[ROOT] floating-point arithmetics

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[ROOT] floating-point arithmetics
Giannis Doxaras 5 January 2005 17:02:04
	Hi all, I am experiencing a problem with high precision integer arithmetic in ROOT. After e^{20}, fmod() function seems to lose precision due to floating point error I presume. I wonder if there exists a class manipulating large integer, or floating point arithmetic in general , something similar to GMP (GNU Multiple Precision Arithmetic Library). If not, it should be rather helpful, if such a feature was included in forthcoming versions. Friendly, Doxaras John University Of Athens Division of Nuclear Physics & Elementary Particles d0x@r@$ //Doxaras Ioannis University of Athens //Division of Nuclear Physics and Elementary Particles /Algorithm for simulating Shor's procedure for factoring quantum mechanicly a large composite number N into primes. First we choose a random number [1...N-1] and using Eucleid's Algorithm we check if the number we generated has no common devisors with N. The distribution of co-prime number lower than N is determined [Hardy] \phi(n)=m\prod_{p\|m}(1-\frac{1}{p}) were m=\prodp^{c}/ void prime(Int_t numb) { gROOT->Reset(); Int_t rand = 7; Int_t remainder; Int_t quotient; Int_t seed = 1; gBenchmark->Start("Prime"); //do //{ gRandom = new TRandom3(seed); rand = ceil(numbgRandom->Rndm()); //Eucleid's Algorithm //remainder = &rand; //initialize //quotient = &numb; //while (remainder != 1) //{ //quotient = quotient / remainder; //remainder = fmod( quotient, remainder); //} // seed += 1; //}while(quotient!= 0 \|\| seed > 20); cout << "The random number generated is: " << rand << endl; //Create the Histograms Int_t nbins = 128; Int_t min = 0; Int_t max = 127; Double_t c2, c3; TH1F order = new TH1F("order","ORDER",nbins,min,max); TH1F * modulo = new TH1F("modulo","modulo",nbins,min,max); for (Int_t k = 0; k < 128; k++ ) { c2 = pow( rand , k ); c3 = fmod(c2, numb); cout << "For: " << k << " show: " << c2 << " and " << c3 << endl; order->Fill(k , k); modulo->Fill(k, c3); } //Draw Options TCanvas *c1 = new TCanvas("Order","",200,10,700,780); c1->SetFillColor(0); c1->Divide(1,2); order->GetXaxis()->SetTitle("Potential orders of probabilistic algorithm"); order->GetXaxis()->SetTitleFont(32); order->GetXaxis()->SetLabelFont(32); order->GetXaxis()->SetLabelSize(0.03); c1->cd(1); order->Draw(); // plot the spectrum c1->cd(2); modulo->Draw(); // plot the spectrum c1->Update(); // update the canvas gBenchmark->Show("Prime"); }
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Rene Brun 5 January 2005 17:02:04 [ permanent link ]
	You can load the GMP library dynamically from an interactive ROOT session. For example with gmp-4.1.4 installed in my home directory, I can do root [0] gSystem.Load("/home/brun/gmp-4.1.4/.libs/libgmp.so") Now you can modify your prime.C file to include all the relevant extern "C" void gmp_xxx prototype declarations and the equivalent includes. Then do root[1] .L prime.C+ (using ACLIC) root[2] prime(4567) I agree that it would be nice to call the GMP library directly from CINT. This requires the dictionary for all GMP functions. If somebody succeeds in building it, let me know. Rene Brun Giannis Doxaras wrote:> Hi all,> I am experiencing a problem with high precision integer arithmetic in ROOT.> After e^{20}, fmod() function seems to lose precision due to> floating point error I presume.> I wonder if there exists a class manipulating large integer, or> floating point arithmetic in general , something similar to GMP (GNU> Multiple Precision Arithmetic Library).> If not, it should be rather helpful, if such a feature was included> in forthcoming versions.> Friendly,> Doxaras John> University Of Athens> Division of Nuclear Physics & Elementary Particles> d0x@r@$> --------------------------------------------------------------------------------> Name: prime.C> prime.C Type: Plain Text (text/plain)> Encoding: quoted-printable
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[ROOT] floating-point arithmetics

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