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# sjs

## geeky ramblings

## Floating point in ElSchemo 0

Posted by sjs
on Sunday, June 24

### Parsing floating point numbers

The first task is extending the `LispVal` type to grok floats.

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    type LispInt = Integer
    type LispFloat = Float

    -- numeric data types
    data LispNum = Integer LispInt
                 | Float LispFloat

    -- data types
    data LispVal = Atom String
                 | List [LispVal]
                 | DottedList [LispVal] LispVal
                 | Number LispNum
                 | Char Char
                 | String String
                 | ...

The reason for using the new `LispNum` type and not just throwing a new `Float Float` constructor in there is so that functions can accept and operate on parameters of any supported numeric type. First the floating point numbers need to be parsed. For now I only parse floating point numbers in decimal because the effort to parse other bases is too great for the benefits gained (none, for me).

ElSchemo now parses negative numbers so I’ll start with 2 helper functions that are used when parsing both integers and floats:

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    parseSign :: Parser Char
    parseSign = do try (char '-')
               <|> do optional (char '+')
                      return '+'

    applySign :: Char -> LispNum -> LispNum
    applySign sign n = if sign == '-' then negate n else n

`parseSign` is straightforward as it follows the convention that a literal number is positive unless explicitly marked as negative with a leading minus sign. A leading plus sign is allowed but not required.

`applySign` takes a sign character and a `LispNum` and negates it if necessary, returning a `LispNum`.

Armed with these 2 functions we can now parse floating point numbers in decimal. Conforming to R5RS an optional `#d` prefix is allowed.

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    parseFloat :: Parser LispVal
    parseFloat = do optional (string "#d")
                    sign <- parseSign
                    whole <- many1 digit
                    char '.'
                    fract <- many1 digit
                    return . Number $ applySign sign (makeFloat whole fract)
        where makeFloat whole fract = Float . fst . head . readFloat $ whole ++ "." ++ fract

The first 6 lines should be clear. Line 7 simply applies the parsed sign to the parsed number and returns it, delegating most of the work to `makeFloat`. `makeFloat` in turn delegates the work to the `readFloat` library function, extracts the result and constructs a `LispNum` for it.

The last step for parsing is to modify `parseExpr` to try and parse floats.

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    -- Integers, floats, characters and atoms can all start with a # so wrap those with try.
    -- (Left factor the grammar in the future)
    parseExpr :: Parser LispVal
    parseExpr = (try parseFloat)
            <|> (try parseInteger)
            <|> (try parseChar)
            <|> parseAtom
            <|> parseString
            <|> parseQuoted
            <|> do char '('
                   x <- (try parseList) <|> parseDottedList
                   char ')'
                   return x
            <|> parseComment

### Displaying the floats

That’s it for parsing, now let’s provide a way to display these suckers. `LispVal` is an instance of show, where `show` = `showVal` so `showVal` is our first stop. Remembering that `LispVal` now has a single `Number` constructor we modify it accordingly:

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    showVal (Number n) = showNum n

    showNum :: LispNum -> String
    showNum (Integer contents) = show contents
    showNum (Float contents) = show contents

    instance Show LispNum where show = showNum

One last, and certainly not least, step is to modify `eval` so that numbers evaluate to themselves.

    eval env val@(Number _) = return val

There’s a little more housekeeping to be done such as fixing `integer?`, `number?`, implementing `float?` but I will leave those as an exercise to the reader, or just wait until I share the full code. As it stands now floating point numbers can be parsed and displayed. If you fire up the interpreter and type `2.5` or `-10.88` they will be understood. Now try adding them:

    (+ 2.5 1.1)
    Invalid type: expected integer, found 2.5

Oops, we don’t know how to operate on floats yet!

### Operating on floats

Parsing was the easy part. Operating on the new floats is not necessarily difficult, but it was more work than I realized it would be. I don’t claim that this is the best or the only way to operate on any `LispNum`, it’s just the way I did it and it seems to work. There’s a bunch of boilerplate necessary to make `LispNum` an instance of the required classes, Eq, Num, Real, and Ord. I don’t think I have done this properly but for now it works. What is clearly necessary is the code that operates on different types of numbers. I think I’ve specified sane semantics for coercion. This will be very handy shortly.

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    lispNumEq :: LispNum -> LispNum -> Bool
    lispNumEq (Integer arg1) (Integer arg2) = arg1 == arg2
    lispNumEq (Integer arg1) (Float arg2) = (fromInteger arg1) == arg2
    lispNumEq (Float arg1) (Float arg2) = arg1 == arg2
    lispNumEq (Float arg1) (Integer arg2) = arg1 == (fromInteger arg2)

    instance Eq LispNum where (==) = lispNumEq

    lispNumPlus :: LispNum -> LispNum -> LispNum
    lispNumPlus (Integer x) (Integer y) = Integer $ x + y
    lispNumPlus (Integer x) (Float y)   = Float $ (fromInteger x) + y
    lispNumPlus (Float x)   (Float y)   = Float $ x + y
    lispNumPlus (Float x)   (Integer y) = Float $ x + (fromInteger y)

    lispNumMinus :: LispNum -> LispNum -> LispNum
    lispNumMinus (Integer x) (Integer y) = Integer $ x - y
    lispNumMinus (Integer x) (Float y)   = Float $ (fromInteger x) - y
    lispNumMinus (Float x)   (Float y)   = Float $ x - y
    lispNumMinus (Float x)   (Integer y) = Float $ x - (fromInteger y)

    lispNumMult :: LispNum -> LispNum -> LispNum
    lispNumMult (Integer x) (Integer y) = Integer $ x * y
    lispNumMult (Integer x) (Float y)   = Float $ (fromInteger x) * y
    lispNumMult (Float x)   (Float y)   = Float $ x * y
    lispNumMult (Float x)   (Integer y) = Float $ x * (fromInteger y)

    lispNumDiv :: LispNum -> LispNum -> LispNum
    lispNumDiv (Integer x) (Integer y) = Integer $ x `div` y
    lispNumDiv (Integer x) (Float y)   = Float $ (fromInteger x) / y
    lispNumDiv (Float x)   (Float y)   = Float $ x / y
    lispNumDiv (Float x)   (Integer y) = Float $ x / (fromInteger y)

    lispNumAbs :: LispNum -> LispNum
    lispNumAbs (Integer x) = Integer (abs x)
    lispNumAbs (Float x) = Float (abs x)

    lispNumSignum :: LispNum -> LispNum
    lispNumSignum (Integer x) = Integer (signum x)
    lispNumSignum (Float x) = Float (signum x)

    instance Num LispNum where
        (+) = lispNumPlus
        (-) = lispNumMinus
        (*) = lispNumMult
        abs = lispNumAbs
        signum = lispNumSignum
        fromInteger x = Integer x

    lispNumToRational :: LispNum -> Rational
    lispNumToRational (Integer x) = toRational x
    lispNumToRational (Float x) = toRational x

    instance Real LispNum where
        toRational = lispNumToRational

    lispIntQuotRem :: LispInt -> LispInt -> (LispInt, LispInt)
    lispIntQuotRem n d = quotRem n d

    lispIntToInteger :: LispInt -> Integer
    lispIntToInteger x = x

    lispNumLessThanEq :: LispNum -> LispNum -> Bool
    lispNumLessThanEq (Integer x) (Integer y) = x <= y
    lispNumLessThanEq (Integer x) (Float y)   = (fromInteger x) <= y
    lispNumLessThanEq (Float x)   (Integer y) = x <= (fromInteger y)
    lispNumLessThanEq (Float x)   (Float y)   = x <= y

    instance Ord LispNum where (<=) = lispNumLessThanEq

Phew, ok with that out of the way now we can actually extend our operators to work with any type of `LispNum`. Our Scheme operators are defined using the functions `numericBinop` and `numBoolBinop`. First we’ll slightly modify our definition of `primitives`:

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    primitives :: [(String, [LispVal] -> ThrowsError LispVal)]
    primitives = [("+", numericBinop (+)),
                  ("-", subtractOp),
                  ("*", numericBinop (*)),
                  ("/", floatBinop (/)),
                  ("mod", integralBinop mod),
                  ("quotient", integralBinop quot),
                  ("remainder", integralBinop rem),
                  ("=", numBoolBinop (==)),
                  ("<", numBoolBinop (<)),
                  (">", numBoolBinop (>)),
                  ("/=", numBoolBinop (/=)),
                  (">=", numBoolBinop (>=)),
                  ("<=", numBoolBinop (<=)),
                  ...]

Note that `mod`, `quotient`, and `remainder` are only defined for integers and as such use `integralBinop`, while division (/) is only defined for floating point numbers using `floatBinop`. `subtractOp` is different to support unary usage, e.g. `(- 4) => -4`, but it uses `numericBinop` internally when more than 1 argument is given. On to the implementation! First extend `unpackNum` to work with any `LispNum`, and provide separate `unpackInt` and `unpackFloat` functions to handle both kinds of `LispNum`.

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    unpackNum :: LispVal -> ThrowsError LispNum
    unpackNum (Number (Integer n)) = return $ Integer n
    unpackNum (Number (Float n)) = return $ Float n
    unpackNum notNum = throwError $ TypeMismatch "number" notNum

    unpackInt :: LispVal -> ThrowsError Integer
    unpackInt (Number (Integer n)) = return n
    unpackInt (List [n]) = unpackInt n
    unpackInt notInt = throwError $ TypeMismatch "integer" notInt

    unpackFloat :: LispVal -> ThrowsError Float
    unpackFloat (Number (Float f)) = return f
    unpackFloat (Number (Integer f)) = return $ fromInteger f
    unpackFloat (List [f]) = unpackFloat f
    unpackFloat notFloat = throwError $ TypeMismatch "float" notFloat

The initial work of separating integers and floats into the `LispNum` abstraction, and the code I said would be handy shortly, are going to be really handy here. There’s relatively no change in `numericBinop` except for the type signature. `integralBinop` and `floatBinop` are just specific versions of the same function. I’m sure there’s a nice Haskelly way of doing this with less repetition, and I welcome such corrections.

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    numericBinop :: (LispNum -> LispNum -> LispNum) -> [LispVal] -> ThrowsError LispVal
    numericBinop op singleVal@[_] = throwError $ NumArgs 2 singleVal
    numericBinop op params = mapM unpackNum params >>= return . Number . foldl1 op

    integralBinop :: (LispInt -> LispInt -> LispInt) -> [LispVal] -> ThrowsError LispVal
    integralBinop op singleVal@[_] = throwError $ NumArgs 2 singleVal
    integralBinop op params = mapM unpackInt params >>= return . Number . Integer . foldl1 op

    floatBinop :: (LispFloat -> LispFloat -> LispFloat) -> [LispVal] -> ThrowsError LispVal
    floatBinop op singleVal@[_] = throwError $ NumArgs 2 singleVal
    floatBinop op params = mapM unpackFloat params >>= return . Number . Float . foldl1 op

    subtractOp :: [LispVal] -> ThrowsError LispVal
    subtractOp num@[_] = unpackNum (head num) >>= return . Number . negate
    subtractOp params = numericBinop (-) params

    numBoolBinop :: (LispNum -> LispNum -> Bool) -> [LispVal] -> ThrowsError LispVal
    numBoolBinop op params = boolBinop unpackNum op params

That was a bit of work but now ElSchemo supports floating point numbers, and if you’re following along then your Scheme might too if I haven’t missed any important details!

Next time I’ll go over some of the special forms I have added, including short-circuiting `and` and `or` forms and the full repetoire of `let`, `let*`, and `letrec`. Stay tuned!

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