ikarus/scheme/ikarus.fixnums.ss

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;;; Ikarus Scheme -- A compiler for R6RS Scheme.
;;; Copyright (C) 2006,2007,2008 Abdulaziz Ghuloum
;;;
;;; This program is free software: you can redistribute it and/or modify
;;; it under the terms of the GNU General Public License version 3 as
;;; published by the Free Software Foundation.
;;;
;;; This program is distributed in the hope that it will be useful, but
;;; WITHOUT ANY WARRANTY; without even the implied warranty of
;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
;;; General Public License for more details.
;;;
;;; You should have received a copy of the GNU General Public License
;;; along with this program. If not, see <http://www.gnu.org/licenses/>.
(library (ikarus fixnums)
(export fxzero? fxadd1 fxsub1 fxlognot fx+ fx- fx* fxquotient
fx+/carry fx*/carry fx-/carry
fxremainder fxmodulo fxlogor fxlogand fxlogxor fxsll fxsra
fx= fx< fx<= fx> fx>=
fx=? fx<? fx<=? fx>? fx>=?
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fxior fxand fxxor fxnot fxif
fxpositive? fxnegative?
fxeven? fxodd?
fixnum->string
fxarithmetic-shift-left fxarithmetic-shift-right fxarithmetic-shift
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fxmin fxmax
error@fx+ error@fx* error@fx- error@fxadd1 error@fxsub1
error@fxarithmetic-shift-left
error@fxarithmetic-shift-right
)
(import
(ikarus system $fx)
(ikarus system $chars)
(ikarus system $pairs)
(ikarus system $strings)
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(prefix (only (ikarus) fx+ fx* fx-) sys:)
(except (ikarus) fxzero? fxadd1 fxsub1 fxlognot fx+ fx- fx*
fxquotient fxremainder fxmodulo fxlogor fxlogand
fxlogxor fxsll fxsra fx= fx< fx<= fx> fx>=
fx=? fx<? fx<=? fx>? fx>=?
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fxior fxand fxxor fxnot fxif
fxpositive? fxnegative?
fxeven? fxodd?
fxarithmetic-shift-left fxarithmetic-shift-right fxarithmetic-shift
fx+/carry fx*/carry fx-/carry
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fxmin fxmax
fixnum->string))
(define (die/overflow who . args)
(raise
(condition
(make-implementation-restriction-violation)
(make-who-condition who)
(make-message-condition "overflow")
(make-irritants-condition args))))
(define fxzero?
(lambda (x)
(cond
[(eq? x 0) #t]
[(fixnum? x) #f]
[else (die 'fxzero? "not a fixnum" x)])))
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(define fxlognot
(lambda (x)
(unless (fixnum? x)
(die 'fxlognot "not a fixnum" x))
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($fxlognot x)))
(define fxnot
(lambda (x)
(unless (fixnum? x)
(die 'fxnot "not a fixnum" x))
($fxlognot x)))
(define (make-fx-error who)
(case-lambda
[(x y)
(if (fixnum? x)
(if (fixnum? y)
(die/overflow who x y)
(die who "not a fixnum" y))
(die who "not a fixnum" x))]
[(x)
(if (fixnum? x)
(die/overflow who x)
(die who "not a fixnum" x))]))
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(define error@fx+ (make-fx-error 'fx+))
(define error@fx- (make-fx-error 'fx-))
(define error@fx* (make-fx-error 'fx*))
(define error@fxadd1 (make-fx-error 'fxadd1))
(define error@fxsub1 (make-fx-error 'fxsub1))
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(define (fx+ x y) (sys:fx+ x y))
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(define (fx* x y) (sys:fx* x y))
(define fx-
(case-lambda
[(x y) (sys:fx- x y)]
[(x) (sys:fx- x)]))
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(define fxadd1
(lambda (n)
(import (ikarus))
(fxadd1 n)))
(define fxsub1
(lambda (n)
(import (ikarus))
(fxsub1 n)))
(define false-loop
(lambda (who ls)
(if (pair? ls)
(if (fixnum? ($car ls))
(false-loop who ($cdr ls))
(die who "not a fixnum" ($car ls)))
#f)))
(define-syntax fxcmp
(syntax-rules ()
[(_ who $op)
(case-lambda
[(x y)
(unless (fixnum? x)
(die 'who "not a fixnum" x))
(unless (fixnum? y)
(die 'who "not a fixnum" y))
($op x y)]
[(x y . ls)
(if (fixnum? x)
(if (fixnum? y)
(if ($op x y)
(let f ([x y] [ls ls])
(if (pair? ls)
(let ([y ($car ls)] [ls ($cdr ls)])
(if (fixnum? y)
(if ($op x y)
(f y ls)
(false-loop 'who ls))
(die 'who "not a fixnum" y)))
#t))
(false-loop 'who ls))
(die 'who "not a fixnum" y))
(die 'who "not a fixnum" x))]
[(x)
(if (fixnum? x) #t (die 'who "not a fixnum" x))])]))
(define fx= (fxcmp fx= $fx=))
(define fx< (fxcmp fx< $fx<))
(define fx<= (fxcmp fx<= $fx<=))
(define fx> (fxcmp fx> $fx>))
(define fx>= (fxcmp fx>= $fx>=))
(define fx=? (fxcmp fx=? $fx=))
(define fx<? (fxcmp fx<? $fx<))
(define fx<=? (fxcmp fx<=? $fx<=))
(define fx>? (fxcmp fx>? $fx>))
(define fx>=? (fxcmp fx>=? $fx>=))
(define fxquotient
(lambda (x y)
(unless (fixnum? x)
(die 'fxquotient "not a fixnum" x))
(unless (fixnum? y)
(die 'fxquotient "not a fixnum" y))
(when ($fxzero? y)
(die 'fxquotient "zero dividend" y))
(if (eq? y -1)
(if (eq? x (least-fixnum))
(die/overflow 'fxquotient x y)
($fx- 0 x))
($fxquotient x y))))
(define fxremainder
(lambda (x y)
(unless (fixnum? x)
(die 'fxremainder "not a fixnum" x))
(unless (fixnum? y)
(die 'fxremainder "not a fixnum" y))
(when ($fxzero? y)
(die 'fxremainder "zero dividend" y))
(let ([q ($fxquotient x y)])
($fx- x ($fx* q y)))))
(define fxmodulo
(lambda (x y)
(unless (fixnum? x)
(die 'fxmodulo "not a fixnum" x))
(unless (fixnum? y)
(die 'fxmodulo "not a fixnum" y))
(when ($fxzero? y)
(die 'fxmodulo "zero dividend" y))
($fxmodulo x y)))
(define-syntax fxbitop
(syntax-rules ()
[(_ who $op identity)
(case-lambda
[(x y)
(if (fixnum? x)
(if (fixnum? y)
($op x y)
(die 'who "not a fixnum" y))
(die 'who "not a fixnum" x))]
[(x y . ls)
(if (fixnum? x)
(if (fixnum? y)
(let f ([a ($op x y)] [ls ls])
(cond
[(pair? ls)
(let ([b ($car ls)])
(if (fixnum? b)
(f ($op a b) ($cdr ls))
(die 'who "not a fixnum" b)))]
[else a]))
(die 'who "not a fixnum" y))
(die 'who "not a fixnum" x))]
[(x) (if (fixnum? x) x (die 'who "not a fixnum" x))]
[() identity])]))
(define fxlogor (fxbitop fxlogor $fxlogor 0))
(define fxlogand (fxbitop fxlogand $fxlogand -1))
(define fxlogxor (fxbitop fxlogxor $fxlogxor 0))
(define fxior (fxbitop fxior $fxlogor 0))
(define fxand (fxbitop fxand $fxlogand -1))
(define fxxor (fxbitop fxxor $fxlogxor 0))
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(define (fxif x y z)
(if (fixnum? x)
(if (fixnum? y)
(if (fixnum? z)
($fxlogor
($fxlogand x y)
($fxlogand ($fxlognot x) z))
(die 'fxif "not a fixnum" z))
(die 'fxif "not a fixnum" y))
(die 'fxif "not a fixnum" x)))
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(define fxsra
(lambda (x y)
(unless (fixnum? x)
(die 'fxsra "not a fixnum" x))
(unless (fixnum? y)
(die 'fxsra "not a fixnum" y))
(unless ($fx>= y 0)
(die 'fxsra "negative shift not allowed" y))
($fxsra x y)))
(define fxarithmetic-shift-right
(lambda (x y)
(import (ikarus))
(fxarithmetic-shift-right x y)))
(define fxsll
(lambda (x y)
(unless (fixnum? x)
(die 'fxsll "not a fixnum" x))
(unless (fixnum? y)
(die 'fxsll "not a fixnum" y))
(unless ($fx>= y 0)
(die 'fxsll "negative shift not allowed" y))
($fxsll x y)))
(define (error@fxarithmetic-shift who x y)
(unless (fixnum? x)
(die who "not a fixnum" x))
(unless (fixnum? y)
(die who "not a fixnum" y))
(unless ($fx>= y 0)
(die who "negative shift not allowed" y))
(unless ($fx< y (fixnum-width))
(die who "shift is not less than fixnum-width" y))
(die/overflow who x y))
(define (error@fxarithmetic-shift-left x y)
(error@fxarithmetic-shift 'arithmetic-shift-left x y))
(define (error@fxarithmetic-shift-right x y)
(error@fxarithmetic-shift 'arithmetic-shift-right x y))
(define fxarithmetic-shift-left
(lambda (x y)
(import (ikarus))
(fxarithmetic-shift-left x y)))
(define fxarithmetic-shift
(lambda (x y)
(import (ikarus))
(define (err str x) (die 'fxarithmetic-shift str x))
(unless (fixnum? x) (err "not a fixnum" x))
(unless (fixnum? y) (err "not a fixnum" y))
(if ($fx>= y 0)
(if ($fx< y (fixnum-width))
(let ([r ($fxsll x y)])
(if ($fx= x ($fxsra r y))
r
(die/overflow 'fxarithmetic-shift x y)))
(err "invalid shift amount" y))
(if ($fx> y (- (fixnum-width)))
($fxsra x ($fx- 0 y))
(err "invalid shift amount" y)))))
(define (fxpositive? x)
(if (fixnum? x)
($fx> x 0)
(die 'fxpositive? "not a fixnum" x)))
(define (fxnegative? x)
(if (fixnum? x)
($fx< x 0)
(die 'fxnegative? "not a fixnum" x)))
(define (fxeven? x)
(if (fixnum? x)
($fxzero? ($fxlogand x 1))
(die 'fxeven? "not a fixnum" x)))
(define (fxodd? x)
(if (fixnum? x)
(not ($fxzero? ($fxlogand x 1)))
(die 'fxodd? "not a fixnum" x)))
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(define fxmin
(case-lambda
[(x y)
(if (fixnum? x)
(if (fixnum? y)
(if ($fx< x y) x y)
(die 'fxmin "not a fixnum" y))
(die 'fxmin "not a fixnum" x))]
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[(x y z . ls)
(fxmin (fxmin x y)
(if (fixnum? z)
(let f ([z z] [ls ls])
(if (null? ls)
z
(let ([a ($car ls)])
(if (fixnum? a)
(if ($fx< a z)
(f a ($cdr ls))
(f z ($cdr ls)))
(die 'fxmin "not a fixnum" a)))))
(die 'fxmin "not a fixnum" z)))]
[(x) (if (fixnum? x) x (die 'fxmin "not a fixnum" x))]))
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(define fxmax
(case-lambda
[(x y)
(if (fixnum? x)
(if (fixnum? y)
(if ($fx> x y) x y)
(die 'fxmax "not a fixnum" y))
(die 'fxmax "not a fixnum" x))]
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[(x y z . ls)
(fxmax (fxmax x y)
(if (fixnum? z)
(let f ([z z] [ls ls])
(if (null? ls)
z
(let ([a ($car ls)])
(if (fixnum? a)
(if ($fx> a z)
(f a ($cdr ls))
(f z ($cdr ls)))
(die 'fxmax "not a fixnum" a)))))
(die 'fxmax "not a fixnum" z)))]
[(x) (if (fixnum? x) x (die 'fxmax "not a fixnum" x))]))
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(define-syntax define-fx
(syntax-rules ()
[(_ (name arg* ...) body)
(define (name arg* ...)
(unless (fixnum? arg*) (die 'name "not a fixnum" arg*)) ...
body)]))
(define-fx (fx*/carry fx1 fx2 fx3)
(let ([s0 ($fx+ ($fx* fx1 fx2) fx3)])
(values
s0
(sra (+ (* fx1 fx2) (- fx3 s0)) (fixnum-width)))))
(define-fx (fx+/carry fx1 fx2 fx3)
(let ([s0 ($fx+ ($fx+ fx1 fx2) fx3)])
(values
s0
(sra (+ (+ fx1 fx2) (- fx3 s0)) (fixnum-width)))))
(define-fx (fx-/carry fx1 fx2 fx3)
(let ([s0 ($fx- ($fx- fx1 fx2) fx3)])
(values
s0
(sra (- (- fx1 fx2) (+ s0 fx3)) (fixnum-width)))))
(module (fixnum->string)
(define mapping-string "0123456789ABCDEF")
(define f
(lambda (n i j radix)
(cond
[($fxzero? n)
(values (make-string i) j)]
[else
(let* ([q ($fxquotient n radix)]
[c ($string-ref mapping-string
($fx- n ($fx* q radix)))])
(call-with-values
(lambda () (f q ($fxadd1 i) j radix))
(lambda (str j)
(string-set! str j c)
(values str ($fxadd1 j)))))])))
(define $fixnum->string
(lambda (x radix)
(cond
[($fxzero? x) (string #\0)]
[($fx> x 0)
(call-with-values
(lambda () (f x 0 0 radix))
(lambda (str j) str))]
[($fx= x (least-fixnum))
(string-append
($fixnum->string ($fxquotient x radix) radix)
($fixnum->string ($fx- radix ($fxmodulo x radix)) radix))]
[else
(call-with-values
(lambda () (f ($fx- 0 x) 1 1 radix))
(lambda (str j)
($string-set! str 0 #\-)
str))])))
(define fixnum->string
(case-lambda
[(x)
(unless (fixnum? x) (die 'fixnum->string "not a fixnum" x))
($fixnum->string x 10)]
[(x r)
(unless (fixnum? x) (die 'fixnum->string "not a fixnum" x))
(case r
[(2) ($fixnum->string x 2)]
[(8) ($fixnum->string x 8)]
[(10) ($fixnum->string x 10)]
[(16) ($fixnum->string x 16)]
[else (die 'fixnum->string "invalid radix" r)])])))
)
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(library (ikarus fixnums div-and-mod)
(export fxdiv fxmod fxdiv-and-mod fxdiv0 fxmod0 fxdiv0-and-mod0)
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(import
(ikarus system $fx)
(except (ikarus) fxdiv fxmod fxdiv-and-mod fxdiv0 fxmod0 fxdiv0-and-mod0))
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(define ($fxdiv-and-mod n m)
(let ([d0 ($fxquotient n m)])
(let ([m0 ($fx- n ($fx* d0 m))])
(if ($fx>= m0 0)
(values d0 m0)
(if ($fx>= m 0)
(values ($fx- d0 1) ($fx+ m0 m))
(values ($fx+ d0 1) ($fx- m0 m)))))))
(define ($fxdiv n m)
(let ([d0 ($fxquotient n m)])
(if ($fx>= n ($fx* d0 m))
d0
(if ($fx>= m 0)
($fx- d0 1)
($fx+ d0 1)))))
(define ($fxmod n m)
(let ([d0 ($fxquotient n m)])
(let ([m0 ($fx- n ($fx* d0 m))])
(if ($fx>= m0 0)
m0
(if ($fx>= m 0)
($fx+ m0 m)
($fx- m0 m))))))
(define-syntax define-div-proc
(syntax-rules ()
[(_ who $unsafe-op overflow-check?)
(define (who x y)
(if (fixnum? x)
(if (fixnum? y)
(if ($fx> y 0)
($unsafe-op x y)
(if ($fx= y 0)
(die 'who "division by 0" x y)
(if (and overflow-check? ($fx= y -1))
(if ($fx= x (least-fixnum))
(die 'who "result not representable as fixnum"
x y)
($unsafe-op x y))
($unsafe-op x y))))
(die 'who "not a fixnum" y))
(die 'who "not a fixnum" x)))]))
(define-div-proc fxdiv $fxdiv #t)
(define-div-proc fxmod $fxmod #f)
(define-div-proc fxdiv-and-mod $fxdiv-and-mod #t)
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(define ($fxdiv0-and-mod0 n m)
(let ([d0 (quotient n m)])
(let ([m0 (- n (* d0 m))])
(if (>= m 0)
(if (< (* m0 2) m)
(if (<= (* m0 -2) m)
(values d0 m0)
(values (- d0 1) (+ m0 m)))
(values (+ d0 1) (- m0 m)))
(if (> (* m0 -2) m)
(if (>= (* m0 2) m)
(values d0 m0)
(values (+ d0 1) (- m0 m)))
(values (- d0 1) (+ m0 m)))))))
(define ($fxdiv0 n m)
(let ([d0 (quotient n m)])
(let ([m0 (- n (* d0 m))])
(if (>= m 0)
(if (< (* m0 2) m)
(if (<= (* m0 -2) m)
d0
(- d0 1))
(+ d0 1))
(if (> (* m0 -2) m)
(if (>= (* m0 2) m)
d0
(+ d0 1))
(- d0 1))))))
(define ($fxmod0 n m)
(let ([d0 (quotient n m)])
(let ([m0 (- n (* d0 m))])
(if (>= m 0)
(if (< (* m0 2) m)
(if (<= (* m0 -2) m)
m0
(+ m0 m))
(- m0 m))
(if (> (* m0 -2) m)
(if (>= (* m0 2) m)
m0
(- m0 m))
(+ m0 m))))))
(define (fxdiv0-and-mod0 x y)
(if (fixnum? x)
(if (fixnum? y)
(if ($fx= y 0)
(die 'fxdiv0-and-mod0 "division by 0")
(let-values ([(d m) ($fxdiv0-and-mod0 x y)])
(if (and (fixnum? d) (fixnum? m))
(values d m)
(die 'fxdiv0-and-mod0
"results not representable as fixnums"
x y))))
(die 'fxdiv0-and-mod0 "not a fixnum" y))
(die 'fxdiv0-and-mod0 "not a fixnum" x)))
(define (fxdiv0 x y)
(if (fixnum? x)
(if (fixnum? y)
(if ($fx= y 0)
(die 'fxdiv0 "division by 0")
(let ([d ($fxdiv0 x y)])
(if (fixnum? d)
d
(die 'fxdiv0
"result not representable as fixnum"
x y))))
(die 'fxdiv0 "not a fixnum" y))
(die 'fxdiv0 "not a fixnum" x)))
(define (fxmod0 x y)
(if (fixnum? x)
(if (fixnum? y)
(if ($fx= y 0)
(die 'fxmod0 "division by 0")
(let ([d ($fxmod0 x y)])
(if (fixnum? d)
d
(die 'fxmod0
"result not representable as fixnum"
x y))))
(die 'fxmod0 "not a fixnum" y))
(die 'fxmod0 "not a fixnum" x)))
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)
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(library (ikarus fixnums unsafe)
(export $fxzero? $fxadd1 $fxsub1
$fx+ $fx* $fx- $fx= $fx< $fx<= $fx> $fx>=
$fxsll $fxsra $fxlogor $fxlogand $fxlognot)
(import (ikarus))
(define $fxzero? fxzero?)
(define $fxadd1 fxadd1)
(define $fxsub1 fxsub1)
(define $fx+ fx+)
(define $fx* fx*)
(define $fx- fx-)
(define $fx= fx=)
(define $fx< fx<)
(define $fx<= fx<=)
(define $fx> fx>)
(define $fx>= fx>=)
(define $fxsll fxsll)
(define $fxsra fxsra)
(define $fxlogor fxlogor)
(define $fxlogand fxlogand)
(define $fxlognot fxlognot))