ikarus/scheme/ikarus.string-to-number.ss

;;; Ikarus Scheme -- A compiler for R6RS Scheme.
;;; Copyright (C) 2008,2009  Abdulaziz Ghuloum
;;; 
;;; This program is free software: you can redistribute it and/or modify
;;; it under the terms of the GNU General Public License version 3 as
;;; published by the Free Software Foundation.
;;; 
;;; This program is distributed in the hope that it will be useful, but
;;; WITHOUT ANY WARRANTY; without even the implied warranty of
;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
;;; General Public License for more details.
;;; 
;;; You should have received a copy of the GNU General Public License
;;; along with this program.  If not, see <http://www.gnu.org/licenses/>.



(library (ikarus.string-to-number)
  (export string->number define-string->number-parser)
  (import (except (ikarus) string->number))

  (define who 'string->number)
  (define (do-sn/ex sn ex ac)
    (* sn (if (eq? ex 'i) (inexact ac) ac)))
  (define (do-dec-sn/ex sn ex ac)
    (* sn (if (eq? ex 'e) ac (inexact ac))))
  (define (digit c r)
    (let ([n (fx- (char->integer c) (char->integer #\0))])
      (cond
        [(and (fx>=? n 0) (fx< n r)) n]
        [(eqv? r 16)
         (let ([n (fx- (char->integer c) (char->integer #\a))])
           (cond
             [(and (fx>=? n 0) (fx< n 6)) (+ n 10)]
             [else
              (let ([n (fx- (char->integer c) (char->integer #\A))])
                (cond
                  [(and (fx>=? n 0) (fx< n 6)) (+ n 10)]
                  [else #f]))]))]
        [else #f])))

  (module (define-parser)
    (define-syntax gen-empty
      (syntax-rules (eof)
        [(_ C Ca) (C EOF-ERROR Ca)]
        [(_ C Ca [(eof) then] . rest) then]
        [(_ C Ca other . rest) (gen-empty C Ca . rest)]))
    (define-syntax gen-delimiter
      (syntax-rules (eof)
        [(_ C Ca c) 
         (C GEN-DELIM-TEST c
            (C FAIL Ca)
            (C FAIL Ca c))]
        [(_ C Ca c [(eof) then] . rest) 
         (C GEN-DELIM-TEST c
             then
             (C FAIL Ca c))]
        [(_ C Ca c other . rest) (gen-delimiter C Ca c . rest)]))
    (define-syntax gen-char
      (syntax-rules (eof =>)
        [(_ C Ca c dc) dc]
        [(_ C Ca c dc [(eof) then] . rest)
         (gen-char C Ca c dc . rest)]
        [(_ C Ca c dc [(test . args) => result then] . rest)
         (cond
           [(test c . args) => 
            (lambda (result) then)]
           [else (gen-char C Ca c dc . rest)])]
        [(_ C Ca c dc [ls then] . rest)
         (if (memv c 'ls)
             then
             (gen-char C Ca c dc . rest))]))
    (define-syntax gen-clause
      (syntax-rules ()
        [(_ (Ca ...) C next fail name (arg* ...) (clause* ...))
         (define (name Ca ... arg* ...)
           (C GEN-TEST c next fail (Ca ...)
              (gen-empty C (Ca ...) clause* ...)
              (gen-char C (Ca ...) c 
                  (gen-delimiter C (Ca ...) c clause* ...)
                  clause* ...)))]))
    (define-syntax define-parser^
      (lambda (x)
        (define (lookup ls1 ls2)
          (lambda (var)
            (let f ([ls1 ls1] [ls2 ls2])
              (cond
                [(null? ls1) 
                 (error 'define-parser "cannot find" var)]
                [(bound-identifier=? var (car ls1))
                 (car ls2)]
                [else (f (cdr ls1) (cdr ls2))]))))
        (syntax-case x ()
          [(_ (entries ...) config next fail
             orig*
             [name* (arg** ...) clause** ...] ...)
           (with-syntax ([(mapped-entries ...)
                          (map 
                            (lookup
                              (syntax->datum #'orig*)
                              #'(name* ...))
                            #'(entries ...))])
             #'(begin
                 (config GEN-ARGS 
                    gen-clause config next fail name* 
                    (arg** ...)
                    (clause** ...))
                 ...
                 (define entries mapped-entries)
                 ...))])))
    (define-syntax define-parser
      (lambda (x)
        (syntax-case x ()
          [(_ definer next fail [name* (arg** ...) clause** ...] ...)
           (with-syntax ([orig* (datum->syntax #'foo #'(name* ...))])
             #'(define-syntax definer
                 (syntax-rules ()
                   [(_ config (entries (... ...)))
                    (define-parser^ (entries (... ...)) config next fail
                      orig*
                      [name* (arg** ...) clause** ...] ...)])))]))))



  (define-parser define-string->number-parser next fail

    (ratio+ (r ex sn num ac)
      [(eof)
       (if (= ac 0)
           (fail)
           (do-sn/ex sn ex (/ num ac)))]
      [(digit r) => d
       (next ratio+ r ex sn num (+ (* ac r) d))]
      [(#\+)
       (if (= ac 0)
           (fail)
           (let ([real (do-sn/ex sn ex (/ num ac))])
             (next im:sign r real ex +1)))]
      [(#\-)
       (if (= ac 0)
           (fail)
           (let ([real (do-sn/ex sn ex (/ num ac))])
             (next im:sign r real ex -1)))]
      [(#\@)
       (if (= ac 0)
           (fail)
           (let ([mag (do-sn/ex sn ex (/ num ac))])
             (next polar r mag ex)))]
      [(#\i)
       (if (= ac 0)
           (fail)
           (next im:done
             (make-rectangular 0 (do-sn/ex sn ex (/ num ac)))))])

    (im:ratio+ (r real ex sn num ac)
      [(digit r) => d
       (next im:ratio+ r real ex sn num (+ (* ac r) d))]
      [(#\i) 
       (if (= ac 0)
           (fail)
           (next im:done 
             (make-rectangular real (do-sn/ex sn ex (/ num ac)))))])

    (im:done (n)
      [(eof) n])

    (ratio (r ex sn num)
      [(digit r) => d
       (next ratio+ r ex sn num d)])

    (im:ratio (r real ex sn num)
      [(digit r) => d
       (next im:ratio+ r real ex sn num d)])

    (exponent+digit (r ex sn ac exp1 exp2 exp-sign)
      [(eof)
       (do-dec-sn/ex sn ex (* ac (expt 10 (+ exp1 (* exp2 exp-sign)))))]
      [(#\+) 
       (let ([real (do-dec-sn/ex sn ex (* ac (expt 10 (+ exp1 (* exp2 exp-sign)))))])
         (next im:sign r real ex +1))]
      [(#\-) 
       (let ([real (do-dec-sn/ex sn ex (* ac (expt 10 (+ exp1 (* exp2 exp-sign)))))])
         (next im:sign r real ex -1))]

      [(#\@) 
       (let ([mag (do-dec-sn/ex sn ex (* ac (expt 10 (+ exp1 (* exp2 exp-sign)))))])
         (next polar r mag ex))]
      [(digit r) => d
       (next exponent+digit r ex sn ac exp1 (+ (* exp2 r) d) exp-sign)]
      [(#\i) 
       (let ([n (do-dec-sn/ex sn ex 
                  (* ac (expt 10 (+ exp1 (* exp2 exp-sign)))))])
         (next im:done (make-rectangular 0 n)))])

    (polar (r mag ex)
      [(digit r) => d 
       (next polar+digit r mag ex d 1)]
      [(#\.) 
       (if (= r 10)
           (next polar+dot r mag ex +1)
           (fail))])
    
    (polar+dot (r mag ex sn)
      [(digit r) => d 
       (next polar+digit+dot r mag ex d sn -1)])

    (polar+digit (r mag ex ang sn)
      [(eof) (make-polar mag (* ang sn))]
      [(digit r) => d 
       (next polar+digit r mag ex (+ (* r ang) d) sn)]
      [(#\.) 
       (if (= r 10)
           (next polar+digit+dot r mag ex ang sn 0)
           (fail))])

    (polar+digit+dot (r mag ex ang sn exp)
      [(eof) 
       (let ([ang (* ang sn (expt 10 exp))])
         (make-polar mag ang))]
      [(digit r) => d
       (next polar+digit+dot r mag ex (+ (* r ang) d) sn (- exp 1))])

    (im:exponent+digit (r real ex sn ac exp1 exp2 exp-sign)
      [(digit r) => d
       (next im:exponent+digit r real ex sn ac exp1 (+ (* exp2 r) d) exp-sign)]
      [(#\i)
       (let ([imag (do-dec-sn/ex sn ex
                     (* ac (expt 10 (+ exp1 (* exp2 exp-sign)))))])
         (next im:done (make-rectangular real imag)))])

    (exponent+sign (r ex sn ac exp1 exp-sign)
      [(digit r) => d
       (next exponent+digit r ex sn ac exp1 d exp-sign)])

    (im:exponent+sign (r real ex sn ac exp1 exp-sign)
      [(digit r) => d
       (next im:exponent+digit r real ex sn ac exp1 d exp-sign)])

    (exponent (r ex sn ac exp1)
      [(digit r) => d
       (next exponent+digit r ex sn ac exp1 d +1)]
      [(#\+) (next exponent+sign r ex sn ac exp1 +1)]
      [(#\-) (next exponent+sign r ex sn ac exp1 -1)])

    (im:exponent (r real ex sn ac exp1)
      [(digit r) => d
       (next im:exponent+digit r real ex sn ac exp1 d +1)]
      [(#\+) (next im:exponent+sign r real ex sn ac exp1 +1)]
      [(#\-) (next im:exponent+sign r real ex sn ac exp1 -1)])

    (digit+dot (r ex sn ac exp)
      [(eof)
       (do-dec-sn/ex sn ex (* ac (expt 10 exp)))]
      [(digit r) => d
       (next digit+dot r ex sn (+ (* ac r) d) (- exp 1))]
      [(#\+)
       (let ([real (do-dec-sn/ex sn ex (* ac (expt 10 exp)))])
         (next im:sign r real ex +1))]
      [(#\-)
       (let ([real (do-dec-sn/ex sn ex (* ac (expt 10 exp)))])
         (next im:sign r real ex -1))]
      [(#\@)
       (let ([mag (do-dec-sn/ex sn ex (* ac (expt 10 exp)))])
         (next polar r mag ex))]
      [(#\i)
       (let ([real (do-dec-sn/ex sn ex (* ac (expt 10 exp)))])
         (next im:done (make-rectangular 0.0 real)))]
      [(#\e #\E #\s #\S #\f #\F #\d #\D #\l #\L)
       (if (fx=? r 10)
           (next exponent r ex sn ac exp)
           (fail))])

    (im:digit+dot (r real ex sn ac exp)
      [(eof)
       (do-dec-sn/ex sn ex (* ac (expt 10 exp)))]
      [(digit r) => d
       (next im:digit+dot r real ex sn (+ (* ac r) d) (- exp 1))]
      [(#\i)
       (let ([imag (do-dec-sn/ex sn ex (* ac (expt 10 exp)))])
         (next im:done (make-rectangular real imag)))]
      [(#\e #\E #\s #\S #\f #\F #\d #\D #\l #\L)
       (next im:exponent r real ex sn ac exp)])

    (digit+ (r ex sn ac)
      [(eof) (do-sn/ex sn ex ac)]
      [(digit r) => d
       (next digit+ r ex sn (+ (* ac r) d))]
      [(#\/) (next ratio r ex sn ac)]
      [(#\.)
       (if (fx=? r 10) 
           (next digit+dot r ex sn ac 0)
           (fail))]
      [(#\+)
       (let ([real (do-sn/ex sn ex ac)])
         (next im:sign r real ex +1))]
      [(#\-)
       (let ([real (do-sn/ex sn ex ac)])
         (next im:sign r real ex -1))]
      [(#\@)
       (let ([mag (do-sn/ex sn ex ac)])
         (next polar r mag ex))]
      [(#\i)
       (next im:done (make-rectangular 0 (do-sn/ex sn ex ac)))]
      [(#\e #\E #\s #\S #\f #\F #\d #\D #\l #\L)
       (if (fx=? r 10) 
           (next exponent r ex sn ac 0)
           (fail))])

    (im:digit+ (r real ex sn ac)
      [(digit r) => d
       (next im:digit+ r real ex sn (+ (* ac r) d))]
      [(#\.)
       (if (fx=? r 10)
           (next im:digit+dot r real ex sn ac 0)
           (fail))]
      [(#\/)
       (next im:ratio r real ex sn ac)]
      [(#\i)
       (next im:done (make-rectangular real (do-sn/ex sn ex ac)))]
      [(#\e #\E #\s #\S #\f #\F #\d #\D #\l #\L)
       (if (fx=? r 10)
           (next im:exponent r real ex sn ac 0)
           (fail))])

    (sign-i (r ex sn)
      [(eof)
       (make-rectangular 
         (if (eq? ex 'i) 0.0 0)
         sn)]
      [(#\n) (next sign-in r ex sn)])
    (sign-in (r ex sn)
      [(#\f) (next sign-inf r ex sn)])
    (sign-inf (r ex sn)
      [(#\.) (next sign-inf. r ex sn)])
    (sign-inf. (r ex sn)
      [(#\0) (next sign-inf.0 r ex sn)])
    (sign-inf.0 (r ex sn)
      [(eof) (* sn +inf.0)]
      [(#\+) (next im:sign r (* sn +inf.0) ex +1)]
      [(#\-) (next im:sign r (* sn +inf.0) ex -1)]
      [(#\@) (next polar r (* sn +inf.0) ex)]
      [(#\i) 
       (next im:done (make-rectangular 0.0 (* sn +inf.0)))])

    (im:sign-i (real ex sn)
      [(eof) (make-rectangular real (do-sn/ex sn ex 1))]
      [(#\n) (next im:sign-in (make-rectangular real (* sn +inf.0)))])
    (im:sign-in (n)
      [(#\f) (next im:sign-inf n)])
    (im:sign-inf (n)
      [(#\.) (next im:sign-inf. n)])
    (im:sign-inf. (n)
      [(#\0) (next im:sign-inf.0 n)])
    (im:sign-inf.0 (n)
      [(#\i) (next im:done n)])

    (im:sign-n (n) [(#\a) (next im:sign-na n)])
    (im:sign-na (n) [(#\n) (next im:sign-nan n)])
    (im:sign-nan (n) [(#\.) (next im:sign-nan. n)])
    (im:sign-nan. (n) [(#\0) (next im:sign-nan.0 n)])
    (im:sign-nan.0 (n) [(#\i) (next im:done n)])

    (dot (r ex sn)
      [(digit r) => d
       (next digit+dot r ex sn d -1)])
    
    (im:dot (r real ex sn)
      [(digit r) => d
       (next im:digit+dot r real ex sn d -1)])

    (im:sign (r real ex sn)
      [(digit r) => d
       (next im:digit+ r real ex sn d)]
      [(#\i) 
       (next im:sign-i real ex sn)]
      [(#\n)
       (next im:sign-n (make-rectangular real +nan.0))]
      [(#\.)
       (if (fx=? r 10)
           (next im:dot r real ex sn)
           (fail))])

    (sign (r ex sn)
      [(digit r) => d
       (next digit+ r ex sn d)]
      [(#\i)
       (next sign-i r ex sn)]
      [(#\.)
       (if (fx=? r 10)
           (next dot r ex sn)
           (fail))]
      [(#\n)
       (next sign-n r ex)])
    (sign-n (r ex) [(#\a) (next sign-na r ex)])
    (sign-na (r ex) [(#\n) (next sign-nan r ex)])
    (sign-nan (r ex) [(#\.) (next sign-nan. r ex)])
    (sign-nan. (r ex) [(#\0) (next sign-nan.0 r ex)])
    (sign-nan.0 (r ex)
      [(eof) +nan.0]
      [(#\+) (next im:sign r +nan.0 ex +1)]
      [(#\-) (next im:sign r +nan.0 ex -1)]
      [(#\@) (next polar r +nan.0 ex)]
      [(#\i) (next sign-nan.0i r ex)])
    (sign-nan.0i (r ex)
      [(eof) (make-rectangular 0.0 +nan.0)])

    (parse-string-h (dr r ex)
      [(#\x #\X)
       (if r (fail) (next parse-string 16 16 ex))]
      [(#\o #\O)
       (if r (fail) (next parse-string 8 8 ex))]
      [(#\b #\B)
       (if r (fail) (next parse-string 2 2 ex))]
      [(#\d #\D)
       (if r (fail) (next parse-string 10 10 ex))]
      [(#\e #\E)
       (if ex (fail) (next parse-string dr r 'e))]
      [(#\i #\I)
       (if ex (fail) (next parse-string dr r 'i))])

    (parse-string (dr r ex)
      [(#\#) (next parse-string-h dr r ex)]
      [(#\+) (next sign dr ex +1)]
      [(#\-) (next sign dr ex -1)]
      [(#\.)
       (if (fx=? dr 10) 
           (next dot dr ex +1)
           (fail))]
      [(digit dr) => d
       (next digit+ dr ex +1 d)])
  )

  (define-syntax string-config
    (syntax-rules (EOF-ERROR GEN-TEST GEN-ARGS FAIL GEN-DELIM-TEST)
      [(_ GEN-ARGS k . rest) (k (s n i) . rest)]
      [(_ FAIL (s n i) c) #f]
      [(_ FAIL (s n i)) #f]
      [(_ EOF-ERROR (s n i)) #f]
      [(_ GEN-DELIM-TEST c sk fk) #f]
      [(_ GEN-TEST var next fail (s n i) sk fk)
       (let ()
         (define-syntax fail
           (syntax-rules ()
             [(_) #f]))
         (if (fx=? i n)
             sk
             (let ([var (string-ref s i)])
               (define-syntax next
                 (syntax-rules ()
                   [(_ who args (... ...))
                    (who s n (fx+ i 1) args (... ...))]))
               fk)))]))

  (define-string->number-parser string-config (parse-string))

  (define string->number
    (case-lambda
      [(s)
       (unless (string? s) (die who "not a string" s))
       (parse-string s (string-length s) 0 10 #f #f)]
      [(s r)
       (unless (string? s) (die who "not a string" s))
       (unless (memv r '(10 16 2 8)) (die who "invalid radix" r))
       (parse-string s (string-length s) 0 r #f #f)]))
  
)



;;; <number>          ::= <num 2>
;;;                     | <num 8>
;;;                     | <num 10> 
;;;                     | <num 16>
;;; <num R>           ::= <prefix R> <complex R>
;;; <complex R>       ::= <real R>
;;;                     | <real R> "@" <real R>
;;;                     | <real R> "+" <ureal R> "i"
;;;                     | <real R> "-" <ureal R> "i"
;;;                     | <real R> "+" <naninf> "i"
;;;                     | <real R> "-" <naninf> "i"
;;;                     | <real R> "+" "i"
;;;                     | <real R> "-"  "i"
;;;                     | "+" <ureal R> "i"
;;;                     | "-" <ureal R> "i"
;;;                     | "+" <naninf> "i"
;;;                     | "-" <naninf> "i"
;;;                     | "+" "i"
;;;                     | "-" "i"
;;; <real R>          ::= <sign> <ureal R>
;;;                     | "+" <naninf>
;;;                     | "-" <naninf>
;;; <naninf>          ::= "nan.0" 
;;;                     | "inf.0"
;;; <ureal R>           | <uinteger R>
;;;                     | <uinteger R> "/" <uinteger R>
;;;                     | <decimal R> <mantissa width>
;;; <decimal 10>      ::= <uinteger 10> <suffix>
;;;                     | "." <digit 10> + <suffix>
;;;                     | <digit 10> + "." <digit 10> * <suffix>
;;;                     | <digit 10> + "." <suffix>
;;; <uinteger R>      ::= <digit R> +
;;; <prefix R>          | <radix R> <exactness>
;;;                     | <exactness <radix R>
;;; <suffix>          ::= epsilon
;;;                     | <exponent-marker> <sign> <digit 10> +
;;; <exponent-marker> ::= "e"
;;;                     | "E"
;;;                     | "s"
;;;                     | "S"
;;;                     | "f"
;;;                     | "F"
;;;                     | "d"
;;;                     | "D"
;;;                     | "l"
;;;                     | "L"
;;; <mantissa-width>  ::= epsilon
;;;                     | "|" <digit +>
;;; <sign>            ::= epsilon
;;;                     | "+"
;;;                     | "-"
;;; <exactness>       ::= epsilon
;;;                     | "#i"
;;;                     | "#I"
;;;                     | "#e"
;;;                     | "#E"
;;; <radix-2>         ::= "#b"
;;;                     | "#B"
;;; <radix-8>         ::= "#o"
;;;                     | "#O"
;;; <radix-10>        ::= epsilon
;;;                     | "#d"
;;;                     | "#D"
;;; <radix-16>        ::= "#x"
;;;                     | "#X"
;;; <digit-2>         ::= "0"
;;;                     | "1"
;;; <digit-8>         ::= "0"
;;;                     | "1"
;;;                     | "2"
;;;                     | "3"
;;;                     | "4"
;;;                     | "5"
;;;                     | "6"
;;;                     | "7"
;;; <digit-10>        ::= <digit>
;;; <digit-16>        ::= <hex-digit>
;;; <digit>           ::= "0"
;;;                     | "1"
;;;                     | "2"
;;;                     | "3"
;;;                     | "4"
;;;                     | "5"
;;;                     | "6"
;;;                     | "7"
;;;                     | "8"
;;;                     | "9"
;;; <hex-digit>       ::= <hex>
;;;                     | "A"
;;;                     | "B"
;;;                     | "C"
;;;                     | "D"
;;;                     | "E"
;;;                     | "F"
;;;                     | "a"
;;;                     | "b"
;;;                     | "c"
;;;                     | "d"
;;;                     | "e"
;;;                     | "f"