/usr/share/scsh-0.6/rts/xnum.scm is in scsh-common-0.6 0.6.7-8.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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; This is file xnum.scm.
;;;; Extended number support
(define-simple-type :extended-number (:number) extended-number?)
(define-record-type extended-number-type :extended-number-type
(really-make-extended-number-type field-names supers priority predicate id)
extended-number-type?
(field-names extended-number-type-field-names)
(supers extended-number-type-supers)
(priority extended-number-type-priority)
(predicate extended-number-predicate)
(id extended-number-type-identity))
(define-record-discloser :extended-number-type
(lambda (e-n-t)
(list 'extended-number-type (extended-number-type-identity e-n-t))))
(define (make-extended-number-type field-names supers id)
(letrec ((t (really-make-extended-number-type
field-names
supers
(+ (apply max
(map type-priority
(cons :extended-number supers)))
10)
(lambda (x)
(and (extended-number? x)
(eq? (extended-number-type x) t)))
id)))
t))
(define (extended-number-type x) (extended-number-ref x 0))
; DEFINE-EXTENDED-NUMBER-TYPE macro
(define-syntax define-extended-number-type
(syntax-rules ()
((define-extended-number-type ?type (?super ...)
(?constructor ?arg1 ?arg ...)
?predicate
(?field ?accessor)
...)
(begin (define ?type
(make-extended-number-type '(?field ...)
(list ?super ...)
'?type))
(define ?constructor
(let ((args '(?arg1 ?arg ...)))
(if (equal? args
(extended-number-type-field-names ?type))
(let ((k (+ (length args) 1)))
(lambda (?arg1 ?arg ...)
(let ((n (make-extended-number k #f))
(i 1))
(extended-number-set! n 0 ?type)
(extended-number-set! n 1 ?arg1)
(begin (set! i (+ i 1))
(extended-number-set! n i ?arg))
...
n)))
(error "ill-formed DEFINE-EXTENDED-NUMBER-TYPE" '?type))))
(define (?predicate x)
(and (extended-number? x)
(eq? (extended-number-type x) ?type)))
(define-extended-number-accessors ?accessor ...)))))
(define-syntax define-extended-number-accessors
(syntax-rules ()
((define-extended-number-accessors ?accessor)
(define (?accessor n) (extended-number-ref n 1)))
((define-extended-number-accessors ?accessor1 ?accessor2)
(begin (define (?accessor1 n) (extended-number-ref n 1))
(define (?accessor2 n) (extended-number-ref n 2))))
((define-extended-number-accessors ?accessor1 ?accessor2 ?accessor3)
(begin (define (?accessor1 n) (extended-number-ref n 1))
(define (?accessor2 n) (extended-number-ref n 2))
(define (?accessor3 n) (extended-number-ref n 3))))))
(define-method &type-priority ((t :extended-number-type))
(extended-number-type-priority t))
(define-method &type-predicate ((t :extended-number-type))
(extended-number-predicate t))
; Make all the numeric instructions be extensible.
(define (make-opcode-generic! opcode mtable)
(let ((perform (method-table-get-perform mtable)))
(extend-opcode! opcode
(lambda (lose)
(set-final-method! mtable
(lambda (next-method . args)
(apply lose args)))
(lambda args
((perform) args))))))
(define-syntax define-opcode-extension
(syntax-rules ()
((define-opcode-extension ?name ?table-name)
(begin (define ?table-name (make-method-table '?name))
(make-opcode-generic! (enum op ?name) ?table-name)))))
(define-opcode-extension + &+)
(define-opcode-extension - &-)
(define-opcode-extension * &*)
(define-opcode-extension / &/)
(define-opcode-extension = &=)
(define-opcode-extension < &<)
(define-opcode-extension quotient "ient)
(define-opcode-extension remainder &remainder)
(define-opcode-extension integer? &integer?)
(define-opcode-extension rational? &rational?)
(define-opcode-extension real? &real?)
(define-opcode-extension complex? &complex?)
(define-opcode-extension number? &number?)
(define-opcode-extension exact? &exact?)
(define-opcode-extension exact->inexact &exact->inexact)
(define-opcode-extension inexact->exact &inexact->exact)
(define-opcode-extension real-part &real-part)
(define-opcode-extension imag-part &imag-part)
(define-opcode-extension floor &floor)
(define-opcode-extension numerator &numerator)
(define-opcode-extension denominator &denominator)
(define-opcode-extension make-rectangular &make-rectangular)
(define-opcode-extension exp &exp)
(define-opcode-extension log &log)
(define-opcode-extension sin &sin)
(define-opcode-extension cos &cos)
(define-opcode-extension tan &tan)
(define-opcode-extension asin &asin)
(define-opcode-extension acos &acos)
(define-opcode-extension atan &atan)
(define-opcode-extension sqrt &sqrt)
; >, <=, and >= are all extended using the table for <.
(let ((perform (method-table-get-perform &<)))
(extend-opcode! (enum op >)
(lambda (lose)
(lambda (x y)
((perform) (list y x)))))
(extend-opcode! (enum op <=)
(lambda (lose)
(lambda (x y)
(not ((perform) (list y x))))))
(extend-opcode! (enum op >=)
(lambda (lose)
(lambda (x y)
(not ((perform) (list x y)))))))
; Default methods.
(define-method &integer? (x) #f)
(define-method &rational? (x) (integer? x))
(define-method &real? (x) (rational? x))
(define-method &complex? (x) (real? x))
(define-method &number? (x) (complex? x))
(define-method &real-part ((x :real)) x)
(define-method &imag-part ((x :real))
(if (exact? x) 0 (exact->inexact 0)))
(define-method &floor ((n :integer)) n)
(define-method &numerator ((n :integer)) n)
(define-method &denominator ((n :integer))
(if (exact? n) 1 (exact->inexact 1)))
; Make sure this has very low priority, so that it's only tried as a
; last resort.
(define-method &/ (m n)
(if (and (integer? m) (integer? n))
(if (= 0 (remainder m n))
(quotient m n)
(let ((z (abs (quotient n 2))))
(set-exactness (quotient (if (< m 0)
(- m z)
(+ m z))
n)
#f)))
(next-method)))
(define-method &sqrt ((n :integer))
(if (>= n 0)
(non-negative-integer-sqrt n) ;Dubious
(next-method)))
(define (non-negative-integer-sqrt n)
(cond ((<= n 1) ; for both 0 and 1
n)
;; ((< n 0)
;; (make-rectangular 0 (integer-sqrt (- 0 n))))
(else
(let loop ((m (quotient n 2)))
(let ((m1 (quotient n m)))
(cond ((< m1 m)
(loop (quotient (+ m m1) 2)))
((= n (* m m))
m)
(else
(exact->inexact m))))))))
(define-simple-type :exact (:number)
(lambda (n) (and (number? n) (exact? n))))
(define-simple-type :inexact (:number)
(lambda (n) (and (number? n) (inexact? n))))
; Whattakludge.
; Replace the default method (which in the initial image always returns #f).
(define-method &really-string->number (s radix xact?)
(let ((len (string-length s)))
(cond ((<= len 1) #f)
((char=? (string-ref s (- len 1)) #\i)
(parse-rectangular s radix xact?))
((string-position #\@ s)
=> (lambda (at)
(let ((r (really-string->number (substring s 0 at)
radix xact?))
(theta (really-string->number (substring s (+ at 1) len)
radix xact?)))
(if (and (real? r) (real? theta))
(make-polar r theta)))))
((string-position #\/ s)
=> (lambda (slash)
(let ((m (string->integer (substring s 0 slash) radix))
(n (string->integer (substring s (+ slash 1) len)
radix)))
(if (and m n)
(set-exactness (/ m n) xact?)
#f))))
((string-position #\# s)
(if xact?
#f
(really-string->number
(list->string (map (lambda (c) (if (char=? c #\#) #\5 c))
(string->list s)))
radix
xact?)))
((string-position #\. s)
=> (lambda (dot)
(parse-decimal s radix xact? dot)))
(else #f))))
(define (parse-decimal s radix xact? dot)
;; Talk about kludges. This is REALLY kludgey.
(let* ((len (string-length s))
(j (if (or (char=? (string-ref s 0) #\+)
(char=? (string-ref s 0) #\-))
1
0))
(m (if (= dot j)
0
(string->integer (substring s j dot)
radix)))
(n (if (= dot (- len 1))
0
(string->integer (substring s (+ dot 1) len)
radix))))
(if (and m n)
(let ((n (+ m (/ n (expt radix
(- len (+ dot 1)))))))
(set-exactness (if (char=? (string-ref s 0) #\-)
(- 0 n)
n)
xact?))
#f)))
(define (parse-rectangular s radix xact?)
(let ((len (string-length s)))
(let loop ((i (- len 2)))
(if (< i 0)
#f
(let ((c (string-ref s i)))
(if (or (char=? c #\+)
(char=? c #\-))
(let ((x (if (= i 0)
0
(really-string->number (substring s 0 i)
radix xact?)))
(y (if (= i (- len 2))
(if (char=? c #\+) 1 -1)
(really-string->number (substring s i (- len 1))
radix xact?))))
(if (and (real? x) (real? y))
(make-rectangular x y)
#f))
(loop (- i 1))))))))
(define (set-exactness n xact?)
(if (exact? n)
(if xact? n (exact->inexact n))
;; ?what to do? (if xact? (inexact->exact n) n)
n))
; Utility
(define (string-position c s)
(let loop ((i 0))
(if (>= i (string-length s))
#f
(if (char=? c (string-ref s i))
i
(loop (+ i 1))))))
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