ROMAN NUMERAL CONVERSION ROUTINES FOR THE HP48                          15Mar92

The following two routines translate between integers and roman numerals.
The Roman system uses 7 letters to represent different weightings:
     M 1000
     D 500
     C 100
     L 50
     X 10
     V 5
     I 1
These are assembled additively into a string, largest numbers being left
justified:
e.g. "MCL" is 1150
In addition any character may be preceeded by one of the following:
     C 100
     X 10
     I 1
and this is subtracted from the character. So 9 is "IX" and NOT "VIIII"
However "IM" is not allowed for 999. The preceeding character must be
the next least significant of the ones listed above, e.g. "CMXCIX" for 999.
Only one preceeding character is allowed at a time, 8 is NOT "IIX" it should 
be represented by "VIII".

Finally a whole expression can be multiplied by 1000 if a bar covers it.
This aspect is not reproduced in the following programs.


->RN: Takes a number from the stack and returns a string containing the
      roman numeral. The result is "tagged" with the original number from
      the stack. If the stack is empty then a message indicating the
      correct syntax for the routine is returned. If the number has a
      fractional part then the fraction is ignored. If the number is greater
      than 10000 then only the part of the number <10000 is processed, the
      resulting string is preceeded with a "+" to indicate this. This
      prevents the creation of very long roman numerals with dozens of
      preceeding "M"'s, that take ages to process.

RN->: Takes a string from the stack and returns the equivalent integer.
      The result is "tagged" with the original string from the stack. 
      If the stack is empty then a message indicating the correct syntax 
      for the routine is returned. If the string contains characters other
      than "MDCLXVI" then the program fails. The routine will translate all
      legal roman numerals, it will also  translate some non legal ones:
      e.g. "VX" (5) "MIM" (1999), however it will not translate "IIV" 
      correctly.

HP48 ASCII CODE for \->RN.....................................................
%%HP: T(3)A(D)F(.);
\<< DEPTH
  IF THEN IP "MDCLXVI" "CCXXII " { 1000 500  @ Create four lists that
     100 50 10 5 1 } { 100 100 10 10 1 1 0 } @ define the translation
     \-> r rs w ws
    \<< DUP DUP 10000 > 
      IF THEN 10000 MOD "+"                  @ If greater than 10000 then
      ELSE ""                                @ truncate input and add "+"
      END 
      1 r SIZE FOR i                         @ For each character in the
        r i i SUB rs i i SUB w i GET ws i GET@ translation get the weighting
        \-> r1 r2 w1 w2                      @ from the list
        \<<
          WHILE OVER w1 \>=
          REPEAT SWAP w1 - SWAP r1 +         @ subtract weighting as
          END                                @ many times as possible.
          IF OVER w2 + w1 \>=                @ Check if one more can be
          THEN SWAP w1 - w2 + SWAP r2 + r1 + @ subtracted with preceeding
          END                                @ character.
        \>>
      NEXT
    \>> SWAP DROP SWAP \->TAG                @ Tag output with input integer
  ELSE
"INT \-> Roman Numeral $"                    @ Print this string as help
DOERR
  END
\>>

HP48 ASCII CODE for RN\->.....................................................
%%HP: T(3)A(D)F(.);
\<< DEPTH IF
  THEN EVAL DUP SIZE "IVXLCDM" { 1 5 10      @ Create two lists for 
  50 100 500 1000 } \-> s l r w              @ the translation
    \<< { } 
      1 l FOR i                              @ for each character in the input
      s i i SUB r SWAP POS w SWAP GET +      @ build a list of the weights
      NEXT 0 + l \-> v l
      \<< 0 1 l FOR i                        @ For the list of weights
        v i GET DUP v i 1 + GET <            @ subtract if followed by a
          IF THEN - ELSE + END               @ larger number else add
        NEXT s \->TAG                        @ Tag output with input string
      \>>
    \>>
  ELSE
"Roman Numeral $ \-> INT"                    @ Print this string as help
DOERR
  END
\>>