Parsing numbers in FParsec - f#

Question

I've started learning FParsec. It has a very flexible way to parse numbers; I can provide a set of number formats I want to use:
type Number =
| Numeral of int
| Decimal of float
| Hexadecimal of int
| Binary of int
let numberFormat = NumberLiteralOptions.AllowFraction
||| NumberLiteralOptions.AllowHexadecimal
||| NumberLiteralOptions.AllowBinary
let pnumber =
numberLiteral numberFormat "number"
|>> fun num -> if num.IsHexadecimal then Hexadecimal (int num.String)
elif num.IsBinary then Binary (int num.String)
elif num.IsInteger then Numeral (int num.String)
else Decimal (float num.String)
However, the language I'm trying to parse is a bit strange. A number could be numeral (non-negative int), decimal (non-negative float), hexadecimal (with prefix #x) or binary (with prefix #b):
numeral: 0, 2
decimal: 0.2, 2.0
hexadecimal: #xA04, #x611ff
binary: #b100, #b001
Right now I have to do parsing twice by substituting # by 0 (if necessary) to make use of pnumber:
let number: Parser<_, unit> =
let isDotOrDigit c = isDigit c || c = '.'
let numOrDec = many1Satisfy2 isDigit isDotOrDigit
let hexOrBin = skipChar '#' >>. manyChars (letter <|> digit) |>> sprintf "0%s"
let str = spaces >>. numOrDec <|> hexOrBin
str |>> fun s -> match run pnumber s with
| Success(result, _, _) -> result
| Failure(errorMsg, _, _) -> failwith errorMsg
What is a better way of parsing in this case? Or how can I alter FParsec's CharStream to be able to make conditional parsing easier?

Answer 1

Parsing numbers can be pretty messy if you want to generate good error messages and properly check for overflows.
The following is a simple FParsec implementation of your number parser:
let numeralOrDecimal : Parser<_, unit> =
// note: doesn't parse a float exponent suffix
numberLiteral NumberLiteralOptions.AllowFraction "number"
|>> fun num ->
// raises an exception on overflow
if num.IsInteger then Numeral(int num.String)
else Decimal(float num.String)
let hexNumber =
pstring "#x" >>. many1SatisfyL isHex "hex digit"
|>> fun hexStr ->
// raises an exception on overflow
Hexadecimal(System.Convert.ToInt32(hexStr, 16))
let binaryNumber =
pstring "#b" >>. many1SatisfyL (fun c -> c = '0' || c = '1') "binary digit"
|>> fun hexStr ->
// raises an exception on overflow
Binary(System.Convert.ToInt32(hexStr, 2))
let number =
choiceL [numeralOrDecimal
hexNumber
binaryNumber]
"number literal"
Generating good error messages on overflows would complicate this implementation a bit, as you would ideally also need to backtrack after the error, so that the error position ends up at the start of the number literal (see the numberLiteral docs for an example).
A simple way to gracefully handle possible overflow exception is to use a little exception handling combinator like the following:
let mayThrow (p: Parser<'t,'u>) : Parser<'t,'u> =
fun stream ->
let state = stream.State
try
p stream
with e -> // catching all exceptions is somewhat dangerous
stream.BacktrackTo(state)
Reply(FatalError, messageError e.Message)
You could then write
let number = mayThrow (choiceL [...] "number literal")
I'm not sure what you meant to say with "alter FParsec's CharStream to be able to make conditional parsing easier", but the following sample demonstrates how you could write a low-level implementation that only uses the CharStream methods directly.
type NumberStyles = System.Globalization.NumberStyles
let invariantCulture = System.Globalization.CultureInfo.InvariantCulture
let number: Parser<Number, unit> =
let expectedNumber = expected "number"
let inline isBinary c = c = '0' || c = '1'
let inline hex2int c = (int c &&& 15) + (int c >>> 6)*9
let hexStringToInt (str: string) = // does no argument or overflow checking
let mutable n = 0
for c in str do
n <- n*16 + hex2int c
n
let binStringToInt (str: string) = // does no argument or overflow checking
let mutable n = 0
for c in str do
n <- n*2 + (int c - int '0')
n
let findIndexOfFirstNonNull (str: string) =
let mutable i = 0
while i < str.Length && str.[i] = '0' do
i <- i + 1
i
let isHexFun = id isHex // tricks the compiler into caching the function object
let isDigitFun = id isDigit
let isBinaryFun = id isBinary
fun stream ->
let start = stream.IndexToken
let cs = stream.Peek2()
match cs.Char0, cs.Char1 with
| '#', 'x' ->
stream.Skip(2)
let str = stream.ReadCharsOrNewlinesWhile(isHexFun, false)
if str.Length <> 0 then
let i = findIndexOfFirstNonNull str
let length = str.Length - i
if length < 8 || (length = 8 && str.[i] <= '7') then
Reply(Hexadecimal(hexStringToInt str))
else
stream.Seek(start)
Reply(Error, messageError "hex number literal is too large for 32-bit int")
else
Reply(Error, expected "hex digit")
| '#', 'b' ->
stream.Skip(2)
let str = stream.ReadCharsOrNewlinesWhile(isBinaryFun, false)
if str.Length <> 0 then
let i = findIndexOfFirstNonNull str
let length = str.Length - i
if length < 32 then
Reply(Binary(binStringToInt str))
else
stream.Seek(start)
Reply(Error, messageError "binary number literal is too large for 32-bit int")
else
Reply(Error, expected "binary digit")
| c, _ ->
if not (isDigit c) then Reply(Error, expectedNumber)
else
stream.SkipCharsOrNewlinesWhile(isDigitFun) |> ignore
if stream.Skip('.') then
let n2 = stream.SkipCharsOrNewlinesWhile(isDigitFun)
if n2 <> 0 then
// we don't parse any exponent, as in the other example
let mutable result = 0.
if System.Double.TryParse(stream.ReadFrom(start),
NumberStyles.AllowDecimalPoint,
invariantCulture,
&result)
then Reply(Decimal(result))
else
stream.Seek(start)
Reply(Error, messageError "decimal literal is larger than System.Double.MaxValue")
else
Reply(Error, expected "digit")
else
let decimalString = stream.ReadFrom(start)
let mutable result = 0
if System.Int32.TryParse(stream.ReadFrom(start),
NumberStyles.None,
invariantCulture,
&result)
then Reply(Numeral(result))
else
stream.Seek(start)
Reply(Error, messageError "decimal number literal is too large for 32-bit int")
While this implementation parses hex and binary numbers without the help of system methods, it eventually delegates the parsing of decimal numbers to the Int32.TryParse and Double.TryParse methods.
As I said: it's messy.