TGaxis.cxx

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// @(#)root/graf:$Id$
// Author: Rene Brun, Olivier Couet   12/12/94
 
/*************************************************************************
 * Copyright (C) 1995-2000, Rene Brun and Fons Rademakers.               *
 * All rights reserved.                                                  *
 *                                                                       *
 * For the licensing terms see $ROOTSYS/LICENSE.                         *
 * For the list of contributors see $ROOTSYS/README/CREDITS.             *
 *************************************************************************/
 
#include "TROOT.h"
#include "TBuffer.h"
#include "TGaxis.h"
#include "TAxisModLab.h"
#include "TVirtualPad.h"
#include "TLine.h"
#include "TArrow.h"
#include "TLatex.h"
#include "TStyle.h"
#include "TF1.h"
#include "TAxis.h"
#include "THashList.h"
#include "TObject.h"
#include "TMath.h"
#include "THLimitsFinder.h"
#include "TColor.h"
#include "TTimeStamp.h"
#include "strlcpy.h"
 
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <cmath>
#include <iostream>
 
const Int_t kHori = BIT(9);
 
 
/** \class TGaxis
\ingroup BasicGraphics
 
The axis painter class.
 
Instances of this class are generated by the histograms and graphs painting
classes when `TAxis` are drawn. `TGaxis` is the "painter class" of
`TAxis`. Therefore it is mainly used via `TAxis`, even if is some
occasion it can be used directly to draw an axis which is not part of a graph
or an instance. For instance to draw an extra scale on a plot.
 
- [Basic definition](\ref GA00)
- [Definition with a function](\ref GA01)
- [Logarithmic axis](\ref GA02)
- [Blank axis](\ref GA03)
- [Arrow on axis](\ref GA03a)
- [Tick marks' orientation](\ref GA04)
- [Tick marks' size](\ref GA05)
- [Labels' positioning](\ref GA06)
- [Labels' orientation](\ref GA07)
- [Labels' position on tick marks](\ref GA08)
- [Labels' format](\ref GA09)
- [Alphanumeric labels](\ref GA10)
- [Changing axis labels](\ref GA10a)
- [Number of divisions optimisation](\ref GA11)
- [Maximum Number of Digits for the axis labels](\ref GA12)
- [Optional grid](\ref GA13)
- [Time axis](\ref GA14)
 
\anchor GA00
## Basic definition
A `TGaxis` is defined the following way:
~~~ {.cpp}
    TGaxis::TGaxis(Double_t xmin, Double_t ymin, Double_t xmax, Double_t ymax,
                   Double_t wmin, Double_t wmax, Int_t ndiv, Option_t *chopt,
                   Double_t gridlength)
~~~
Where:
 
- xmin : X origin coordinate in user's coordinates space.
- xmax : X end axis coordinate in user's coordinates space.
- ymin : Y origin coordinate in user's coordinates space.
- ymax : Y end axis coordinate in user's coordinates space.
- wmin : Lowest value for the tick mark labels written on the axis.
- wmax : Highest value for the tick mark labels written on the axis.
- ndiv : Number of divisions.
   - ndiv=N1 + 100*N2 + 10000*N3
   - N1=number of 1st divisions.
   - N2=number of 2nd divisions.
   - N3=number of 3rd divisions. e.g.:
      - ndiv=0 --> no tick marks.
      - ndiv=2 --> 2 divisions, one tick mark in the middle of the axis.
- chopt : Drawing options (see below).
- gridlength: grid length on main tick marks.
 
The example below generates various kind of axis.
 
Begin_Macro(source)
../../../tutorials/visualisation/graphics/gaxis.C
End_Macro
 
\anchor GA01
## Definition with a function
 
Instead of the wmin,wmax arguments of the normal definition, the
name of a `TF1` function can be specified. This function will be used to
map the user coordinates to the axis values and ticks.
 
A `TGaxis` is defined the following way:
~~~ {.cpp}
    TGaxis::TGaxis(Double_t xmin, Double_t ymin, Double_t xmax, Double_t ymax,
                   const char *func, Int_t ndiv,   Option_t *chopt,
                   Double_t gridlength)
~~~
Where:
 
- xmin : X origin coordinate in user's coordinates space.
- xmax : X end axis coordinate in user's coordinates space.
- ymin : Y origin coordinate in user's coordinates space.
- ymax : Y end axis coordinate in user's coordinates space.
- func : function defining axis labels and tick marks.
- ndiv : Number of divisions.
   - ndiv=N1 + 100*N2 + 10000*N3
   - N1=number of 1st divisions.
   - N2=number of 2nd divisions.
   - N3=number of 3rd divisions. e.g.:
      - ndiv=0 --> no tick marks.
      - ndiv=2 --> 2 divisions, one tick mark in the middle of the axis.
- chopt : Drawing options (see below).
- gridlength: grid length on main tick marks.
 
It should be noted that `func` is not defined in the user's coordinate space,
but in the new TGaxis space. If `x` is the original axis, `w` the new axis,
and `w = f(x)` (for example, `f` is a calibration function converting ADC
channels `x` to energy `w`), then `func` must be supplied as `f^{-1}(w)`.
 
Examples:
 
Begin_Macro(source)
{
   TCanvas *c2 = new TCanvas("c2","c2",10,10,700,500);
 
   gPad->DrawFrame(0.,-2.,10.,2);
 
   TF1 *f1=new TF1("f1","-x",-10,10);
   TGaxis *A1 = new TGaxis(0,2,10,2,"f1",510,"-");
   A1->SetTitle("axis with decreasing values");
   A1->Draw();
 
   TF1 *f2=new TF1("f2","exp(x)",0,2);
   TGaxis *A2 = new TGaxis(1,1,9,1,"f2");
   A2->SetTitle("exponential axis");
   A2->SetLabelSize(0.03);
   A2->SetTitleSize(0.03);
   A2->SetTitleOffset(1.2);
   A2->Draw();
 
   TF1 *f3=new TF1("f3","log10(x)",1,1000);
   TGaxis *A3 = new TGaxis(2,-2,2,0,"f3",505,"");
   A3->SetTitle("logarithmic axis");
   A3->SetLabelSize(0.02);
   A3->SetTitleSize(0.03);
   A3->SetTitleOffset(0.); // Axis title automatically placed
   A3->Draw();
}
End_Macro
 
Note that this functionality has some limitations and does not follow all the TGaxis setting.
In particular the number of divisions or the maximum number digits do not apply.
 
\anchor GA02
## Logarithmic axis
 
By default axis are linear. To define a `TGaxis` as logarithmic, it is
enough to create it with the option `"G"`.
 
When plotting an histogram or a graph the logarithmic scale can be set using:
 
  - `gPad->SetLogx(1);` set the logarithmic scale on the X axis
  - `gPad->SetLogy(1);` set the logarithmic scale on the Y axis
 
When the `SetMoreLogLabels()` method is called more labels are drawn
when in logarithmic scale and there is a small number of decades  (less than 3).
 
\anchor GA03
## Blank axis
To draw only the axis tick marks without the axis body, it is enough to specify
the option `"B"`. It useful to superpose axis.
 
\anchor GA03a
## Arrow on axis
\since **ROOT version 6.27/01:**
 
To draw an arrow at the end of the axis use the option `">"`. To draw it at the beginning
of the axis use the option `"<"`. To draw it on both ends use `"<>"`.
 
Begin_Macro(source)
{
   auto c = new TCanvas("c","c",0,0,500,500);
   c->Range(-11,-11,11,11);
 
   auto f2 = new TF1("x2","x*x",-10,10);
   f2->SetLineColor(kRed);
   f2->Draw("same");
 
   auto f3 = new TF1("x3","x*x*x",-10,10);
   f3->SetLineColor(kBlue);
   f3->Draw("same");
 
   // Draw the axis with arrows
   auto ox = new TGaxis(-10,0,10,0,-10.,10.,510,"+-S>");
   ox->SetTickSize(0.009);
   ox->SetLabelFont(42);
   ox->SetLabelSize(0.025);
   ox->Draw();
   auto oy = new TGaxis(0,-10,0,10,-10,10,510,"+-S>");
   oy->SetTickSize(0.009);
   oy->SetLabelFont(42);
   oy->SetLabelSize(0.025);
   oy->Draw();
}
End_Macro
 
\anchor GA04
## Tick marks' orientation
 
By default tick marks are drawn on the positive side of the axis, except for
vertical axis for which the default is negative. The `chop` parameter
allows to control the tick marks orientation:
 
  - `chopt = "+"`:  tick marks are drawn on Positive side. (default)
  - `chopt ="-"`:   tick mark are drawn on the negative side.
  - `chopt = "+-"`: tick marks are drawn on both sides of the axis.
  - `chopt = "U"`:  Unlabelled axis, default is labeled.
 
\anchor GA05
## Tick marks' size
 
By default, tick marks have a length equal to 3 per cent of the axis length.
When the option "S" is specified, the length of the tick marks is equal to
`fTickSize*axis_length`, where `fTickSize` may be set via
`TGaxis::SetTickSize`.
 
When plotting an histogram `h` the tick marks size can be changed using:
 
  - `h->GetXaxis()->SetTickLength(0.02);` set the tick length for the X axis
  - `gStyle->SetTickLength(0.02,"x");` set the tick length for the X axis
     of all histograms drawn after this instruction.
 
A good way to remove tick marks on an axis is to set the tick length to 0:
`h->GetXaxis()->SetTickLength(0.);`
 
\anchor GA06
## Labels' positioning
 
Labels are normally drawn on side opposite to tick marks. However the option
`"="` allows to draw them on the same side. The distance between the labels and
the axis body can be changed with `SetLabelOffset`.
 
\anchor GA07
## Labels' orientation
 
By default axis labels are drawn parallel to the axis. However if the axis is vertical
then are drawn perpendicular to the axis.
 
\anchor GA08
## Labels' position on tick marks
 
By default axis labels are centered on tick marks. However, for vertical axis,
they are right adjusted. The `chop` parameter allows to control the labels'
position on tick marks:
 
  - `chopt = "R"`: labels are Right adjusted on tick mark.(default is centered)
  - `chopt = "L"`: labels are Left adjusted on tick mark.
  - `chopt = "C"`: labels are Centered on tick mark.
  - `chopt = "M"`: In the Middle of the divisions.
 
\anchor GA09
## Labels' format
 
Blank characters are stripped, and then the label is correctly aligned. the dot,
if last character of the string, is also stripped, unless the option `"."`
(a dot, or period) is specified. if `SetDecimals(kTRUE)` has been called
all labels have the same number of decimals after the `"."`
The same is true if `gStyle->SetStripDecimals(kFALSE)` has been called.
 
In the following, we have some parameters, like tick marks length and characters
height (in percentage of the length of the axis (user's coordinates))
The default values are as follows:
 
  - Primary tick marks: 3.0 %
  - Secondary tick marks: 1.5 %
  - Third order tick marks: .75 %
  - Characters height for labels: 4%
  - Labels offset: 1.0 %
 
By default, an exponent of the form 10^N is used when the label values are either
all very small or very large. One can disable the exponent by calling
`axis.SetNoExponent(kTRUE)`.
 
`TGaxis::SetExponentOffset(Float_t xoff, Float_t yoff, Option_t *axis)` is
static function to set X and Y offset of the axis 10^n notation. It is in % of
the pad size. It can be negative. `axis` specifies which axis
(`"x"` or/and `"y"`), default is `"x"` if `axis = "xz"`
set the two axes
 
\anchor GA10
## Alphanumeric labels
 
Axis labels can be any alphanumeric character strings. Such axis can be produced
only with histograms because the labels'definition is stored in `TAxis`.
The following example demonstrates how to create such labels.
 
Begin_Macro(source)
../../../tutorials/hist/hist036_TH2_labels.C
End_Macro
 
Because the alphanumeric labels are usually longer that the numeric labels, their
size is by default equal to `0.66666 * the_numeric_labels_size`.
 
\anchor GA10a
## Changing axis labels
\since **ROOT version 6.07/07:**
 
After an axis has been created, TGaxis::ChangeLabel allows to define new text
attributes for a given label. A fine tuning of the labels can be done. All the
attributes can be changed as well as the text label itself.
 
When plotting an histogram or a graph the labels can be changed like in the
following example which shows a way to produce \f$\pi\f$-axis :
 
Begin_Macro(source)
{
   Double_t pi = TMath::Pi();
   TF1*   f = new TF1("f","TMath::Cos(x/TMath::Pi())", -pi, pi);
   TAxis* a = f->GetXaxis();
   a->SetNdivisions(-502);
   a->ChangeLabel(1,-1,-1,-1,-1,-1,"-#pi");
   a->ChangeLabel(-1,-1,-1,-1,-1,-1,"#pi");
   f->Draw();
}
End_Macro
 
\anchor GA11
## Number of divisions optimisation
 
By default the number of divisions on axis is optimised to show a coherent
labelling of the main tick marks. The number of division (`ndiv`) is a
composite integer given by:
 
` ndiv = N1 + 100*N2 + 10000*N3`
 
  - `N1` = number of 1st divisions.
  - `N2` = number of 2nd divisions.
  - `N3` = number of 3rd divisions.
 
by default the value of `N1`, `N2` and `N3` are maximum
values. After optimisation the real number of divisions will be smaller or
equal to these value. If one wants to bypass the optimisation, the option `"N"`
should be given when the `TGaxis` is created. The option  `"I"`
also act on the number of division as it will force an integer labelling of
the axis.
 
On an histogram pointer `h` the number of divisions can be set in different ways:.
 
- Directly on the histogram. The following will set the number of division
  to 510 on the X axis of `h`. To avoid optimization the number of divisions
  should be negative (ie: -510);
~~~ {.cpp}
    h->SetNdivisions(510, "X");
~~~
- On the axis itself:
~~~ {.cpp}
    h->GetXaxis()->SetNdivisions(510, kTRUE);
~~~
 
The first parameter is the number of division. If it is negative of if the
second parameter is kFALSE then the number of divisions is not optimised.
And other signature is also allowed:
~~~ {.cpp}
    h->GetXaxis()->SetNdivisions(10, 5, 0, kTRUE);
~~~
\anchor GA12
## Maximum Number of Digits for the axis labels
 
The static method `TGaxis::SetMaxDigits` sets the maximum number of
digits permitted for the axis labels above which the notation with 10^N is used.
For example, to accept 6 digits number like 900000 on an axis call
`TGaxis::SetMaxDigits(6)`. The default value is 5.
`fgMaxDigits` must be greater than 0.
Warning: even when called on a particular TGaxis* instance, this static function
changes globally the number of digits for all axes (X, Y, ...) in the canvas.
If you want to change the maximum number of digits N only of the current TGaxis*,
and not all the others, use axis->SetNdivisions(N*1000000 + (axis->GetNdiv()%1000000))
instead of axis->SetMaxDigits(N).
 
\anchor GA13
## Optional grid
 
The option `"W"` allows to draw a grid on the primary tick marks. In case
of a log axis, the grid is only drawn for the primary tick marks if the number
of secondary and tertiary divisions is 0. `SetGridLength()` allows to define
the length of the grid.
 
When plotting an histogram or a graph the grid can be set ON or OFF using:
 
  - `gPad->SetGridy(1);` set the grid on the X axis
  - `gPad->SetGridx(1);` set the grid on the Y axis
  - `gPad->SetGrid(1,1);` set the grid on both axis.
 
\anchor GA14
## Time axis
 
Histograms' axis can be defined as "time axis". To do that it is enough to activate
the TAxis::SetTimeDisplay attribute on a given axis. If `h` is an histogram, it is
done the following way:
 
~~~ {.cpp}
    h->GetXaxis()->SetTimeDisplay(1);  // The X axis is a time axis
~~~
 
Two parameters can be adjusted in order to define time axis:
 
### The time format:
 
Defines the format of the labels along the time axis. It can be changed using the TAxis
TAxis::SetTimeFormat. The time format is the one used by the C function **strftime()**.
It's a string containing the following formatting characters:
 
  - for date :
    - **%a** abbreviated weekday name
    - **%b** abbreviated month name
    - **%d** day of the month (01-31)
    - **%m** month (01-12)
    - **%y** year without century
    - **%Y** year with century
  - for time :
    - **%H** hour (24-hour clock)
    - **%I** hour (12-hour clock)
    - **%p** local equivalent of AM or PM
    - **%M** minute (00-59)
    - **%S** seconds (00-61)
    - **%%** %
 
 The other characters are output as is. For example to have a format like
 `dd/mm/yyyy` one should do:
 
~~~ {.cpp}
    h->GetXaxis()->SetTimeFormat("%d\/%m\/%Y");
~~~
 
### The time offset:
 
This is a time in seconds in the UNIX standard UTC format (this is an universal
time, not the local time), defining the starting date of an histogram axis.
This date should be greater than 01/01/95 and is given in seconds. There are
three ways to define the time offset:
 
#### By setting the global default time offset:
 
~~~ {.cpp}
    TDatime da(2003,02,28,12,00,00);
    gStyle->SetTimeOffset(da.Convert());
~~~
 
  If no time offset is defined for a particular axis, the default time offset
  will be used. In the example above, notice the usage of TDateTime to translate
  an explicit date into the time in seconds required by TAxis::SetTimeFormat.
 
#### By setting a time offset to a particular axis:
 
~~~ {.cpp}
    TDatime dh(2001,09,23,15,00,00);
    h->GetXaxis()->SetTimeOffset(dh.Convert());
~~~
 
#### Together with the time format using TAxis::SetTimeFormat:
 
The time offset can be specified using the control character `%F` after
the normal time format. **%F** is followed by the date in the format:
`yyyy-mm-dd hh:mm:ss`.
 
Example:
 
~~~ {.cpp}
    h->GetXaxis()->SetTimeFormat("%d\/%m\/%y%F2000-02-28 13:00:01");
~~~
 
 
 
Notice that this date format is the same used by the TDateString function
`AsSQLString`. If needed, this function can be used to translate a time in
seconds into a character string which can be appended after `%F`. If the time
format is not specified (before `%F), the automatic one will be used.
 
If a time axis has no specified time offset, the global time offset will be
stored in the axis data structure.
 
The following example illustrates the various possibilities.
 
Begin_Macro(source)
{
   gStyle->SetTitleH(0.08);
 
   TDatime da(2003,2,28,12,00,00);
   gStyle->SetTimeOffset(da.Convert());
 
   auto ct = new TCanvas("ct","Time on axis",0,0,600,600);
   ct->Divide(1,3);
 
   auto ht1 = new TH1F("ht1","ht1",30000,0.,200000.);
   auto ht2 = new TH1F("ht2","ht2",30000,0.,200000.);
   auto ht3 = new TH1F("ht3","ht3",30000,0.,200000.);
   for (Int_t i=1;i<30000;i++) {
      auto noise = gRandom->Gaus(0,120);
      ht1->SetBinContent(i,noise);
      ht2->SetBinContent(i,noise*noise);
      ht3->SetBinContent(i,noise*noise*noise);
   }
 
   ct->cd(1);
   ht1->GetXaxis()->SetLabelSize(0.06);
   ht1->GetXaxis()->SetTimeDisplay(1);
   ht1->GetXaxis()->SetTimeFormat("%d/%m/%y%F2000-02-28 13:00:01");
   ht1->Draw();
 
   ct->cd(2);
   ht2->GetXaxis()->SetLabelSize(0.06);
   ht2->GetXaxis()->SetTimeDisplay(1);
   ht2->GetXaxis()->SetTimeFormat("%d/%m/%y");
   ht2->Draw();
 
   ct->cd(3);
   ht3->GetXaxis()->SetLabelSize(0.06);
   TDatime dh(2001,9,23,15,00,00);
   ht3->GetXaxis()->SetTimeDisplay(1);
   ht3->GetXaxis()->SetTimeOffset(dh.Convert());
   ht3->Draw();
}
End_Macro
 
The histogram limits times in seconds. If `wmin` and `wmax` are the histogram
limits, the time axis will spread around the time offset value from `TimeOffset+wmin`
to `TimeOffset+wmax`. Until now all the examples had a lowest value equal to 0.
The following example demonstrates how to define the histogram limits relatively
to the time offset value.
 
Begin_Macro(source)
{
   // Define the time offset as 2003, January 1st
   TDatime T0(2003,1,1,0,0,0);
   auto X0 = T0.Convert();
   gStyle->SetTimeOffset(X0);
 
   // Define the lowest histogram limit as 2002, September 23rd
   TDatime T1(2002,9,23,0,0,0);
   auto X1 = T1.Convert()-X0;
 
   // Define the highest histogram limit as 2003, March 7th
   TDatime T2(2003,3,7,0,0,0);
   auto X2 = T2.Convert(1)-X0;
 
   auto h1 = new TH1F("h1","test",100,X1,X2);
 
   TRandom r;
   for (Int_t i=0;i<30000;i++) {
      Double_t noise = r.Gaus(0.5*(X1+X2),0.1*(X2-X1));
      h1->Fill(noise);
   }
 
   h1->GetXaxis()->SetTimeDisplay(1);
   h1->GetXaxis()->SetLabelSize(0.03);
   h1->GetXaxis()->SetTimeFormat("%Y/%m/%d");
   h1->Draw();
}
End_Macro
 
 
Usually time axis are created automatically via histograms, but one may also want
to draw a time axis outside an "histogram context". Therefore it is useful to
understand how TGaxis works for such axis.
 
The time offset can be defined using one of the three methods described before.
The time axis will spread around the time offset value. Actually it will go from
`TimeOffset+wmin` to `TimeOffset+wmax` where `wmin` and `wmax` are the minimum
and maximum values (in seconds) of the axis. Let's take again an example. Having
defined "2003, February 28 at 12h" we would like to see the axis a day before and
a day after. A TGaxis can be created the following way (a day has 86400 seconds):
 
~~~ {.cpp}
    TGaxis *axis = new TGaxis(x1,y1,x2,y2,-100000,150000,2405,"t");
~~~
 
the `t` option (in lower case) means it is a "time axis". The axis goes form
100000 seconds before `TimeOffset` and 150000 seconds after.
 
So the complete macro is:
 
Begin_Macro(source)
{
   auto c1 = new TCanvas("c1","Examples of TGaxis",10,10,700,100);
   c1->Range(-10,-1,10,1);
 
   TGaxis *axis = new TGaxis(-8,0.,8,0.,-100000,150000,2405,"tS");
   axis->SetLabelSize(0.2);
   axis->SetTickSize(0.2);
 
   TDatime da(2003,02,28,12,00,00);
   axis->SetTimeOffset(da.Convert());
   axis->SetTimeFormat("%d-%m-%Y");
   axis->Draw();
   return c1;
}
End_Macro
 
 
Thanks to the TLatex directive `#splitline` it is possible to write the time
labels on two lines. In the previous example changing the `SetTimeFormat` line by
 
~~~ {.cpp}
    axis->SetLabelOffset(0.15);
    axis->SetTimeFormat("#splitline{%Y}{%d\/%m}");
~~~
 
will produce the following axis:
 
Begin_Macro
{
   auto c1 = new TCanvas("c1","Examples of TGaxis",10,10,700,100);
   c1->Range(-10,-1,10,1);
 
   TGaxis *axis = new TGaxis(-8,0.,8,0.,-100000,150000,2405,"tS");
   axis->SetLabelSize(0.2);
   axis->SetTickSize(0.2);
 
   TDatime da(2003,02,28,12,00,00);
   axis->SetTimeOffset(da.Convert());
   axis->SetLabelOffset(0.15);
   axis->SetTimeFormat("#splitline{%Y}{%d/%m}");
   axis->Draw();
   return c1;
}
End_Macro
 
 
The following example shows time axis on a TGraph:
 
Begin_Macro(source)
{
   TDatime da1(2008,02,28,15,52,00);
   TDatime da2(2008,02,28,15,53,00);
 
   double x[2],y[2];
 
   y[0] = 1.;
   y[1] = 2.;
   x[0] = da1.Convert();
   x[1] = da2.Convert();
 
   TGraph mgr(2,x,y);
   mgr.SetMarkerStyle(20);
 
   mgr.Draw("apl");
   mgr.GetXaxis()->SetTimeDisplay(1);
   mgr.GetXaxis()->SetNdivisions(-503);
   mgr.GetXaxis()->SetTimeFormat("%Y-%m-%d %H:%M");
   mgr.GetXaxis()->SetTimeOffset(0,"gmt");
}
End_Macro
 
The following example compares what the system time function `gmtime`
and `localtime` give with what gives `TGaxis`. It can be used
as referenced test to check if the time option of `TGaxis` is working properly.
 
Begin_Macro(source)
../../../tutorials/visualisation/graphics/timeonaxis3.C
End_Macro
 
 
The following macro illustrates the use, with histograms axis, of the time mode on the axis
with different time intervals and time formats.
 
Begin_Macro(source)
../../../tutorials/hist/hist061_TH1_timeonaxis.C
End_Macro
 
*/
 
////////////////////////////////////////////////////////////////////////////////
/// TGaxis default constructor.
 
TGaxis::TGaxis(): TLine(), TAttText(11,0,1,62,0.040)
{
 
   fGridLength  = 0.;
   fLabelOffset = 0.005;
   fLabelSize   = 0.040;
   fLabelFont   = 62;
   fLabelColor  = 1;
   fTickSize    = 0.030;
   fTitleOffset = 1;
   fTitleSize   = fLabelSize;
   fChopt       = "";
   fName        = "";
   fTitle       = "";
   fTimeFormat  = "";
   fFunctionName= "";
   fFunction    = nullptr;
   fAxis        = nullptr;
   fNdiv        = 0;
   fNModLabs    = 0;
   fModLabs     = nullptr;
   fWmin        = 0.;
   fWmax        = 0.;
}
 
////////////////////////////////////////////////////////////////////////////////
/// TGaxis normal constructor.
 
TGaxis::TGaxis(Double_t xmin, Double_t ymin, Double_t xmax, Double_t ymax,
               Double_t wmin, Double_t wmax, Int_t ndiv,   Option_t *chopt,
               Double_t gridlength)
       : TLine(xmin,ymin,xmax,ymax), TAttText(11,0,1,62,0.040)
{
 
   fWmin        = wmin;
   fWmax        = wmax;
   fNdiv        = ndiv;
   fNModLabs    = 0;
   fModLabs     = nullptr;
   fGridLength  = gridlength;
   fLabelOffset = 0.005;
   fLabelSize   = 0.040;
   fLabelFont   = 62;
   fLabelColor  = 1;
   fTickSize    = 0.030;
   fTitleOffset = 1;
   fTitleSize   = fLabelSize;
   fChopt       = chopt;
   fName        = "";
   fTitle       = "";
   fTimeFormat  = "";
   fFunctionName= "";
   fFunction    = nullptr;
   fAxis        = nullptr;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Constructor with a `TF1` to map axis values.
///
/// \note The function `func` (with name `funcname`) is not defined in the user's
/// coordinate space, but in the new TGaxis space. If `x` is the original axis,
/// `w` the new axis, and `w = f(x)` (for example, `f` is a calibration function
/// converting ADC channels `x` to energy `w`), then `func` must be supplied as
/// `f^{-1}(w)`.
 
TGaxis::TGaxis(Double_t xmin, Double_t ymin, Double_t xmax, Double_t ymax,
               const char *funcname, Int_t ndiv,   Option_t *chopt,
               Double_t gridlength)
       : TLine(xmin,ymin,xmax,ymax), TAttText(11,0,1,62,0.040)
{
 
   fFunction = (TF1*)gROOT->GetFunction(funcname);
   if (!fFunction) {
      Error("TGaxis", "calling constructor with an unknown function: %s", funcname);
      fWmin = 0;
      fWmax = 1;
   } else {
      fWmin = fFunction->GetXmin();
      fWmax = fFunction->GetXmax();
   }
   fFunctionName= funcname;
   fNdiv        = ndiv;
   fNModLabs    = 0;
   fModLabs     = nullptr;
   fGridLength  = gridlength;
   fLabelOffset = 0.005;
   fLabelSize   = 0.040;
   fLabelFont   = 62;
   fLabelColor  = 1;
   fTickSize    = 0.030;
   fTitleOffset = 1;
   fTitleSize   = fLabelSize;
   fChopt       = chopt;
   fName        = "";
   fTitle       = "";
   fTimeFormat  = "";
   fAxis        = nullptr;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Copy constructor.
 
TGaxis::TGaxis(const TGaxis& ax) :
  TLine(ax),
  TAttText(ax),
  fWmin(ax.fWmin),
  fWmax(ax.fWmax),
  fGridLength(ax.fGridLength),
  fTickSize(ax.fTickSize),
  fLabelOffset(ax.fLabelOffset),
  fLabelSize(ax.fLabelSize),
  fTitleOffset(ax.fTitleOffset),
  fTitleSize(ax.fTitleSize),
  fNdiv(ax.fNdiv),
  fLabelColor(ax.fLabelColor),
  fLabelFont(ax.fLabelFont),
  fNModLabs(ax.fNModLabs),
  fChopt(ax.fChopt),
  fName(ax.fName),
  fTitle(ax.fTitle),
  fTimeFormat(ax.fTimeFormat),
  fFunctionName(ax.fFunctionName),
  fFunction(ax.fFunction),
  fAxis(ax.fAxis)
{
   if (ax.IsOwnedModLabs())
      fModLabs = (TList *) ax.fModLabs->Clone();
   else
      fModLabs = ax.fModLabs;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Assignment operator.
 
TGaxis& TGaxis::operator=(const TGaxis& ax)
{
 
   if(this!=&ax) {
      TLine::operator=(ax);
      TAttText::operator=(ax);
      fWmin=ax.fWmin;
      fWmax=ax.fWmax;
      fGridLength=ax.fGridLength;
      fTickSize=ax.fTickSize;
      fLabelOffset=ax.fLabelOffset;
      fLabelSize=ax.fLabelSize;
      fTitleOffset=ax.fTitleOffset;
      fTitleSize=ax.fTitleSize;
      fNdiv=ax.fNdiv;
      fLabelColor=ax.fLabelColor;
      fLabelFont=ax.fLabelFont;
      fChopt=ax.fChopt;
      fName=ax.fName;
      fTitle=ax.fTitle;
      fTimeFormat=ax.fTimeFormat;
      fFunctionName=ax.fFunctionName;
      fFunction=ax.fFunction;
      fAxis=ax.fAxis;
      fNModLabs=ax.fNModLabs;
      fModLabs = ax.IsOwnedModLabs() ? (TList *) ax.fModLabs->Clone() : ax.fModLabs;
   }
   return *this;
}
 
////////////////////////////////////////////////////////////////////////////////
/// TGaxis default destructor.
 
TGaxis::~TGaxis()
{
   CleanupModLabs();
}
 
////////////////////////////////////////////////////////////////////////////////
/// Returns kTRUE when fModLabs owned by TGaxis and should be cleaned up
 
Bool_t TGaxis::IsOwnedModLabs() const
{
   if (!fModLabs) return kFALSE;
   if (fAxis && (fAxis->GetModifiedLabels() == fModLabs)) return kFALSE;
   // TList created by TGaxis configured with owner flag
   // If TGaxis object from old ROOT file will be read, memory will be leaked
   return fModLabs->IsOwner();
}
 
////////////////////////////////////////////////////////////////////////////////
/// Correctly cleanup fModLabs - delete content when owned by TGaxis
 
void TGaxis::CleanupModLabs()
{
   if (IsOwnedModLabs()) {
      fModLabs->Delete();
      delete fModLabs;
   }
   fModLabs = nullptr;
   fNModLabs = 0;
}
 
////////////////////////////////////////////////////////////////////////////////
/// If center = kTRUE axis labels are centered in the center of the bin.
/// The default is to center on the primary tick marks.
/// This option does not make sense if there are more bins than tick marks.
 
void TGaxis::CenterLabels(Bool_t center)
{
 
   if (center) SetBit(TAxis::kCenterLabels);
   else        ResetBit(TAxis::kCenterLabels);
}
 
////////////////////////////////////////////////////////////////////////////////
/// If center = kTRUE axis title will be centered. The default is right adjusted.
 
void TGaxis::CenterTitle(Bool_t center)
{
 
   if (center) SetBit(TAxis::kCenterTitle);
   else        ResetBit(TAxis::kCenterTitle);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Draw this axis with new attributes.
 
TGaxis *TGaxis::DrawAxis(Double_t xmin, Double_t ymin, Double_t xmax, Double_t ymax,
                         Double_t wmin, Double_t wmax, Int_t ndiv,   Option_t *chopt,
                         Double_t gridlength)
{
 
   TGaxis *newaxis = new TGaxis(xmin,ymin,xmax,ymax,wmin,wmax,ndiv,chopt,gridlength);
   newaxis->SetLineColor(fLineColor);
   newaxis->SetLineWidth(fLineWidth);
   newaxis->SetLineStyle(fLineStyle);
   newaxis->SetTextAlign(fTextAlign);
   newaxis->SetTextAngle(fTextAngle);
   newaxis->SetTextColor(fTextColor);
   newaxis->SetTextFont(fTextFont);
   newaxis->SetTextSize(fTextSize);
   newaxis->SetTitleSize(fTitleSize);
   newaxis->SetTitleOffset(fTitleOffset);
   newaxis->SetLabelFont(fLabelFont);
   newaxis->SetLabelColor(fLabelColor);
   newaxis->SetLabelSize(fLabelSize);
   newaxis->SetLabelOffset(fLabelOffset);
   newaxis->SetTickSize(fTickSize);
   newaxis->SetBit(kCanDelete);
   newaxis->SetTitle(GetTitle());
   newaxis->SetBit(TAxis::kCenterTitle,TestBit(TAxis::kCenterTitle));
   newaxis->AppendPad();
   return newaxis;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Static function returning `gStyle->GetAxisMaxDigits()`.
 
Int_t TGaxis::GetMaxDigits()
{
   return gStyle->GetAxisMaxDigits();
}
 
////////////////////////////////////////////////////////////////////////////////
/// Internal method to import TAxis attributes to this TGaxis.
 
void TGaxis::ImportAxisAttributes(TAxis *axis)
{
   // cleanup previously configured custom labels
   CleanupModLabs();
 
   fAxis = axis;
   SetLineColor(axis->GetAxisColor());
   SetTextColor(axis->GetTitleColor());
   SetTextFont(axis->GetTitleFont());
   SetLabelColor(axis->GetLabelColor());
   SetLabelFont(axis->GetLabelFont());
   SetLabelSize(axis->GetLabelSize());
   SetLabelOffset(axis->GetLabelOffset());
   SetTickSize(axis->GetTickLength());
   SetTitle(axis->GetTitle());
   SetTitleOffset(axis->GetTitleOffset());
   SetTitleSize(axis->GetTitleSize());
   SetBit(TAxis::kCenterTitle,   axis->TestBit(TAxis::kCenterTitle));
   SetBit(TAxis::kCenterLabels,  axis->TestBit(TAxis::kCenterLabels));
   SetBit(TAxis::kRotateTitle,   axis->TestBit(TAxis::kRotateTitle));
   SetBit(TAxis::kNoExponent,    axis->TestBit(TAxis::kNoExponent));
   SetBit(TAxis::kTickPlus,      axis->TestBit(TAxis::kTickPlus));
   SetBit(TAxis::kTickMinus,     axis->TestBit(TAxis::kTickMinus));
   SetBit(TAxis::kMoreLogLabels, axis->TestBit(TAxis::kMoreLogLabels));
   if (axis->GetDecimals())      SetBit(TAxis::kDecimals); //the bit is in TAxis::fAxis2
   SetTimeFormat(axis->GetTimeFormat());
}
 
////////////////////////////////////////////////////////////////////////////////
/// Draw this axis with its current attributes.
 
void TGaxis::Paint(Option_t *)
{
   if (!gPad) return;
 
   Double_t wmin = fWmin;
   Double_t wmax = fWmax;
   Int_t    ndiv = fNdiv;
 
   // following code required to support toggle of lin/log scales
   Double_t x1 = gPad->XtoPad(fX1);
   Double_t y1 = gPad->YtoPad(fY1);
   Double_t x2 = gPad->XtoPad(fX2);
   Double_t y2 = gPad->YtoPad(fY2);
 
   PaintAxis(x1,y1,x2,y2,wmin,wmax,ndiv,fChopt.Data(),fGridLength);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Control function to draw an axis.
/// Original authors: O.Couet C.E.Vandoni N.Cremel-Somon.
/// Modified and converted to C++ class by Rene Brun.
 
void TGaxis::PaintAxis(Double_t xmin, Double_t ymin, Double_t xmax, Double_t ymax,
                       Double_t &wmin, Double_t &wmax, Int_t &ndiv,   Option_t *chopt,
                       Double_t gridlength, Bool_t drawGridOnly)
{
   if (!gPad) return;
 
   const char *where = "PaintAxis";
 
   Double_t alfa, beta, ratio1, ratio2, grid_side;
   Double_t axis_lengthN = 0;
   Double_t axis_length0 = 0;
   Double_t axis_length1 = 0;
   Double_t axis_length;
   Double_t atick[3];
   Double_t tick_side;
   Double_t charheight;
   Double_t phil, phi, sinphi, cosphi;
   Double_t binLow = 0.,  binLow2 = 0.,  binLow3 = 0.;
   Double_t binHigh = 0., binHigh2 = 0., binHigh3 = 0.;
   Double_t binWidth = 0., binWidth2 = 0., binWidth3 = 0.;
   Double_t xpl1, xpl2, ypl1, ypl2;
   Double_t dxtick=0;
   Double_t wlabel, dwlabel, axis_value;
   Double_t xfactor, yfactor;
   Double_t xlabel, ylabel, dxlabel;
   Double_t xone, xtwo;
   Double_t rlab;
   Double_t x0, x1, y0, y1, xx0, xx1, yy0, yy1;
   xx0 = xx1 = yy0 = yy1 = 0;
   Double_t xxmin, xxmax, yymin, yymax;
   xxmin = xxmax = yymin = yymax = 0;
   Double_t xlside, xmside;
   Double_t ww, af, rne;
   Double_t xx, yy;
   Double_t xmnlog, x00, x11, h2, h2sav, axmul, y;
   Double_t rtxw, rtyw;
   Int_t nlabels, nticks, nticks0 = 0, nticks1 = 0;
   Int_t i, j, k, l, decade;
   Int_t mside, lside;
   Int_t nexe  = 0;
   Int_t lnlen = 0;
   Int_t iexe, if1, if2, na, nf, ih1, ih2, nbinin, nch, kmod;
   Int_t optionLog,optionBlank,optionVert,optionPlus,optionMinus,optionUnlab,optionPara;
   Int_t optionDown,optionRight,optionLeft,optionCent,optionEqual,optionDecimals=0,optionDot;
   Int_t optionY,optionText,optionGrid,optionSize,optionNoopt,optionInt,optionM,optionUp,optionX;
   Int_t optionTime, optionArrow;
   Int_t first=0,last=0,labelnumber;
   Int_t xalign, yalign;
   Int_t nn1, nn2, nn3, n1a, n2a, n3a, nb2, nb3;
   Int_t nbins=10, n1aold, nn1old;
   Int_t maxDigits;
   n1aold = nn1old = 0;
   Int_t ndyn;
   Int_t nhilab = 0;
   Int_t idn;
   Bool_t flexe = false;
   Bool_t flexpo,flexne;
   char *label;
   char *chtemp;
   char chlabel[256];
   char kchtemp[256];
   char chcoded[64];
   TLine linegrid;
   TString timeformat;
   TString typolabel;
   time_t timelabel;
   Double_t timed, wTimeIni;
   struct tm* utctis;
   Double_t rangeOffset = 0;
 
   Double_t epsilon   = 1e-5;
   const Double_t kPI = TMath::Pi();
 
   Double_t rwmi = wmin;
   Double_t rwma = wmax;
   chtemp = &kchtemp[0];
   label  = &chlabel[0];
 
   fFunction = (TF1*)gROOT->GetFunction(fFunctionName.Data());
 
   Bool_t noExponent = TestBit(TAxis::kNoExponent);
 
// If moreLogLabels = kTRUE more Log Intermediate Labels are drawn.
   Bool_t moreLogLabels = TestBit(TAxis::kMoreLogLabels);
 
// the following parameters correspond to the pad range in NDC
// and the user's coordinates in the pad
 
   Double_t padh   = gPad->GetWh()*gPad->GetAbsHNDC();
   Double_t padw   = gPad->GetWw()*gPad->GetAbsWNDC();
   Double_t rwxmin = gPad->GetX1();
   Double_t rwxmax = gPad->GetX2();
   Double_t rwymin = gPad->GetY1();
   Double_t rwymax = gPad->GetY2();
 
   if(strchr(chopt,'G')) optionLog  = 1;  else optionLog  = 0;
   if(strchr(chopt,'B')) optionBlank= 1;  else optionBlank= 0;
   if(strchr(chopt,'V')) optionVert = 1;  else optionVert = 0;
   if(strchr(chopt,'+')) optionPlus = 1;  else optionPlus = 0;
   if(strchr(chopt,'-')) optionMinus= 1;  else optionMinus= 0;
   if(strchr(chopt,'U')) optionUnlab= 1;  else optionUnlab= 0;
   if(strchr(chopt,'P')) optionPara = 1;  else optionPara = 0;
   if(strchr(chopt,'O')) optionDown = 1;  else optionDown = 0;
   if(strchr(chopt,'R')) optionRight= 1;  else optionRight= 0;
   if(strchr(chopt,'L')) optionLeft = 1;  else optionLeft = 0;
   if(strchr(chopt,'C')) optionCent = 1;  else optionCent = 0;
   if(strchr(chopt,'=')) optionEqual= 1;  else optionEqual= 0;
   if(strchr(chopt,'Y')) optionY    = 1;  else optionY    = 0;
   if(strchr(chopt,'T')) optionText = 1;  else optionText = 0;
   if(strchr(chopt,'W')) optionGrid = 1;  else optionGrid = 0;
   if(strchr(chopt,'S')) optionSize = 1;  else optionSize = 0;
   if(strchr(chopt,'N')) optionNoopt= 1;  else optionNoopt= 0;
   if(strchr(chopt,'I')) optionInt  = 1;  else optionInt  = 0;
   if(strchr(chopt,'M')) optionM    = 1;  else optionM    = 0;
   if(strchr(chopt,'0')) optionUp   = 1;  else optionUp   = 0;
   if(strchr(chopt,'X')) optionX    = 1;  else optionX    = 0;
   if(strchr(chopt,'t')) optionTime = 1;  else optionTime = 0;
   if(strchr(chopt,'.')) optionDot  = 1;  else optionDot  = 0;
   if (TestBit(TAxis::kTickPlus))     optionPlus  = 2;
   if (TestBit(TAxis::kTickMinus))    optionMinus = 2;
   if (TestBit(TAxis::kCenterLabels)) optionM     = 1;
   if (TestBit(TAxis::kDecimals))     optionDecimals = 1;
   if (!gStyle->GetStripDecimals())   optionDecimals = 1;
   optionArrow= 0;
   if(strchr(chopt,'>')) optionArrow = 1;
   if(strchr(chopt,'<')) optionArrow = optionArrow+2;
   if (fAxis) {
      if (fAxis->GetLabels()) {
         optionM     = 1;
         optionText  = 1;
         optionNoopt = 1;
         ndiv = fAxis->GetLast()-fAxis->GetFirst()+1;
      }
      TList *ml = fAxis->GetModifiedLabels();
      if (ml) {
         fModLabs = ml;
         fNModLabs = fModLabs->GetSize();
      } else {
         fModLabs  = nullptr;
         fNModLabs = 0;
      }
   }
   if (ndiv < 0) {
      Error(where, "Invalid number of divisions: %d",ndiv);
      return;
   }
 
// Set the grid length
 
   if (optionGrid) {
      if (gridlength == 0) gridlength = 0.8;
      linegrid.SetLineColor(gStyle->GetGridColor());
      if (linegrid.GetLineColor() == 0) linegrid.SetLineColor(GetLineColor());
      linegrid.SetLineStyle(gStyle->GetGridStyle());
      linegrid.SetLineWidth(gStyle->GetGridWidth());
   }
 
// No labels if the axis label offset is big.
// In that case the labels are not visible anyway.
 
   if (GetLabelOffset() > 1.1 ) optionUnlab = 1;
 
// Determine time format
 
   Int_t idF = fTimeFormat.Index("%F");
   if (idF>=0) {
      timeformat = fTimeFormat(0,idF);
   } else {
      timeformat = fTimeFormat;
   }
 
   //GMT option
   if (fTimeFormat.Index("GMT")>=0) optionTime =2;
 
   // Determine the time offset and correct for time offset not being integer.
   Double_t timeoffset =0;
   if (optionTime) {
      if (idF>=0) {
         Int_t lnF = fTimeFormat.Length();
         TString stringtimeoffset = fTimeFormat(idF+2,lnF);
         Int_t year, mm, dd, hh, mi, ss;
         if (sscanf(stringtimeoffset.Data(), "%d-%d-%d %d:%d:%d", &year, &mm, &dd, &hh, &mi, &ss) == 6) {
            //Get time offset in seconds since EPOCH:
            struct tm tp;
            tp.tm_year   = year-1900;
            tp.tm_mon    = mm-1;
            tp.tm_mday   = dd;
            tp.tm_hour   = hh;
            tp.tm_min    = mi;
            tp.tm_sec    = ss;
            tp.tm_isdst  = 0; //no DST for UTC (and forced to 0 in MktimeFromUTC function)
            timeoffset = TTimeStamp::MktimeFromUTC(&tp);
 
            // Add the time offset's decimal part if it is there
            Int_t ids   = stringtimeoffset.Index("s");
            if (ids >= 0) {
               Float_t dp;
               Int_t lns   = stringtimeoffset.Length();
               TString sdp = stringtimeoffset(ids+1,lns);
               sscanf(sdp.Data(),"%g",&dp);
               timeoffset += dp;
            }
         } else {
            Error(where, "Time offset has not the right format");
         }
      } else {
         timeoffset = gStyle->GetTimeOffset();
      }
      wmin += timeoffset - (int)(timeoffset);
      wmax += timeoffset - (int)(timeoffset);
 
      // correct for time offset at a good limit (min, hour, day, month, year)
      struct tm* tp0;
      time_t timetp = (time_t)((Long_t)(timeoffset));
      Double_t range = wmax - wmin;
      Long_t rangeBase = 60;
      if (range>60)       rangeBase = 60*20;       // minutes
      if (range>3600)     rangeBase = 3600*20;     // hours
      if (range>86400)    rangeBase = 86400*20;    // days
      if (range>2419200)  rangeBase = 31556736;    // months (average # days)
      rangeOffset = (Double_t) ((Long_t)(timeoffset)%rangeBase);
      if (range>31536000) {
         tp0 = gmtime(&timetp);
         tp0->tm_mon   = 0;
         tp0->tm_mday  = 1;
         tp0->tm_hour  = 0;
         tp0->tm_min   = 0;
         tp0->tm_sec   = 0;
         tp0->tm_isdst = 1; // daylight saving time is on.
         rangeBase = (timetp-mktime(tp0)); // years
         rangeOffset = (Double_t) (rangeBase);
      }
      wmax += rangeOffset;
      wmin += rangeOffset;
   }
 
// Determine number of divisions 1, 2 and 3 and the maximum digits for this axis
   n1a       = (ndiv%100);
   n2a       = (ndiv%10000 - n1a)/100;
   n3a       = (ndiv%1000000 - n2a -n1a)/10000;
   nn3       = TMath::Max(n3a,1);
   nn2       = TMath::Max(n2a,1)*nn3;
   nn1       = TMath::Max(n1a,1)*nn2+1;
   nticks    = nn1;
   maxDigits = (ndiv/1000000);
   if (maxDigits==0) maxDigits = gStyle->GetAxisMaxDigits();
 
// Axis bining optimisation is ignored if:
//   - the first and the last label are equal
//   - the number of divisions is 0
//   - less than 1 primary division is requested
//   - logarithmic scale is requested
 
   if (wmin == wmax || ndiv == 0 || n1a <= 1 || optionLog) {
      optionNoopt = 1;
      optionInt   = 0;
   }
 
// Axis bining optimisation
   if ( (wmax-wmin) < 1 && optionInt) {
      Error(where, "option I not available");
      optionInt = 0;
   }
   if (!optionNoopt || optionInt ) {
 
// Primary divisions optimisation
// When integer labelling is required, Optimize is invoked first
// and only if the result is not an integer labelling, AdjustBinSize is invoked.
 
      THLimitsFinder::Optimize(wmin,wmax,n1a,binLow,binHigh,nbins,binWidth,fChopt.Data());
      if (optionInt) {
         if (binLow != Double_t(int(binLow)) || binWidth != Double_t(int(binWidth))) {
            AdjustBinSize(wmin,wmax,n1a,binLow,binHigh,nbins,binWidth);
         }
      }
      if ((wmin-binLow)  > epsilon) { binLow  += binWidth; nbins--; }
      if ((binHigh-wmax) > epsilon) { binHigh -= binWidth; nbins--; }
      if (xmax == xmin) {
         rtyw  = (ymax-ymin)/(wmax-wmin);
         xxmin = xmin;
         xxmax = xmax;
         yymin = rtyw*(binLow-wmin)  + ymin;
         yymax = rtyw*(binHigh-wmin) + ymin;
      }
      else {
         rtxw  = (xmax-xmin)/(wmax-wmin);
         xxmin = rtxw*(binLow-wmin)  + xmin;
         xxmax = rtxw*(binHigh-wmin) + xmin;
         if (ymax == ymin) {
            yymin = ymin;
            yymax = ymax;
         }
         else {
            alfa  = (ymax-ymin)/(xmax-xmin);
            beta  = (ymin*xmax-ymax*xmin)/(xmax-xmin);
            yymin = alfa*xxmin + beta;
            yymax = alfa*xxmax + beta;
         }
      }
      if (fFunction) {
         yymin = ymin;
         yymax = ymax;
         xxmin = xmin;
         xxmax = xmax;
      } else {
         wmin = binLow;
         wmax = binHigh;
      }
 
// Secondary divisions optimisation
      nb2 = n2a;
      if (!optionNoopt && n2a > 1 && binWidth > 0) {
         THLimitsFinder::Optimize(wmin,wmin+binWidth,n2a,binLow2,binHigh2,nb2,binWidth2,fChopt.Data());
      }
 
// Tertiary divisions optimisation
      nb3 = n3a;
      if (!optionNoopt && n3a > 1 && binWidth2 > 0) {
         THLimitsFinder::Optimize(binLow2,binLow2+binWidth2,n3a,binLow3,binHigh3,nb3,binWidth3,fChopt.Data());
      }
      n1aold = n1a;
      nn1old = nn1;
      n1a    = nbins;
      nn3    = TMath::Max(nb3,1);
      nn2    = TMath::Max(nb2,1)*nn3;
      nn1    = TMath::Max(n1a,1)*nn2+1;
      nticks = nn1;
   }
 
// Coordinates are normalized
 
   ratio1 = 1/(rwxmax-rwxmin);
   ratio2 = 1/(rwymax-rwymin);
   x0     = ratio1*(xmin-rwxmin);
   x1     = ratio1*(xmax-rwxmin);
   y0     = ratio2*(ymin-rwymin);
   y1     = ratio2*(ymax-rwymin);
   if (!optionNoopt || optionInt ) {
      xx0 = ratio1*(xxmin-rwxmin);
      xx1 = ratio1*(xxmax-rwxmin);
      yy0 = ratio2*(yymin-rwymin);
      yy1 = ratio2*(yymax-rwymin);
   }
 
   if ((x0 == x1) && (y0 == y1)) {
      Error(where, "length of axis is 0");
      return;
   }
 
// Title offset. If 0 it is automatically computed
   Double_t toffset  = GetTitleOffset();
   Bool_t   autotoff = kFALSE;
   if (toffset==0 && x1 == x0) autotoff = kTRUE;
 
// Return wmin, wmax and the number of primary divisions
   if (optionX) {
      ndiv = n1a;
      return;
   }
 
   TLatex textaxis;
   SetLineStyle(1); // axis line style
   Int_t TitleColor = GetTextColor();
   Int_t TitleFont  = GetTextFont();
 
// Compute length of axis
   axis_length = TMath::Sqrt((x1-x0)*(x1-x0)+(y1-y0)*(y1-y0));
   if (axis_length == 0) {
      Error(where, "length of axis is 0");
      return;
   }
   if (!optionNoopt || optionInt) {
      axis_lengthN = TMath::Sqrt((xx1-xx0)*(xx1-xx0)+(yy1-yy0)*(yy1-yy0));
      axis_length0 = TMath::Sqrt((xx0-x0)*(xx0-x0)+(yy0-y0)*(yy0-y0));
      axis_length1 = TMath::Sqrt((x1-xx1)*(x1-xx1)+(y1-yy1)*(y1-yy1));
      if (axis_lengthN < epsilon) {
         optionNoopt = 1;
         optionInt   = 0;
         wmin        = rwmi;
         wmax        = rwma;
         n1a         = n1aold;
         nn1         = nn1old;
         nticks      = nn1;
         if (optionTime) {
            wmin        += timeoffset - (int)(timeoffset) + rangeOffset;
            wmax        += timeoffset - (int)(timeoffset) + rangeOffset;
         }
      }
   }
 
   if (x0 == x1) {
      if (y1>=y0) phi  = 0.5*kPI;
      else        phi  = 1.5*kPI;
      phil = phi;
   } else {
      phi = TMath::ATan2((y1-y0),(x1-x0));
      Int_t px0 = gPad->UtoPixel(x0);
      Int_t py0 = gPad->VtoPixel(y0);
      Int_t px1 = gPad->UtoPixel(x1);
      Int_t py1 = gPad->VtoPixel(y1);
      if (x0 < x1) phil = TMath::ATan2(Double_t(py0-py1), Double_t(px1-px0));
      else         phil = TMath::ATan2(Double_t(py1-py0), Double_t(px0-px1));
   }
   cosphi  = TMath::Cos(phi);
   sinphi  = TMath::Sin(phi);
   if (TMath::Abs(cosphi) <= epsilon)
      cosphi  = 0;
   if (TMath::Abs(sinphi) <= epsilon)
      sinphi  = 0;
 
// mside positive, tick marks on positive side
// mside negative, tick marks on negative side
// mside zero, tick marks on both sides
// Default is positive except for vertical axis
 
   mside=1;
   if (x0 == x1 && y1 > y0)       mside = -1;
   if (optionPlus)                mside = 1;
   if (optionMinus)               mside = -1;
   if (optionPlus && optionMinus) mside = 0;
   xmside = mside;
   lside = -mside;
   if (optionEqual) lside = mside;
   if (optionPlus && optionMinus) {
      lside = -1;
      if (optionEqual) lside=1;
   }
   xlside = lside;
 
// Tick marks size
   if(xmside >= 0) tick_side = 1;
   else            tick_side = -1;
   if (optionSize) atick[0] = tick_side*axis_length*fTickSize;
   else            atick[0] = tick_side*axis_length*0.03;
 
   atick[1] = 0.5*atick[0];
   atick[2] = 0.5*atick[1];
 
// Set the side of the grid
   if ((x0 == x1) && (y1 > y0))  grid_side =-1;
   else                          grid_side = 1;
 
// Compute Values if Function is given
   if(fFunction) {
      rwmi = fFunction->Eval(wmin);
      rwma = fFunction->Eval(wmax);
      if(rwmi > rwma) {
         Double_t t = rwma;
         rwma = rwmi;
         rwmi = t;
      }
   }
 
// Draw the axis if needed...
   if (!optionBlank) {
      xpl1 = x0;
      xpl2 = x1;
      ypl1 = y0;
      ypl2 = y1;
      if (optionArrow) {
         TArrow a;
         a.SetLineColor(GetLineColor());
         a.SetFillColor(GetLineColor());
         a.SetLineWidth(GetLineWidth());
         a.SetAngle(30);
         Double_t as = 0.04*axis_length;
         if (optionArrow==1) a.PaintArrowNDC(xpl1, ypl1, xpl2, ypl2, as,"|>");
         if (optionArrow==2) a.PaintArrowNDC(xpl1, ypl1, xpl2, ypl2, as,"<|");
         if (optionArrow==3) a.PaintArrowNDC(xpl1, ypl1, xpl2, ypl2, as,"<|>");
      } else {
         PaintLineNDC(xpl1, ypl1, xpl2, ypl2);
      }
   }
 
// No bining
 
   if (ndiv == 0) return;
   if (wmin == wmax) {
      Error(where, "wmin (%f) == wmax (%f)", wmin, wmax);
      return;
   }
 
// Labels preparation:
// Get character height
// Compute the labels orientation in case of overlaps
// (with alphanumeric labels for horizontal axis).
 
   charheight = GetLabelSize();
   if (optionText && GetLabelFont()%10 != 3) charheight *= 0.66666;
   textaxis.SetTextFont(GetLabelFont());
   if ((GetLabelFont()%10 < 2) && optionLog) // force TLatex mode in PaintLatex
      textaxis.SetTextFont((Int_t)(GetLabelFont()/10)*10+2);
   textaxis.SetTextColor(GetLabelColor());
   textaxis.SetTextSize (charheight);
   textaxis.SetTextAngle(GetTextAngle());
   if (GetLabelFont()%10 > 2) {
      charheight /= padh;
   }
   if (!optionUp && !optionDown && !optionY && !optionUnlab) {
      if (!drawGridOnly && optionText && ((ymin == ymax) || (xmin == xmax))) {
         textaxis.SetTextAlign(32);
         optionText = 2;
         Int_t nl = fAxis->GetLast()-fAxis->GetFirst()+1;
         Double_t angle     = 0;
         for (i=fAxis->GetFirst(); i<=fAxis->GetLast(); i++) {
            textaxis.SetText(0,0,fAxis->GetBinLabel(i));
            if (textaxis.GetXsize() < (xmax-xmin)/nl) continue;
            angle = -20;
            break;
         }
         for (i=fAxis->GetFirst(); i<=fAxis->GetLast(); i++) {
            if ((!strcmp(fAxis->GetName(),"xaxis") && !gPad->TestBit(kHori))
              ||(!strcmp(fAxis->GetName(),"yaxis") &&  gPad->TestBit(kHori))) {
               if (nl > 50) angle = 90;
               if (fAxis->TestBit(TAxis::kLabelsHori)) angle = 0;
               if (fAxis->TestBit(TAxis::kLabelsVert)) angle = 90;
               if (fAxis->TestBit(TAxis::kLabelsUp))   angle = 20;
               if (fAxis->TestBit(TAxis::kLabelsDown)) angle =-20;
               if (angle ==   0) textaxis.SetTextAlign(23);
               if (angle == -20) textaxis.SetTextAlign(12);
               textaxis.SetTextAngle(angle);
               Double_t s = -3;
               if (ymin == gPad->GetUymax()) {
                  if (angle == 0) textaxis.SetTextAlign(21);
                  s = 3;
               }
               strlcpy(chtemp, fAxis->GetBinLabel(i), 255);
               if (fNModLabs) ChangeLabelAttributes(i, fAxis->GetLabels()->GetSize()-1, &textaxis, chtemp, i, 0.1);
               textaxis.PaintLatex(fAxis->GetBinCenter(i),
                                   ymin + s*fAxis->GetLabelOffset()*(gPad->GetUymax()-gPad->GetUymin()),
                                   textaxis.GetTextAngle(),
                                   textaxis.GetTextSize(),
                                   chtemp);
               if (fNModLabs) ResetLabelAttributes(&textaxis);
            } else if ((!strcmp(fAxis->GetName(),"yaxis") && !gPad->TestBit(kHori))
                    || (!strcmp(fAxis->GetName(),"xaxis") &&  gPad->TestBit(kHori))) {
               Double_t s = -3;
               if (xmin == gPad->GetUxmax()) {
                  textaxis.SetTextAlign(12);
                  s = 3;
               }
               if (autotoff) {
                  UInt_t w,h;
                  textaxis.SetText(0.,0., fAxis->GetBinLabel(i));
                  textaxis.GetBoundingBox(w,h);
                  double scale=gPad->GetWw()*gPad->GetWNDC();
                  if (scale>0.0) toffset = TMath::Max(toffset,(double)w/scale);
               }
               strlcpy(chtemp, fAxis->GetBinLabel(i), 255);
               if (fNModLabs) ChangeLabelAttributes(i, fAxis->GetLabels()->GetSize()-1, &textaxis, chtemp, i, 0.1);
               textaxis.PaintLatex(xmin + s*fAxis->GetLabelOffset()*(gPad->GetUxmax()-gPad->GetUxmin()),
                                   fAxis->GetBinCenter(i),
                                   0,
                                   textaxis.GetTextSize(),
                                   chtemp);
               if (fNModLabs) ResetLabelAttributes(&textaxis);
            } else {
               strlcpy(chtemp, fAxis->GetBinLabel(i), 255);
               if (fNModLabs) ChangeLabelAttributes(i, fAxis->GetLabels()->GetSize()-1, &textaxis, chtemp, i, 0.1);
               textaxis.PaintLatex(xmin - 3*fAxis->GetLabelOffset()*(gPad->GetUxmax()-gPad->GetUxmin()),
                                   ymin +(i-0.5)*(ymax-ymin)/nl,
                                   0,
                                   textaxis.GetTextSize(),
                                   chtemp);
               if (fNModLabs) ResetLabelAttributes(&textaxis);
            }
         }
      }
   }
 
// Now determine text alignment
   xalign = 2;
   yalign = 1;
   if (x0 == x1)    xalign = 3;
   if (y0 != y1)    yalign = 2;
   if (optionCent)  xalign = 2;
   if (optionRight) xalign = 3;
   if (optionLeft)  xalign = 1;
   if (TMath::Abs(cosphi) > 0.9) {
      xalign = 2;
   } else {
      if (cosphi*sinphi > 0)  xalign = 1;
      if (cosphi*sinphi < 0)  xalign = 3;
   }
   textaxis.SetTextAlign(10*xalign+yalign);
 
// Position of labels in Y
   if (x0 == x1) {
      if (optionPlus && !optionMinus) {
         if (optionEqual) ylabel =  fLabelOffset/2 + atick[0];
         else             ylabel = -fLabelOffset;
      } else {
         ylabel = fLabelOffset;
         if (lside < 0)  ylabel += atick[0];
      }
   } else if (y0 == y1) {
      if (optionMinus && !optionPlus) {
         if ((GetLabelFont() % 10) == 3 ) {
            ylabel = fLabelOffset+0.5*
            ((gPad->AbsPixeltoY(0)-gPad->AbsPixeltoY((Int_t)fLabelSize))/
            (gPad->GetY2() - gPad->GetY1()));
         } else {
            ylabel = fLabelOffset+0.5*fLabelSize;
         }
         ylabel += TMath::Abs(atick[0]);
      } else {
         ylabel = -fLabelOffset;
         if (mside <= 0) ylabel -= TMath::Abs(atick[0]);
      }
      if (optionLog)  ylabel -= 0.5*charheight;
   } else {
      if (mside+lside >= 0) ylabel =  fLabelOffset;
      else                  ylabel = -fLabelOffset;
   }
   if (optionText) ylabel /= 2;
 
// Draw the linear tick marks if needed...
   if (!optionLog && ndiv) {
      if (fFunction) {
         dxtick = (binHigh-binLow)/Double_t(nticks-1);
         axis_length0 = binLow-wmin;
         axis_length1 = wmax-binHigh;
      } else {
         if (optionNoopt && !optionInt) dxtick = axis_length/Double_t(nticks-1);
         else                           dxtick = axis_lengthN/Double_t(nticks-1);
      }
      if (!optionNoopt || optionInt) {
         if (axis_length0)
            nticks0 = TMath::Min(Int_t(axis_length0/dxtick + epsilon), 1000);
         if (axis_length1)
            nticks1 = TMath::Min(Int_t(axis_length1/dxtick + epsilon), 1000);
      }
 
      std::vector<Double_t> ticksx, ticksy, gridx, gridy;
      if (!drawGridOnly) {
         ticksx.reserve(nticks + nticks0 + nticks1);
         ticksy.reserve(nticks + nticks0 + nticks1);
      }
      if (optionGrid) {
         gridx.reserve((nticks + nticks0 + nticks1) / nn2 + 2);
         gridy.reserve((nticks + nticks0 + nticks1) / nn2 + 2);
      }
 
      auto draw_tick = [&](int indx, double xtick, double xf) {
         int ltick;
         if (indx % nn2 == 0)
            ltick = 0;
         else if (indx % nn3 == 0)
            ltick = 1;
         else
            ltick = 2;
 
         if (fFunction) {
            Double_t zz = fFunction->Eval(xf)-rwmi;
            xtick = zz * axis_length / TMath::Abs(rwma-rwmi);
         }
 
         Double_t ytick = mside ? 0. : -atick[ltick];
         if (optionNoopt && !optionInt) {
            Rotate(xtick,ytick,cosphi,sinphi,x0,y0, xpl2,ypl2);
            Rotate(xtick,atick[ltick],cosphi,sinphi,x0,y0, xpl1,ypl1);
         } else {
            Rotate(xtick,ytick,cosphi,sinphi,xx0,yy0, xpl2,ypl2);
            Rotate(xtick,atick[ltick],cosphi,sinphi,xx0,yy0, xpl1,ypl1);
         }
         if (optionVert) {
            if ((x0 != x1) && (y0 != y1)) {
               if (mside) {
                  xpl1 = xpl2;
                  if (cosphi > 0) ypl1 = ypl2 + atick[ltick];
                  else            ypl1 = ypl2 - atick[ltick];
               } else {
                  xpl1 = 0.5*(xpl1 + xpl2);
                  xpl2 = xpl1;
                  ypl1 = 0.5*(ypl1 + ypl2) + atick[ltick];
                  ypl2 = 0.5*(ypl1 + ypl2) - atick[ltick];
               }
            }
         }
         if (!drawGridOnly) {
            Bool_t paint_tick = kTRUE;
            if (optionArrow == 1)
               paint_tick = (x1 != x0) ? (xpl2 < x1) : (ypl2 < y1);
            else if (optionArrow == 2)
               paint_tick = (x1 != x0) ? (xpl1 > x0) : (ypl1 > y0);
            else if (optionArrow == 3)
               paint_tick = (x1 != x0) ? (xpl1 > x0 && xpl2 < x1) : (ypl1 > y0 && ypl2 < y1);
            if (paint_tick) {
               ticksx.push_back(xpl1);
               ticksx.push_back(xpl2);
               ticksy.push_back(ypl1);
               ticksy.push_back(ypl2);
            }
         }
 
         if (optionGrid && (ltick == 0)) {
            if (optionNoopt && !optionInt) {
               Rotate(xtick,0,cosphi,sinphi,x0,y0, xpl2,ypl2);
               Rotate(xtick,grid_side*gridlength,cosphi,sinphi,x0,y0, xpl1,ypl1);
            } else {
               Rotate(xtick,0,cosphi,sinphi,xx0,yy0, xpl2,ypl2);
               Rotate(xtick,grid_side*gridlength,cosphi,sinphi,xx0,yy0, xpl1,ypl1);
            }
            gridx.push_back(xpl1);
            gridx.push_back(xpl2);
            gridy.push_back(ypl1);
            gridy.push_back(ypl2);
         }
      };
 
      for (k = 0; k < nticks; k++)
         draw_tick(k, Double_t(k) * dxtick, binLow + Double_t(k)*dxtick);
 
      for (k = 1; k <= nticks0; k++)
         draw_tick(k, -1. * Double_t(k) * dxtick, binLow - Double_t(k)*dxtick);
 
      for (k = 1; k <= nticks1; k++)
         draw_tick(k, Double_t(nticks-1 + k) * dxtick, binHigh + Double_t(k)*dxtick);
 
      // paint ticks all together with one command
      if (ticksx.size() > 0) {
         TAttLine::Modify();
         gPad->PaintSegmentsNDC(ticksx.size() / 2, ticksx.data(), ticksy.data());
      }
 
      // paint grid lines all together after ticks
      if (gridx.size() > 0) {
         linegrid.TAttLine::Modify();
         gPad->PaintSegmentsNDC(gridx.size() / 2, gridx.data(), gridy.data());
      }
   }
 
// Draw the numeric labels if needed...
   if (!drawGridOnly && !optionUnlab) {
      if (!optionLog) {
         if (n1a) {
// Spacing of labels
            if ((wmin == wmax) || (ndiv == 0)) {
               Error(where, "wmin (%f) == wmax (%f), or ndiv == 0", wmin, wmax);
               return;
            }
            wlabel  = wmin;
            dwlabel = (wmax-wmin)/Double_t(n1a);
            if (optionNoopt && !optionInt) dxlabel = axis_length/Double_t(n1a);
            else                           dxlabel = axis_lengthN/Double_t(n1a);
 
            if (!optionText && !optionTime) {
 
// We have to decide what format to generate
// (for numeric labels only)
// Test the magnitude, decide format
               flexe  = kFALSE;
               nexe   = 0;
               flexpo = kFALSE;
               flexne = kFALSE;
               ww     = TMath::Max(TMath::Abs(wmin),TMath::Abs(wmax));
 
// First case : (wmax-wmin)/n1a less than 0.001
// (0.001 fgMaxDigits of 5 (fgMaxDigits) characters). Then we use x 10 n
// format. If af >=0 x10 n cannot be used
               Double_t xmicros = 0.00099;
               if (maxDigits) xmicros = TMath::Power(10,-maxDigits);
               if (!noExponent && (TMath::Abs(wmax-wmin)/Double_t(n1a)) < xmicros) {
                  af    = TMath::Log10(ww) + epsilon;
                  if (af < 0) {
                     flexe   = kTRUE;
                     nexe    = int(af);
                     iexe    = TMath::Abs(nexe);
                     if (iexe%3 == 1)     iexe += 2;
                     else if(iexe%3 == 2) iexe += 1;
                     if (nexe < 0) nexe = -iexe;
                     else          nexe =  iexe;
                     wlabel  = wlabel*TMath::Power(10,iexe);
                     dwlabel = dwlabel*TMath::Power(10,iexe);
                     if1     = maxDigits;
                     if2     = maxDigits-2;
                     goto L110;
                  }
               }
               if (ww >= 1) af = TMath::Log10(ww);
               else         af = TMath::Log10(ww*0.0001);
               af += epsilon;
               nf  = Int_t(af)+1;
               if (!noExponent && nf > maxDigits)  flexpo = kTRUE;
               if (!noExponent && nf < -maxDigits) flexne = kTRUE;
 
// Use x 10 n format. (only powers of 3 allowed)
 
               if (flexpo) {
                  flexe = kTRUE;
                  while (true) {
                     nexe++;
                     ww      /= 10;
                     wlabel  /= 10;
                     dwlabel /= 10;
                     if (nexe%3 == 0 && ww <= TMath::Power(10,maxDigits-1)) break;
                  }
               }
 
               if (flexne) {
                  flexe = kTRUE;
                  rne   = 1/TMath::Power(10,maxDigits-2);
                  while (true) {
                     nexe--;
                     ww      *= 10;
                     wlabel  *= 10;
                     dwlabel *= 10;
                     if (nexe%3 == 0 && ww >= rne) break;
                  }
               }
 
               na = 0;
               for (i=maxDigits-1; i>0; i--) {
                  if (TMath::Abs(ww) < TMath::Power(10,i)) na = maxDigits-i;
               }
               ndyn = n1a;
               while (ndyn) {
                  Double_t wdyn = TMath::Abs((wmax-wmin)/ndyn);
                  if (wdyn <= 0.999 && na < maxDigits-2) {
                     na++;
                     ndyn /= 10;
                  }
                  else break;
               }
// if1 and if2 are the two digits defining the format used to produce the
// labels. The format used will be %[if1].[if2]f .
// if1 and if2 are positive (small) integers.
               if2 = na;
               if1 = TMath::Max(nf+na,maxDigits)+1;
L110:
               if (TMath::Min(wmin,wmax) < 0)if1 = if1+1;
               if1 = TMath::Min(if1,32);
 
// In some cases, if1 and if2 are too small....
               while (dwlabel < TMath::Power(10,-if2)) {
                  if1++;
                  if2++;
               }
               if (if1 > 14) if1 = 14;
               if (if2 > 14) if2 = 14;
               if (if1 <  0) if1 = 0;
               int len = 0;
               if (if2 > 0) {
                  len = snprintf(chcoded,sizeof(chcoded),"%%%d.%df",if1,if2);
               } else {
                  len = snprintf(chcoded,sizeof(chcoded),"%%%d.%df",if1+1,1);
               }
               // check improbable error condition, suppress gcc9 warnings
               if ((len < 0) || (len >= (int) sizeof(chcoded)))
                  strcpy(chcoded,"%7.3f");
            }
 
// We draw labels
 
            snprintf(chtemp,256,"%g",dwlabel);
            Int_t ndecimals = 0;
            if (optionDecimals) {
               char *dot = strchr(chtemp,'.');
               if (dot) {
                  ndecimals = chtemp + strlen(chtemp) -dot;
               } else {
                  char *exp;
                  exp = strstr(chtemp,"e-");
                  if (exp) {
                     sscanf(&exp[2],"%d",&ndecimals);
                     ndecimals++;
                  }
               }
            }
            if (optionM) nlabels = n1a-1;
            else         nlabels = n1a;
            wTimeIni = wlabel;
            for ( k=0; k<=nlabels; k++) {
               if (fFunction) {
                  Double_t xf = binLow+Double_t(k*nn2)*dxtick;
                  Double_t zz = fFunction->Eval(xf)-rwmi;
                  wlabel = xf;
                  xlabel = zz* axis_length / TMath::Abs(rwma-rwmi);
               } else {
                  xlabel = dxlabel*k;
               }
               if (optionM)    xlabel += 0.5*dxlabel;
 
               axis_value = wlabel;
 
               if (!optionText && !optionTime) {
                  snprintf(label,256,chcoded,wlabel);
 
                  label[28] = 0;
                  wlabel += dwlabel;
 
                  LabelsLimits(label,first,last);  //Eliminate blanks
 
                  if (label[first] == '.') { //check if '.' is preceded by a digit
                     strncpy(chtemp, "0", 256);
                     strlcat(chtemp, &label[first],256);
                     strlcpy(label, chtemp, 256);
                     first = 1; last = strlen(label);
                  }
                  if (label[first] == '-' && label[first+1] == '.') {
                     strncpy(chtemp, "-0",256);
                     strlcat(chtemp, &label[first+1],256);
                     strlcpy(label, chtemp, 256);
                     first = 1; last = strlen(label);
                  }
 
// We eliminate the non significant 0 after '.'
                  if (ndecimals) {
                     char *adot = strchr(label,'.');
                     if (adot) adot[ndecimals] = 0;
                  } else {
                     while (label[last] == '0') { label[last] = 0; last--;}
                  }
 
// We eliminate the dot, unless dot is forced.
                  if (label[last] == '.') {
                     if (!optionDot) { label[last] = 0; last--;}
                  }
 
// Make sure the label is not "-0"
                  if (last-first == 1 && label[first] == '-'
                                      && label[last]  == '0') {
                     strncpy(label, "0", 256);
                     label[last] = 0;
                  }
               }
 
// Generate the time labels
 
               if (optionTime) {
                  timed = wlabel + (int)(timeoffset) - rangeOffset;
                  timelabel = (time_t)((Long_t)(timed));
                  if (optionTime == 1) {
                     utctis = localtime(&timelabel);
                  } else {
                     utctis = gmtime(&timelabel);
                  }
                  TString timeformattmp;
                  if (timeformat.Length() < 220) timeformattmp = timeformat;
                  else timeformattmp = "#splitline{Format}{too long}";
 
// Appends fractional part if seconds displayed
                  if (dwlabel<0.9) {
                     double tmpdb;
                     int tmplast;
                     snprintf(label, 256, "%%S%7.5f", modf(timed,&tmpdb));
                     tmplast = strlen(label)-1;
 
// We eliminate the non significant 0 after '.'
                     while (label[tmplast] == '0') {
                        label[tmplast] = 0; tmplast--;
                     }
 
                     timeformattmp.ReplaceAll("%S",label);
// replace the "0." at the beginning by "s"
                     timeformattmp.ReplaceAll("%S0.","%Ss");
 
                  }
 
                  if (utctis != nullptr) {
                     strftime(label, 256, timeformattmp.Data(), utctis);
                  } else {
                     strncpy(label, "invalid", 256);
                  }
                  strlcpy(chtemp, &label[0], 256);
                  first = 0; last=strlen(label)-1;
                  wlabel = wTimeIni + (k+1)*dwlabel;
               }
 
// We generate labels (numeric or alphanumeric).
 
               if (optionNoopt && !optionInt)
                        Rotate (xlabel,ylabel,cosphi,sinphi,x0,y0,xx,yy);
               else     Rotate (xlabel,ylabel,cosphi,sinphi,xx0,yy0,xx,yy);
               if (y0 == y1 && !optionDown && !optionUp) {
                  yy -= 0.80*charheight;
               }
               if (optionVert) {
                  if (x0 != x1 && y0 != y1) {
                     if (optionNoopt && !optionInt)
                           Rotate (xlabel,0,cosphi,sinphi,x0,y0,xx,yy);
                     else  Rotate (xlabel,0,cosphi,sinphi,xx0,yy0,xx,yy);
                     if (cosphi > 0 ) yy += ylabel;
                     if (cosphi < 0 ) yy -= ylabel;
                  }
               }
               if (!optionY || (x0 == x1)) {
                  if (!optionText) {
                     if (first > last)  strncpy(chtemp, " ", 256);
                     else               strlcpy(chtemp, &label[first], 255);
                     if (fNModLabs) ChangeLabelAttributes(k+1, nlabels, &textaxis, chtemp, axis_value, dwlabel*0.01);
                     typolabel = chtemp;
                     if (!optionTime) typolabel.ReplaceAll("-", "#minus");
                     if (autotoff) {
                        UInt_t w,h;
                        textaxis.SetText(0.,0., typolabel.Data());
                        textaxis.GetBoundingBox(w,h);
                        double scale=gPad->GetWw()*gPad->GetWNDC();
                        if (scale>0.0) toffset = TMath::Max(toffset,(double)w/scale);
                     }
                     textaxis.PaintLatex(gPad->GetX1() + xx*(gPad->GetX2() - gPad->GetX1()),
                           gPad->GetY1() + yy*(gPad->GetY2() - gPad->GetY1()),
                           textaxis.GetTextAngle(),
                           textaxis.GetTextSize(),
                           typolabel.Data());
                     if (fNModLabs) ResetLabelAttributes(&textaxis);
                  } else  {
                     strlcpy(chtemp, fAxis->GetBinLabel(k+fAxis->GetFirst()), 255);
                     if (fNModLabs) ChangeLabelAttributes(k+fAxis->GetFirst(), fAxis->GetLabels()->GetSize()-1, &textaxis, chtemp, k+fAxis->GetFirst(), 0.1);
                     if (optionText == 1) textaxis.PaintLatex(gPad->GetX1() + xx*(gPad->GetX2() - gPad->GetX1()),
                                                   gPad->GetY1() + yy*(gPad->GetY2() - gPad->GetY1()),
                                                   0,
                                                   textaxis.GetTextSize(),
                                                   chtemp);
                     if (fNModLabs) ResetLabelAttributes(&textaxis);
                  }
               } else {
 
// Text alignment is down
                  if (!optionText)     lnlen = last-first+1;
                  else {
                     if (k+1 > nhilab) lnlen = 0;
                  }
                  for ( l=1; l<=lnlen; l++) {
                     if (!optionText) *chtemp = label[first+l-2];
                     else {
                        if (lnlen == 0) strncpy(chtemp, " ", 256);
                        else            strncpy(chtemp, "1", 256);
                     }
                     typolabel = chtemp;
                     typolabel.ReplaceAll("-", "#minus");
                     textaxis.PaintLatex(gPad->GetX1() + xx*(gPad->GetX2() - gPad->GetX1()),
                           gPad->GetY1() + yy*(gPad->GetY2() - gPad->GetY1()),
                           0,
                           textaxis.GetTextSize(),
                           typolabel.Data());
                     yy -= charheight*1.3;
                  }
               }
            }
 
//   We use the format x 10 ** n
 
            if (flexe && !optionText && nexe)  {
               snprintf(label,256,"#times10^{%d}", nexe);
               if (x0 != x1) { xfactor = axis_length+0.1*charheight; yfactor = 0; }
               else          { xfactor = y1-y0+0.1*charheight; yfactor = 0; }
               Rotate (xfactor,yfactor,cosphi,sinphi,x0,y0,xx,yy);
               textaxis.SetTextAlign(11);
               if (GetLabelFont()%10 < 2) // force TLatex mode in PaintLatex
                  textaxis.SetTextFont((Int_t)(GetLabelFont()/10)*10+2);
               if (fAxis && !strcmp(fAxis->GetName(),"xaxis")) {
                  Float_t xoff = 0., yoff = 0.;
                  gStyle->GetExponentOffset(xoff, yoff, "x");
                  xx += xoff;
                  yy += yoff;
               }
               if (fAxis && !strcmp(fAxis->GetName(),"yaxis")) {
                  Float_t xoff = 0., yoff = 0.;
                  gStyle->GetExponentOffset(xoff, yoff, "y");
                  xx += xoff;
                  yy += yoff;
               }
               typolabel = label;
               typolabel.ReplaceAll("-", "#minus");
               textaxis.PaintLatex(gPad->GetX1() + xx*(gPad->GetX2() - gPad->GetX1()),
                           gPad->GetY1() + yy*(gPad->GetY2() - gPad->GetY1()),
                           0,
                           textaxis.GetTextSize(),
                           typolabel.Data());
            }
         }
      }
   }
 
// Log axis
 
   if (optionLog && ndiv) {
      UInt_t xi1=0,xi2=0,wi=0,yi1=0,yi2=0,hi=0,xl=0,xh=0;
      Bool_t firstintlab = kTRUE, overlap = kFALSE;
      if ((wmin == wmax) || (ndiv == 0))  {
         Error(where, "wmin (%f) == wmax (%f), or ndiv == 0", wmin, wmax);
         return;
      }
      if (wmin <= 0)   {
         Error(where, "negative logarithmic axis");
         return;
      }
      if (wmax <= 0)     {
         Error(where, "negative logarithmic axis");
         return;
      }
      xmnlog = TMath::Log10(wmin);
      if (xmnlog > 0) xmnlog += 1.E-6;
      else            xmnlog -= 1.E-6;
      x00    = 0;
      x11    = axis_length;
      h2     = TMath::Log10(wmax);
      h2sav  = h2;
      if (h2 > 0) h2 += 1.E-6;
      else        h2 -= 1.E-6;
      ih1    = int(xmnlog);
      ih2    = 1+int(h2);
      nbinin = ih2-ih1+1;
      axmul  = (x11-x00)/(h2sav-xmnlog);
 
      std::vector<Double_t> ticksx, ticksy, gridsx, gridsy;
 
      if (!drawGridOnly) {
         ticksx.reserve(nbinin*2);
         ticksy.reserve(nbinin*2);
      }
      if (optionGrid) {
         gridsx.reserve(nbinin*2);
         gridsy.reserve(nbinin*2);
      }
 
      struct LogLabel {
         Int_t id = 0, num = 0;
         Double_t u = 0., v = 0., value = 0.;
         TString lbl;
      };
      std::vector<LogLabel> loglabels;
      if (!drawGridOnly && !optionUnlab)
         loglabels.reserve(nbinin);
 
 
// Plot decade and intermediate tick marks
      decade      = ih1-2;
      labelnumber = ih1;
      if ( xmnlog > 0 && (xmnlog-Double_t(ih1) > 0) ) labelnumber++;
      Int_t changelablogid  = 0;
      Int_t changelablognum = 0;
      for (j=1; j<=nbinin; j++) {
 
// Plot decade
         firstintlab = kTRUE, overlap = kFALSE;
         decade++;
         if (x0 == x1 && j == 1) ylabel += charheight*0.33;
         if (y0 == y1 && j == 1) ylabel -= charheight*0.65;
         xone = x00+axmul*(Double_t(decade)-xmnlog);
         //the following statement is a trick to circumvent a gcc bug
         if (j < 0) printf("j=%d\n",j);
         if (x00 > xone) goto L160;
         if ((xone-x11)>epsilon) break;
         xtwo = xone;
         y    = 0;
         if (!mside) y -= atick[0];
         Rotate(xone,y,cosphi,sinphi,x0,y0,xpl2,ypl2);
         Rotate(xtwo,atick[0],cosphi,sinphi,x0,y0,xpl1,ypl1);
         if (optionVert) {
            if ((x0 != x1) && (y0 != y1)) {
               if (mside) {
                  xpl1=xpl2;
                  if (cosphi > 0) ypl1 = ypl2 + atick[0];
                  else            ypl1 = ypl2 - atick[0];
               }
               else {
                  xpl1 = 0.5*(xpl1 + xpl2);
                  xpl2 = xpl1;
                  ypl1 = 0.5*(ypl1 + ypl2) + atick[0];
                  ypl2 = 0.5*(ypl1 + ypl2) - atick[0];
               }
            }
         }
         if (!drawGridOnly) {
            ticksx.emplace_back(xpl1);
            ticksx.emplace_back(xpl2);
            ticksy.emplace_back(ypl1);
            ticksy.emplace_back(ypl2);
         }
 
         if (optionGrid) {
            Rotate(xone,0,cosphi,sinphi,x0,y0,xpl2,ypl2);
            Rotate(xone,grid_side*gridlength,cosphi,sinphi,x0,y0,xpl1,ypl1);
            gridsx.emplace_back(xpl1);
            gridsx.emplace_back(xpl2);
            gridsy.emplace_back(ypl1);
            gridsy.emplace_back(ypl2);
         }
 
         if (!drawGridOnly && !optionUnlab)  {
 
// We generate labels (numeric only).
            axis_value = TMath::Power(10,labelnumber);
            if (noExponent) {
               rlab = TMath::Power(10,labelnumber);
               snprintf(label,256, "%f", rlab);
               LabelsLimits(label,first,last);
               while (last > first) {
                  if (label[last] != '0') break;
                  label[last] = 0;
                  last--;
               }
               if (label[last] == '.') {label[last] = 0; last--;}
            } else {
               snprintf(label,256, "%d", labelnumber);
               LabelsLimits(label,first,last);
            }
            Rotate (xone,ylabel,cosphi,sinphi,x0,y0,xx,yy);
            if ((x0 == x1) && !optionPara) {
               if (lside < 0) {
                  if (mside < 0) {
                     if (labelnumber == 0) nch=1;
                     else                  nch=2;
                     xx    += nch*charheight;
                  } else {
                     xx += 0.25*charheight;
                  }
               }
               xx += 0.25*charheight;
            }
            if ((y0 == y1) && !optionDown && !optionUp) {
               if (noExponent) yy += 0.33*charheight;
            }
            if (n1a == 0) return;
            kmod = nbinin/n1a;
            if (kmod == 0) kmod=1000000;
            if ((nbinin <= n1a) || (j == 1) || (j == nbinin) || ((nbinin > n1a) && (j%kmod == 0))) {
               if (labelnumber == 0) {
                  snprintf(chtemp,256, "1");
               } else if (labelnumber == 1) {
                  snprintf(chtemp,256, "10");
               } else {
                  if (noExponent) {
                     chtemp = &label[first];
                  } else {
                     snprintf(chtemp,256, "10^{%d}", labelnumber);
                  }
               }
               if (fNModLabs) {
                  if (changelablogid  == 0) changelablognum = nbinin-j;
                  changelablogid++;
                  ChangeLabelAttributes(changelablogid, changelablognum, &textaxis, chtemp, axis_value, axis_value*1e-6);
               }
               typolabel = chtemp;
               typolabel.ReplaceAll("-", "#minus");
               if (autotoff) {
                  UInt_t w,h;
                  textaxis.SetText(0.,0., typolabel.Data());
                  textaxis.GetBoundingBox(w,h);
                  double scale=gPad->GetWw()*gPad->GetWNDC();
                  if (scale>0.0) toffset = TMath::Max(toffset,(double)w/scale);
               }
               loglabels.emplace_back();
               auto &back = loglabels.back();
               back.id = changelablogid;
               back.num = changelablognum;
               back.u = gPad->GetX1() + xx*(gPad->GetX2() - gPad->GetX1());
               back.v = gPad->GetY1() + yy*(gPad->GetY2() - gPad->GetY1());
               back.value = axis_value;
               back.lbl = typolabel;
               if (fNModLabs) ResetLabelAttributes(&textaxis);
            }
            labelnumber++;
         }
L160:
         for (k=2;k<10;k++) {
 
// Plot intermediate tick marks
            xone = x00+axmul*(TMath::Log10(Double_t(k))+Double_t(decade)-xmnlog);
            if (x00 > xone) continue;
            if (xone > x11) goto L200;
            y = 0;
            if (!mside)  y -= atick[1];
            xtwo = xone;
            Rotate(xone,y,cosphi,sinphi,x0,y0,xpl2,ypl2);
            Rotate(xtwo,atick[1],cosphi,sinphi,x0,y0,xpl1,ypl1);
            if (optionVert) {
               if ((x0 != x1) && (y0 != y1)) {
                  if (mside) {
                     xpl1 = xpl2;
                     if (cosphi > 0) ypl1 = ypl2 + atick[1];
                     else            ypl1 = ypl2 - atick[1];
                  }
                  else {
                     xpl1 = 0.5*(xpl1+xpl2);
                     xpl2 = xpl1;
                     ypl1 = 0.5*(ypl1+ypl2) + atick[1];
                     ypl2 = 0.5*(ypl1+ypl2) - atick[1];
                  }
               }
            }
            idn = n1a*2;
            if ((nbinin <= idn) || ((nbinin > idn) && (k == 5))) {
               if (!drawGridOnly) {
                  ticksx.emplace_back(xpl1);
                  ticksx.emplace_back(xpl2);
                  ticksy.emplace_back(ypl1);
                  ticksy.emplace_back(ypl2);
               }
 
// Draw the intermediate LOG labels if requested
 
               if (moreLogLabels && !optionUnlab && !drawGridOnly && !overlap) {
                  axis_value = Double_t(k)*TMath::Power(10,labelnumber-1);
                  if (noExponent) {
                     rlab = axis_value;
                     snprintf(chtemp,256, "%g", rlab);
                  } else {
                     if (labelnumber-1 == 0) {
                        snprintf(chtemp,256, "%d", k);
                     } else if (labelnumber-1 == 1) {
                        snprintf(chtemp,256, "%d", 10*k);
                     } else {
                        snprintf(chtemp,256, "%d#times10^{%d}", k, labelnumber-1);
                     }
                  }
                  Rotate (xone,ylabel,cosphi,sinphi,x0,y0,xx,yy);
                  if ((x0 == x1) && !optionPara) {
                     if (lside < 0) {
                        if (mside < 0) {
                           if (labelnumber == 0) nch=1;
                           else                  nch=2;
                           xx    += nch*charheight;
                        } else {
                           if (labelnumber >= 0) xx    += 0.25*charheight;
                           else                  xx    += 0.50*charheight;
                        }
                     }
                     xx += 0.25*charheight;
                  }
                  if ((y0 == y1) && !optionDown && !optionUp) {
                     if (noExponent) yy += 0.33*charheight;
                  }
                  if (optionVert) {
                     if ((x0 != x1) && (y0 != y1)) {
                        Rotate(xone,ylabel,cosphi,sinphi,x0,y0,xx,yy);
                        if (cosphi > 0) yy += ylabel;
                        else            yy -= ylabel;
                     }
                  }
                  textaxis.SetTitle(chtemp);
                  Double_t u = gPad->GetX1() + xx*(gPad->GetX2() - gPad->GetX1());
                  Double_t v = gPad->GetY1() + yy*(gPad->GetY2() - gPad->GetY1());
                  if (firstintlab) {
                     textaxis.GetBoundingBox(wi, hi); wi=(UInt_t)(wi*1.3); hi=(UInt_t)(hi*1.3);
                     xi1 = gPad->XtoAbsPixel(u);
                     yi1 = gPad->YtoAbsPixel(v);
                     firstintlab = kFALSE;
                     if (fNModLabs) {
                        changelablogid++;
                        ChangeLabelAttributes(changelablogid, 0, &textaxis, chtemp, axis_value, axis_value*1e-6);
                     }
                     typolabel = chtemp;
                     typolabel.ReplaceAll("-", "#minus");
                     loglabels.emplace_back();
                     auto &back = loglabels.back();
                     back.id = changelablogid;
                     back.num = 0;
                     back.u = u;
                     back.v = v;
                     back.value = axis_value;
                     back.lbl = typolabel;
                     if (fNModLabs) ResetLabelAttributes(&textaxis);
                  } else {
                     xi2 = gPad->XtoAbsPixel(u);
                     yi2 = gPad->YtoAbsPixel(v);
                     xl = TMath::Min(xi1,xi2);
                     xh = TMath::Max(xi1,xi2);
                     if ((x0 == x1 && yi1-hi <= yi2) || (y0 == y1 && xl+wi >= xh)){
                        overlap = kTRUE;
                     } else {
                        xi1 = xi2;
                        yi1 = yi2;
                        textaxis.GetBoundingBox(wi, hi); wi=(UInt_t)(wi*1.3); hi=(UInt_t)(hi*1.3);
                        if (fNModLabs) {
                           changelablogid++;
                           ChangeLabelAttributes(changelablogid, 0, &textaxis, chtemp, axis_value, axis_value*1e-6);
                        }
                        typolabel = chtemp;
                        typolabel.ReplaceAll("-", "#minus");
                        loglabels.emplace_back();
                        auto &back = loglabels.back();
                        back.id = changelablogid;
                        back.num = 0;
                        back.u = u;
                        back.v = v;
                        back.value = axis_value;
                        back.lbl = typolabel;
                        if (fNModLabs) ResetLabelAttributes(&textaxis);
                     }
                  }
               }
 
// Draw the intermediate LOG grid if only three decades are requested
               if (optionGrid && nbinin <= 5 && ndiv > 100) {
                  Rotate(xone,0,cosphi,sinphi,x0,y0, xpl2, ypl2);
                  Rotate(xone,grid_side*gridlength,cosphi,sinphi,x0,y0, xpl1,ypl1);
                  gridsx.emplace_back(xpl1);
                  gridsx.emplace_back(xpl2);
                  gridsy.emplace_back(ypl1);
                  gridsy.emplace_back(ypl2);
               }
            }  //endif ((nbinin <= idn) ||
         }  //endfor (k=2;k<10;k++)
      } //endfor (j=1; j<=nbinin; j++)
L200:
      // paint ticks all together with one command
      if (ticksx.size() > 0) {
         TAttLine::Modify();
         gPad->PaintSegmentsNDC(ticksx.size() / 2, ticksx.data(), ticksy.data());
      }
 
      // paint all labels after ticks
      for(auto & lbl : loglabels) {
         if (fNModLabs)
            ChangeLabelAttributes(lbl.id, lbl.num, &textaxis, chtemp, lbl.value, lbl.value*1e-6);
         textaxis.PaintLatex(lbl.u, lbl.v, 0, textaxis.GetTextSize(), lbl.lbl.Data());
         if (fNModLabs)
            ResetLabelAttributes(&textaxis);
      }
 
      // paint grid lines all together at the end
      if (gridsx.size() > 0) {
         linegrid.TAttLine::Modify();
         gPad->PaintSegmentsNDC(gridsx.size() / 2, gridsx.data(), gridsy.data());
      }
 
   }  //endif (optionLog && ndiv)
 
// Draw axis title if it exists
   if (!drawGridOnly && strlen(GetTitle())) {
      textaxis.SetTextSize (GetTitleSize());
      charheight = GetTitleSize();
      if ((GetTextFont() % 10) > 2) {
         charheight /= ((x1==x0) ? padw : padh);
      }
      if (x1 == x0) {
         if (autotoff) {
            if (toffset) ylabel = xlside*charheight+toffset;
            else         ylabel = xlside*1.6*charheight;
         } else {
            ylabel = xlside*1.6*charheight*toffset;
         }
      } else {
        ylabel = xlside*1.3*charheight*toffset;
      }
      if (y1 == y0) {
         if (toffset == 0.) toffset = gStyle->GetTitleOffset("X");
         ylabel = xlside*1.6*charheight*toffset;
      }
      Double_t axispos;
      if (TestBit(TAxis::kCenterTitle)) axispos = 0.5*axis_length;
      else                              axispos = axis_length;
      if (TestBit(TAxis::kRotateTitle)) {
         if (x1 >= x0) {
            if (TestBit(TAxis::kCenterTitle)) textaxis.SetTextAlign(22);
            else                              textaxis.SetTextAlign(12);
         } else {
            if (TestBit(TAxis::kCenterTitle)) textaxis.SetTextAlign(22);
            else                              textaxis.SetTextAlign(32);
         }
         phil+=kPI;
      } else {
         if (x1 >= x0) {
            if (TestBit(TAxis::kCenterTitle)) textaxis.SetTextAlign(22);
            else                              textaxis.SetTextAlign(32);
         } else {
            if (TestBit(TAxis::kCenterTitle)) textaxis.SetTextAlign(22);
            else                              textaxis.SetTextAlign(12);
         }
      }
      Rotate(axispos,ylabel,cosphi,sinphi,x0,y0,xpl1,ypl1);
      textaxis.SetTextColor(TitleColor);
      textaxis.SetTextFont(TitleFont);
      textaxis.PaintLatex(gPad->GetX1() + xpl1*(gPad->GetX2() - gPad->GetX1()),
                           gPad->GetY1() + ypl1*(gPad->GetY2() - gPad->GetY1()),
                           phil*180/kPI,
                           GetTitleSize(),
                           GetTitle());
   }
 
}
 
////////////////////////////////////////////////////////////////////////////////
/// Internal method for axis labels optimisation. This method adjusts the bining
/// of the axis in order to have integer values for the labels.
///
/// \param[in]  A1,A2            Old WMIN,WMAX
/// \param[out] binLow,binHigh   New WMIN,WMAX
/// \param[in]  nold             Old NDIV (primary divisions)
/// \param[out] nbins            New NDIV
/// \param[out] binWidth         Bin width
 
void TGaxis::AdjustBinSize(Double_t A1,  Double_t A2,  Int_t nold
                          ,Double_t &binLow, Double_t &binHigh, Int_t &nbins, Double_t &binWidth)
{
 
   binWidth = TMath::Abs(A2-A1)/Double_t(nold);
   if (binWidth <= 1) { binWidth = 1; binLow = int(A1); }
   else {
      Int_t width = int(binWidth/5) + 1;
      binWidth = 5*width;
      binLow   = int(A1/binWidth)*binWidth;
 
// We determine binLow to have one tick mark at 0
// if there are negative labels.
 
      if (A1 < 0) {
         for (Int_t ic=0; ic<1000; ic++) {
            Double_t rbl = binLow/binWidth;
            Int_t   ibl = int(binLow/binWidth);
            if ( (rbl-ibl) == 0 || ic > width) { binLow -= 5; break;}
         }
      }
   }
   binHigh     = int(A2);
   nbins       = 0;
   Double_t xb  = binLow;
   while (xb <= binHigh) {
      xb += binWidth;
      nbins++;
   }
   binHigh = xb - binWidth;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Internal method to find first and last character of a label.
 
void TGaxis::LabelsLimits(const char *label, Int_t &first, Int_t &last)
{
   last = strlen(label)-1;
   for (Int_t i=0; i<=last; i++) {
      if (strchr("1234567890-+.", label[i]) ) { first = i; return; }
   }
   Error("LabelsLimits", "attempt to draw a blank label");
}
 
////////////////////////////////////////////////////////////////////////////////
///    Internal method to rotate axis coordinates.
 
void TGaxis::Rotate(Double_t X,  Double_t Y,  Double_t CFI, Double_t SFI
                   ,Double_t XT, Double_t YT, Double_t &U,   Double_t &V)
{
   U = CFI*X-SFI*Y+XT;
   V = SFI*X+CFI*Y+YT;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Save primitive as a C++ statement(s) on output stream out
 
void TGaxis::SavePrimitive(std::ostream &out, Option_t *option)
{
   SavePrimitiveConstructor(out, Class(), "gaxis",
                            TString::Format("%g, %g, %g, %g, %14.12g, %14.12g, %d, \"%s\", %g", fX1, fY1, fX2, fY2,
                                            fWmin, fWmax, fNdiv, fChopt.Data(), GetGridLength()));
 
   SaveLineAttributes(out, "gaxis", 1, 1, 1);
   SaveTextAttributes(out, "gaxis", 11, 0, 1, 62, 0.04);
 
   if (strlen(GetName()))
      out << "   gaxis->SetName(\"" << GetName() << "\");\n";
   if (strlen(GetTitle()))
      out << "   gaxis->SetTitle(\"" << TString(GetTitle()).ReplaceSpecialCppChars() << "\");\n";
   if (fTimeFormat.Length() > 0)
      out << "   gaxis->SetTimeFormat(\"" << TString(fTimeFormat).ReplaceSpecialCppChars() << "\");\n";
 
   out << "   gaxis->SetLabelOffset(" << GetLabelOffset() << ");\n";
   out << "   gaxis->SetLabelSize(" << GetLabelSize() << ");\n";
   if (fLabelColor != 1)
      out << "   gaxis->SetLabelColor(" << TColor::SavePrimitiveColor(GetLabelColor()) << ");\n";
   if (fLabelFont != 62)
      out << "   gaxis->SetLabelFont(" << GetLabelFont() << ");\n";
   if (TestBit(TAxis::kMoreLogLabels))
      out << "   gaxis->SetMoreLogLabels();\n";
 
   out << "   gaxis->SetTickSize(" << GetTickSize() << ");\n";
   out << "   gaxis->SetTitleOffset(" << GetTitleOffset() << ");\n";
   out << "   gaxis->SetTitleSize(" << GetTitleSize() << ");\n";
 
   if (TestBit(TAxis::kNoExponent))
      out << "   gaxis->SetNoExponent();\n";
   if (fModLabs) {
      TIter next(fModLabs);
      while (auto ml = static_cast<TAxisModLab *>(next())) {
         if (ml->GetLabNum() == 0)
            out << "   gaxis->ChangeLabelByValue(" << ml->GetLabValue();
         else
            out << "   gaxis->ChangeLabel(" << ml->GetLabNum();
         out << ", " << ml->GetAngle() << ", " << ml->GetSize() << ", " << ml->GetAlign() << ", "
             << TColor::SavePrimitiveColor(ml->GetColor()) << ", " << ml->GetFont() << ", \""
             << TString(ml->GetText()).ReplaceSpecialCppChars() << "\");\n";
      }
   }
 
   SavePrimitiveDraw(out, "gaxis", option);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Set the decimals flag. By default, blank characters are stripped, and then the
/// label is correctly aligned. The dot, if last character of the string, is also
/// stripped, unless this option is specified. One can disable the option by
/// calling `axis.SetDecimals(kTRUE)`.
/// Note the bit is set in fBits (as opposed to fBits2 in TAxis!)
 
void TGaxis::SetDecimals(Bool_t dot)
{
   if (dot) SetBit(TAxis::kDecimals);
   else     ResetBit(TAxis::kDecimals);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Specify a function to map the axis values.
 
void TGaxis::SetFunction(const char *funcname)
{
   fFunctionName = funcname;
   if (!funcname || !funcname[0]) {
      fFunction = nullptr;
      return;
   }
   fFunction = (TF1*)gROOT->GetFunction(funcname);
   if (!fFunction) {
      Error("SetFunction", "unknown function: %s", funcname);
   } else {
      fWmin = fFunction->GetXmin();
      fWmax = fFunction->GetXmax();
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Search for axis modifier by index or value
 
TAxisModLab *TGaxis::FindModLab(Int_t indx, Int_t numlabels, Double_t v, Double_t eps) const
{
   if (!fModLabs)
      return nullptr;
 
   TIter next(fModLabs);
   while (auto ml = (TAxisModLab*)next()) {
 
      if (ml->GetLabNum() == 0) {
         if (TMath::Abs(v - ml->GetLabValue()) <= eps)
            return ml;
      } else if (indx != 0) {
         Bool_t match = ml->GetLabNum() == indx;
         if (!match && (ml->GetLabNum() < 0) && (indx > 0) && (numlabels > 0)) {
            if (TestBit(TAxis::kMoreLogLabels)) {
               Error("FindModLab", "reverse numbering in ChangeLabel doesn't work when more log labels are requested");
               return nullptr;
            }
 
            match = indx == (ml->GetLabNum() + 2 + numlabels);
         }
         if (match) return ml;
      }
   }
 
   return nullptr;
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// Define new text attributes for the label number "labNum". It allows to do a
/// fine tuning of the labels. All the attributes can be changed, even the
/// label text itself.
///
/// \param[in] labNum    Number of the label to be changed, negative numbers start from the end
/// \param[in] labAngle  New angle value
/// \param[in] labSize   New size (0 erase the label)
/// \param[in] labAlign  New alignment value
/// \param[in] labColor  New label color
/// \param[in] labFont   New label font
/// \param[in] labText   New label text
///
/// #### Example:
///
/// Begin_Macro(source)
/// {
///   auto c = new TCanvas("c1","Examples of TGaxis",900,100);
///   c->Range(-6,-0.1,6,0.1);
///   auto *axis = new TGaxis(-5.5,0.,5.5,0.,0.0,100,510,"S");
///   axis->SetName("axis1");
///   axis->SetTitle("Axis Title");
///   axis->SetTitleSize(0.2);
///   axis->SetLabelSize(0.2);
///   axis->SetTickSize(0.15);
///   axis->SetTitleColor(kBlue);
///   axis->SetTitleFont(42);
///   axis->ChangeLabel(1,-1,-1,-1,2);
///   axis->ChangeLabel(3,-1,0.);
///   axis->ChangeLabel(5,30.,-1,0);
///   axis->ChangeLabel(6,-1,-1,-1,3,-1,"6th label");
///   axis->ChangeLabel(-2,-1,-1,-1,3,-1,"2nd to last label");
///   axis->Draw();
/// }
/// End_Macro
///
///  #### Notes:
///
///  - If an attribute should not be changed just give the value "-1".
///  - If labnum=0 the list of modified labels is reset.
///  - To erase a label set labSize to 0.
///  - If labText is not specified or is an empty string, the text label is not changed.
 
void TGaxis::ChangeLabel(Int_t labNum, Double_t labAngle, Double_t labSize,
                         Int_t labAlign, Int_t labColor, Int_t labFont,
                         const TString &labText)
{
   // special situation when mod labs taken from axis - one have to reset pointer
   if (fModLabs && !IsOwnedModLabs()) {
      fModLabs = nullptr;
      fNModLabs = 0;
   }
 
   // Reset the list of modified labels.
   if (labNum == 0) {
      CleanupModLabs();
      return;
   }
 
   fNModLabs++;
   if (!fModLabs) {
      fModLabs = new TList();
      fModLabs->SetOwner(kTRUE);
   }
 
   TAxisModLab *ml = FindModLab(labNum);
   if (!ml) {
      ml = new TAxisModLab();
      ml->SetLabNum(labNum);
      fModLabs->Add(ml);
   }
 
   ml->SetAngle(labAngle);
   ml->SetSize(labSize);
   ml->SetAlign(labAlign);
   ml->SetColor(labColor);
   ml->SetFont(labFont);
   ml->SetText(labText);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Define new text attributes for the label value "labValue". It allows to do a
/// fine tuning of the labels. All the attributes can be changed, even the
/// label text itself.
///
/// \param[in] labValue  Axis value to be changed
/// \param[in] labAngle  New angle value
/// \param[in] labSize   New size (0 erase the label)
/// \param[in] labAlign  New alignment value
/// \param[in] labColor  New label color
/// \param[in] labFont   New label font
/// \param[in] labText   New label text
///
/// #### Example:
///
/// Begin_Macro(source)
/// {
///   auto c = new TCanvas("c1","Examples of TGaxis",900,100);
///   c->Range(-6,-0.1,6,0.1);
///   auto *axis = new TGaxis(-5.5,0.,5.5,0.,0.0,100,510,"S");
///   axis->SetName("axis1");
///   axis->SetTitle("Axis Title");
///   axis->SetTitleSize(0.2);
///   axis->SetLabelSize(0.2);
///   axis->SetTickSize(0.15);
///   axis->SetTitleColor(kBlue);
///   axis->SetTitleFont(42);
///   axis->ChangeLabelByValue(0., -1, -1, -1, kRed);
///   axis->ChangeLabelByValue(20., -1, 0);
///   axis->ChangeLabelByValue(40., 30.);
///   axis->ChangeLabelByValue(50., -1, -1, -1, kBlue, -1, "blue for 50.");
///   axis->ChangeLabelByValue(90., -1, -1, -1, kGreen, -1, "green for 90.");
///   axis->Draw();
/// }
/// End_Macro
///
///  #### Notes:
///
///  - If an attribute should not be changed just give the value "-1".
///  - To erase a label set labSize to 0
///  - If labText is not specified or is an empty string, the text label is not changed.
 
void TGaxis::ChangeLabelByValue(Double_t labValue, Double_t labAngle, Double_t labSize,
                              Int_t labAlign, Int_t labColor, Int_t labFont,
                              const TString &labText)
{
   // special situation when mod labs taken from axis - one have to reset pointer
   if (fModLabs && !IsOwnedModLabs()) {
      fModLabs = nullptr;
      fNModLabs = 0;
   }
 
   fNModLabs++;
   if (!fModLabs) {
      fModLabs = new TList();
      fModLabs->SetOwner(kTRUE);
   }
 
   TAxisModLab *ml = FindModLab(0, 0, labValue, 0.);
   if (!ml) {
      ml = new TAxisModLab();
      ml->SetLabValue(labValue);
      fModLabs->Add(ml);
   }
 
   ml->SetAngle(labAngle);
   ml->SetSize(labSize);
   ml->SetAlign(labAlign);
   ml->SetColor(labColor);
   ml->SetFont(labFont);
   ml->SetText(labText);
}
 
 
static TAttText SavedAttText;  ///< Global variable saving the current label's text angle. Used by TGaxis::ChangeLabelAttributes.
 
////////////////////////////////////////////////////////////////////////////////
/// Helper method used by TGaxis::ChangeLabel.
/// Change the label attributes of label number i. If needed.
///
/// \param[in] i        Current label number to be changed if needed
/// \param[in] nlabels  Totals number of labels for this axis (useful when i is counted from the end)
/// \param[in] t        Original TLatex string holding the label to be changed
/// \param[in] c        Text string to be drawn
/// \param[in] value    Axis value which should be changed
/// \param[in] eps      Epsilon parameter for axis value, -1 means ignore axis value at all
 
 
void TGaxis::ChangeLabelAttributes(Int_t i, Int_t nlabels, TLatex* t, char* c, Double_t value, Double_t eps)
{
   t->TAttText::Copy(SavedAttText);
 
   auto ml = FindModLab(i, nlabels, value, eps);
 
   if (ml) {
      if (ml->GetAngle()>=0.) t->SetTextAngle(ml->GetAngle());
      if (ml->GetSize()>=0.)  t->SetTextSize(ml->GetSize());
      if (ml->GetAlign()>0)   t->SetTextAlign(ml->GetAlign());
      if (ml->GetColor()>=0)  t->SetTextColor(ml->GetColor());
      if (ml->GetFont()>0)    t->SetTextFont(ml->GetFont());
      if (!ml->GetText().IsNull()) strlcpy(c, ml->GetText().Data(), 256);
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Helper method used by TGaxis::ChangeLabel.
/// Reset the labels' attributes to the values they had before the last call to
/// TGaxis::ChangeLabelAttributes.
 
void TGaxis::ResetLabelAttributes(TLatex* t)
{
   SavedAttText.Copy(*t);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Static function to set `fgMaxDigits` for axis.`fgMaxDigits` is
/// the maximum number of digits permitted for the axis labels above which the
/// notation with 10^N is used.For example, to accept 6 digits number like 900000
/// on an axis call `TGaxis::SetMaxDigits(6)`. The default value is 5.
/// `fgMaxDigits` must be greater than 0.
/// Warning: this static function changes the max number of digits in all axes.
/// If you only want to change the digits of the current TGaxis instance, use
/// axis->SetNdivisions(N*1000000 + (axis->GetNdiv()%1000000))
/// instead of axis->SetMaxDigits(N).
 
void TGaxis::SetMaxDigits(Int_t maxd)
{
   gStyle->SetAxisMaxDigits(maxd);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Change the name of the axis.
 
void TGaxis::SetName(const char *name)
{
   fName = name;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Set the kMoreLogLabels bit flag. When this option is selected more labels are
/// drawn when in logarithmic scale and there is a small number of decades (less than 3).
/// Note that this option is automatically inherited from TAxis
 
void TGaxis::SetMoreLogLabels(Bool_t more)
{
   if (more) SetBit(TAxis::kMoreLogLabels);
   else      ResetBit(TAxis::kMoreLogLabels);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Set the NoExponent flag. By default, an exponent of the form 10^N is used
/// when the label values are either all very small or very large. One can disable
/// the exponent by calling axis.SetNoExponent(kTRUE).
 
void TGaxis::SetNoExponent(Bool_t noExponent)
{
   if (noExponent) SetBit(TAxis::kNoExponent);
   else            ResetBit(TAxis::kNoExponent);
}
 
////////////////////////////////////////////////////////////////////////////////
/// To set axis options.
 
void TGaxis::SetOption(Option_t *option)
{
   fChopt = option;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Change the title of the axis.
 
void TGaxis::SetTitle(const char *title)
{
   fTitle = title;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Change the format used for time plotting.
/// The format string for date and time use the same options as the one used
/// in the standard strftime C function, i.e. :
///
/// for date :
///
///  - `%a` abbreviated weekday name
///  - `%b` abbreviated month name
///  - `%d` day of the month (01-31)
///  - `%m` month (01-12)
///  - `%y` year without century
///
/// for time :
///
///  - `%H` hour (24-hour clock)
///  - `%I` hour (12-hour clock)
///  - `%p` local equivalent of AM or PM
///  - `%M` minute (00-59)
///  - `%S` seconds (00-61)
///  - `%%` %
 
void TGaxis::SetTimeFormat(const char *tformat)
{
   TString timeformat = tformat;
 
   if (timeformat.Index("%F")>=0 || timeformat.IsNull()) {
      fTimeFormat = timeformat;
      return;
   }
 
   Int_t idF = fTimeFormat.Index("%F");
   if (idF>=0) {
      Int_t lnF = fTimeFormat.Length();
      TString stringtimeoffset = fTimeFormat(idF,lnF);
      fTimeFormat = tformat;
      fTimeFormat.Append(stringtimeoffset);
   } else {
      fTimeFormat = tformat;
      SetTimeOffset(gStyle->GetTimeOffset());
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Change the time offset. If option = "gmt", set display mode to GMT.
 
void TGaxis::SetTimeOffset(Double_t toffset, Option_t *option)
{
   TString opt = option;
   opt.ToLower();
 
   char tmp[20];
   time_t timeoff;
   struct tm* utctis;
   Int_t idF = fTimeFormat.Index("%F");
   if (idF>=0) fTimeFormat.Remove(idF);
   fTimeFormat.Append("%F");
 
   timeoff = (time_t)((Long_t)(toffset));
 
   // offset is always saved in GMT to allow file transport
   // to different time zones
   utctis = gmtime(&timeoff);
 
   if (utctis != nullptr) {
      strftime(tmp, 20,"%Y-%m-%d %H:%M:%S",utctis);
      fTimeFormat.Append(tmp);
   } else {
      fTimeFormat.Append("1970-01-01 00:00:00");
   }
 
   // append the decimal part of the time offset
   Double_t ds = toffset-(Int_t)toffset;
   snprintf(tmp,20,"s%g",ds);
   fTimeFormat.Append(tmp);
 
   // add GMT/local option
   if (opt.Contains("gmt")) fTimeFormat.Append(" GMT");
}
 
////////////////////////////////////////////////////////////////////////////////
/// Static method to set X and Y offset of the axis 10^n notation.
/// It applies on axis belonging to an histogram (TAxis). It has no effect on standalone TGaxis.
/// It is in % of the pad size. It can be negative.
/// axis specifies which axis ("x","y"), default = "x"
/// if axis="xz" set the two axes
/// Redirected to TStyle::SetExponentOffset
 
void TGaxis::SetExponentOffset(Float_t xoff, Float_t yoff, Option_t *axis)
{
   gStyle->SetExponentOffset(xoff, yoff, axis);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Stream an object of class TGaxis.
 
void TGaxis::Streamer(TBuffer &R__b)
{
   if (R__b.IsReading()) {
      UInt_t R__s, R__c;
      Version_t R__v = R__b.ReadVersion(&R__s, &R__c);
      if (R__v > 3) {
         R__b.ReadClassBuffer(TGaxis::Class(), this, R__v, R__s, R__c);
         return;
      }
      //====process old versions before automatic schema evolution
      TLine::Streamer(R__b);
      TAttText::Streamer(R__b);
      R__b >> fNdiv;
      R__b >> fWmin;
      R__b >> fWmax;
      R__b >> fGridLength;
      R__b >> fTickSize;
      R__b >> fLabelOffset;
      R__b >> fLabelSize;
      R__b >> fTitleOffset;
      R__b >> fTitleSize;
      R__b >> fLabelFont;
      if (R__v > 2) {
         R__b >> fLabelColor;
      }
      fChopt.Streamer(R__b);
      fName.Streamer(R__b);
      fTitle.Streamer(R__b);
      fTimeFormat.Streamer(R__b);
      if (R__v > 1) {
         fFunctionName.Streamer(R__b);
         fFunction = (TF1*)gROOT->GetFunction(fFunctionName.Data());
      }
      R__b.CheckByteCount(R__s, R__c, TGaxis::IsA());
      //====end of old versions
 
   } else {
      R__b.WriteClassBuffer(TGaxis::Class(),this);
   }
}
 
void TGaxis::SetLabelColor(TColorNumber lcolor)
{
   SetLineColor(lcolor.number());
}