function floatgui(callbackarg)
%FLOATGUI  Show structure of floating point numbers.
%  The set of positive model floating point numbers is determined
%  by three parameters: t, emin, and emax.  It is the set of rational
%  numbers of the form x = (1+f)*2^e where f = (integer)/2^t,
%  0 <= f < 1, e = integer, and emin <= e <= emax.
%
%  IEEE 754 double precision has t = 52, emin = -1022, emax = 1023.

%   Copyright 2014 Cleve Moler
%   Copyright 2014 The MathWorks, Inc.

% Initialize parameters

if nargin == 0
   t = 3;
   emin = -4;
   emax = 2;
   logscale = 0;
   Fpos=[50 300 900 250];
else
   t = round(get(findobj('tag','t'),'value'));
   emin = round(get(findobj('tag','emin'),'value'));
   emax = round(get(findobj('tag','emax'),'value'));
   logscale = get(findobj('style','check'),'value');
   Fpos=get(gcf,'pos');
end

% Position figure window

shg
clf reset
set(gcf,'pos',Fpos,'name','floatgui', ...
   'resize','on','defaultuicontrolunits','normalized',...
   'numbertitle','off','menubar','none')

% Generate and plot floating point numbers

f = (0:2^t-1)/2^t;
F = [];
for e = emin:emax
   F = [F (1+f)*2^e];
end
for x = F
   text(x,0,'|','fontunits','normalized','fontsize',0.3)
end

% Set axes

set(gca,'pos',[.05 .6 .9 .2],'fontunits','normalized','fontsize',0.22)
if logscale
   set(gca,'xscale','log')
   xmin = 1/2^(-emin+.5);
   xmax = 2^(emax+1.5);
else
   set(gca,'xscale','linear')
   xmin = 0;
   xmax = 2^(emax+1);
end
axis([xmin xmax -1 1])

% Set tick marks

fmin = min(F);
fmax = max(F);
xtick = 1;
xticklab = {'1'};
if fmin < 1
   xtick = [1/2 xtick];
   xticklab = ['1/2' xticklab];
end
if logscale & (fmin < 1/4)
   xtick = [1/4 xtick];
   xticklab = ['1/4' xticklab];
end
if fmin < 1/2
   xtick = [fmin xtick];
   xticklab = [['1/' int2str(1/fmin)] xticklab];
end
if 2 < fmax
   xtick = [xtick 2];
   xticklab = [xticklab '2'];
end
if 4 < fmax
   xtick = [xtick 4];
   xticklab = [xticklab '4'];
end
if max(xtick) < fmax
   xtick = [xtick fmax];
   if fmax == round(fmax)
      fmaxlab = int2str(fmax);
   else
      over = 2^(emax+1);
      fmaxlab = [int2str(over) '-1/' int2str(1/(over-fmax))];
   end
   xticklab = [xticklab fmaxlab];
end
set(gca,'xtick',xtick,'xticklabel',xticklab,'xminortick','off','ytick',[])

% Create uicontrols

uicontrol('style','slider','tag','emin','value',emin, ...
   'min',-8,'max',0,...
   'pos',[0.15 0.26 0.13 0.07],'sliderstep',[1/8 1/8], ...
   'callback','floatgui(1)');
uicontrol('style','slider','tag','t','value',t, ...
   'min',0,'max',8,...
   'pos',[0.435 0.26 0.13 0.07],'sliderstep',[1/8 1/8], ...
   'callback','floatgui(1)');
uicontrol('style','slider','tag','emax','value',emax, ...
   'min',0,'max',8,...
   'pos',[0.72 0.26 0.13 0.07],'sliderstep',[1/8 1/8], ...
   'callback','floatgui(1)');
uicontrol('style','text','string',['emin = ' int2str(emin)], ...
   'pos',[0.15 0.35 0.13 0.07],'fontunits','normalized','fontsize',0.7)
uicontrol('style','text','string',['t = ' int2str(t)], ...
   'pos',[0.435 0.35 0.13 0.07],'fontunits','normalized','fontsize',0.7)
uicontrol('style','text','string',['emax = ' int2str(emax)], ...
   'pos',[0.72 0.35 0.13 0.07],'fontunits','normalized','fontsize',0.7)
uicontrol('style','check','string','log scale','value',logscale, ...
   'pos',[0.435 0.15 0.13 0.07],'fontunits','normalized','fontsize',0.7, ...
   'callback','floatgui(1)');
uicontrol('style','push','pos',[0.88 0.1 0.07 0.07], ...
   'fontunits','normalized','fontsize',0.7, ...
   'string','close','callback','close(gcf)')

% eps

if fmax > 1
   eps = 2^(-t);
   text(1,0,'|','color','r','fontunits','normalized','fontsize',0.3)
   text(1+eps,0,'|','color','r','fontunits','normalized','fontsize',0.3)
   if eps < 1
      text(1.0,1.5,['eps = 1/' int2str(1/eps)], ...
      'fontunits','normalized','fontsize',0.3,'fontweight','bold')
   else
      text(1.0,1.5,'eps = 1', 'fontunits','normalized','fontsize',0.3,'fontweight','bold')
   end
end

% Number of numbers

% Exercise:
% How many "floating point" numbers are in the set?
% Complete this statement.
% text(.9*xmax,2,num2str(???)