ikarus/lib/libnumerics.ss

414 lines
12 KiB
Scheme

(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 binary+
(lambda (x y)
(cond
[(fixnum? x)
(cond
[(fixnum? y)
(foreign-call "ikrt_fxfxplus" x y)]
[(bignum? y)
(foreign-call "ikrt_fxbnplus" 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)]
[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)]
[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)]
[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)]
[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)]
[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 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 number?
(lambda (x)
(or (fixnum? x)
(bignum? x))))
(define positive-bignum?
(lambda (x)
(foreign-call "ikrt_positive_bn" x)))
(define even-bignum?
(lambda (x) (error 'even-bignum? "not implemented")))
(define number->string
(lambda (x)
(cond
[(fixnum? x) (fixnum->string x)]
[(bignum? x) (foreign-call "ikrt_bntostring" x)]
[else (error 'number->string "~s is not a number" x)])))
(define-syntax mk<
(syntax-rules ()
[(_ name fxfx< fxbn< bnfx< bnbn<)
(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))))]
[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))))]
[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)]
[else (err y)])]
[(bignum? x)
(cond
[(fixnum? y) (bnfx< x y)]
[(bignum? y) (bnbn< 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))]
[else (err z)])]
[(bignum? y)
(cond
[(fixnum? z) #f]
[(bignum? z)
(and (fxbn< x y) (bnbn< y z))]
[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))]
[else (err z)])]
[(bignum? y)
(cond
[(fixnum? z) (and (bnfx< y z) (bnbn< x y))]
[(bignum? z) (and (bnbn< x y) (bnbn< 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)]
[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 #%$fx>=)]))
(define-syntax fxbn< (syntax-rules () [(_ x y) (positive-bignum? y)]))
(define-syntax bnfx< (syntax-rules () [(_ x y) (not (positive-bignum? x))]))
(define-syntax fxbn> (syntax-rules () [(_ x y) (not (positive-bignum? y))]))
(define-syntax bnfx> (syntax-rules () [(_ x y) (positive-bignum? x)]))
(primitive-set! '+ +)
(primitive-set! '- -)
(primitive-set! '* *)
(primitive-set! '= (mk< = #%$fx= false false bnbn=))
(primitive-set! '< (mk< < #%$fx< fxbn< bnfx< bnbn<))
(primitive-set! '> (mk< > #%$fx> fxbn> bnfx> bnbn>))
(primitive-set! '<= (mk< <= #%$fx<= fxbn< bnfx< bnbn<=))
(primitive-set! '>= (mk< >= #%$fx>= fxbn> bnfx> bnbn>=))
(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)])))
)