{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "101bc26e",
   "metadata": {},
   "source": [
    "# float16\n",
    "Tutorial illustrating use and precision of the Float16_t data type.\n",
    "See the double32.C tutorial for all the details.\n",
    "\n",
    "\n",
    "\n",
    "**Author:** Danilo Piparo  \n",
    "<i><small>This notebook tutorial was automatically generated with <a href= \"https://github.com/root-project/root/blob/master/documentation/doxygen/converttonotebook.py\">ROOTBOOK-izer</a> from the macro found in the ROOT repository  on Tuesday, May 19, 2026 at 08:14 PM.</small></i>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0b7eea77",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%%cpp -d\n",
    "\n",
    "#include \"ROOT/TSeq.hxx\"\n",
    "#include \"TCanvas.h\"\n",
    "#include \"TFile.h\"\n",
    "#include \"TGraph.h\"\n",
    "#include \"TH1.h\"\n",
    "#include \"TLegend.h\"\n",
    "#include \"TMath.h\"\n",
    "#include \"TRandom3.h\"\n",
    "#include \"TTree.h\"\n",
    "\n",
    "class DemoFloat16 {\n",
    "private:\n",
    "   float fF32;     // reference member with full single precision\n",
    "   Float16_t fF16; // saved as a 16 bit floating point number\n",
    "   Float16_t fI16; //[-pi,pi]    saved as a 16 bit unsigned int\n",
    "   Float16_t fI14; //[-pi,pi,14] saved as a 14 bit unsigned int\n",
    "   Float16_t fI10; //[-pi,pi,10] saved as a 10 bit unsigned int\n",
    "   Float16_t fI8;  //[-pi,pi,8] saved as a 8 bit unsigned int\n",
    "   Float16_t fI6;  //[-pi,pi,6] saved as a 6 bit unsigned int\n",
    "   Float16_t fI4;  //[-pi,pi,4] saved as a 4 bit unsigned int\n",
    "   Float16_t fR8;  //[0, 0, 8] saved as a 16 bit float with a 8 bits mantissa\n",
    "   Float16_t fR6;  //[0, 0, 6] saved as a 16 bit float with a 6 bits mantissa\n",
    "   Float16_t fR4;  //[0, 0, 4] saved as a 16 bit float with a 4 bits mantissa\n",
    "   Float16_t fR2;  //[0, 0, 2] saved as a 16 bit float with a 2 bits mantissa\n",
    "\n",
    "public:\n",
    "   DemoFloat16() = default;\n",
    "   void Set(float ref) { fF32 = fF16 = fI16 = fI14 = fI10 = fI8 = fI6 = fI4 = fR8 = fR6 = fR4 = fR2 = ref; }\n",
    "};"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7ee06842",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "const auto nEntries = 200000;\n",
    "const auto xmax = TMath::Pi();\n",
    "const auto xmin = -xmax;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "514db242",
   "metadata": {},
   "source": [
    "create a Tree with nEntries objects DemoFloat16"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "158be865",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "TFile::Open(\"DemoFloat16.root\", \"recreate\");\n",
    "TTree tree(\"tree\", \"DemoFloat16\");\n",
    "DemoFloat16 demoInstance;\n",
    "auto demoInstanceBranch = tree.Branch(\"d\", \"DemoFloat16\", &demoInstance, 4000);\n",
    "TRandom3 r;\n",
    "for (auto i : ROOT::TSeqI(nEntries)) {\n",
    "   demoInstance.Set(r.Uniform(xmin, xmax));\n",
    "   tree.Fill();\n",
    "}\n",
    "tree.Write();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f079341f",
   "metadata": {},
   "source": [
    "Now we can proceed with the analysis of the sizes on disk of all branches"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22771c86",
   "metadata": {},
   "source": [
    "Create the frame histogram and the graphs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "12c4b71a",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "auto branches = demoInstanceBranch->GetListOfBranches();\n",
    "const auto nb = branches->GetEntries();\n",
    "auto br = static_cast<TBranch *>(branches->At(0));\n",
    "const Long64_t zip64 = br->GetZipBytes();\n",
    "\n",
    "auto h = new TH1F(\"h\", \"Float16_t compression and precision\", nb, 0, nb);\n",
    "h->SetMaximum(18);\n",
    "h->SetStats(false);\n",
    "\n",
    "auto gcx = new TGraph();\n",
    "gcx->SetName(\"gcx\");\n",
    "gcx->SetMarkerStyle(kFullSquare);\n",
    "gcx->SetMarkerColor(kBlue);\n",
    "\n",
    "auto gdrange = new TGraph();\n",
    "gdrange->SetName(\"gdrange\");\n",
    "gdrange->SetMarkerStyle(kFullCircle);\n",
    "gdrange->SetMarkerColor(kRed);\n",
    "\n",
    "auto gdval = new TGraph();\n",
    "gdval->SetName(\"gdval\");\n",
    "gdval->SetMarkerStyle(kFullTriangleUp);\n",
    "gdval->SetMarkerColor(kBlack);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b4c83b8",
   "metadata": {},
   "source": [
    "loop on branches to get the precision and compression factors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "396f1c79",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "for (auto i : ROOT::TSeqI(nb)) {\n",
    "   br = static_cast<TBranch *>(branches->At(i));\n",
    "   const auto brName = br->GetName();\n",
    "   h->GetXaxis()->SetBinLabel(i + 1, brName);\n",
    "   auto const cx = double(zip64) / br->GetZipBytes();\n",
    "   gcx->SetPoint(i, i + 0.5, cx);\n",
    "   if (i == 0) continue;\n",
    "\n",
    "   tree.Draw(Form(\"(fF32-%s)/(%g)\", brName, xmax - xmin), \"\", \"goff\");\n",
    "   const auto rmsDrange = TMath::RMS(nEntries, tree.GetV1());\n",
    "   const auto drange = TMath::Max(0., -TMath::Log10(rmsDrange));\n",
    "   gdrange->SetPoint(i - 1, i + 0.5, drange);\n",
    "\n",
    "   tree.Draw(Form(\"(fF32-%s)/fF32 >> hdval_%s\", brName, brName), \"\", \"goff\");\n",
    "   const auto rmsDval = TMath::RMS(nEntries, tree.GetV1());\n",
    "   const auto dval = TMath::Max(0., -TMath::Log10(rmsDval));\n",
    "   gdval->SetPoint(i - 1, i + 0.5, dval);\n",
    "\n",
    "   tree.Draw(Form(\"(fF32-%s) >> hdvalabs_%s\", brName, brName), \"\", \"goff\");\n",
    "   auto hdval = gDirectory->Get<TH1F>(Form(\"hdvalabs_%s\", brName));\n",
    "   hdval->GetXaxis()->SetTitle(\"Difference wrt reference value\");\n",
    "   auto c = new TCanvas(brName, brName, 800, 600);\n",
    "   c->SetGrid();\n",
    "   c->SetLogy();\n",
    "   hdval->DrawClone();\n",
    "}\n",
    "\n",
    "auto c1 = new TCanvas(\"c1\", \"c1\", 800, 600);\n",
    "c1->SetGrid();\n",
    "\n",
    "h->Draw();\n",
    "h->GetXaxis()->LabelsOption(\"v\");\n",
    "gcx->Draw(\"lp\");\n",
    "gdrange->Draw(\"lp\");\n",
    "gdval->Draw(\"lp\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8aafc927",
   "metadata": {},
   "source": [
    "Finally build a legend"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8055a413",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "auto legend = new TLegend(0.3, 0.6, 0.9, 0.9);\n",
    "legend->SetHeader(Form(\"%d entries within the [-#pi, #pi] range\", nEntries));\n",
    "legend->AddEntry(gcx, \"Compression factor\", \"lp\");\n",
    "legend->AddEntry(gdrange, \"Log of precision wrt range: p = -Log_{10}( RMS( #frac{Ref - x}{range} ) ) \", \"lp\");\n",
    "legend->AddEntry(gdval, \"Log of precision wrt value: p = -Log_{10}( RMS( #frac{Ref - x}{Ref} ) ) \", \"lp\");\n",
    "legend->Draw();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "45c102d0",
   "metadata": {},
   "source": [
    "Draw all canvases "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8d76a7ab",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%jsroot on\n",
    "gROOT->GetListOfCanvases()->Draw()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "ROOT C++",
   "language": "c++",
   "name": "root"
  },
  "language_info": {
   "codemirror_mode": "text/x-c++src",
   "file_extension": ".C",
   "mimetype": " text/x-c++src",
   "name": "c++"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}