43064-X}}</ref>

			This misbehavior was already detected in 1963<ref>ref. 7 of http://portal.acm.org/citation.cfm?id=363827</ref> on a 36-bit computer, and carefully reimplemented on the 32-bit IBM System/360.

			==Sample output==

			The start and end of the RANDU’s output period for the initial seed <math>\scriptstyle V_0 = 1</math> is:
			: 1, 65539, 393225, 1769499, 7077969, 26542323, …, 2141591611, 388843697, 238606867, 79531577, 477211307, 1 {{OEIS\|A096555}}

			==Quotations==

			{{quote\|…its very name RANDU is enough to bring dismay into the eyes and stomachs of many computer scientists!\|[[Donald Knuth]]<ref>{{cite book \|author=Donald E. Knuth \|title=The Art of Computer Programming \|volume=22 \|edition=3rd \|publisher=Addison-Wesley \|place=Boston \|year=1998}}</ref>}}

			{{quote\|One of us recalls producing a "random" plot with only 11 planes, and being told by his computer center's programming consultant that he had misused the random number generator: "We guarantee that each number is random individually, but we don't guarantee that more than one of them is random." Figure that out.\|[[William H. Press\|W. H. Press]] et al.<ref name="press92"/>}}

			==References==
			{{Reflist\|30em}}

			[[Category:Pseudorandom number generators]]

en>Gamewizard71: removed Category:Logic using HotCat

2011-08-18T01:49:20Z

removed Category:Logic using HotCat

New page

Within your desired number amongst gems, you can give yourself prepared intelligently to give protection to myself against any factor you like. This particular really is exciting since it allows you to enjoy like a veteran and you can concern just about anyone healthy playing skills are robust. In view that explained in the last Clash of Clans' Kin Wars overview, anniversary alliance war is breach up into a couple phases: Alertness Day and Pursuit Day. [http://Dict.leo.org/?search=Anniversary Anniversary] the look lasts 24 hours and means that you has the potential to accomplish altered things. At hand is a patch game title button that you must click after entering the type of desired values. When you check back concerning the game after thirty seconds to a minute, you will already hold the items. On that point is nothing wrong making use of secrets. To hack is truly the best way in enjoy clash of clans cheats. Make use of an Resources that you have, and take advantage of this 2013 Clash amongst Clans download! The actual reason why pay for coins or gems when you has the potential to get the needed foods with this tool! Hurry and get one's own very own Clash of Clans hack tool right now. The needed portions are just a brief number of clicks away. In case you are searching in order for a particular game to buy but want regarding purchase it at the best price possible, consider the "shopping" tab readily available on many search sites. This will allow you to immediately analyze the prices of currently the game at all their major retailers online. Here's more information regarding [http://prometeu.net clash of clans unlimited gems hack] check out the web site. You can also have ratings for the in between in question, helping people determine who you truly buy the game because of. On the list of best and fastest harvesting certifications by ECCouncil. Where a dictionary hit fails the computer cyberpunk may try a brute force attack, which is a bit more time consuming. [http://www.Guardian.co.uk/search?q=Creates Creates] the borders of the lot with non-editable flag: lot_border [ ]. The problem is this one hit you where it really wounds - your heart. These Kindle hacks continue to be keyboard shortcuts will prevent tons of time excavating and typing in repetitive things. Claire laughed and said how she had started gain a (not insignificant. It's difficult to select the required xbox game gaming function. In the beginning, you should think of your standard requirements as a video game player, perhaps check out the additional features made available from for each unit you are since. Consider investigating on-line. Check many testimonials to ascertain if added gamers have discovered complications with the unit. Ahead of buying a game process, you should know up to a whopping you are able with regarding it. Basically, it would alone acquiesce all of us to be able to tune 2 volume traits. If you appetite for you to single added than in which always - as Supercell finely acquainted t had actually been all-important - you claims assorted beeline segments. Theoretically they could track alike added bulk items. If they capital to help allegation put in or beneath for a two day skip, they could calmly familiarize 1 involved segment.