;;;; srfi-27-numbers.scm
;;;; Kon Lovett, Mar '21
;;;; Kon Lovett, Feb '10

(module srfi-27-numbers

(;export
  ;
  #;check-nonzero-real
  #;check-nonnegative-real
  #;check-positive-real
  #;check-real-open-interval
  #;check-real-closed-interval
  check-real-precision
  #;check-real-unit
  ;
  random-large-integer
  random-large-real
  ;
  native-real-precision?)

;NOTE that the module language is not Scheme so one cannot create a list of identifiers,
;respective of context, then use that list for import except or only, or declare.

(import scheme
  (chicken base)
  (chicken type)
  (chicken fixnum)
  (type-checks-numbers scheme)
  (type-errors-numbers interval)
  type-checks-basic
  type-errors-basic)

;;;

(include-relative "srfi-27-common-types")

(: random-power (procedure * number integer fixnum -> number))
(: random-large-integer (procedure * number integer integer -> number))
(: random-large-real (procedure * number integer number -> number))

(: native-real-precision? (maybe-number number -> boolean))

;;;

;;

; use 'number' conditioned checks

#;
(define (nonzero-real? obj)
  (and (real? obj) (not (zero? obj))) )

#;
(define (nonnegative-real? obj)
  (and (real? obj) (not (negative? obj))) )

#;
(define (positive-real? obj)
  (and (real? obj) (positive? obj)) )

#;(define-check+error-type real)
#;(define-check+error-type nonzero-real)
#;(define-check+error-type nonnegative-real)
#;(define-check+error-type positive-real)

(define (check-real-open-interval loc obj mn mx #!optional argnam)
  (check-real loc obj argnam)
  (unless (< mn obj mx)
    (error-open-interval loc obj mn mx argnam) )
  obj )

#;
(define (check-real-closed-interval loc obj mn mx #!optional argnam)
  (check-real loc obj argnam)
  (unless (<= mn obj mx)
    (error-closed-interval loc obj mn mx argnam) )
  obj )

(define (check-real-precision loc obj #!optional argnam)
  (check-real-open-interval loc obj 0 1 argnam) )

#;
(define (check-real-unit loc obj #!optional argnam)
  (check-real-closed-interval loc obj 0 1 argnam) )

;;;

; 'prec-max - maximum range of "core" random integer generator (maybe inexact)
; 'm        - exact maximum range (passed so conversion performed by caller)

(define (random-power rndint state prec-max m k) ;n = m^k, k >= 1
  (let ((max (inexact->exact prec-max)))
    (do ((k k (fx- k 1))
         (n (rndint state max) (+ (rndint state max) (* n m))) )
        ((fx= 1 k) n)) ) )

; Large Integers
; ==============
;
; To produce large integer random deviates, for n > m, we first
; construct large random numbers in the range {0..m^k-1} for some
; k such that m^k >= n and then use the rejection method to choose
; uniformly from the range {0..n-1}.

(define (random-large-integer rndint state prec-max m n) ;n > m
  (do ((k 2 (fx+ k 1))
       (mk (* m m) (* mk m)))
      ((<= n mk)
        (let* ((mk-by-n (quotient mk n))
               (a (* mk-by-n n)) )
          (let loop ()
            (let ((x (random-power rndint state prec-max m k)))
              (if (< x a)
                  (quotient x mk-by-n)
                  (loop) ) ) ) ) ) ) )

; Multiple Precision Reals
; ========================
;
; To produce multiple precision reals we produce a large integer value
; and convert it into a real value. This value is then normalized.
; The precision goal is prec <= 1/(m^k + 1), or 1/prec - 1 <= m^k.
; If you know more about the floating point number types of the
; Scheme system, this can be improved.

(define (random-large-real rndint state prec-max m prec)
  (do ((k 1 (fx+ k 1))
       (u (- (/ 1 prec) 1) (/ u m)) )
      ((<= u 1)
        (exact->inexact
          (/ (+ 1 (random-power rndint state prec-max m k))
             (+ 1 (expt m k)))) ) ) )

; Representation Check
; ====================
;
; required bits within native generator range?

(define (native-real-precision? prec prec-max)
  (or (not prec)
      (<= (- (/ 1 prec) 1) prec-max)) )

) ;module srfi-27-numbers