TrigTable2.tex

\documentclass{article}

\usepackage[mathbf]{euler}
\usepackage{longtable}
\usepackage{geometry}
\geometry{head=14pt,hmargin=0.5in,vmargin=1.35in}

%% Set up indexing headers and footer for fast lookup while
%% flipping pages.
\usepackage{fancyhdr}
\pagestyle{fancy}
\setlength{\headheight}{14.0pt}
\renewcommand{\headrulewidth}{0pt}
\lhead{\large\mathversion{bold}\firstmark}
\rhead{\large\mathversion{bold}\botmark}

\begin{document}

%% This function is a utility to help the sprintf
%% function keep the number of digits after the decimal
%% place at the right level to come out to 9 digits in total
%% both before and after the decimal point.
{:  def digs(x)
      if ("%0.8f" % x) =~ /[-+]?([0-9]*)\./
        l = 10 - $1.length  #$
        l = (l > 0 ? l : 0)
        return l
      end
      return(0)
    end
:}

\def\tstrut{\rule[-1pt]{0pt}{11pt}}

%% Set up the longtable environment by specifying the header for
%% each page and the footer.
\begin{longtable}[c]{c|llllll}
\hline\hline
\multicolumn{1}{c|}{\mathversion{bold}$x$}&
\multicolumn{1}{c}{\mathversion{bold}$\sin(x)$}&
\multicolumn{1}{c}{\mathversion{bold}$\cos(x)$}&
\multicolumn{1}{c}{\mathversion{bold}$\tan(x)$}&
\multicolumn{1}{c}{\mathversion{bold}$\cot(x)$}&
\multicolumn{1}{c}{\mathversion{bold}$\sec(x)$}&
\multicolumn{1}{c}{\mathversion{bold}$\csc(x)$}\\
\hline\hline
\endhead
\hline\hline
\endfoot

{:
## Set up variables needed for computing the values that go into
## the table, taking care to use ruby's BigDecimal class to ensure
## accuracy.  The table is set up here to go from 0 to pi/2 in
## increments of step.

   require 'bigdecimal'
   require 'dms'
   DMS.precision = 0
   step = DMS.new(0, 0, 30)
   one = BigDecimal("1.0")
   d0 = DMS.new(0)
   d90 = DMS.new(90)
-:}

%% Treat the first line of the table, for an x value of 0 specially
%% by giving exact answers in symbolic form.
{:= "\\multicolumn{1}{c|}{\\tstrut{\\mathversion{bold}\\mark{%s}$0$}}" % d0.to_tex :}&
{:= "\\multicolumn{1}{c}{{$0$}}" :}&
{:= "\\multicolumn{1}{c}{{$1$}}" :}&
{:= "\\multicolumn{1}{c}{{$0$}}" :}&
{:= "\\multicolumn{1}{c}{{$\\infty$}}" :}&
{:= "\\multicolumn{1}{c}{{$1$}}" :}&
{:= "\\multicolumn{1}{c}{{$\\infty$}}" :}\\

%% Here is the loop for the body of the table, which starts with
%% x one step beyond 0 and pre-computes some of the functions
{:   x = d0 + step
     while (x < d90) do
      tanx = x.tan
      cotx = x.cotan
      secx = x.sec
      cscx = x.csc
:}

{:
## Here is where each line of the main body of the table is set.
## We use the digs function defined above to make sure that every
## column has the same number of significant digits for the functions
## that tend toward infinity.
##
## NB: I could write this comment as a LaTeX comment outside a code
## segment, but then it would end up in the generated LaTeX file,
## TrigTable.etx.  Doing so made that file about 6MB in size; by
## putting the comments inside this ruby code block, the size was
## around 2MB.
-:}
\mark{{:= x.to_tex :}}
\tstrut{:= "\\mathversion{bold}#{x.to_tex}" :}&
{:= "$%0.8f$" % x.sin :}&
{:= "$%0.8f$" % x.cos :}&
{:= "$%0.*f$" % [ digs(tanx), tanx ] :}&
{:= "$%0.*f$" % [ digs(cotx), cotx ] :}&
{:= "$%0.*f$" % [ digs(secx), secx ] :}&
{:= "$%0.*f$" % [ digs(cscx), cscx ] :}\\

%% Step and loop
{:
      x += step
    end
:}

%% This causes a LaTeX error, but nonetheless gets the final line of
%% the table squeezed onto the last page instead of on a page by
%% itself.  Uncomment if that's what you want.
%{\enlargethispage{20pt}}

%% Finally, treat the last row of the table for pi/2 specially
%% by giving exact values symbolically.
{:= "\\multicolumn{1}{c|}{\\mark{%s}\\mathversion{bold}%s}" %
 [d90.to_tex, d90.to_tex]  :}&
{:= "\\multicolumn{1}{c}{$1$}" :}&
{:= "\\multicolumn{1}{c}{$0$}" :}&
{:= "\\multicolumn{1}{c}{$\\infty$}" :}&
{:= "\\multicolumn{1}{c}{$0$}" :}&
{:= "\\multicolumn{1}{c}{$\\infty$}" :}&
{:= "\\multicolumn{1}{c}{$1$}" :}\\

%% End the table and document---this version comes to 649 pages!
\end{longtable}
\end{document}

% Take /that/ Charles Babbage!