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float16.C
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1/// \file
2/// \ingroup tutorial_io
3/// \notebook -js
4/// Tutorial illustrating use and precision of the Float16_t data type.
5/// See the double32.C tutorial for all the details.
6/// \macro_image
7/// \macro_code
8///
9/// \author Danilo Piparo
10
11#include "ROOT/TSeq.hxx"
12#include "TCanvas.h"
13#include "TFile.h"
14#include "TGraph.h"
15#include "TH1.h"
16#include "TLegend.h"
17#include "TMath.h"
18#include "TRandom3.h"
19#include "TTree.h"
20
21class DemoFloat16 {
22private:
23 float fF32; // reference member with full single precision
24 Float16_t fF16; // saved as a 16 bit floating point number
25 Float16_t fI16; //[-pi,pi] saved as a 16 bit unsigned int
26 Float16_t fI14; //[-pi,pi,14] saved as a 14 bit unsigned int
27 Float16_t fI10; //[-pi,pi,10] saved as a 10 bit unsigned int
28 Float16_t fI8; //[-pi,pi,8] saved as a 8 bit unsigned int
29 Float16_t fI6; //[-pi,pi,6] saved as a 6 bit unsigned int
30 Float16_t fI4; //[-pi,pi,4] saved as a 4 bit unsigned int
31 Float16_t fR8; //[0, 0, 8] saved as a 16 bit float with a 8 bits mantissa
32 Float16_t fR6; //[0, 0, 6] saved as a 16 bit float with a 6 bits mantissa
33 Float16_t fR4; //[0, 0, 4] saved as a 16 bit float with a 4 bits mantissa
34 Float16_t fR2; //[0, 0, 2] saved as a 16 bit float with a 2 bits mantissa
35
36public:
37 DemoFloat16() = default;
38 void Set(float ref) { fF32 = fF16 = fI16 = fI14 = fI10 = fI8 = fI6 = fI4 = fR8 = fR6 = fR4 = fR2 = ref; }
39};
40
41void float16()
42{
43 const auto nEntries = 200000;
44 const auto xmax = TMath::Pi();
45 const auto xmin = -xmax;
46
47 // create a Tree with nEntries objects DemoFloat16
48 TFile::Open("DemoFloat16.root", "recreate");
49 TTree tree("tree", "DemoFloat16");
50 DemoFloat16 demoInstance;
51 auto demoInstanceBranch = tree.Branch("d", "DemoFloat16", &demoInstance, 4000);
52 TRandom3 r;
53 for (auto i : ROOT::TSeqI(nEntries)) {
54 demoInstance.Set(r.Uniform(xmin, xmax));
55 tree.Fill();
56 }
57 tree.Write();
58
59 // Now we can proceed with the analysis of the sizes on disk of all branches
60
61 // Create the frame histogram and the graphs
62 auto branches = demoInstanceBranch->GetListOfBranches();
63 const auto nb = branches->GetEntries();
64 auto br = static_cast<TBranch *>(branches->At(0));
65 const Long64_t zip64 = br->GetZipBytes();
66
67 auto h = new TH1F("h", "Float16_t compression and precision", nb, 0, nb);
68 h->SetMaximum(18);
69 h->SetStats(false);
70
71 auto gcx = new TGraph();
72 gcx->SetName("gcx");
73 gcx->SetMarkerStyle(kFullSquare);
74 gcx->SetMarkerColor(kBlue);
75
76 auto gdrange = new TGraph();
77 gdrange->SetName("gdrange");
78 gdrange->SetMarkerStyle(kFullCircle);
79 gdrange->SetMarkerColor(kRed);
80
81 auto gdval = new TGraph();
82 gdval->SetName("gdval");
83 gdval->SetMarkerStyle(kFullTriangleUp);
84 gdval->SetMarkerColor(kBlack);
85
86 // loop on branches to get the precision and compression factors
87 for (auto i : ROOT::TSeqI(nb)) {
88 br = static_cast<TBranch *>(branches->At(i));
89 const auto brName = br->GetName();
90 h->GetXaxis()->SetBinLabel(i + 1, brName);
91 auto const cx = double(zip64) / br->GetZipBytes();
92 gcx->SetPoint(i, i + 0.5, cx);
93 if (i == 0) continue;
94
95 tree.Draw(Form("(fF32-%s)/(%g)", brName, xmax - xmin), "", "goff");
96 const auto rmsDrange = TMath::RMS(nEntries, tree.GetV1());
97 const auto drange = TMath::Max(0., -TMath::Log10(rmsDrange));
98 gdrange->SetPoint(i - 1, i + 0.5, drange);
99
100 tree.Draw(Form("(fF32-%s)/fF32 >> hdval_%s", brName, brName), "", "goff");
101 const auto rmsDval = TMath::RMS(nEntries, tree.GetV1());
102 const auto dval = TMath::Max(0., -TMath::Log10(rmsDval));
103 gdval->SetPoint(i - 1, i + 0.5, dval);
104
105 tree.Draw(Form("(fF32-%s) >> hdvalabs_%s", brName, brName), "", "goff");
106 auto hdval = gDirectory->Get<TH1F>(Form("hdvalabs_%s", brName));
107 hdval->GetXaxis()->SetTitle("Difference wrt reference value");
108 auto c = new TCanvas(brName, brName, 800, 600);
109 c->SetGrid();
110 c->SetLogy();
111 hdval->DrawClone();
112 }
113
114 auto c1 = new TCanvas("c1", "c1", 800, 600);
115 c1->SetGrid();
116
117 h->Draw();
118 h->GetXaxis()->LabelsOption("v");
119 gcx->Draw("lp");
120 gdrange->Draw("lp");
121 gdval->Draw("lp");
122
123 // Finally build a legend
124 auto legend = new TLegend(0.3, 0.6, 0.9, 0.9);
125 legend->SetHeader(Form("%d entries within the [-#pi, #pi] range", nEntries));
126 legend->AddEntry(gcx, "Compression factor", "lp");
127 legend->AddEntry(gdrange, "Log of precision wrt range: p = -Log_{10}( RMS( #frac{Ref - x}{range} ) ) ", "lp");
128 legend->AddEntry(gdval, "Log of precision wrt value: p = -Log_{10}( RMS( #frac{Ref - x}{Ref} ) ) ", "lp");
129 legend->Draw();
130}
#define c(i)
Definition RSha256.hxx:101
#define h(i)
Definition RSha256.hxx:106
float Float16_t
Definition RtypesCore.h:58
long long Long64_t
Definition RtypesCore.h:80
@ kRed
Definition Rtypes.h:66
@ kBlack
Definition Rtypes.h:65
@ kBlue
Definition Rtypes.h:66
@ kFullSquare
Definition TAttMarker.h:55
@ kFullTriangleUp
Definition TAttMarker.h:55
@ kFullCircle
Definition TAttMarker.h:55
#define gDirectory
Definition TDirectory.h:384
Option_t Option_t TPoint TPoint const char GetTextMagnitude GetFillStyle GetLineColor GetLineWidth GetMarkerStyle GetTextAlign GetTextColor GetTextSize void char Point_t Rectangle_t WindowAttributes_t Float_t r
float xmin
float xmax
char * Form(const char *fmt,...)
Formats a string in a circular formatting buffer.
Definition TString.cxx:2489
A TTree is a list of TBranches.
Definition TBranch.h:93
Long64_t GetZipBytes(Option_t *option="") const
Return total number of zip bytes in the branch if option ="*" includes all sub-branches of this branc...
Definition TBranch.cxx:2238
The Canvas class.
Definition TCanvas.h:23
static TFile * Open(const char *name, Option_t *option="", const char *ftitle="", Int_t compress=ROOT::RCompressionSetting::EDefaults::kUseCompiledDefault, Int_t netopt=0)
Create / open a file.
Definition TFile.cxx:4067
A TGraph is an object made of two arrays X and Y with npoints each.
Definition TGraph.h:41
1-D histogram with a float per channel (see TH1 documentation)
Definition TH1.h:621
TAxis * GetXaxis()
Definition TH1.h:324
This class displays a legend box (TPaveText) containing several legend entries.
Definition TLegend.h:23
virtual void SetTitle(const char *title="")
Set the title of the TNamed.
Definition TNamed.cxx:164
const char * GetName() const override
Returns name of object.
Definition TNamed.h:47
Random number generator class based on M.
Definition TRandom3.h:27
A TTree represents a columnar dataset.
Definition TTree.h:79
return c1
Definition legend1.C:41
This file contains a specialised ROOT message handler to test for diagnostic in unit tests.
TSeq< int > TSeqI
Definition TSeq.hxx:203
Double_t RMS(Long64_t n, const T *a, const Double_t *w=nullptr)
Returns the Standard Deviation of an array a with length n.
Definition TMath.h:1188
Short_t Max(Short_t a, Short_t b)
Returns the largest of a and b.
Definition TMathBase.h:250
constexpr Double_t Pi()
Definition TMath.h:37
Double_t Log10(Double_t x)
Returns the common (base-10) logarithm of x.
Definition TMath.h:762