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

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;;; 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))))
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(define (sign c)
(case c
[(#\+) +1]
[(#\-) -1]
[else #f]))
(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** ...] ...)])))]))))
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(define (mkrec0 n0 n1)
(cond
[(not n0) (make-rectangular 0 n1)]
[(and (pair? n0) (eq? (car n0) 'polar))
(make-polar (cdr n0) n1)]
[else (make-rectangular n0 n1)]))
(define (mkrec1 n0 n1)
(cond
[(not n0) n1]
[(and (pair? n0) (eq? (car n0) 'polar))
(make-polar (cdr n0) n1)]
[else (make-rectangular n0 n1)]))
(define-parser define-string->number-parser next fail
(u:ratio+ (r n0 ex sn num ac)
[(eof)
(if (or n0 (= ac 0))
(fail)
(do-sn/ex sn ex (/ num ac)))]
[(digit r) => d
(next u:ratio+ r n0 ex sn num (+ (* ac r) d))]
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[(sign) => sn2
(if (or n0 (= ac 0))
(fail)
(let ([real (do-sn/ex sn ex (/ num ac))])
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(next u:sign r real ex sn2)))]
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[(#\@)
(if (or n0 (= ac 0))
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(fail)
(let ([mag (do-sn/ex sn ex (/ num ac))])
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(next u:polar r mag ex)))]
[(#\i)
(if (= ac 0)
(fail)
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(next u:done (mkrec0 n0 (do-sn/ex sn ex (/ num ac)))))])
(u:ratio (r n0 ex sn num)
[(digit r) => d
(next u:ratio+ r n0 ex sn num d)])
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(u:done (n)
[(eof) n])
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(u:polar (r mag ex)
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[(digit r) => d
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(next u:digit+ r (cons 'polar mag) ex +1 d)]
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[(#\.)
(if (= r 10)
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(next u:dot r (cons 'polar mag) ex +1)
(fail))]
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[(sign) => sn
(next u:sign r (cons 'polar mag) ex sn)])
(u:exponent+digit (r n0 ex sn ac exp1 exp2 exp-sign)
[(eof)
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(if (number? n0)
(fail)
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(mkrec1 n0 (do-dec-sn/ex sn ex
(* ac (expt 10 (+ exp1 (* exp2 exp-sign)))))))]
[(digit r) => d
(next u:exponent+digit r n0 ex sn ac exp1 (+ (* exp2 r) d) exp-sign)]
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[(sign) => sn2
(if n0
(fail)
(let ([real (do-dec-sn/ex sn ex (* ac (expt 10 (+ exp1 (* exp2 exp-sign)))))])
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(next u:sign r real ex sn2)))]
[(#\@)
(if n0
(fail)
(let ([mag (do-dec-sn/ex sn ex (* ac (expt 10 (+ exp1 (* exp2 exp-sign)))))])
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(next u:polar r mag ex)))]
[(#\i)
(let ([n1 (do-dec-sn/ex sn ex
(* ac (expt 10 (+ exp1 (* exp2 exp-sign)))))])
(next u:done (mkrec0 n0 n1)))]
[(#\|)
(let ([n1 (do-dec-sn/ex sn ex
(* ac (expt 10 (+ exp1 (* exp2 exp-sign)))))])
(next u:mant r n0 n1 ex))])
(u:exponent+sign (r n0 ex sn ac exp1 exp-sign)
[(digit r) => d
(next u:exponent+digit r n0 ex sn ac exp1 d exp-sign)])
(u:exponent (r n0 ex sn ac exp1)
[(digit r) => d
(next u:exponent+digit r n0 ex sn ac exp1 d +1)]
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[(sign) => sn2 (next u:exponent+sign r n0 ex sn ac exp1 sn2)])
(u:digit+dot (r n0 ex sn ac exp)
[(eof)
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(mkrec1 n0 (do-dec-sn/ex sn ex (* ac (expt 10 exp))))]
[(digit r) => d
(next u:digit+dot r n0 ex sn (+ (* ac r) d) (- exp 1))]
[(#\i)
(let ([n1 (do-dec-sn/ex sn ex (* ac (expt 10 exp)))])
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(next u:done (mkrec0 n0 n1)))]
[(sign) => sn2
(if n0
(fail)
(let ([real (do-dec-sn/ex sn ex (* ac (expt 10 exp)))])
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(next u:sign r real ex sn2)))]
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[(#\@)
(if n0
(fail)
(let ([mag (do-dec-sn/ex sn ex (* ac (expt 10 exp)))])
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(next u:polar r mag ex)))]
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[(#\e #\E #\s #\S #\f #\F #\d #\D #\l #\L)
(if (fx=? r 10)
(next u:exponent r n0 ex sn ac exp)
(fail))]
[(#\|)
(let ([n1 (do-dec-sn/ex sn ex (* ac (expt 10 exp)))])
(next u:mant r n0 n1 ex))]
)
(u:digit+ (r n0 ex sn ac)
[(eof)
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(mkrec1 n0 (do-sn/ex sn ex ac))]
[(digit r) => d
(next u:digit+ r n0 ex sn (+ (* ac r) d))]
[(#\.)
(if (fx=? r 10)
(next u:digit+dot r n0 ex sn ac 0)
(fail))]
[(#\/) (next u:ratio r n0 ex sn ac)]
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[(sign) => sn2
(if n0
(fail)
(let ([real (do-sn/ex sn ex ac)])
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(next u:sign r real ex sn2)))]
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[(#\i)
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(next u:done (mkrec0 n0 (do-sn/ex sn ex ac)))]
[(#\@)
(if n0
(fail)
(let ([mag (do-sn/ex sn ex ac)])
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(next u:polar r mag ex)))]
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[(#\e #\E #\s #\S #\f #\F #\d #\D #\l #\L)
(if (fx=? r 10)
(next u:exponent r n0 ex sn ac 0)
(fail))]
[(#\|)
(next u:mant r n0 (do-sn/ex sn 'i ac) ex)])
(u:mant (r n0 n1 ex)
[(digit r) => d_
(next u:mant+ r n0 n1 ex)])
(u:mant+ (r n0 n1 ex)
[(eof) (mkrec1 n0 n1)]
[(digit r) => d_
(next u:mant+ r n0 n1 ex)]
[(sign) => sn2
(if n0 (fail) (next u:sign r n1 ex sn2))]
[(#\@) (if n0 (fail) (next u:polar r n1 ex))]
[(#\i) (if (pair? n0) (fail) (next u:done (mkrec0 n0 n1)))])
(u:sign-i (r n0 ex sn)
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[(eof) (mkrec0 n0 (do-sn/ex sn ex 1))]
[(#\n) (next u:sign-in r n0 (* sn +inf.0) ex)])
(u:sign-in (r n0 n1 ex)
[(#\f) (next u:sign-inf r n0 n1 ex)])
(u:sign-inf (r n0 n1 ex)
[(#\.) (next u:sign-inf. r n0 n1 ex)])
(u:sign-inf. (r n0 n1 ex)
[(#\0) (next u:sign-inf.0 r n0 n1 ex)])
(u:sign-inf.0 (r n0 n1 ex)
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[(eof) (mkrec1 n0 n1)]
[(sign) => sn2
(if n0 (fail) (next u:sign r n1 ex sn2))]
[(#\@) (if n0 (fail) (next u:polar r n1 ex))]
[(#\i) (next u:done (mkrec0 n0 n1))])
(u:dot (r n0 ex sn)
[(digit r) => d
(next u:digit+dot r n0 ex sn d -1)])
(u:sign (r n0 ex sn)
[(digit r) => d
(next u:digit+ r n0 ex sn d)]
[(#\i) (next u:sign-i r n0 ex sn)]
[(#\n) (next u:sign-n r n0 ex)]
[(#\.)
(if (= r 10)
(next u:dot r n0 ex sn)
(fail))])
(u:sign-n (r n0 ex) [(#\a) (next u:sign-na r n0 ex)])
(u:sign-na (r n0 ex) [(#\n) (next u:sign-nan r n0 ex)])
(u:sign-nan (r n0 ex) [(#\.) (next u:sign-nan. r n0 ex)])
(u:sign-nan. (r n0 ex) [(#\0) (next u:sign-nan.0 r n0 ex)])
(u:sign-nan.0 (r n0 ex)
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[(eof) (mkrec1 n0 +nan.0)]
[(sign) => sn2 (if n0 (fail) (next u:sign r +nan.0 ex sn2))]
[(#\@) (if n0 (fail) (next u:polar r +nan.0 ex))]
[(#\i) (next u:done (mkrec0 n0 +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)]
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[(sign) => sn2 (next u:sign dr #f ex sn2)]
[(#\.)
(if (fx=? dr 10)
(next u:dot dr #f ex +1)
(fail))]
[(digit dr) => d
(next u:digit+ dr #f 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"