Example 14.3. roman2.py

This file is available in py/roman/stage2/ in the examples directory.

If you have not already done so, you can download this and other examples used in this book.

"""Convert to and from Roman numerals"""

#Define exceptions
class RomanError(Exception): pass
class OutOfRangeError(RomanError): pass
class NotIntegerError(RomanError): pass
class InvalidRomanNumeralError(RomanError): pass

#Define digit mapping
romanNumeralMap = (('M',  1000), 
                   ('CM', 900),
                   ('D',  500),
                   ('CD', 400),
                   ('C',  100),
                   ('XC', 90),
                   ('L',  50),
                   ('XL', 40),
                   ('X',  10),
                   ('IX', 9),
                   ('V',  5),
                   ('IV', 4),
                   ('I',  1))

def toRoman(n):
    """convert integer to Roman numeral"""
    result = ""
    for numeral, integer in romanNumeralMap:
        while n >= integer:      
            result += numeral
            n -= integer
    return result

def fromRoman(s):
    """convert Roman numeral to integer"""
    pass

romanNumeralMap is a tuple of tuples which defines three things: The character representations of the most basic Roman numerals. Note that this is not just the single-character Roman numerals; you're also defining two-character pairs like CM (“one hundred less than one thousand”); this will make the toRoman code simpler later. The order of the Roman numerals. They are listed in descending value order, from M all the way down to I. The value of each Roman numeral. Each inner tuple is a pair of (numeral, value).

Here's where your rich data structure pays off, because you don't need any special logic to handle the subtraction rule. To convert to Roman numerals, you simply iterate through romanNumeralMap looking for the largest integer value less than or equal to the input. Once found, you add the Roman numeral representation to the end of the output, subtract the corresponding integer value from the input, lather, rinse, repeat.

Example 14.4. How toRoman works

If you're not clear how toRoman works, add a print statement to the end of the while loop:

        while n >= integer:
            result += numeral
            n -= integer
            print 'subtracting', integer, 'from input, adding', numeral, 'to output'

>>> import roman2
>>> roman2.toRoman(1424)
subtracting 1000 from input, adding M to output
subtracting 400 from input, adding CD to output
subtracting 10 from input, adding X to output
subtracting 10 from input, adding X to output
subtracting 4 from input, adding IV to output
'MCDXXIV'

Example 14.5. Output of romantest2.py against roman2.py

Remember to run romantest2.py with the -v command-line flag to enable verbose mode.

fromRoman should only accept uppercase input ... FAIL
toRoman should always return uppercase ... ok                  
fromRoman should fail with malformed antecedents ... FAIL
fromRoman should fail with repeated pairs of numerals ... FAIL
fromRoman should fail with too many repeated numerals ... FAIL
fromRoman should give known result with known input ... FAIL
toRoman should give known result with known input ... ok       
fromRoman(toRoman(n))==n for all n ... FAIL
toRoman should fail with non-integer input ... FAIL            
toRoman should fail with negative input ... FAIL
toRoman should fail with large input ... FAIL
toRoman should fail with 0 input ... FAIL

	toRoman does, in fact, always return uppercase, because romanNumeralMap defines the Roman numeral representations as uppercase. So this test passes already.
	Here's the big news: this version of the toRoman function passes the known values test. Remember, it's not comprehensive, but it does put the function through its paces with a variety of good inputs, including inputs that produce every single-character Roman numeral, the largest possible input (3999), and the input that produces the longest possible Roman numeral (3888). At this point, you can be reasonably confident that the function works for any good input value you could throw at it.
	However, the function does not “work” for bad values; it fails every single bad input test. That makes sense, because you didn't include any checks for bad input. Those test cases look for specific exceptions to be raised (via assertRaises), and you're never raising them. You'll do that in the next stage.

Here's the rest of the output of the unit test, listing the details of all the failures. You're down to 10.

======================================================================
FAIL: fromRoman should only accept uppercase input
----------------------------------------------------------------------
Traceback (most recent call last):
  File "C:\docbook\dip\py\roman\stage2\romantest2.py", line 156, in testFromRomanCase
    roman2.fromRoman, numeral.lower())
  File "c:\python21\lib\unittest.py", line 266, in failUnlessRaises
    raise self.failureException, excName
AssertionError: InvalidRomanNumeralError
======================================================================
FAIL: fromRoman should fail with malformed antecedents
----------------------------------------------------------------------
Traceback (most recent call last):
  File "C:\docbook\dip\py\roman\stage2\romantest2.py", line 133, in testMalformedAntecedent
    self.assertRaises(roman2.InvalidRomanNumeralError, roman2.fromRoman, s)
  File "c:\python21\lib\unittest.py", line 266, in failUnlessRaises
    raise self.failureException, excName
AssertionError: InvalidRomanNumeralError
======================================================================
FAIL: fromRoman should fail with repeated pairs of numerals
----------------------------------------------------------------------
Traceback (most recent call last):
  File "C:\docbook\dip\py\roman\stage2\romantest2.py", line 127, in testRepeatedPairs
    self.assertRaises(roman2.InvalidRomanNumeralError, roman2.fromRoman, s)
  File "c:\python21\lib\unittest.py", line 266, in failUnlessRaises
    raise self.failureException, excName
AssertionError: InvalidRomanNumeralError
======================================================================
FAIL: fromRoman should fail with too many repeated numerals
----------------------------------------------------------------------
Traceback (most recent call last):
  File "C:\docbook\dip\py\roman\stage2\romantest2.py", line 122, in testTooManyRepeatedNumerals
    self.assertRaises(roman2.InvalidRomanNumeralError, roman2.fromRoman, s)
  File "c:\python21\lib\unittest.py", line 266, in failUnlessRaises
    raise self.failureException, excName
AssertionError: InvalidRomanNumeralError
======================================================================
FAIL: fromRoman should give known result with known input
----------------------------------------------------------------------
Traceback (most recent call last):
  File "C:\docbook\dip\py\roman\stage2\romantest2.py", line 99, in testFromRomanKnownValues
    self.assertEqual(integer, result)
  File "c:\python21\lib\unittest.py", line 273, in failUnlessEqual
    raise self.failureException, (msg or '%s != %s' % (first, second))
AssertionError: 1 != None
======================================================================
FAIL: fromRoman(toRoman(n))==n for all n
----------------------------------------------------------------------
Traceback (most recent call last):
  File "C:\docbook\dip\py\roman\stage2\romantest2.py", line 141, in testSanity
    self.assertEqual(integer, result)
  File "c:\python21\lib\unittest.py", line 273, in failUnlessEqual
    raise self.failureException, (msg or '%s != %s' % (first, second))
AssertionError: 1 != None
======================================================================
FAIL: toRoman should fail with non-integer input
----------------------------------------------------------------------
Traceback (most recent call last):
  File "C:\docbook\dip\py\roman\stage2\romantest2.py", line 116, in testNonInteger
    self.assertRaises(roman2.NotIntegerError, roman2.toRoman, 0.5)
  File "c:\python21\lib\unittest.py", line 266, in failUnlessRaises
    raise self.failureException, excName
AssertionError: NotIntegerError
======================================================================
FAIL: toRoman should fail with negative input
----------------------------------------------------------------------
Traceback (most recent call last):
  File "C:\docbook\dip\py\roman\stage2\romantest2.py", line 112, in testNegative
    self.assertRaises(roman2.OutOfRangeError, roman2.toRoman, -1)
  File "c:\python21\lib\unittest.py", line 266, in failUnlessRaises
    raise self.failureException, excName
AssertionError: OutOfRangeError
======================================================================
FAIL: toRoman should fail with large input
----------------------------------------------------------------------
Traceback (most recent call last):
  File "C:\docbook\dip\py\roman\stage2\romantest2.py", line 104, in testTooLarge
    self.assertRaises(roman2.OutOfRangeError, roman2.toRoman, 4000)
  File "c:\python21\lib\unittest.py", line 266, in failUnlessRaises
    raise self.failureException, excName
AssertionError: OutOfRangeError
======================================================================
FAIL: toRoman should fail with 0 input
----------------------------------------------------------------------
Traceback (most recent call last):
  File "C:\docbook\dip\py\roman\stage2\romantest2.py", line 108, in testZero
    self.assertRaises(roman2.OutOfRangeError, roman2.toRoman, 0)
  File "c:\python21\lib\unittest.py", line 266, in failUnlessRaises
    raise self.failureException, excName
AssertionError: OutOfRangeError
----------------------------------------------------------------------
Ran 12 tests in 0.320s

FAILED (failures=10)