A Roman numeral calculator written in Erlang.
- Adds Roman numeral literals to Erlang!
- Never converts numerals into integers — be assured that your calculations remain in Roman numerals throughout the entire process!
- Absolutely no concept of zero.
- Supports calculations in the range of Ⅰ to ⅯⅯⅯⅭⅯⅩⅭⅨ, inclusive.
Right now, you have to compile it yourself, but you can pop into the
erl console and do the following:
1> c(roman).
{ok,roman}
2> roman:add(ii, ii).
iv
3> roman:add(cdxx, lxix).
cdlxxxix
4> roman:subtract(mmi, mcmlxviii).
xxxiiiI overheard somebody saying that creating a calculator without converting Roman numeral into integers would be painful. They were right.
I chose to implement it in Erlang because I saw the opportunity to fake literals into the language without having to modify the language's parser. Also, pattern matching rules.
It parses atoms as Roman numerals into an internal representation. Calculations are done by incrementing or decrementing numbers one-by-one.
The parser is a "generic" finite state machine. Since the same logic that is used to parse units (Ⅰ) can be reused to parse tens (Ⅹ) and hundreds (Ⅽ), the finite state machine can be parameterized for its symbols for unit (Ⅰ), half (Ⅴ), and next (Ⅹ).
fsm digraph G { rankdir = "LR"; node [shape = doublecircle]; start -> i [label="i"]; start -> v [label="v"]; i -> iv [label = "v"]; i -> ii [label = "i"]; i -> ix [label = "x"]; ii -> iii [label = "i"]; v -> vi [label = "i"]; vi -> ii [label = "i"]; start [shape=point]; ii [label = "ii or vii"]; iii [label = "iii or viii"]; } fsm
Numbers are represented internally as a non-empty list of decimal terms.
Each term in the list is a tuple of {Magnitude, Value}, where
Magnitude can be one of unus (units), decem (tens), centum
(hundreds), and—to a limited extent—mille (thousands). Value is the
literal Roman numeral for that decimal place.
Terms are always ordered from least significant to most significant term. There is no zero value, so terms that would ordinarily be zero in place-value notation are omitted from the list.
Examples:
- Ⅳ =
[{unus, iv}] - ⅩⅩⅦ =
[{unus, vii}, {decem, xx}] - ⅮⅬⅤ =
[{unus, v}, {decem, l}, {centum, d}] - ⅯⅯⅩⅡ =
[{unus, ii}, {decem, xx}, {mille, ii}]
It turns out that Claude Shannon had this idea LVIX years earlier than me.
Claude E. Shannon, "THROBAC I, Bell Laboratories Memorandum, April 9, 1953.," in Claude E. Shannon: Collected Papers, IEEE, 1993, pp.695-698, doi: 10.1109/9780470544242.b ch47.
MIT License.