//////////////////////////////////////////////////////////////////////////////
//
//+ 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;i<n;i++) {
d->Set(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;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();
}