ikarus/src/libnumerics.ss

808 lines
25 KiB
Scheme

(let ()
(define (flonum? x)
(foreign-call "ikrt_is_flonum" x))
(define (flonum->string x)
(or (foreign-call "ikrt_flonum_to_string" x)
(error 'flonum->string "~s is not a flonum" x)))
(define (string->flonum x)
(cond
[(string? x) (foreign-call "ikrt_string_to_flonum" x)]
[else
(error 'string->flonum "~s is not a string" x)]))
(primitive-set! 'flonum? flonum?)
(primitive-set! 'flonum->string flonum->string)
(primitive-set! 'string->flonum string->flonum)
)
(let ()
(define bignum?
; FIXME: temporary definition. Compiler should be made aware
; of numeric representation once it's stable enough.
(lambda (x)
(foreign-call "ikrt_isbignum" x)))
(define (fixnum->flonum x)
(foreign-call "ikrt_fixnum_to_flonum" x))
(define (bignum->flonum x)
(foreign-call "ikrt_bignum_to_flonum" x))
(define ($fl+ x y)
(foreign-call "ikrt_fl_plus" x y))
(define ($fl- x y)
(foreign-call "ikrt_fl_minus" x y))
(define ($fl* x y)
(foreign-call "ikrt_fl_times" x y))
(define binary+
(lambda (x y)
(cond
[(fixnum? x)
(cond
[(fixnum? y)
(foreign-call "ikrt_fxfxplus" x y)]
[(bignum? y)
(foreign-call "ikrt_fxbnplus" x y)]
[(flonum? y)
($fl+ (fixnum->flonum x) y)]
[else
(error '+ "~s is not a number" y)])]
[(bignum? x)
(cond
[(fixnum? y)
(foreign-call "ikrt_fxbnplus" y x)]
[(bignum? y)
(foreign-call "ikrt_bnbnplus" x y)]
[(flonum? y)
($fl+ (bignum->flonum x) y)]
[else
(error '+ "~s is not a number" y)])]
[(flonum? x)
(cond
[(fixnum? y)
($fl+ x (fixnum->flonum y))]
[(bignum? y)
($fl+ x (bignum->flonum y))]
[(flonum? y)
($fl+ x y)]
[else
(error '+ "~s is not a number" y)])]
[else (error '+ "~s is not a number" x)])))
(define binary-logand
(lambda (x y)
(cond
[(fixnum? x)
(cond
[(fixnum? y) (#%$fxlogand x y)]
[(bignum? y)
(foreign-call "ikrt_fxbnlogand" x y)]
[else
(error 'logand "~s is not a number" y)])]
[(bignum? x)
(cond
[(fixnum? y)
(foreign-call "ikrt_fxbnlogand" y x)]
[(bignum? y)
(foreign-call "ikrt_bnbnlogand" x y)]
[else
(error 'logand "~s is not a number" y)])]
[else (error 'logand "~s is not a number" x)])))
(define binary-
(lambda (x y)
(cond
[(fixnum? x)
(cond
[(fixnum? y)
(foreign-call "ikrt_fxfxminus" x y)]
[(bignum? y)
(foreign-call "ikrt_fxbnminus" x y)]
[(flonum? y)
($fl- (fixnum->flonum x) y)]
[else
(error '- "~s is not a number" y)])]
[(bignum? x)
(cond
[(fixnum? y)
(foreign-call "ikrt_bnfxminus" x y)]
[(bignum? y)
(foreign-call "ikrt_bnbnminus" x y)]
[(flonum? y)
($fl- (bignum->flonum x) y)]
[else
(error '- "~s is not a number" y)])]
[(flonum? x)
(cond
[(fixnum? y)
($fl- x (fixnum->flonum y))]
[(bignum? y)
($fl- x (bignum->flonum y))]
[(flonum? y)
($fl- x y)]
[else
(error '- "~s is not a number" y)])]
[else (error '- "~s is not a number" x)])))
(define binary*
(lambda (x y)
(cond
[(fixnum? x)
(cond
[(fixnum? y)
(foreign-call "ikrt_fxfxmult" x y)]
[(bignum? y)
(foreign-call "ikrt_fxbnmult" x y)]
[(flonum? y)
($fl* (fixnum->flonum x) y)]
[else
(error '* "~s is not a number" y)])]
[(bignum? x)
(cond
[(fixnum? y)
(foreign-call "ikrt_fxbnmult" y x)]
[(bignum? y)
(foreign-call "ikrt_bnbnmult" x y)]
[(flonum? y)
($fl* (bignum->flonum x) y)]
[else
(error '* "~s is not a number" y)])]
[(flonum? x)
(cond
[(fixnum? y)
($fl* x (fixnum->flonum y))]
[(bignum? y)
($fl* x (bignum->flonum y))]
[(flonum? y)
($fl* x y)]
[else
(error '* "~s is not a number" y)])]
[else (error '* "~s is not a number" x)])))
(define +
(case-lambda
[(x y) (binary+ x y)]
[(x y z) (binary+ (binary+ x y) z)]
[(a)
(cond
[(fixnum? a) a]
[(bignum? a) a]
[else (error '+ "~s is not a number" a)])]
[() 0]
[(a b c d . e*)
(let f ([ac (binary+ (binary+ (binary+ a b) c) d)]
[e* e*])
(cond
[(null? e*) ac]
[else (f (binary+ ac (car e*)) (cdr e*))]))]))
(define logand
(case-lambda
[(x y) (binary-logand x y)]
[(x y z) (binary-logand (binary-logand x y) z)]
[(a)
(cond
[(fixnum? a) a]
[(bignum? a) a]
[else (error 'logand "~s is not a number" a)])]
[() -1]
[(a b c d . e*)
(let f ([ac (binary-logand (binary-logand (binary-logand a b) c) d)]
[e* e*])
(cond
[(null? e*) ac]
[else (f (binary-logand ac (car e*)) (cdr e*))]))]))
(define -
(case-lambda
[(x y) (binary- x y)]
[(x y z) (binary- (binary- x y) z)]
[(a) (binary- 0 a)]
[(a b c d . e*)
(let f ([ac (binary- (binary- (binary- a b) c) d)]
[e* e*])
(cond
[(null? e*) ac]
[else (f (binary- ac (car e*)) (cdr e*))]))]))
(define *
(case-lambda
[(x y) (binary* x y)]
[(x y z) (binary* (binary* x y) z)]
[(a)
(cond
[(fixnum? a) a]
[(bignum? a) a]
[else (error '* "~s is not a number" a)])]
[() 1]
[(a b c d . e*)
(let f ([ac (binary* (binary* (binary* a b) c) d)]
[e* e*])
(cond
[(null? e*) ac]
[else (f (binary* ac (car e*)) (cdr e*))]))]))
(define binary/
(lambda (x y)
(cond
[(flonum? x)
(cond
[(flonum? y)
(foreign-call "ikrt_fl_div" x y)]
[(fixnum? y)
(foreign-call "ikrt_fl_div" x (fixnum->flonum y))]
[else (error '/ "unspported ~s ~s" x y)])]
[(fixnum? x)
(cond
[(flonum? y)
(foreign-call "ikrt_fl_div" (fixnum->flonum x) y)]
[else (error '/ "unsupported ~s ~s" x y)])]
[else (error '/ "unsupported ~s ~s" x y)])))
(define /
(case-lambda
[(x y) (binary/ x y)]
[(x)
(cond
[(flonum? x) (foreign-call "ikrt_fl_invert" x)]
[else (error '/ "unspported argument ~s" x)])]
[(x y z . rest)
(let f ([a (binary/ x y)] [b z] [ls rest])
(cond
[(null? rest) (binary/ a b)]
[else (f (binary/ a b) (car ls) (cdr ls))]))]))
(define expt
(lambda (n m)
(cond
[(#%$fxzero? m) 1]
[(#%$fxzero? (#%$fxlogand m 1))
(expt (binary* n n) (#%$fxsra m 1))]
[else
(binary* n (expt (binary* n n) (#%$fxsra m 1)))])))
(define max
(case-lambda
[(x y)
(cond
[(fixnum? x)
(cond
[(fixnum? y)
(if ($fx> x y) x y)]
[(bignum? y)
(if (positive-bignum? y) y x)]
[else (error 'max "~s is not a number" y)])]
[(bignum? x)
(cond
[(fixnum? y)
(if (positive-bignum? x) x y)]
[(bignum? y)
(if (bnbn> x y) x y)]
[else (error 'max "~s is not a number" y)])]
[else (error 'max "~s is not a number" x)])]
[(x y z . rest)
(let f ([a (max x y)] [b z] [ls rest])
(cond
[(null? ls) (max a b)]
[else
(f (max a b) (car ls) (cdr ls))]))]
[(x)
(if (number? x)
x
(error 'max "~s is not a number" x))]))
(define min
(case-lambda
[(x y)
(cond
[(fixnum? x)
(cond
[(fixnum? y)
(if ($fx> x y) y x)]
[(bignum? y)
(if (positive-bignum? y) x y)]
[else (error 'min "~s is not a number" y)])]
[(bignum? x)
(cond
[(fixnum? y)
(if (positive-bignum? x) y x)]
[(bignum? y)
(if (bnbn> x y) y x)]
[else (error 'min "~s is not a number" y)])]
[else (error 'min "~s is not a number" x)])]
[(x y z . rest)
(let f ([a (min x y)] [b z] [ls rest])
(cond
[(null? ls) (min a b)]
[else
(f (min a b) (car ls) (cdr ls))]))]
[(x)
(if (number? x)
x
(error 'min "~s is not a number" x))]))
(define number?
(lambda (x)
(or (fixnum? x)
(bignum? x)
(flonum? x))))
(define complex?
(lambda (x) (number? x)))
(define real?
(lambda (x) (number? x)))
(define rational?
(lambda (x)
(cond
[(fixnum? x) #t]
[(bignum? x) #t]
[(flonum? x) #f]
[else (error 'rational? "~s is not a number" x)])))
(define integer?
(lambda (x) (number? x)))
(define exact?
(lambda (x)
(cond
[(fixnum? x) #t]
[(bignum? x) #t]
[(flonum? x) #f]
[else
(error 'exact? "~s is not a number" x)])))
(define exact->inexact
(lambda (x)
(cond
[(fixnum? x) (fixnum->flonum x)]
[(bignum? x) (bignum->flonum x)]
[else
(error 'exact->inexact
"~s is not an exact number" x)])))
(define inexact?
(lambda (x)
(cond
[(fixnum? x) #f]
[(bignum? x) #f]
[(flonum? x) #t]
[else
(error 'inexact? "~s is not a number" x)])))
(define positive-bignum?
(lambda (x)
(foreign-call "ikrt_positive_bn" x)))
(define even-bignum?
(lambda (x)
(foreign-call "ikrt_even_bn" x)))
(define ($fxeven? x)
($fxzero? ($fxlogand x 1)))
(define (even? x)
(cond
[(fixnum? x) ($fxeven? x)]
[(bignum? x) (even-bignum? x)]
[else (error 'even? "~s is not an integer" x)]))
(define (odd? x)
(not
(cond
[(fixnum? x) ($fxeven? x)]
[(bignum? x) (even-bignum? x)]
[else (error 'odd? "~s is not an integer" x)])))
(define number->string
(lambda (x)
(cond
[(fixnum? x) (fixnum->string x)]
[(bignum? x) (foreign-call "ikrt_bntostring" x)]
[(flonum? x) (foreign-call "ikrt_flonum_to_string" x)]
[else (error 'number->string "~s is not a number" x)])))
(define modulo
(lambda (n m)
(cond
[(fixnum? n)
(cond
[(fixnum? m) ($fxmodulo n m)]
[else (error 'modulo "unsupported ~s" m)])]
[else (error 'modulo "unsupported ~s" n)])))
(define-syntax mk<
(syntax-rules ()
[(_ name fxfx< fxbn< bnfx< bnbn<
fxfl< flfx< bnfl< flbn< flfl<)
(let ()
(define err
(lambda (x) (error 'name "~s is not a number" x)))
(define fxloopt
(lambda (x y ls)
(cond
[(fixnum? y)
(if (null? ls)
(fxfx< x y)
(if (fxfx< x y)
(fxloopt y (car ls) (cdr ls))
(loopf (car ls) (cdr ls))))]
[(bignum? y)
(if (null? ls)
(fxbn< x y)
(if (fxbn< x y)
(bnloopt y (car ls) (cdr ls))
(loopf (car ls) (cdr ls))))]
[(flonum? y)
(if (null? ls)
(fxfl< x y)
(if (fxfl< x y)
(flloopt y (car ls) (cdr ls))
(loopf (car ls) (cdr ls))))]
[else (err y)])))
(define bnloopt
(lambda (x y ls)
(cond
[(fixnum? y)
(if (null? ls)
(bnfx< x y)
(if (bnfx< x y)
(fxloopt y (car ls) (cdr ls))
(loopf (car ls) (cdr ls))))]
[(bignum? y)
(if (null? ls)
(bnbn< x y)
(if (bnbn< x y)
(bnloopt y (car ls) (cdr ls))
(loopf (car ls) (cdr ls))))]
[(flonum? y)
(if (null? ls)
(bnfl< x y)
(if (bnfl< x y)
(flloopt y (car ls) (cdr ls))
(loopf (car ls) (cdr ls))))]
[else (err y)])))
(define flloopt
(lambda (x y ls)
(cond
[(fixnum? y)
(if (null? ls)
(flfx< x y)
(if (flfx< x y)
(fxloopt y (car ls) (cdr ls))
(loopf (car ls) (cdr ls))))]
[(bignum? y)
(if (null? ls)
(flbn< x y)
(if (flbn< x y)
(bnloopt y (car ls) (cdr ls))
(loopf (car ls) (cdr ls))))]
[(flonum? y)
(if (null? ls)
(flfl< x y)
(if (flfl< x y)
(flloopt y (car ls) (cdr ls))
(loopf (car ls) (cdr ls))))]
[else (err y)])))
(define loopf
(lambda (x ls)
(cond
[(number? x)
(or (null? ls) (loopf (car ls) (cdr ls)))]
[else (err x)])))
(case-lambda
[(x y)
(cond
[(fixnum? x)
(cond
[(fixnum? y) (fxfx< x y)]
[(bignum? y) (fxbn< x y)]
[(flonum? y) (fxfl< x y)]
[else (err y)])]
[(bignum? x)
(cond
[(fixnum? y) (bnfx< x y)]
[(bignum? y) (bnbn< x y)]
[(flonum? y) (bnfl< x y)]
[else (err y)])]
[(flonum? x)
(cond
[(fixnum? y) (flfx< x y)]
[(bignum? y) (flbn< x y)]
[(flonum? y) (flfl< x y)]
[else (err y)])]
[else (err x)])]
[(x y z)
(cond
[(fixnum? x)
(cond
[(fixnum? y)
(cond
[(fixnum? z) (and (fxfx< x y) (fxfx< y z))]
[(bignum? z)
(and (fxfx< x y) (fxbn< y z))]
[(flonum? z)
(and (fxfx< x y) (fxfl< y z))]
[else (err z)])]
[(bignum? y)
(cond
[(fixnum? z) #f]
[(bignum? z)
(and (fxbn< x y) (bnbn< y z))]
[(flonum? z)
(and (fxbn< x y) (bnfl< y z))]
[else (err z)])]
[(flonum? y)
(cond
[(fixnum? z)
(and (fxfx< x z)
(fxfl< x y)
(flfx< y z))]
[(bignum? z)
(and (fxbn< x z)
(fxfl< x y)
(flbn< y z))]
[(flonum? z)
(and (flfl< y z)
(fxfl< x y))]
[else (err z)])]
[else (err y)])]
[(bignum? x)
(cond
[(fixnum? y)
(cond
[(fixnum? z) (and (fxfx< y z) (bnfx< x y))]
[(bignum? z)
(and (bnfx< x y) (bnfx< y z))]
[(flonum? z)
(and (bnfx< x y) (fxfl< y z))]
[else (err z)])]
[(bignum? y)
(cond
[(fixnum? z) (and (bnfx< y z) (bnbn< x y))]
[(bignum? z) (and (bnbn< x y) (bnbn< y z))]
[(flonum? z) (and (bnfl< y z) (bnbn< x y))]
[else (err z)])]
[(flonum? y)
(cond
[(fixnum? z)
(and (flfx< y z) (bnfl< x y))]
[(bignum? z)
(and (bnfl< x y) (flbn< y z))]
[(flonum? z)
(and (flfl< y z) (bnfl< x y))]
[else (err z)])]
[else (err y)])]
[(flonum? x)
(cond
[(fixnum? y)
(cond
[(fixnum? z)
(and (fxfx< y z) (flfx< x y))]
[(bignum? z)
(and (flfx< x y) (fxbn< y z))]
[(flonum? z)
(and (flfx< x y) (fxfl< y z))]
[else (err z)])]
[(bignum? y)
(cond
[(fixnum? z)
(and (bnfx< y z) (flbn< x y))]
[(bignum? z)
(and (bnbn< y z) (flbn< x y))]
[(flonum? z)
(and (flbn< x y) (bnfl< y z))]
[else (err z)])]
[(flonum? y)
(cond
[(fixnum? z)
(and (flfx< y z) (flfl< x y))]
[(bignum? z)
(and (flfl< x y) (flbn< y z))]
[(flonum? z)
(and (flfl< x y) (flfl< y z))]
[else (err z)])]
[else (err y)])]
[else (err x)])]
[(x) (if (number? x) #t (err x))]
[(x y . ls)
(cond
[(fixnum? x) (fxloopt x y ls)]
[(bignum? x) (bnloopt x y ls)]
[(flonum? x) (flloopt x y ls)]
[else (err x)])]))]))
(define-syntax false (syntax-rules () [(_ x y) #f]))
(define-syntax bnbncmp
(syntax-rules ()
[(_ x y cmp)
(cmp (foreign-call "ikrt_bnbncomp" x y) 0)]))
(define-syntax bnbn= (syntax-rules () [(_ x y) (bnbncmp x y #%$fx=)]))
(define-syntax bnbn< (syntax-rules () [(_ x y) (bnbncmp x y #%$fx<)]))
(define-syntax bnbn> (syntax-rules () [(_ x y) (bnbncmp x y #%$fx>)]))
(define-syntax bnbn<= (syntax-rules () [(_ x y) (bnbncmp x y #%$fx<=)]))
(define-syntax bnbn>= (syntax-rules () [(_ x y) (bnbncmp x y #%$fx>=)]))
(define-syntax fxbn< (syntax-rules () [(_ x y) (positive-bignum? y)]))
(define-syntax bnfx< (syntax-rules () [(_ x y) (not (positive-bignum? x))]))
(define-syntax fxbn> (syntax-rules () [(_ x y) (not (positive-bignum? y))]))
(define-syntax bnfx> (syntax-rules () [(_ x y) (positive-bignum? x)]))
(define-syntax flcmp
(syntax-rules ()
[(_ flfl? flfx? fxfl? flbn? bnfl? fl?)
(begin
(define-syntax flfl?
(syntax-rules () [(_ x y) (fl? x y)]))
(define-syntax flfx?
(syntax-rules () [(_ x y) (fl? x (fixnum->flonum y))]))
(define-syntax flbn?
(syntax-rules () [(_ x y) (fl? x (bignum->flonum y))]))
(define-syntax fxfl?
(syntax-rules () [(_ x y) (fl? (fixnum->flonum x) y)]))
(define-syntax bnfl?
(syntax-rules () [(_ x y) (fl? (bignum->flonum x) y)])))]))
(define-syntax $fl=
(syntax-rules () [(_ x y) (foreign-call "ikrt_fl_equal" x y)]))
(define-syntax $fl<
(syntax-rules () [(_ x y) (foreign-call "ikrt_fl_less" x y)]))
(define-syntax $fl<=
(syntax-rules () [(_ x y) (foreign-call "ikrt_fl_less_or_equal" x y)]))
(define-syntax $fl>
(syntax-rules () [(_ x y) (foreign-call "ikrt_fl_less" y x)]))
(define-syntax $fl>=
(syntax-rules () [(_ x y) (foreign-call "ikrt_fl_less_or_equal" y x)]))
(flcmp flfl= flfx= fxfl= flbn= bnfl= $fl=)
(flcmp flfl< flfx< fxfl< flbn< bnfl< $fl<)
(flcmp flfl> flfx> fxfl> flbn> bnfl> $fl>)
(flcmp flfl<= flfx<= fxfl<= flbn<= bnfl<= $fl<=)
(flcmp flfl>= flfx>= fxfl>= flbn>= bnfl>= $fl>=)
(primitive-set! '+ +)
(primitive-set! '- -)
(primitive-set! '* *)
(primitive-set! '/ /)
(primitive-set! '= (mk< = #%$fx= false false bnbn=
fxfl= flfx= bnfl= flbn= flfl=))
(primitive-set! '< (mk< < #%$fx< fxbn< bnfx< bnbn<
fxfl< flfx< bnfl< flbn< flfl<))
(primitive-set! '> (mk< > #%$fx> fxbn> bnfx> bnbn>
fxfl> flfx> bnfl> flbn> flfl>))
(primitive-set! '<= (mk< <= #%$fx<= fxbn< bnfx< bnbn<=
fxfl<= flfx<= bnfl<= flbn<= flfl<=))
(primitive-set! '>= (mk< >= #%$fx>= fxbn> bnfx> bnbn>=
fxfl>= flfx>= bnfl>= flbn>= flfl>=))
(primitive-set! 'logand logand)
(primitive-set! 'number? number?)
(primitive-set! 'number->string number->string)
(primitive-set! 'add1
(lambda (x)
(cond
[(fixnum? x)
(foreign-call "ikrt_fxfxplus" x 1)]
[(bignum? x)
(foreign-call "ikrt_fxbnplus" 1 x)]
[else (error 'add1 "~s is not a number" x)])))
(primitive-set! 'sub1
(lambda (x)
(cond
[(fixnum? x)
(foreign-call "ikrt_fxfxplus" x -1)]
[(bignum? x)
(foreign-call "ikrt_fxbnplus" -1 x)]
[else (error 'sub1 "~s is not a number" x)])))
(primitive-set! 'zero?
(lambda (x)
(cond
[(fixnum? x) (eq? x 0)]
[(bignum? x) #f]
[else (error 'zero? "~s is not a number" x)])))
(primitive-set! 'expt
(lambda (n m)
(unless (number? n)
(error 'expt "~s is not a numebr" n))
(cond
[(fixnum? m)
(if (#%$fx>= m 0)
(expt n m)
(error 'expt "power should be positive, got ~s" m))]
[(bignum? m)
(cond
[(eq? n 0) 0]
[(eq? n 1) 1]
[(eq? n -1)
(if (positive-bignum? m)
(if (even-bignum? m)
1
-1)
(error 'expt "power should be positive, got ~s" m))]
[else
(if (positive-bignum? m)
(error 'expt "(expt ~s ~s) is too big to compute" n m)
(error 'expt "power should be positive, got ~s" m))])]
[else (error 'expt "~s is not a number" m)])))
(primitive-set! 'quotient
(lambda (x y)
(let-values ([(q r) (quotient+remainder x y)])
q)))
(primitive-set! 'remainder
(lambda (x y)
(let-values ([(q r) (quotient+remainder x y)])
r)))
(primitive-set! 'quotient+remainder
(lambda (x y)
(cond
[(eq? y 0)
(error 'quotient+remainder
"second argument must be non-zero")]
[(fixnum? x)
(cond
[(fixnum? y)
(values (fxquotient x y)
(fxremainder x y))]
[(bignum? y) (values 0 x)]
[else (error 'quotient+remainder
"~s is not a number" y)])]
[(bignum? x)
(cond
[(fixnum? y)
(let ([p (foreign-call "ikrt_bnfxdivrem" x y)])
(values (car p) (cdr p)))]
[(bignum? y)
(let ([p (foreign-call "ikrt_bnbndivrem" x y)])
(values (car p) (cdr p)))]
[else (error 'quotient+remainder
"~s is not a number" y)])]
[else (error 'quotient+remainder
"~s is not a number" x)])))
(primitive-set! 'positive?
(lambda (x)
(cond
[(fixnum? x) (#%$fx> x 0)]
[(bignum? x) (positive-bignum? x)]
[else (error 'positive? "~s is not a number" x)])))
(primitive-set! 'negative?
(lambda (x)
(cond
[(fixnum? x) (#%$fx< x 0)]
[(bignum? x) (not (positive-bignum? x))]
[else (error 'negative? "~s is not a number" x)])))
(primitive-set! 'sin
(lambda (x)
(cond
[(flonum? x) (foreign-call "ikrt_fl_sin" x)]
[(fixnum? x) (foreign-call "ikrt_fx_sin" x)]
[else (error 'sin "unsupported ~s" x)])))
(primitive-set! 'even? even?)
(primitive-set! 'odd? odd?)
(primitive-set! 'max max)
(primitive-set! 'min min)
(primitive-set! 'complex? complex?)
(primitive-set! 'real? real?)
(primitive-set! 'rational? rational?)
(primitive-set! 'exact? exact?)
(primitive-set! 'inexact? inexact?)
(primitive-set! 'integer? integer?)
(primitive-set! 'exact->inexact exact->inexact)
(primitive-set! 'modulo modulo)
)