precision_scheme.rb

# Make sure to first bundle install gem 'terminal-table' 

require 'terminal-table'

MAX_EXP = 16

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_num(mantis_bits,available_bits) > 10**(MAX_EXP+1) &&  
  max_num(mantis_bits+1,available_bits) < 10**(MAX_EXP+1)
end

def calculate_scheme
  max_supported_number = 10**MAX_EXP
  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..10).each do |total_bytes|
      total_bits = 8*total_bytes
      available_bits = total_bits - 2
      break_condition = 2**available_bits > 10**MAX_EXP
      byte_flag_bits = (break_condition ? 2 : 3)
      available_bits = total_bits - byte_flag_bits
      until threshold_mantis?(mantis_bits,available_bits) do
        break if mantis_bits == available_bits -1 
        mantis_bits +=1 
      end			
      mantis_bits = ((total_bytes==1 || break_condition) ? available_bits : mantis_bits)
      exponent_bits = ((total_bytes==1 || break_condition) ? 0 : 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]
      break if break_condition
    end		
  end
  puts table
end

calculate_scheme