From e78c0f3a78e7325700140abb1493dac683fcf49a Mon Sep 17 00:00:00 2001 From: Abdulaziz Ghuloum Date: Mon, 21 May 2007 19:35:16 -0400 Subject: [PATCH] * Added gcd --- src/ikarus.boot | Bin 2915926 -> 2934233 bytes src/ikarus.numerics.ss | 194 +++++++++++++++++++++++++++++++++++++---- src/makefile.ss | 1 + 3 files changed, 177 insertions(+), 18 deletions(-) diff --git a/src/ikarus.boot b/src/ikarus.boot index 2a12786b8ba59ed8aa4750c9566aca75ea0e60b8..48bad49a74434a8afa8148ec2fbdc5373167c3c1 100644 GIT binary patch delta 810517 zcmcGX30ziH`uMr`Wm8l@kWE2Qa942G6curaTmUz;Ou;S76iqEmOC7Ui7&E)oX{OwM zEz_=MCAo!}Ex)F+sir+`a!Se)Cn}~i{?GT^dtcrc(3$zs|NVTP_ug~Q_Uz9&=bn4- z-_GtbJ}ljB+>sc1Zo^>DzNPQStD@V&<3rvk^z550iO5?$@ge1dJo_d}V#!#ut>@HT zgRD)hqC&cv0Ra(f9^ACOICD%uK)@1#Ap+wCh6+q_&KJsYqCii9YX#;CUn30xwOEs%3uIvTAO-(#k!VT&Sz3QFW+x{1Q&K>skpi%0oWLjthRcx-=@@KbDXg6*09&b7Adr(G%&Oa2cvCAcuwG}wts{X+ znXq820BnN%#R3Zi=zt>~W(t4+oxwsnMo!DDv~qdvX5 z%c4eVLPqdq(S;9qZacZ|Na(t9&*62|)#2;^r?{!LHF$jdhWSf8uZ&1NxuvRur*uSW 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--git a/src/ikarus.numerics.ss b/src/ikarus.numerics.ss index e339b2f..c3b665e 100644 --- a/src/ikarus.numerics.ss +++ b/src/ikarus.numerics.ss @@ -28,7 +28,7 @@ (library (ikarus generic-arithmetic) (export + - * / zero? = < <= > >= add1 sub1 quotient remainder - positive? expt + positive? expt gcd quotient+remainder number->string string->number) (import (ikarus system $fx) @@ -38,20 +38,25 @@ (ikarus system $strings) (except (ikarus) + - * / zero? = < <= > >= add1 sub1 quotient remainder quotient+remainder number->string positive? - string->number expt)) - - ;(define (ratnum? c) #f) + string->number expt gcd)) (define (fixnum->flonum x) (foreign-call "ikrt_fixnum_to_flonum" x)) (define (bignum->flonum x) (foreign-call "ikrt_bignum_to_flonum" x)) + (define (ratnum->flonum x) + (binary/ (exact->inexact ($ratnum-n x)) + (exact->inexact ($ratnum-d x)))) (define ($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 ($fl/ x y) + (foreign-call "ikrt_fl_div" x y)) + + (define binary+ (lambda (x y) @@ -64,6 +69,10 @@ (foreign-call "ikrt_fxbnplus" x y)] [(flonum? y) ($fl+ (fixnum->flonum x) y)] + [(ratnum? y) + ($make-ratnum + (+ (* x ($ratnum-d y)) ($ratnum-n y)) + ($ratnum-d y))] [else (error '+ "~s is not a number" y)])] [(bignum? x) @@ -74,6 +83,10 @@ (foreign-call "ikrt_bnbnplus" x y)] [(flonum? y) ($fl+ (bignum->flonum x) y)] + [(ratnum? y) + ($make-ratnum + (+ (* x ($ratnum-d y)) ($ratnum-n y)) + ($ratnum-d y))] [else (error '+ "~s is not a number" y)])] [(flonum? x) @@ -84,8 +97,25 @@ ($fl+ x (bignum->flonum y))] [(flonum? y) ($fl+ x y)] + [(ratnum? y) + ($fl+ x (ratnum->flonum y))] [else (error '+ "~s is not a number" y)])] + [(ratnum? x) + (cond + [(or (fixnum? y) (bignum? y)) + ($make-ratnum + (+ (* y ($ratnum-d x)) ($ratnum-n x)) + ($ratnum-d x))] + [(flonum? y) + ($fl+ y (ratnum->flonum x))] + [(ratnum? y) + (let ([n0 ($ratnum-n x)] [n1 ($ratnum-n y)] + [d0 ($ratnum-d x)] [d1 ($ratnum-d y)]) + ;;; FIXME: inefficient + (/ (+ (* n0 d1) (* n1 d0)) (* d0 d1)))] + [else + (error '+ "~s is not a number" y)])] [else (error '+ "~s is not a number" x)]))) (define binary-logand @@ -242,28 +272,155 @@ [(null? e*) ac] [else (f (binary* ac (car e*)) (cdr e*))]))])) - (define binary/ + (define (binary-gcd x y) + (define (gcd x y) + (cond + [($fx= y 0) x] + [else (gcd y (remainder x y))])) + (let ([x (if (< x 0) (- x) x)] + [y (if (< y 0) (- y) y)]) + (cond + [(> x y) (gcd x y)] + [(< x y) (gcd y x)] + [else x]))) + + (define gcd + (case-lambda + [(x y) + (cond + [(or (fixnum? x) (bignum? x)) + (cond + [(or (fixnum? y) (bignum? y)) + (binary-gcd x y)] + [(number? y) + (error 'gcd "~s is not an exact integer" y)] + [else + (error 'gcd "~s is not a number" y)])] + [(number? x) + (error 'gcd "~s is not an exact integer" x)] + [else + (error 'gcd "~s is not a number" x)])] + [(x) + (cond + [(or (fixnum? x) (bignum? x)) x] + [(number? x) + (error 'gcd "~s is not an exact integer" x)] + [else + (error 'gcd "~s is not a number" x)])] + [() 0] + [(x y z . ls) + (let f ([g (gcd (gcd x y) z)] [ls ls]) + (cond + [(null? ls) g] + [else (f (gcd g (car ls)) (cdr ls))]))])) + + + + + + + (define binary/ ;;; implements ratnums (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))] + [(flonum? y) ($fl/ x y)] + [(fixnum? y) ($fl/ x (fixnum->flonum y))] + [(bignum? y) ($fl/ x (bignum->flonum y))] + [(ratnum? y) ($fl/ x (ratnum->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)))] + [(flonum? y) ($fl/ (fixnum->flonum x) y)] + [(fixnum? y) + (cond + [($fx= y 0) (error '/ "division by 0")] + [($fx> y 0) + (if ($fx= y 1) + x + (let ([g (binary-gcd x y)]) + (cond + [($fx= g y) (fxquotient x g)] + [($fx= g 1) ($make-ratnum x y)] + [else ($make-ratnum (fxquotient x g) (fxquotient y g))])))] + [else + (if ($fx= y -1) + (binary- 0 x) + (let ([g (binary-gcd x y)]) + (cond + [($fx= ($fx- 0 g) y) (binary- 0 (fxquotient x g))] + [($fx= g 1) ($make-ratnum (binary- 0 x) (binary- 0 y))] + [else + ($make-ratnum + (binary- 0 (fxquotient x g)) + (binary- 0 (fxquotient y g)))])))])] + [(bignum? y) + (let ([g (binary-gcd x y)]) + (cond + [(= g y) (quotient x g)] ;;; should not happen + [($bignum-positive? y) + (if ($fx= g 1) + ($make-ratnum x y) + ($make-ratnum (fxquotient x g) (quotient y g)))] + [else + (if ($fx= g 1) + ($make-ratnum (binary- 0 x) (binary- 0 y)) + ($make-ratnum + (binary- 0 (fxquotient x g)) + (binary- 0 (quotient y g))))]))] + [(ratnum? y) + (/ (* x ($ratnum-d y)) ($ratnum-n y))] [else (error '/ "unsupported ~s ~s" x y)])] - [else (error '/ "unsupported ~s ~s" x y)]))) + [(bignum? x) + (cond + [(fixnum? y) + (cond + [($fx= y 0) (error '/ "division by 0")] + [($fx> y 0) + (if ($fx= y 1) + x + (let ([g (binary-gcd x y)]) + (cond + [($fx= g 1) ($make-ratnum x y)] + [($fx= g y) (quotient x g)] + [else + ($make-ratnum (quotient x g) (quotient y g))])))] + [else + (if ($fx= y -1) + (- x) + (let ([g (binary-gcd x y)]) + (cond + [(= (- g) y) (- (quotient x g))] + [else + ($make-ratnum + (- (quotient x g)) + (- (quotient y g)))])))])] + [(bignum? y) + (let ([g (binary-gcd x y)]) + (cond + [($fx= g 1) ($make-ratnum x y)] + [($bignum-positive? y) + (if (= g y) + (quotient x g) + ($make-ratnum (quotient x g) (quotient y g)))] + [else + (let ([y (binary- 0 y)]) + (if (= g y) + (binary- 0 (quotient x g)) + ($make-ratnum (binary- 0 (quotient x g)) + (quotient y g))))]))] + [(flonum? y) ($fl/ (bignum->flonum x) y)] + [(ratnum? y) + (binary/ (binary* x ($ratnum-n y)) ($ratnum-d y))] + [else (error '/ "~s is not a number" y)])] + [(ratnum? x) + (cond + [(ratnum? y) + (binary/ + (binary* ($ratnum-n x) ($ratnum-d y)) + (binary* ($ratnum-n y) ($ratnum-d x)))] + [else (binary/ 1 (binary/ y x))])] + [else (error '/ "~s is not a number" x)]))) (define / (case-lambda @@ -359,6 +516,7 @@ (if (number? x) x (error 'min "~s is not a number" x))])) + (define exact->inexact (lambda (x) (cond diff --git a/src/makefile.ss b/src/makefile.ss index 080cc80..e9ef50a 100755 --- a/src/makefile.ss +++ b/src/makefile.ss @@ -379,6 +379,7 @@ [number->string i r] [string->number i r] [flonum->string i] + [gcd i r] [symbol? i r symbols] [gensym? i symbols] [gensym i symbols]

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