precision.rb

require 'terminal-table'

def max_num(mantis_bits,available_bits)
	mantis(mantis_bits)*(10**exponent(mantis_bits,available_bits))
end

def mantis(mantis_bits)
	2**mantis_bits
end

def exponent(mantis_bits,available_bits)
	2**(available_bits-mantis_bits)
end

def threshold_mantis?(mantis_bits,available_bits, max_supported_number)
	 max_num(mantis_bits,available_bits) > 10**(max_supported_number.to_s.length) &&  
	 max_num(mantis_bits+1,available_bits) < 10**(max_supported_number.to_s.length)
end

def calculate_table(max_supported_number, max_bytes)
	table = Terminal::Table.new do |t|
		t.title = "Encoding for maximum #{max_supported_number.to_s.reverse.gsub(/...(?=.)/,'\&,').reverse} Units"		
		t << ['Flag (bits)','Significant Digits','Mantis (bits)','Exponent (bits)','Bits','Bytes']
		t.add_separator
		mantis_bits = 0
		(1..max_bytes).each do |total_bytes|
			total_bits = 8*total_bytes
			byte_flag_bits = (total_bytes == max_bytes ? 2 : 3)
			available_bits = total_bits - byte_flag_bits	
			until threshold_mantis?(mantis_bits,available_bits, max_supported_number) do
				break if mantis_bits == available_bits -1
				mantis_bits +=1 
			end
			exponent_bits = ([1,max_bytes].include?(total_bytes) ? 0 : available_bits - mantis_bits)
			mantis_bits = ([1,max_bytes].include?(total_bytes) ? available_bits : mantis_bits)
			significant = total_bytes==1 ? '1-31' : (2**mantis_bits).to_s.size-1
			# minus one because e.g. 2^10 is 1024 which is 4 digits but is smaller than 9999 so with 10 bits we cannot support all 4 digit numbers, only all 3 digit numbers			
			t<<[byte_flag_bits,significant,mantis_bits,exponent_bits, total_bits, total_bytes]
		end		
	end
	puts table
end
MAX_BYTES = 7
MAX_UNITS = 10**16
calculate_table(MAX_UNITS, MAX_BYTES)