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

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(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 FAIL Ca)]
[(_ C Ca [(eof) then] . rest) then]
[(_ C Ca other . rest) (gen-empty C Ca . rest)]))
(define-syntax gen-char
(syntax-rules (eof =>)
[(_ C Ca c) (C FAIL Ca)]
[(_ C Ca c [(eof) then] . rest)
(gen-char C Ca c . rest)]
[(_ C Ca c [(test . args) => result then] . rest)
(cond
[(test c . args) =>
(lambda (result) then)]
[else (gen-char C Ca c . rest)])]
[(_ C Ca c [ls then] . rest)
(if (memv c 'ls)
then
(gen-char C Ca c . rest))]))
(define-syntax gen-clause
(syntax-rules ()
[(_ (Ca ...) C next fail name (arg* ...) (clause* ...))
(define (name Ca ... arg* ...)
(define-syntax fail
(syntax-rules ()
[(_) (C FAIL (Ca ...))]))
(C GEN-TEST c next (Ca ...)
(gen-empty C (Ca ...) clause* ...)
(gen-char C (Ca ...) c 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
(car (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 (list #'(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)))]
[(#\i)
(if (= ac 0)
(fail)
(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)))))]
[(digit r) => d
(next exponent+digit r ex sn ac exp1 (+ (* exp2 r) d) exp-sign)])
(exponent+sign (r ex sn ac exp1 exp-sign)
[(digit r) => d
(next exponent+digit r 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)])
(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))]
[(#\i)
(let ([real (do-dec-sn/ex sn ex (* ac (expt 10 exp)))])
(next im:done (make-rectangular 0.0 real)))]
[(#\e)
(if (fx=? r 10)
(next exponent r ex sn ac exp)
(fail))])
(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))]
[(#\i)
(make-rectangular 0 (do-sn/ex sn ex ac))]
[(#\e)
(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))]
[(#\/)
(next im:ratio r real ex sn ac)]
[(#\i)
(next im:done (make-rectangular real (do-sn/ex sn ex ac)))])
(sign-i (r ex sn)
[(eof)
(make-rectangular
(if (eq? ex 'i) 0.0 0)
sn)]
[(#\n) (next sign-in r sn)])
(sign-in (r sn)
[(#\f) (next sign-inf r sn)])
(sign-inf (r sn)
[(#\.) (next sign-inf. r sn)])
(sign-inf. (r sn)
[(#\0) (next sign-inf.0 r sn)])
(sign-inf.0 (r sn)
[(eof) (* sn +inf.0)]
[(#\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)])
(dot (r ex sn)
[(digit r) => d
(next digit+dot r 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)])
(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)])
(sign-n () [(#\a) (next sign-na)])
(sign-na () [(#\n) (next sign-nan)])
(sign-nan () [(#\.) (next sign-nan.)])
(sign-nan. () [(#\0) (next sign-nan.0)])
(sign-nan.0 ()
[(eof) +nan.0]
[(#\i) (next sign-nan.0i)])
(sign-nan.0i ()
[(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 (GEN-TEST GEN-ARGS FAIL)
[(_ GEN-ARGS k . rest) (k (s n i) . rest)]
[(_ FAIL (s n i)) #f]
[(_ GEN-TEST var next (s n i) sk fk)
(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"