Very Large number Calculations with No Loss in Accuracy ? Given a 1700 digit number, we want to store the value and perform two functions on it with NO loss of accuracy, its ok if calc time takes longer but better if faster.
Where x = a 1700 digit long numeric value The two calcs to be computed with be ; X * (up to a four digit value ) then we take the modulus of this resultant of 400 ; ( x % 400 ) If we cant multiply [ X * (up to a four digit value ) ] and then take the modulus due to processing bottlenecks, ceilings - then can this be done where we first take the modulus of the original x = 1700 digits and then multiply this by the four digit value and then take the modulus of this after? Ideally Id prefer to be able to do the first scenario. Constraints Im aware of regarding this to date ; Firstly, Im only running on a WinXp 32 bit system and not able to upgrade currently. Secondly, Ive been becoming aware of a lot of issues, bugs, errors with python, sympy, etc.. in properly handling very large number calcs. These problems seem to arise out of data loss through use of floats and related. Details on a number of different approaches can be viewed here ; https://groups.google.com/forum/#!topic/sympy/eUfW6C_nHdI https://groups.google.com/forum/#!topic/sympy/hgoQ74iZLkk My system will not properly handle "float128" floats, although Ive been told by one person this would be able to handle wsuch a computation - altho the prob is it seems that float128 is rarely actually a 128 float and certainly not on my system. Also due to internal processing peculiarties it seems that most floats will lose data on these kinds of computations. If I understand correctly, one of the best candidates for getting the most accurate values returned involves the use of arbitrary precision and representing the inputs as strings and not just straight numeroc values? Also, ideally, Id like the formula to be able to handle rationals without accuracy loss. So "x" starts off as a whole number, but when I multiply it by the four digit value, Id like that value to be any numeric value such as an integer, whole number or rational like "2243.0456". Structure of one of the methods Ive been experimenting with ; from sympy import mpmath mpmath.mp.dps = 1700 x = (mpmath.mpf" INSERT 1700 DIGIT NUMBER HERE" (x % 400) An example with live data ; from sympy import mpmath mpmath.mp.dps = 1700 x = (mpmath.mpf"4224837741562986738552195234618134569391350587851527986076117152972791626026988760293885754068768475423919991676816860701478996539715076968649431668262941552499272851934021744703799728797962346859481772141964720120813934781420732260156446701740408591264289745960985811289070246238359268267313892549883722768575435935465369820850766441187744058828599331364172396647692768693734233545999439071435129082764340446292057962343360114463696515950803159895238667237356887294549618489296157716384494295159851060500050371940523385701946860964162569067371175357615144192344763876540813882107379891591055307476597279137714860430053785074855035948744902479909111840444834198237419177418965268614345042634655648237818899253116247916585686713243193074635608527160273611309051938762676520507404815180792793701259216609316118483835216791263172902470123821111779223204735647931377027227055312940934756325611832463728974558417085791096461266371917752574370345933533929245534623041989305973992490523694190318284666464757159324866096861573704540654160644711274766759520501013633999706244117691235878123489694261724158073725644897527727473450037615295487637338687848351441331386946416003718795419822246935787682977520303924734875834943985619000970655639767984458204513958680501990182471695393372003272654902387493955849775308922901631024199011283441050881608686856746206012270890984260424834329551281249797545775091226433669036680463406283858413423722935297859778786945935751468048494081427689669730664660260908636113264573712854536295005312934569838992758429422872122606102877623867968067833225444280667381025371705347744037508121975424674439904984528128036994803804742198422695627759844248" (x % 400) But I have no idea if accurate results are being returned with this, would love to hear anyones suggestions? -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/6330cf73-4307-4086-b842-2d34cec517b2%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
