construct53.rb

def f2(n)
	return n.odd? ? (n * 3 + 1) / 2 : n / 2

end

def dense(w, d)
	w2 = w - 1
	
	a = (0...w2).to_a
	s = '0' * w2
	(1..(d * w - 1)).map { a.delete_at(rand(a.size)) }.each { |x| s[x, 1] = '1' }
	return ('1' + s)
	
end

def seq(n)

	n1 = n
	l = []
	begin
		l << n
		n = f2(n)
	end while (n != 1)
	
	return l
end

def outa(f, l, t = '', c)
#	$stderr.puts([t, c].inspect)
	f.puts('$dat << eof')
	k = l[0].keys
	
	f.puts(k.join("\t"))
	l.each { |x| f.puts(x.values.join("\t")) }

	f.puts('eof')
	f.puts("set colors classic; set title '#{t}'; plot \\")
	
	f.puts("'$dat' using (column('m1')):(column('m2')) lc #{c} pt 5 ps 0.5 title 'm2 vs m1',\\") 
	f.puts
	f.puts("reset; pause -1;")

end

def slope(l)
	n = l.size / 2

	m1 = (l[n].to_f - l[0]) / n
	m2 = (l[-1].to_f - l[n]) / n
	return {'n' => n, 'm1' => m1, 'm2' => m2}
end

def slopes(c)
	l1 = []
	l2 = []
	
	c.times \
	{

		l = seq(dense(100, 0.5).to_i(2))

		l1 << slope(l.map { |x| x.to_s(2).length })
		l2 << slope(l.map { |x| Math.log(x) })
	}
	return l1, l2
end

f = File.open('gnuplot.cmd', 'w')
3.times \
{
	|n|
	c = 50 * 4 ** (n + 1)
	$stderr.puts(c)
	l1, l2 = slopes(c)
	outa(f, l1, "c=#{c} bitwidth", 1)
	outa(f, l2, "c=#{c} log", 2)
}
f.close