double32.C: Tutorial illustrating use and precision of the Double32_t data type

///////////////////////////////////////////////////////////////////////////
//
//  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();
}