ikarus/src/ikarus.numerics.ss

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(library (ikarus flonums)
(export string->flonum flonum->string)
(import
(except (ikarus) flonum->string string->flonum))
(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)])))
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(library (ikarus generic-arithmetic)
(export + - * = < <= > >= add1 sub1 quotient remainder
quotient+remainder number->string)
(import
(only (scheme) $fxlogand $fx= $fx< $fx<= $fx> $fx>= $fxzero?
$fxsll $fxsra $fxmodulo)
(except (ikarus) + - * = < <= > >= add1 sub1 quotient remainder
quotient+remainder number->string))
(define (fixnum->flonum x)
(foreign-call "ikrt_fixnum_to_flonum" x))
(define (bignum->flonum x)
(foreign-call "ikrt_bignum_to_flonum" x))
(define ($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))
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(define binary+
(lambda (x y)
(cond
[(fixnum? x)
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(cond
[(fixnum? y)
(foreign-call "ikrt_fxfxplus" x y)]
[(bignum? y)
(foreign-call "ikrt_fxbnplus" x y)]
[(flonum? y)
($fl+ (fixnum->flonum x) y)]
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[else
(error '+ "~s is not a number" y)])]
[(bignum? x)
(cond
[(fixnum? y)
(foreign-call "ikrt_fxbnplus" y x)]
[(bignum? y)
(foreign-call "ikrt_bnbnplus" x y)]
[(flonum? y)
($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)
($fl+ x y)]
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[else
(error '+ "~s is not a number" y)])]
[else (error '+ "~s is not a number" x)])))
(define binary-logand
(lambda (x y)
(cond
[(fixnum? x)
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(cond
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[(fixnum? y) ($fxlogand x y)]
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[(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)
($fl- (fixnum->flonum x) y)]
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[else
(error '- "~s is not a number" y)])]
[(bignum? x)
(cond
[(fixnum? y)
(foreign-call "ikrt_bnfxminus" x y)]
[(bignum? y)
(foreign-call "ikrt_bnbnminus" x y)]
[(flonum? y)
($fl- (bignum->flonum x) y)]
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[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)
($fl- x y)]
[else
(error '- "~s is not a number" y)])]
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[else (error '- "~s is not a number" x)])))
(define binary*
(lambda (x y)
(cond
[(fixnum? x)
(cond
[(fixnum? y)
(foreign-call "ikrt_fxfxmult" x y)]
[(bignum? y)
(foreign-call "ikrt_fxbnmult" x y)]
[(flonum? y)
($fl* (fixnum->flonum x) y)]
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[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)
($fl* (bignum->flonum x) y)]
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[else
(error '* "~s is not a number" y)])]
[(flonum? x)
(cond
[(fixnum? y)
($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)])]
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[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)]
[(fixnum? y)
(let ([q (fxquotient x y)]
[r (fxremainder x y)])
(if (fxzero? r)
q
(error '/ "no ratnum for ~s/~s" 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))]))]))
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(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 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)])))
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(define positive-bignum?
(lambda (x)
(foreign-call "ikrt_positive_bn" x)))
(define even-bignum?
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(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) ($fxeven? x)]
[(bignum? x) (even-bignum? x)]
[else (error 'odd? "~s is not an integer" x)])))
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(define number->string
(lambda (x)
(cond
[(fixnum? x) (fixnum->string x)]
[(bignum? x) (foreign-call "ikrt_bntostring" x)]
[(flonum? x) (foreign-call "ikrt_flonum_to_string" x)]
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[else (error 'number->string "~s is not a number" x)])))
(define modulo
(lambda (n m)
(cond
[(fixnum? n)
(cond
[(fixnum? m) ($fxmodulo n m)]
[else (error 'modulo "unsupported ~s" m)])]
[else (error 'modulo "unsupported ~s" n)])))
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(define-syntax mk<
(syntax-rules ()
[(_ name fxfx< fxbn< bnfx< bnbn<
fxfl< flfx< bnfl< flbn< flfl<)
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(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))))]
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[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))))]
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[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)]
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[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)]
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[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))]
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[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))]
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[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))]
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[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))]
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[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)]
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[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)]))
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(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>=)]))
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(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>=)
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(define =
(mk< = $fx= false false bnbn= fxfl= flfx= bnfl= flbn= flfl=))
(define <
(mk< < $fx< fxbn< bnfx< bnbn< fxfl< flfx< bnfl< flbn< flfl<))
(define >
(mk< > $fx> fxbn> bnfx> bnbn> fxfl> flfx> bnfl> flbn> flfl>))
(define <=
(mk< <= $fx<= fxbn< bnfx< bnbn<= fxfl<= flfx<= bnfl<= flbn<= flfl<=))
(define >=
(mk< >= $fx>= fxbn> bnfx> bnbn>= fxfl>= flfx>= bnfl>= flbn>= flfl>=))
(define add1
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(lambda (x)
(cond
[(fixnum? x)
(foreign-call "ikrt_fxfxplus" x 1)]
[(bignum? x)
(foreign-call "ikrt_fxbnplus" 1 x)]
[else (error 'add1 "~s is not a number" x)])))
(define sub1
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(lambda (x)
(cond
[(fixnum? x)
(foreign-call "ikrt_fxfxplus" x -1)]
[(bignum? x)
(foreign-call "ikrt_fxbnplus" -1 x)]
[else (error 'sub1 "~s is not a number" x)])))
(define zero?
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(lambda (x)
(cond
[(fixnum? x) (eq? x 0)]
[(bignum? x) #f]
[(flonum? x) (= x (exact->inexact 0))]
[else (error 'zero? "tag=~s / ~s is not a number"
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($fxlogand 255
($fxsll x 2))
($fxlogand x -1)
)])))
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(define expt
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(lambda (n m)
(define fxexpt
(lambda (n m)
(cond
[($fxzero? m) 1]
[($fxzero? ($fxlogand m 1))
(fxexpt (binary* n n) ($fxsra m 1))]
[else
(binary* n (fxexpt (binary* n n) ($fxsra m 1)))])))
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(unless (number? n)
(error 'expt "~s is not a numebr" n))
(cond
[(fixnum? m)
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(if ($fx>= m 0)
(fxexpt n m)
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(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)])))
(define quotient
(lambda (x y)
(let-values ([(q r) (quotient+remainder x y)])
q)))
(define remainder
(lambda (x y)
(let-values ([(q r) (quotient+remainder x y)])
r)))
(define 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)])))
(define positive?
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(lambda (x)
(cond
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[(fixnum? x) ($fx> x 0)]
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[(bignum? x) (positive-bignum? x)]
[else (error 'positive? "~s is not a number" x)])))
(define negative?
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(lambda (x)
(cond
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[(fixnum? x) ($fx< x 0)]
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[(bignum? x) (not (positive-bignum? x))]
[else (error 'negative? "~s is not a number" x)])))
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(define 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)])))
(define cos
(lambda (x)
(cond
[(flonum? x) (foreign-call "ikrt_fl_cos" x)]
[(fixnum? x) (foreign-call "ikrt_fx_cos" x)]
[else (error 'cos "unsupported ~s" x)])))
(define atan
(lambda (x)
(cond
[(flonum? x) (foreign-call "ikrt_fl_atan" x)]
[(fixnum? x) (foreign-call "ikrt_fx_atan" x)]
[else (error 'atan "unsupported ~s" x)])))
(define sqrt
(lambda (x)
(cond
[(flonum? x) (foreign-call "ikrt_fl_sqrt" x)]
[(fixnum? x) (foreign-call "ikrt_fx_sqrt" x)]
[else (error 'sqrt "unsupported ~s" x)])))
)