;;;============================================================================

;;; File: "_num#.scm"

;;; Copyright (c) 1994-2015 by Marc Feeley, All Rights Reserved.

;;;============================================================================

;;; Representation of exceptions.

(define-library-type-of-exception range-exception
  id: 10aa6857-6f27-45ab-ac38-2318ef2f277c
  constructor: #f
  opaque:

  (procedure unprintable: read-only:)
  (arguments unprintable: read-only:)
  (arg-num   unprintable: read-only:)
)

(define-library-type-of-exception divide-by-zero-exception
  id: c4319ec5-29d5-43f3-bd16-fad15b238e82
  constructor: #f
  opaque:

  (procedure unprintable: read-only:)
  (arguments unprintable: read-only:)
)

(define-library-type-of-exception fixnum-overflow-exception
  id: dd080472-485f-4f09-8e9e-924194042ff3
  constructor: #f
  opaque:

  (procedure unprintable: read-only:)
  (arguments unprintable: read-only:)
)

;;;----------------------------------------------------------------------------

;;; Define type checking macros.

(##define-macro (macro-index? var)
  `(##not (##fxnegative? ,var)))

(##define-macro (macro-index-range? var lo hi)
  `(macro-fixnum-range? ,var ,lo ,hi))

(##define-macro (macro-index-range-incl? var lo hi)
  `(macro-fixnum-range-incl? ,var ,lo ,hi))

(##define-macro (macro-fixnum-range? var lo hi)
  `(and (##not (##fx< ,var ,lo))
        (##fx< ,var ,hi)))

(##define-macro (macro-fixnum-range-incl? var lo hi)
  `(and (##not (##fx< ,var ,lo))
        (##not (##fx< ,hi ,var))))

(##define-macro (macro-fixnum-and-fixnum-range-incl? var lo hi)
  `(and (##fixnum? ,var)
        (macro-fixnum-range-incl? ,var ,lo ,hi)))

(##define-macro (macro-range-incl? var lo hi)
  `(and (macro-exact-int? ,var)
        (##not (##< ,var ,lo))
        (##not (##< ,hi ,var))))

(define-check-index-range-macro
  index
  macro-index?)

(define-check-index-range-macro
  index-range
  macro-index-range?
  lo
  hi)

(define-check-index-range-macro
  index-range-incl
  macro-index-range-incl?
  lo
  hi)

(define-check-index-range-macro
  fixnum-range
  macro-fixnum-range?
  lo
  hi)

(define-check-index-range-macro
  fixnum-range-incl
  macro-fixnum-range-incl?
  lo
  hi)

(define-check-type exact-signed-int8 'exact-signed-int8
  macro-fixnum-and-fixnum-range-incl?
  -128
  127)

(define-check-type exact-signed-int8-list 'exact-signed-int8-list
  macro-fixnum-and-fixnum-range-incl?
  -128
  127)

(define-check-type exact-unsigned-int8 'exact-unsigned-int8
  macro-fixnum-and-fixnum-range-incl?
  0
  255)

(define-check-type exact-unsigned-int8-list 'exact-unsigned-int8-list
  macro-fixnum-and-fixnum-range-incl?
  0
  255)

(define-check-type exact-signed-int16 'exact-signed-int16
  macro-fixnum-and-fixnum-range-incl?
  -32768
  32767)

(define-check-type exact-signed-int16-list 'exact-signed-int16-list
  macro-fixnum-and-fixnum-range-incl?
  -32768
  32767)

(define-check-type exact-unsigned-int16 'exact-unsigned-int16
  macro-fixnum-and-fixnum-range-incl?
  0
  65535)

(define-check-type exact-unsigned-int16-list 'exact-unsigned-int16-list
  macro-fixnum-and-fixnum-range-incl?
  0
  65535)

(define-check-type exact-signed-int32 'exact-signed-int32
  macro-range-incl?
  -2147483648
  2147483647)

(define-check-type exact-signed-int32-list 'exact-signed-int32-list
  macro-range-incl?
  -2147483648
  2147483647)

(define-check-type exact-unsigned-int32 'exact-unsigned-int32
  macro-range-incl?
  0
  4294967295)

(define-check-type exact-unsigned-int32-list 'exact-unsigned-int32-list
  macro-range-incl?
  0
  4294967295)

(define-check-type exact-signed-int64 'exact-signed-int64
  macro-range-incl?
  -9223372036854775808
  9223372036854775807)

(define-check-type exact-signed-int64-list 'exact-signed-int64-list
  macro-range-incl?
  -9223372036854775808
  9223372036854775807)

(define-check-type exact-unsigned-int64 'exact-unsigned-int64
  macro-range-incl?
  0
  18446744073709551615)

(define-check-type exact-unsigned-int64-list 'exact-unsigned-int64-list
  macro-range-incl?
  0
  18446744073709551615)

(define-check-type inexact-real 'inexact-real
  ##flonum?)

(define-check-type inexact-real-list 'inexact-real-list
  ##flonum?)

(define-check-type real 'real
  ##real?)

(define-check-type fixnum 'fixnum
  ##fixnum?)

(define-check-type flonum 'flonum
  ##flonum?)

;;;============================================================================

;;; Number representation.

;; There are 5 internal representations for numbers:
;;
;; fixnum, bignum, ratnum, flonum, cpxnum
;;
;; Fixnums and bignums form the class of exact-int.
;; Fixnums, bignums and ratnums form the class of exact-real.
;; Fixnums, bignums, ratnums and flonums form the class of noncpxnum.

;; The representation has some invariants:
;;
;; The numerator of a ratnum is a non-zero exact-int.
;; The denominator of a ratnum is an exact-int greater than 1.
;; The numerator and denominator have no common divisors greater than 1.
;;
;; The real part of a cpxnum is a noncpxnum.
;; The imaginary part of a cpxnum is a noncpxnum != fixnum 0

;; The following table gives the mapping of the Scheme exact numbers to their
;; internal representation:
;;
;;    type          representation
;; exact integer  = exact-int (fixnum, bignum)
;; exact rational = exact-real (fixnum, bignum, ratnum)
;; exact real     = exact-real (fixnum, bignum, ratnum)
;; exact complex  = exact-real or cpxnum with exact-real real and imag parts

;; For inexact numbers, the representation is not quite as straightforward.
;;
;; There are 3 special classes of inexact representation:
;; flonum-int : flonum with integer value
;; cpxnum-real: cpxnum with imag part = flonum 0.0 or -0.0
;; cpxnum-int : cpxnum-real with exact-int or flonum-int real part
;;
;; Note: cpxnum-real and cpxnum-int only exist if
;; (macro-cpxnum-are-possibly-real?) returns #t.
;;
;; This gives the following table for Scheme's inexact numbers:
;;
;;      type          representation
;; inexact integer  = flonum-int or cpxnum-int if it exists
;; inexact rational = flonum     or cpxnum-real if it exists
;; inexact real     = flonum     or cpxnum-real if it exists
;; inexact complex  = flonum     or cpxnum with flonum real or imag part

(##define-macro (macro-special-case-exact-zero?) #t); (+ -0. 0)=-0.  (* 4. 0)=0
(##define-macro (macro-cpxnum-are-possibly-real?) #f)

(##define-macro (macro-exact-int? obj) ;; obj can be any object
  `(or (##fixnum? ,obj)
       (##bignum? ,obj)))

(##define-macro (macro-exact-real? obj) ;; obj can be any object
  `(or (macro-exact-int? ,obj)
       (##ratnum? ,obj)))

(##define-macro (macro-flonum-int? obj) ;; obj must be a flonum
  `(##flinteger? ,obj))

(##define-macro (macro-flonum-rational? obj) ;; obj must be a flonum
  `(##flfinite? ,obj))

(##define-macro (macro-noncpxnum-int? obj) ;; obj must be in fixnum/bignum/ratnum/flonum
  `(if (##flonum? ,obj)
     (macro-flonum-int? ,obj)
     (##not (##ratnum? ,obj))))

(##define-macro (macro-noncpxnum-rational? obj) ;; obj must be in fixnum/bignum/ratnum/flonum
  `(or (##not (##flonum? ,obj))
       (macro-flonum-rational? ,obj)))

(##define-macro (macro-cpxnum-int? obj) ;; obj must be a cpxnum
  `(and (macro-cpxnum-are-possibly-real?)
        (macro-cpxnum-real? ,obj)
        (let ((real (macro-cpxnum-real ,obj)))
          (macro-noncpxnum-int? real))))

(##define-macro (macro-cpxnum-rational? obj) ;; obj must be a cpxnum
  `(and (macro-cpxnum-are-possibly-real?)
        (let ((imag (macro-cpxnum-imag ,obj)))
          (and (##flonum? imag)
               (##flzero? imag)
               (let ((real (macro-cpxnum-real ,obj)))
                 (macro-noncpxnum-rational? real))))))

(##define-macro (macro-cpxnum-real? obj) ;; obj must be a cpxnum
  `(and (macro-cpxnum-are-possibly-real?)
        (let ((imag (macro-cpxnum-imag ,obj)))
          (and (##flonum? imag)
               (##flzero? imag)))))

;; Dispatch for number representation

(macro-define-syntax macro-number-dispatch
  (lambda (stx)
    (syntax-case stx ()
      ((_ num err fix big rat flo cpx)
       #'(cond ((##fixnum? num) fix)
               ((##flonum? num) flo)
               ((##bignum? num) big)
               ((##ratnum? num) rat)
               ((##cpxnum? num) cpx)
               (else            err))))))

;;; - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

;;; Miscellaneous constants.

(##define-macro (macro-inexact-+2)     2.0)
(##define-macro (macro-inexact--2)    -2.0)
(##define-macro (macro-inexact-+1)     1.0)
(##define-macro (macro-inexact--1)    -1.0)
(##define-macro (macro-inexact-+1/2)   0.5)
(##define-macro (macro-inexact-+0)     0.0)
(##define-macro (macro-inexact--0)    -0.0)
(##define-macro (macro-inexact-+pi)    3.141592653589793)
(##define-macro (macro-inexact--pi)   -3.141592653589793)
(##define-macro (macro-inexact-+pi/2)  1.5707963267948966)
(##define-macro (macro-inexact--pi/2) -1.5707963267948966)
(##define-macro (macro-inexact-+pi/4)   .7853981633974483)
(##define-macro (macro-inexact-+3pi/4) 2.356194490192345)
(##define-macro (macro-inexact-+inf)  (/ +1. 0.))
(##define-macro (macro-inexact--inf)  (/ -1. 0.))
(##define-macro (macro-inexact-+nan)  (/ 0. 0.))
(##define-macro (macro-cpxnum-+2i)    +2i)
(##define-macro (macro-cpxnum--i)     -i)
(##define-macro (macro-cpxnum-+i)     +i)

(##define-macro (macro-cpxnum-+1/2+sqrt3/2i)
  (make-rectangular 1/2 (/ (sqrt 3) 2)))

(##define-macro (macro-cpxnum-+1/2-sqrt3/2i)
  (make-rectangular 1/2 (- (/ (sqrt 3) 2))))

(##define-macro (macro-cpxnum--1/2+sqrt3/2i)
  (make-rectangular -1/2 (/ (sqrt 3) 2)))

(##define-macro (macro-cpxnum--1/2-sqrt3/2i)
  (make-rectangular -1/2 (- (/ (sqrt 3) 2))))

(##define-macro (macro-cpxnum-+sqrt3/2+1/2i)
  (make-rectangular (/ (sqrt 3) 2) 1/2))

(##define-macro (macro-cpxnum-+sqrt3/2-1/2i)
  (make-rectangular (/ (sqrt 3) 2) -1/2))

(##define-macro (macro-cpxnum--sqrt3/2+1/2i)
  (make-rectangular (- (/ (sqrt 3) 2)) 1/2))

(##define-macro (macro-cpxnum--sqrt3/2-1/2i)
  (make-rectangular (- (/ (sqrt 3) 2)) -1/2))

(##define-macro (macro-inexact-exp-+1/2) (exp +1/2))
(##define-macro (macro-inexact-exp--1/2) (exp -1/2))
(##define-macro (macro-inexact-log-2)    (log 2))

;;; The next constants are for 64-bit, IEEE 754 binary arithmetic

(##define-macro (macro-inexact-epsilon) 1.1102230246251565e-16)     ; (- 1 epsilon) <> 1, epsilon smallest
(##define-macro (macro-inexact-lambda)  2.2250738585072014e-308)    ; smallest positive flonum
(##define-macro (macro-inexact-omega)   1.7976931348623157e308)     ; largest finite flonum

;;; - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

;;; Bignum related constants.

(##define-macro (macro-max-lines)                  65536)
(##define-macro (macro-max-fixnum32-div-max-lines)  8191)
(##define-macro (macro-max-fixnum32)           536870911)
(##define-macro (macro-max-fixnum32-div-10)     53687091)

;;; - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

;;; Flonum related constants.

(##define-macro (macro-flonum-m-bits)
  52)

(##define-macro (macro-flonum-m-bits-plus-1)
  53)

(##define-macro (macro-flonum-m-bits-plus-1*2)
  106)

(##define-macro (macro-flonum-e-bits)
  11)

(##define-macro (macro-flonum-sign-bit) ;; (expt 2 (+ (macro-flonum-e-bits) (macro-flonum-m-bits)))
  #x8000000000000000)

(##define-macro (macro-flonum-m-min) ;; (expt 2.0 (macro-flonum-m-bits))
  4503599627370496.0)

(##define-macro (macro-flonum-+m-min) ;; (expt 2 (macro-flonum-m-bits))
  4503599627370496)

(##define-macro (macro-flonum-+m-max-plus-1) ;; (expt 2 (macro-flonum-m-bits-plus-1))
  9007199254740992)

(##define-macro (macro-flonum-+m-max) ;; (- (macro-flonum-+m-max-plus-1) 1)
  9007199254740991)

(##define-macro (macro-flonum-+m-max-plus-1-inexact);; (exact->inexact (macro-flonum-+m-max-plus-1))
  9007199254740992.0)

(##define-macro (macro-flonum-inverse-+m-max-plus-1-inexact);; (/ (macro-flonum-+m-max-plus-1-inexact))
  (/ 9007199254740992.0))

(##define-macro (macro-flonum--m-min) ;; (- (macro-flonum-+m-min))
  -4503599627370496)

(##define-macro (macro-flonum--m-max) ;; (- (macro-flonum-+m-max))
  -9007199254740991)

(##define-macro (macro-flonum-e-bias) ;; (- (expt 2 (- (macro-flonum-e-bits) 1)) 1)
  1023)

(##define-macro (macro-flonum-e-bias-plus-1) ;; (+ (macro-flonum-e-bias) 1)
  1024)

(##define-macro (macro-flonum-e-bias-minus-1) ;; (- (macro-flonum-e-bias) 1)
  1022)

(##define-macro (macro-flonum-e-min) ;; (- (+ (macro-flonum-e-bias) (macro-flonum-m-bits) -1))
  -1074)

(##define-macro (macro-flonum-min-normal) ;; (expt 2.0 (+ (macro-flonum-m-bits) (macro-flonum-e-min)))
  (expt 2.0 (+ 52 -1074)))

(##define-macro (macro-scale-down) ;; (expt 2 (- (+ (quotient (macro-flonum-e-bias-plus-1) 2) 1)))
  (expt 2 -513))

(##define-macro (macro-inexact-scale-down) ;; (expt 2.0 (- (+ (quotient (macro-flonum-e-bias-plus-1) 2) 1)))
  (expt 2.0 -513))

(##define-macro (macro-scale-up) ;; (expt 2 (+ (quotient (macro-flonum-e-bias-plus-1) 2) (macro-flonum-m-bits-plus-1)))
  (expt 2 565))

(##define-macro (macro-inexact-scale-up) ;; (expt 2.0 (+ (quotient (macro-flonum-e-bias-plus-1) 2) (macro-flonum-m-bits-plus-1)))
  (expt 2.0 565))

(##define-macro (macro-inexact-radix) ;; (exact->inexact (macro-radix))
  16384.0)

;;; - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

;;; Ratnum objects.

;; A ratnum is represented by an object vector of length 2
;; slot 0 = numerator
;; slot 1 = denominator

;;TODO: replace with ##ratnum-make

(macro-case-target

 ((C)

  (##define-macro (macro-ratnum-make num den)
    `(##subtype-set!
      (##vector ,num ,den)
      (macro-subtype-ratnum)))

  (##define-macro (macro-ratnum-numerator r)   `(macro-slot 0 ,r))
  (##define-macro (macro-ratnum-denominator r) `(macro-slot 1 ,r)))

 (else

  (##define-macro (macro-ratnum-make num den) `(##ratnum-make ,num ,den))
  (##define-macro (macro-ratnum-numerator r) `(##ratnum-numerator ,r))
  (##define-macro (macro-ratnum-denominator r) `(##ratnum-denominator ,r))))

;;; - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

;;; Cpxnum objects.

;; A cpxnum is represented by an object vector of length 2
;; slot 0 = real
;; slot 1 = imag

;;TODO: replace with ##cpxnum-make

(macro-case-target

 ((C)

  (##define-macro (macro-cpxnum-make r i)
    `(##subtype-set!
      (##vector ,r ,i)
      (macro-subtype-cpxnum)))

  (##define-macro (macro-cpxnum-real c) `(macro-slot 0 ,c))
  (##define-macro (macro-cpxnum-imag c) `(macro-slot 1 ,c)))

 (else

  (##define-macro (macro-cpxnum-make r i) `(##cpxnum-make ,r ,i))
  (##define-macro (macro-cpxnum-real c) `(##cpxnum-real ,c))
  (##define-macro (macro-cpxnum-imag c) `(##cpxnum-imag ,c))))

;;; - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

(##define-macro (macro-bignum-odd? x);;;;;;;;;;;;;;;;;;;;
  `(##fxodd? (##bignum.mdigit-ref ,x 0)))

(##define-macro (macro-real->inexact x)
  `(let ((x ,x))
     (if (##flonum? x)
       x
       (##exact->inexact
        (if (macro-cpxnum-are-possibly-real?)
          (##real-part x)
          x)))))

;;;============================================================================
