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

554 lines
18 KiB
Scheme
Executable File

(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"