////////////////////////////////////////////////////////////////////////////// // //+ Tutorial illustrating use and precision of the Double32_t data type // // You must run this tutorial with ACLIC // root > .x double32.C+ // // The following cases are supported for streaming a Double32_t type // depending on the range declaration in the comment field of the data member: // A- Double32_t fNormal; // B- Double32_t fTemperature; //[0,100] // C- Double32_t fCharge; //[-1,1,2] // D- Double32_t fVertex[3]; //[-30,30,10] // E- Double32_t fChi2; //[0,0,6] // F- Int_t fNsp; // Double32_t* fPointValue; //[fNsp][0,3] // // In case A fNormal is converted from a Double_t to a Float_t // In case B fTemperature is converted to a 32 bit unsigned integer // In case C fCharge is converted to a 2 bits unsigned integer // In case D the array elements of fVertex are converted to an unsigned 10 bits integer // In case E fChi2 is converted to a Float_t with truncated precision at 6 bits // In case F the fNsp elements of array fPointvalue are converted to an unsigned 32 bit integer // Note that the range specifier must follow the dimension specifier. // the case B has more precision (9 to 10 significative digits than case A (6 to 7 digits). // // The range specifier has the general format: [xmin,xmax] or [xmin,xmax,nbits] // [0,1] // [-10,100]; // [-pi,pi], [-pi/2,pi/4],[-2pi,2*pi] // [-10,100,16] // [0,0,8] // if nbits is not specified, or nbits <2 or nbits>32 it is set to 32 // if (xmin==0 and xmax==0 and nbits <=14) the double word will be converted // to a float and its mantissa truncated to nbits significative bits. // // IMPORTANT NOTE // -------------- // Lets assume an original variable double x: // When using the format [0,0,8] (ie range not specified) you get the best // relative precision when storing and reading back the truncated x, say xt. // The variance of (x-xt)/x will be better than when specifying a range // for the same number of bits. However the precision relative to the // range (x-xt)/(xmax-xmin) will be worst, and vice-versa. // The format [0,0,8] is also interesting when the range of x is infinite // or unknown. // //Author: Rene Brun // /////////////////////////////////////////////////////////////////////////// #include "TFile.h" #include "TCanvas.h" #include "TTree.h" #include "TH1.h" #include "TMath.h" #include "TRandom3.h" #include "TGraph.h" #include "TLegend.h" #include "TFrame.h" #include "TPaveLabel.h" class DemoDouble32 { private: Double_t fD64; //reference member with full double precision Double32_t fF32; //saved as a 32 bit Float_t Double32_t fI32; //[-pi,pi] saved as a 32 bit unsigned int Double32_t fI30; //[-pi,pi,30] saved as a 30 bit unsigned int Double32_t fI28; //[-pi,pi,28] saved as a 28 bit unsigned int Double32_t fI26; //[-pi,pi,26] saved as a 26 bit unsigned int Double32_t fI24; //[-pi,pi,24] saved as a 24 bit unsigned int Double32_t fI22; //[-pi,pi,22] saved as a 22 bit unsigned int Double32_t fI20; //[-pi,pi,20] saved as a 20 bit unsigned int Double32_t fI18; //[-pi,pi,18] saved as a 18 bit unsigned int Double32_t fI16; //[-pi,pi,16] saved as a 16 bit unsigned int Double32_t fI14; //[-pi,pi,14] saved as a 14 bit unsigned int Double32_t fI12; //[-pi,pi,12] saved as a 12 bit unsigned int Double32_t fI10; //[-pi,pi,10] saved as a 10 bit unsigned int Double32_t fI8; //[-pi,pi, 8] saved as a 8 bit unsigned int Double32_t fI6; //[-pi,pi, 6] saved as a 6 bit unsigned int Double32_t fI4; //[-pi,pi, 4] saved as a 4 bit unsigned int Double32_t fI2; //[-pi,pi, 2] saved as a 2 bit unsigned int Double32_t fR14; //[0, 0, 14] saved as a 32 bit float with a 14 bits mantissa Double32_t fR12; //[0, 0, 12] saved as a 32 bit float with a 12 bits mantissa Double32_t fR10; //[0, 0, 10] saved as a 32 bit float with a 10 bits mantissa Double32_t fR8; //[0, 0, 8] saved as a 32 bit float with a 8 bits mantissa Double32_t fR6; //[0, 0, 6] saved as a 32 bit float with a 6 bits mantissa Double32_t fR4; //[0, 0, 4] saved as a 32 bit float with a 4 bits mantissa Double32_t fR2; //[0, 0, 2] saved as a 32 bit float with a 2 bits mantissa public: DemoDouble32() {;} void Set(Double_t ref); }; void DemoDouble32::Set(Double_t ref) { fD64 = fF32 = fI32 = fI30 = fI28 = fI26 = fI24 = fI22 = fI20 = ref; fI18 = fI16 = fI14 = fI12 = fI10 = fI8 = fI6 = fI4 = fI2 = ref; fR14 = fR12 = fR10 = fR8 = fR6 = fR4 = fR2 = ref; } void double32() { // show the use and precision of the Double32_t data type DemoDouble32 *d = new DemoDouble32(); //create a Tree with 40000 objects DemoDouble32 TFile::Open("DemoDouble32.root","recreate"); TTree *T = new TTree("T","DemoDouble32"); TBranch *bd = T->Branch("d","DemoDouble32",&d,4000); TRandom3 r; Double_t xmax = TMath::Pi(); Double_t xmin = -xmax; Int_t i, n = 40000; for (i=0;iSet(r.Uniform(xmin,xmax)); T->Fill(); } T->Write(); //Create the frame histogram and the graphs TObjArray *branches = bd->GetListOfBranches(); Int_t nb = branches->GetEntries(); TBranch *br = (TBranch*)branches->At(0); Long64_t zip64 = br->GetZipBytes(); Double_t cx = 1; Double_t drange = 15; Double_t dval = 15; TCanvas *c1 = new TCanvas("c1","c1",800,600); c1->SetGrid(); c1->SetHighLightColor(0); c1->SetFillColor(17); c1->SetFrameFillColor(20); c1->SetFrameBorderSize(10); TH1F *h = new TH1F("h","",nb,0,nb); h->SetMaximum(16); h->SetStats(0); h->Draw(); c1->GetFrame()->SetFillColor(21); c1->GetFrame()->SetBorderSize(12); TGraph *gcx = new TGraph(nb); gcx->SetName("gcx"); gcx->SetMarkerStyle(21); gcx->SetMarkerColor(kBlue); TGraph *gdrange = new TGraph(nb); gdrange->SetName("gdrange"); gdrange->SetMarkerStyle(20); gdrange->SetMarkerColor(kRed); TGraph *gdval = new TGraph(nb); gdval->SetName("gdval"); gdval->SetMarkerStyle(20); gdval->SetMarkerColor(kBlack); TPaveLabel *title = new TPaveLabel(.15,.92,.85,.97,"Double32_t compression and precision","brNDC"); title->Draw(); //loop on branches to get the precision and compression factors for (i=0;iAt(i); h->GetXaxis()->SetBinLabel(i+1,br->GetName()); cx = Double_t(zip64)/Double_t(br->GetZipBytes()); gcx->SetPoint(i,i+0.5,cx); if (i > 0) { T->Draw(Form("(fD64-%s)/(%g)",br->GetName(),xmax-xmin),"","goff"); Double_t rms = TMath::RMS(n,T->GetV1()); drange = TMath::Max(0.,-TMath::Log10(rms)); } gdrange->SetPoint(i,i+0.5,drange); if (i > 0) { T->Draw(Form("(fD64-%s)/(fD64+0.01)",br->GetName()),"","goff"); Double_t rms = TMath::RMS(n,T->GetV1()); dval = TMath::Max(0.,-TMath::Log10(rms)); } gdval->SetPoint(i,i+0.5,dval); } gcx->Draw("lp"); gdrange->Draw("lp"); gdval->Draw("lp"); TLegend *legend = new TLegend(0.2,0.7,0.7,0.85); legend->SetTextFont(72); legend->SetTextSize(0.04); legend->AddEntry(gcx,"Compression factor","lp"); legend->AddEntry(gdrange,"Log of precision wrt range","lp"); legend->AddEntry(gdval,"Log of precision wrt value","lp"); legend->Draw(); TPaveLabel *rang = new TPaveLabel(.75,.75,.88,.80,"[-pi,pi]","brNDC"); rang->Draw(); }