Double 3 2

Tutorial illustrating use and precision of the Double32_t data type You must run this tutorial with ACLIC: a dictionary will be automatically created.

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:

Case	Declaration
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]

Case A fNormal is converted from a Double_t to a Float_t
Case B fTemperature is converted to a 32 bit unsigned integer
Case C fCharge is converted to a 2 bits unsigned integer
Case D the array elements of fVertex are converted to an unsigned 10 bits integer
Case E fChi2 is converted to a Float_t with truncated precision at 6 bits
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.

Case B has more precision than case A: 9 to 10 significative digits and 6 to 7 digits respectively. The range specifier has the general format: [xmin,xmax] or [xmin,xmax,nbits]. Examples

[0,1]
[-10,100];
[-pi,pi], [-pi/2,pi/4],[-2pi,2*pi]
[-10,100,16]
[0,0,8] Note that:
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] (i.e. 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
This notebook tutorial was automatically generated with ROOTBOOK-izer (Beta) from the macro found in the ROOT repository on Thursday, January 19, 2017 at 04:29 PM.



In [1]:

    
%%cpp -d
#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);
};

A helper function is created:



In [2]:

    
%%cpp -d
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;
}

Show the use and precision of the double32_t data type



In [3]:

    
DemoDouble32 *d = new DemoDouble32();

Create a tree with 40000 objects demodouble32



In [4]:

    
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;i<n;i++) {
   d->Set(r.Uniform(xmin,xmax));
   T->Fill();
}
T->Write();

Create the frame histogram and the graphs



In [5]:

    
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



In [6]:

    
for (i=0;i<nb;i++) {
   br = (TBranch*)branches->At(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();

Draw all canvases



In [7]:

    
%jsroot on
gROOT->GetListOfCanvases()->Draw()