3215 lines
107 KiB
Scheme
3215 lines
107 KiB
Scheme
;;; Ikarus Scheme -- A compiler for R6RS Scheme.
|
|
;;; Copyright (C) 2006,2007 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 flonums)
|
|
(export $flonum->exact $flonum->integer flonum-parts
|
|
inexact->exact exact $flonum-rational? $flonum-integer? $flzero?
|
|
$flnegative? flpositive? flabs fixnum->flonum
|
|
flsin flcos fltan flasin flacos flatan fleven? flodd?
|
|
flfloor flceiling flnumerator fldenominator flexp fllog
|
|
flinteger? flonum-bytes flnan? flfinite? flinfinite?
|
|
flexpt $flround flround)
|
|
(import
|
|
(ikarus system $bytevectors)
|
|
(ikarus system $fx)
|
|
(only (ikarus system $flonums) $fl>= $flonum-sbe)
|
|
(ikarus system $bignums)
|
|
(except (ikarus system $flonums) $flonum-rational?
|
|
$flonum-integer? $flround)
|
|
(except (ikarus) inexact->exact exact flpositive? flabs fixnum->flonum
|
|
flsin flcos fltan flasin flacos flatan fleven? flodd?
|
|
flfloor flceiling flnumerator fldenominator flexp fllog
|
|
flexpt flinteger? flonum-parts flonum-bytes flnan? flfinite?
|
|
flinfinite? flround))
|
|
|
|
(define (flonum-bytes f)
|
|
(unless (flonum? f)
|
|
(error 'flonum-bytes "not a flonum" f))
|
|
(values
|
|
($flonum-u8-ref f 0)
|
|
($flonum-u8-ref f 1)
|
|
($flonum-u8-ref f 2)
|
|
($flonum-u8-ref f 3)
|
|
($flonum-u8-ref f 4)
|
|
($flonum-u8-ref f 5)
|
|
($flonum-u8-ref f 6)
|
|
($flonum-u8-ref f 7)))
|
|
(define (flonum-parts x)
|
|
(unless (flonum? x)
|
|
(error 'flonum-parts "not a flonum" x))
|
|
(let-values ([(b0 b1 b2 b3 b4 b5 b6 b7) (flonum-bytes x)])
|
|
(values
|
|
(zero? (fxlogand b0 128))
|
|
(+ (fxsll (fxlogand b0 127) 4)
|
|
(fxsra b1 4))
|
|
(+ (+ b7 (fxsll b6 8) (fxsll b5 16))
|
|
(* (+ b4
|
|
(fxsll b3 8)
|
|
(fxsll b2 16)
|
|
(fxsll (fxlogand b1 #b1111) 24))
|
|
(expt 2 24))))))
|
|
(define ($zero-m? f)
|
|
(and ($fxzero? ($flonum-u8-ref f 7))
|
|
($fxzero? ($flonum-u8-ref f 6))
|
|
($fxzero? ($flonum-u8-ref f 5))
|
|
($fxzero? ($flonum-u8-ref f 4))
|
|
($fxzero? ($flonum-u8-ref f 3))
|
|
($fxzero? ($flonum-u8-ref f 2))
|
|
($fxzero? ($fxlogand ($flonum-u8-ref f 1) #b1111))))
|
|
|
|
(define ($flonum-rational? x)
|
|
(let ([be ($fxlogand ($flonum-sbe x)
|
|
($fxsub1 ($fxsll 1 11)))])
|
|
($fx< be 2047)))
|
|
|
|
(define ($flonum-integer? x)
|
|
(let ([be ($fxlogand ($flonum-sbe x)
|
|
($fxsub1 ($fxsll 1 11)))])
|
|
(cond
|
|
[($fx= be 2047) ;;; nans and infs
|
|
#f]
|
|
[($fx>= be 1075) ;;; magnitue large enough
|
|
#t]
|
|
[($fx= be 0) ;;; denormalized double, only +/-0.0 is integer
|
|
(and ($fx= ($flonum-u8-ref x 7) 0)
|
|
($fx= ($flonum-u8-ref x 6) 0)
|
|
($fx= ($flonum-u8-ref x 5) 0)
|
|
($fx= ($flonum-u8-ref x 4) 0)
|
|
($fx= ($flonum-u8-ref x 3) 0)
|
|
($fx= ($flonum-u8-ref x 2) 0)
|
|
($fx= ($flonum-u8-ref x 1) 0))]
|
|
[($fx< be ($fx+ 1075 -52)) ;;; too small to be an integer
|
|
#f]
|
|
[else ($fl= x ($flround x))])))
|
|
|
|
|
|
(define ($flround x)
|
|
(foreign-call "ikrt_fl_round" x ($make-flonum)))
|
|
|
|
(define (flround x)
|
|
(if (flonum? x)
|
|
($flround x)
|
|
(error 'flround "not a flonum" x)))
|
|
|
|
(module ($flonum->integer $flonum->exact)
|
|
(define ($flonum-signed-mantissa x)
|
|
(let ([b0 ($flonum-u8-ref x 0)])
|
|
(let ([m0 ($fx+ ($flonum-u8-ref x 7)
|
|
($fx+ ($fxsll ($flonum-u8-ref x 6) 8)
|
|
($fxsll ($flonum-u8-ref x 5) 16)))]
|
|
[m1 ($fx+ ($flonum-u8-ref x 4)
|
|
($fx+ ($fxsll ($flonum-u8-ref x 3) 8)
|
|
($fxsll ($flonum-u8-ref x 2) 16)))]
|
|
[m2 (let ([b1 ($flonum-u8-ref x 1)])
|
|
(if (and ($fx= ($fxlogand b0 #x7F) 0)
|
|
($fx= ($fxsra b1 4) 0))
|
|
($fxlogand b1 #xF)
|
|
($fxlogor ($fxlogand b1 #xF) #x10)))])
|
|
(if ($fx= 0 ($fxlogand #x80 b0))
|
|
(+ (bitwise-arithmetic-shift-left ($fxlogor m1 ($fxsll m2 24)) 24) m0)
|
|
(+ (bitwise-arithmetic-shift-left
|
|
($fx- 0 ($fxlogor m1 ($fxsll m2 24))) 24)
|
|
($fx- 0 m0))))))
|
|
(define ($flonum->integer x)
|
|
(let ([sbe ($flonum-sbe x)])
|
|
(let ([be ($fxlogand sbe #x7FF)])
|
|
(cond
|
|
[($fx= be 2047) #f] ;;; nans/infs
|
|
[($fx>= be 1075) ;;; magnitude large enough to be an integer
|
|
(bitwise-arithmetic-shift-left
|
|
($flonum-signed-mantissa x)
|
|
(- be 1075))]
|
|
[else
|
|
(let-values ([(pos? be m) (flonum-parts x)])
|
|
(cond
|
|
[(<= 1 be 2046) ; normalized flonum
|
|
(let ([n (+ m (expt 2 52))]
|
|
[d (expt 2 (- be 1075))])
|
|
(let-values ([(q r) (quotient+remainder n d)])
|
|
(if (= r 0)
|
|
(if pos? q (- q))
|
|
#f)))]
|
|
[(= be 0) (if (= m 0) 0 #f)]
|
|
[else #f]))]))))
|
|
(define-syntax ctexpt
|
|
(lambda (x)
|
|
(import (ikarus))
|
|
(syntax-case x ()
|
|
[(_ n m)
|
|
(expt (syntax->datum #'n) (syntax->datum #'m))])))
|
|
(define ($flonum->exact x)
|
|
(import (ikarus))
|
|
(let ([sbe ($flonum-sbe x)])
|
|
(let ([be ($fxlogand sbe #x7FF)])
|
|
(cond
|
|
[($fx= be 2047) #f] ;;; nans/infs
|
|
[($fx>= be 1075) ;;; magnitude large enough to be an integer
|
|
(bitwise-arithmetic-shift-left
|
|
($flonum-signed-mantissa x)
|
|
(- be 1075))]
|
|
[else
|
|
;;; this really needs to get optimized.
|
|
(let-values ([(pos? be m) (flonum-parts x)])
|
|
(cond
|
|
[(= be 0) ;;; denormalized
|
|
(if (= m 0)
|
|
0
|
|
(* (if pos? 1 -1)
|
|
(/ m (ctexpt 2 1074))))]
|
|
[else ; normalized flonum
|
|
(/ (+ m (ctexpt 2 52))
|
|
(bitwise-arithmetic-shift-left
|
|
(if pos? 1 -1)
|
|
(- 1075 be)))]))])))))
|
|
|
|
(define (flnumerator x)
|
|
(unless (flonum? x)
|
|
(error 'flnumerator "not a flonum" x))
|
|
(cond
|
|
[($flonum-integer? x) x]
|
|
[($flonum-rational? x)
|
|
(exact->inexact (numerator ($flonum->exact x)))]
|
|
[else x]))
|
|
|
|
(define (fldenominator x)
|
|
(unless (flonum? x)
|
|
(error 'fldenominator "not a flonum" x))
|
|
(cond
|
|
[($flonum-integer? x) 1.0]
|
|
[($flonum-rational? x)
|
|
(exact->inexact (denominator ($flonum->exact x)))]
|
|
[(flnan? x) x]
|
|
[else 1.0]))
|
|
|
|
(define (fleven? x)
|
|
;;; FIXME: optimize
|
|
(unless (flonum? x)
|
|
(error 'fleven? "not a flonum" x))
|
|
(let ([v ($flonum->exact x)])
|
|
(cond
|
|
[(fixnum? v) ($fx= ($fxlogand v 1) 0)]
|
|
[(bignum? v)
|
|
(foreign-call "ikrt_even_bn" v)]
|
|
[else (error 'fleven? "not an integer flonum" x)])))
|
|
|
|
(define (flodd? x)
|
|
(unless (flonum? x)
|
|
(error 'flodd? "not a flonum" x))
|
|
;;; FIXME: optimize
|
|
(let ([v ($flonum->exact x)])
|
|
(cond
|
|
[(fixnum? v) ($fx= ($fxlogand v 1) 1)]
|
|
[(bignum? v)
|
|
(not (foreign-call "ikrt_even_bn" v))]
|
|
[else (error 'flodd? "not an integer flonum" x)])))
|
|
|
|
(define (flinteger? x)
|
|
(if (flonum? x)
|
|
($flonum-integer? x)
|
|
(error 'flinteger? "not a flonum" x)))
|
|
|
|
(define (flinfinite? x)
|
|
(if (flonum? x)
|
|
(let ([be (fxlogand ($flonum-sbe x) (sub1 (fxsll 1 11)))])
|
|
(and (fx= be 2047) ;;; nans and infs
|
|
($zero-m? x)))
|
|
(error 'flinfinite? "not a flonum" x)))
|
|
|
|
(define (flnan? x)
|
|
(if (flonum? x)
|
|
(let ([be (fxlogand ($flonum-sbe x) (sub1 (fxsll 1 11)))])
|
|
(and (fx= be 2047) ;;; nans and infs
|
|
(not ($zero-m? x))))
|
|
(error 'flnan? "not a flonum" x)))
|
|
|
|
(define (flfinite? x)
|
|
(if (flonum? x)
|
|
(let ([be (fxlogand ($flonum-sbe x) (sub1 (fxsll 1 11)))])
|
|
(not (fx= be 2047)))
|
|
(error 'flfinite? "not a flonum" x)))
|
|
|
|
(define ($flzero? x)
|
|
(let ([be (fxlogand ($flonum-sbe x) (sub1 (fxsll 1 11)))])
|
|
(and
|
|
(fx= be 0) ;;; denormalized double, only +/-0.0 is integer
|
|
(and (fx= ($flonum-u8-ref x 7) 0)
|
|
(fx= ($flonum-u8-ref x 6) 0)
|
|
(fx= ($flonum-u8-ref x 5) 0)
|
|
(fx= ($flonum-u8-ref x 4) 0)
|
|
(fx= ($flonum-u8-ref x 3) 0)
|
|
(fx= ($flonum-u8-ref x 2) 0)
|
|
(fx= ($flonum-u8-ref x 1) 0)))))
|
|
|
|
(define ($flnegative? x)
|
|
(let ([b0 ($flonum-u8-ref x 0)])
|
|
(fx> b0 127)))
|
|
|
|
|
|
|
|
|
|
|
|
(define (inexact->exact x)
|
|
(cond
|
|
[(flonum? x)
|
|
(or ($flonum->exact x)
|
|
(error 'inexact->exact "no real value" x))]
|
|
[(or (fixnum? x) (ratnum? x) (bignum? x)) x]
|
|
[else
|
|
(error 'inexact->exact "not an inexact number" x)]))
|
|
|
|
(define (exact x)
|
|
(cond
|
|
[(flonum? x)
|
|
(or ($flonum->exact x)
|
|
(error 'exact "no real value" x))]
|
|
[(or (fixnum? x) (ratnum? x) (bignum? x)) x]
|
|
[else
|
|
(error 'exact "not an inexact number" x)]))
|
|
|
|
|
|
(define (flpositive? x)
|
|
(if (flonum? x)
|
|
($fl> x 0.0)
|
|
(error 'flpositive? "not a flonum" x)))
|
|
|
|
(define (flabs x)
|
|
(if (flonum? x)
|
|
(if ($fx> ($flonum-u8-ref x 0) 127)
|
|
($fl* x -1.0)
|
|
x)
|
|
(error 'flabs "not a flonum" x)))
|
|
|
|
(define (fixnum->flonum x)
|
|
(if (fixnum? x)
|
|
($fixnum->flonum x)
|
|
(error 'fixnum->flonum "not a fixnum")))
|
|
|
|
(define (flsin x)
|
|
(if (flonum? x)
|
|
(foreign-call "ikrt_fl_sin" x)
|
|
(error 'flsin "not a flonum" x)))
|
|
|
|
(define (flcos x)
|
|
(if (flonum? x)
|
|
(foreign-call "ikrt_fl_cos" x)
|
|
(error 'flcos "not a flonum" x)))
|
|
|
|
(define (fltan x)
|
|
(if (flonum? x)
|
|
(foreign-call "ikrt_fl_tan" x)
|
|
(error 'fltan "not a flonum" x)))
|
|
|
|
(define (flasin x)
|
|
(if (flonum? x)
|
|
(foreign-call "ikrt_fl_asin" x)
|
|
(error 'flasin "not a flonum" x)))
|
|
|
|
(define (flacos x)
|
|
(if (flonum? x)
|
|
(foreign-call "ikrt_fl_acos" x)
|
|
(error 'flacos "not a flonum" x)))
|
|
|
|
(define (flatan x)
|
|
(if (flonum? x)
|
|
(foreign-call "ikrt_fl_atan" x)
|
|
(error 'flatan "not a flonum" x)))
|
|
|
|
|
|
(define (flfloor x)
|
|
(define (ratnum-floor x)
|
|
(let ([n (numerator x)] [d (denominator x)])
|
|
(let ([q (quotient n d)])
|
|
(if (>= n 0) q (- q 1)))))
|
|
(cond
|
|
[(flonum? x)
|
|
;;; optimize for integer flonums case
|
|
(let ([e ($flonum->exact x)])
|
|
(cond
|
|
[(ratnum? e)
|
|
(exact->inexact (ratnum-floor e))]
|
|
[else x]))]
|
|
[else (error 'flfloor "not a flonum" x)]))
|
|
|
|
(define (flceiling x)
|
|
(cond
|
|
[(flonum? x)
|
|
;;; optimize for integer flonums case
|
|
(let ([e ($flonum->exact x)])
|
|
(cond
|
|
[(ratnum? e)
|
|
(exact->inexact (ceiling e))]
|
|
[else x]))]
|
|
[else (error 'flceiling "not a flonum" x)]))
|
|
|
|
(define (flexp x)
|
|
(if (flonum? x)
|
|
(foreign-call "ikrt_fl_exp" x ($make-flonum))
|
|
(error 'flexp "not a flonum" x)))
|
|
|
|
(define (fllog x)
|
|
(if (flonum? x)
|
|
(if ($fl>= x 0.0)
|
|
(foreign-call "ikrt_fl_log" x)
|
|
(error 'fllog "argument should not be negative" x))
|
|
(error 'fllog "not a flonum" x)))
|
|
|
|
(define (flexpt x y)
|
|
(if (flonum? x)
|
|
(if (flonum? y)
|
|
(let ([y^ ($flonum->exact y)])
|
|
;;; FIXME: performance bottleneck?
|
|
(cond
|
|
[(fixnum? y^) (inexact (expt x y^))]
|
|
[(bignum? y^) (inexact (expt x y^))]
|
|
[else
|
|
(foreign-call "ikrt_flfl_expt" x y ($make-flonum))]))
|
|
(error 'flexpt "not a flonum" y))
|
|
(error 'fllog "not a flonum" x)))
|
|
|
|
|
|
)
|
|
|
|
|
|
|
|
|
|
|
|
(library (ikarus generic-arithmetic)
|
|
(export + - * / zero? = < <= > >= add1 sub1 quotient remainder
|
|
modulo even? odd? bitwise-and bitwise-not
|
|
bitwise-arithmetic-shift-right bitwise-arithmetic-shift-left
|
|
bitwise-arithmetic-shift
|
|
positive? negative? expt gcd lcm numerator denominator exact-integer-sqrt
|
|
quotient+remainder number->string string->number min max
|
|
abs truncate fltruncate sra sll real->flonum
|
|
exact->inexact inexact floor ceiling round log fl=? fl<? fl<=? fl>?
|
|
fl>=? fl+ fl- fl* fl/ flsqrt flmin flzero? flnegative?
|
|
sin cos tan asin acos atan sqrt exp
|
|
flmax random)
|
|
(import
|
|
(ikarus system $fx)
|
|
(ikarus system $flonums)
|
|
(ikarus system $ratnums)
|
|
(ikarus system $bignums)
|
|
(ikarus system $chars)
|
|
(ikarus system $strings)
|
|
(only (ikarus flonums) $flonum->exact $flzero? $flnegative?
|
|
$flonum->integer $flround)
|
|
(except (ikarus) + - * / zero? = < <= > >= add1 sub1 quotient
|
|
remainder modulo even? odd? quotient+remainder number->string
|
|
bitwise-arithmetic-shift-right bitwise-arithmetic-shift-left
|
|
bitwise-arithmetic-shift
|
|
positive? negative? bitwise-and bitwise-not
|
|
string->number expt gcd lcm numerator denominator
|
|
exact->inexact inexact floor ceiling round log
|
|
exact-integer-sqrt min max abs real->flonum
|
|
fl=? fl<? fl<=? fl>? fl>=? fl+ fl- fl* fl/ flsqrt flmin
|
|
flzero? flnegative? sra sll exp
|
|
sin cos tan asin acos atan sqrt truncate fltruncate
|
|
flmax random))
|
|
|
|
|
|
(module (bignum->flonum)
|
|
; sbe f6 f5 f4 f3 f2 f1 f0
|
|
;SEEEEEEE|EEEEmmmm|mmmmmmmm|mmmmmmmm|mmmmmmmm|mmmmmmmm|mmmmmmmm|mmmmmmmm
|
|
; | | | | | | |
|
|
; v0 v1 v2 v3 v4 v5 v6 v7
|
|
(define ($flonum pos? e f6 f5 f4 f3 f2 f1 f0)
|
|
(let ([be (fx+ e 1075)])
|
|
(let ([v ($make-flonum)])
|
|
(cond
|
|
[(fx< be 2047)
|
|
(let ([sbe (if pos? be (fxlogor be (fxsll 1 11)))])
|
|
($flonum-set! v 0 (fxsra sbe 4))
|
|
($flonum-set! v 1 (fxlogor (fxsll sbe 4) (fxlogand f6 #b1111)))
|
|
($flonum-set! v 2 f5)
|
|
($flonum-set! v 3 f4)
|
|
($flonum-set! v 4 f3)
|
|
($flonum-set! v 5 f2)
|
|
($flonum-set! v 6 f1)
|
|
($flonum-set! v 7 f0))]
|
|
[else ;;; inf
|
|
(let ([sbe (if pos? 2047 (fxlogor 2047 (fxsll 1 11)))])
|
|
($flonum-set! v 0 (fxsra sbe 4))
|
|
($flonum-set! v 1 (fxsll sbe 4))
|
|
($flonum-set! v 2 0)
|
|
($flonum-set! v 3 0)
|
|
($flonum-set! v 4 0)
|
|
($flonum-set! v 5 0)
|
|
($flonum-set! v 6 0)
|
|
($flonum-set! v 7 0))])
|
|
v)))
|
|
(define ($flonum/c0 pos? e f6 f5 f4 f3 f2 f1 f0 c)
|
|
(define ($fxeven? x)
|
|
(fxzero? (fxlogand x 1)))
|
|
(define-syntax cond*
|
|
(syntax-rules (else)
|
|
[(_ [test conseq] [else val])
|
|
(if test conseq val)]
|
|
[(_ [test conseq] [var val] rest ...)
|
|
(if test conseq (let ([var val]) (cond* rest ...)))]))
|
|
(cond*
|
|
[($fxeven? c) ($flonum pos? e f6 f5 f4 f3 f2 f1 f0)]
|
|
[f0 (fx+ (fxlogand f0 255) 1)]
|
|
[(fx< f0 256) ($flonum pos? e f6 f5 f4 f3 f2 f1 f0)]
|
|
[f1 (fx+ (fxlogand f1 255) 1)]
|
|
[(fx< f1 256) ($flonum pos? e f6 f5 f4 f3 f2 f1 0)]
|
|
[f2 (fx+ (fxlogand f2 255) 1)]
|
|
[(fx< f2 256) ($flonum pos? e f6 f5 f4 f3 f2 0 0)]
|
|
[f3 (fx+ (fxlogand f3 255) 1)]
|
|
[(fx< f3 256) ($flonum pos? e f6 f5 f4 f3 0 0 0)]
|
|
[f4 (fx+ (fxlogand f4 255) 1)]
|
|
[(fx< f4 256) ($flonum pos? e f6 f5 f4 0 0 0 0)]
|
|
[f5 (fx+ (fxlogand f5 255) 1)]
|
|
[(fx< f5 256) ($flonum pos? e f6 f5 0 0 0 0 0)]
|
|
[f6 (fx+ (fxlogand f6 #b1111) 1)]
|
|
[(fx< f6 16) ($flonum pos? e f6 0 0 0 0 0 0)]
|
|
[else ($flonum pos? (+ e 1) 0 0 0 0 0 0 0)]))
|
|
(define ($flonum/aux pos? e b7 b6 b5 b4 b3 b2 b1 b0)
|
|
(cond
|
|
[(fx>= b7 #x80)
|
|
($flonum/c0 pos? (fx+ e 3)
|
|
(fxsra b7 3)
|
|
(fxlogor (fxsll b7 5) (fxsra b6 3))
|
|
(fxlogor (fxsll b6 5) (fxsra b5 3))
|
|
(fxlogor (fxsll b5 5) (fxsra b4 3))
|
|
(fxlogor (fxsll b4 5) (fxsra b3 3))
|
|
(fxlogor (fxsll b3 5) (fxsra b2 3))
|
|
(fxlogor (fxsll b2 5) (fxsra b1 3))
|
|
(fxsra b1 2))]
|
|
[(fx>= b7 #x40)
|
|
($flonum/c0 pos? (fx+ e 2)
|
|
(fxsra b7 2)
|
|
(fxlogor (fxsll b7 6) (fxsra b6 2))
|
|
(fxlogor (fxsll b6 6) (fxsra b5 2))
|
|
(fxlogor (fxsll b5 6) (fxsra b4 2))
|
|
(fxlogor (fxsll b4 6) (fxsra b3 2))
|
|
(fxlogor (fxsll b3 6) (fxsra b2 2))
|
|
(fxlogor (fxsll b2 6) (fxsra b1 2))
|
|
(fxsra b1 1))]
|
|
[(fx>= b7 #x20)
|
|
($flonum/c0 pos? (fx+ e 1)
|
|
(fxsra b7 1)
|
|
(fxlogor (fxsll b7 7) (fxsra b6 1))
|
|
(fxlogor (fxsll b6 7) (fxsra b5 1))
|
|
(fxlogor (fxsll b5 7) (fxsra b4 1))
|
|
(fxlogor (fxsll b4 7) (fxsra b3 1))
|
|
(fxlogor (fxsll b3 7) (fxsra b2 1))
|
|
(fxlogor (fxsll b2 7) (fxsra b1 1))
|
|
b1)]
|
|
[(fx>= b7 #x10)
|
|
($flonum/c0 pos? e b7 b6 b5 b4 b3 b2 b1
|
|
(fxsra b0 7))]
|
|
[(fx>= b7 #x08)
|
|
($flonum/c0 pos? (fx- e 1)
|
|
(fxlogor (fxsll b7 1) (fxsra b6 7))
|
|
(fxlogor (fxsll b6 1) (fxsra b5 7))
|
|
(fxlogor (fxsll b5 1) (fxsra b4 7))
|
|
(fxlogor (fxsll b4 1) (fxsra b3 7))
|
|
(fxlogor (fxsll b3 1) (fxsra b2 7))
|
|
(fxlogor (fxsll b2 1) (fxsra b1 7))
|
|
(fxlogor (fxsll b1 1) (fxsra b0 7))
|
|
(fxsra b0 6))]
|
|
[(fx>= b7 #x04)
|
|
($flonum/c0 pos? (fx- e 2)
|
|
(fxlogor (fxsll b7 2) (fxsra b6 6))
|
|
(fxlogor (fxsll b6 2) (fxsra b5 6))
|
|
(fxlogor (fxsll b5 2) (fxsra b4 6))
|
|
(fxlogor (fxsll b4 2) (fxsra b3 6))
|
|
(fxlogor (fxsll b3 2) (fxsra b2 6))
|
|
(fxlogor (fxsll b2 2) (fxsra b1 6))
|
|
(fxlogor (fxsll b1 2) (fxsra b0 6))
|
|
(fxsra b0 5))]
|
|
[(fx>= b7 #x02)
|
|
($flonum/c0 pos? (fx- e 3)
|
|
(fxlogor (fxsll b7 3) (fxsra b6 5))
|
|
(fxlogor (fxsll b6 3) (fxsra b5 5))
|
|
(fxlogor (fxsll b5 3) (fxsra b4 5))
|
|
(fxlogor (fxsll b4 3) (fxsra b3 5))
|
|
(fxlogor (fxsll b3 3) (fxsra b2 5))
|
|
(fxlogor (fxsll b2 3) (fxsra b1 5))
|
|
(fxlogor (fxsll b1 3) (fxsra b0 5))
|
|
(fxsra b0 4))]
|
|
[(fx>= b7 #x01)
|
|
($flonum/c0 pos? (fx- e 4)
|
|
(fxlogor (fxsll b7 4) (fxsra b6 4))
|
|
(fxlogor (fxsll b6 4) (fxsra b5 4))
|
|
(fxlogor (fxsll b5 4) (fxsra b4 4))
|
|
(fxlogor (fxsll b4 4) (fxsra b3 4))
|
|
(fxlogor (fxsll b3 4) (fxsra b2 4))
|
|
(fxlogor (fxsll b2 4) (fxsra b1 4))
|
|
(fxlogor (fxsll b1 4) (fxsra b0 4))
|
|
(fxsra b0 3))]
|
|
[else (error '$float/aux "BUG: invalid b7" b7)]))
|
|
(define (bignum->flonum x)
|
|
(define (bignum/4->flonum x)
|
|
($flonum/aux ($bignum-positive? x) -24
|
|
($bignum-byte-ref x 3)
|
|
($bignum-byte-ref x 2)
|
|
($bignum-byte-ref x 1)
|
|
($bignum-byte-ref x 0)
|
|
0 0 0 0))
|
|
(define (bignum/8->flonum x)
|
|
;;; bignum: [b0 b1 b2 b3 b4 b5 b6 b7]
|
|
(let ([b0 ($bignum-byte-ref x 0)]
|
|
[b1 ($bignum-byte-ref x 1)]
|
|
[b2 ($bignum-byte-ref x 2)]
|
|
[b3 ($bignum-byte-ref x 3)]
|
|
[b4 ($bignum-byte-ref x 4)]
|
|
[b5 ($bignum-byte-ref x 5)]
|
|
[b6 ($bignum-byte-ref x 6)]
|
|
[b7 ($bignum-byte-ref x 7)]
|
|
[pos? ($bignum-positive? x)])
|
|
(if (fx= b7 0)
|
|
(if (fx= b6 0)
|
|
(if (fx= b5 0)
|
|
(if (fx= b4 0)
|
|
(error 'bignum8->flonum "malformed bignum")
|
|
($flonum/aux pos? -16 b4 b3 b2 b1 b0 0 0 0))
|
|
($flonum/aux pos? -8 b5 b4 b3 b2 b1 b0 0 0))
|
|
($flonum/aux pos? 0 b6 b5 b4 b3 b2 b1 b0 0))
|
|
($flonum/aux pos? 8 b7 b6 b5 b4 b3 b2 b1 b0))))
|
|
(define (bignum/n->flonum x bytes)
|
|
(define (aux x b7 bytes)
|
|
($flonum/aux ($bignum-positive? x) (+ (* bytes 8) -48)
|
|
b7
|
|
($bignum-byte-ref x (fx- bytes 1))
|
|
($bignum-byte-ref x (fx- bytes 2))
|
|
($bignum-byte-ref x (fx- bytes 3))
|
|
($bignum-byte-ref x (fx- bytes 4))
|
|
($bignum-byte-ref x (fx- bytes 5))
|
|
($bignum-byte-ref x (fx- bytes 6))
|
|
($bignum-byte-ref x (fx- bytes 7))))
|
|
;;; bignum: [b0 b1 b2 b3 ... b_{bytes-1}]
|
|
(let* ([bytes (fxsub1 bytes)] [bn ($bignum-byte-ref x bytes)])
|
|
(if (fx= bn 0)
|
|
(let* ([bytes (fxsub1 bytes)] [bn ($bignum-byte-ref x bytes)])
|
|
(if (fx= bn 0)
|
|
(let* ([bytes (fxsub1 bytes)] [bn ($bignum-byte-ref x bytes)])
|
|
(if (fx= bn 0)
|
|
(let* ([bytes (fxsub1 bytes)] [bn ($bignum-byte-ref x bytes)])
|
|
(if (fx= bn 0)
|
|
(error 'bignum/n->flonum "malformed bignum")
|
|
(aux x bn bytes)))
|
|
(aux x bn bytes)))
|
|
(aux x bn bytes)))
|
|
(aux x bn bytes))))
|
|
|
|
(unless (bignum? x)
|
|
(error 'bignum->flonum "not a bignum" x))
|
|
(let ([bytes ($bignum-size x)])
|
|
(case bytes
|
|
[(4) (bignum/4->flonum x)]
|
|
[(8) (bignum/8->flonum x)]
|
|
[else (bignum/n->flonum x bytes)]))))
|
|
|
|
|
|
|
|
;;; (define (ratnum->flonum x)
|
|
;;; (define (->flonum n d)
|
|
;;; (let-values ([(q r) (quotient+remainder n d)])
|
|
;;; (if (= r 0)
|
|
;;; (inexact q)
|
|
;;; (if (= q 0)
|
|
;;; (/ (->flonum d n))
|
|
;;; (+ q (->flonum r d))))))
|
|
;;; (let ([n (numerator x)] [d (denominator x)])
|
|
;;; (let ([b (bitwise-first-bit-set n)])
|
|
;;; (if (eqv? b 0)
|
|
;;; (let ([b (bitwise-first-bit-set d)])
|
|
;;; (if (eqv? b 0)
|
|
;;; (->flonum n d)
|
|
;;; (/ (->flonum n (bitwise-arithmetic-shift-right d b))
|
|
;;; (expt 2.0 b))))
|
|
;;; (* (->flonum (bitwise-arithmetic-shift-right n b) d)
|
|
;;; (expt 2.0 b))))))
|
|
(define (ratnum->flonum x)
|
|
(let f ([n ($ratnum-n x)] [d ($ratnum-d x)])
|
|
(let-values ([(q r) (quotient+remainder n d)])
|
|
(if (= q 0)
|
|
(/ 1.0 (f d n))
|
|
(if (= r 0)
|
|
(inexact q)
|
|
(+ q (f r d)))))))
|
|
|
|
(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)]
|
|
[(ratnum? y)
|
|
($make-ratnum
|
|
(+ (* x ($ratnum-d y)) ($ratnum-n y))
|
|
($ratnum-d y))]
|
|
[else
|
|
(error '+ "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)
|
|
($fl+ (bignum->flonum x) y)]
|
|
[(ratnum? y)
|
|
($make-ratnum
|
|
(+ (* x ($ratnum-d y)) ($ratnum-n y))
|
|
($ratnum-d y))]
|
|
[else
|
|
(error '+ "not a number" y)])]
|
|
[(flonum? x)
|
|
(cond
|
|
[(fixnum? y)
|
|
($fl+ x ($fixnum->flonum y))]
|
|
[(bignum? y)
|
|
($fl+ x (bignum->flonum y))]
|
|
[(flonum? y)
|
|
($fl+ x y)]
|
|
[(ratnum? y)
|
|
($fl+ x (ratnum->flonum y))]
|
|
[else
|
|
(error '+ "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 ($ratnum-d y)])
|
|
;;; FIXME: inefficient
|
|
(/ (+ (* n0 d1) (* n1 d0)) (* d0 d1)))]
|
|
[else
|
|
(error '+ "not a number" y)])]
|
|
[else (error '+ "not a number" x)])))
|
|
|
|
(define binary-bitwise-and
|
|
(lambda (x y)
|
|
(cond
|
|
[(fixnum? x)
|
|
(cond
|
|
[(fixnum? y) ($fxlogand x y)]
|
|
[(bignum? y)
|
|
(foreign-call "ikrt_fxbnlogand" x y)]
|
|
[else
|
|
(error 'bitwise-and "not an exact integer" y)])]
|
|
[(bignum? x)
|
|
(cond
|
|
[(fixnum? y)
|
|
(foreign-call "ikrt_fxbnlogand" y x)]
|
|
[(bignum? y)
|
|
(foreign-call "ikrt_bnbnlogand" x y)]
|
|
[else
|
|
(error 'bitwise-and "not an exact integer" y)])]
|
|
[else (error 'bitwise-and "not an exact integer" 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)
|
|
(if ($fx= x 0)
|
|
($fl* y -1.0)
|
|
($fl- ($fixnum->flonum x) y))]
|
|
[(ratnum? y)
|
|
(let ([n ($ratnum-n y)] [d ($ratnum-d y)])
|
|
(binary/ (binary- (binary* d x) n) d))]
|
|
[else
|
|
(error '- "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)
|
|
($fl- (bignum->flonum x) y)]
|
|
[(ratnum? y)
|
|
(let ([n ($ratnum-n y)] [d ($ratnum-d y)])
|
|
(binary/ (binary- (binary* d x) n) d))]
|
|
[else
|
|
(error '- "not a number" y)])]
|
|
[(flonum? x)
|
|
(cond
|
|
[(fixnum? y)
|
|
($fl- x ($fixnum->flonum y))]
|
|
[(bignum? y)
|
|
($fl- x (bignum->flonum y))]
|
|
[(flonum? y)
|
|
($fl- x y)]
|
|
[(ratnum? y)
|
|
(let ([n ($ratnum-n y)] [d ($ratnum-d y)])
|
|
(binary/ (binary- (binary* d x) n) d))]
|
|
[else
|
|
(error '- "not a number" y)])]
|
|
[(ratnum? x)
|
|
(let ([nx ($ratnum-n x)] [dx ($ratnum-d x)])
|
|
(cond
|
|
[(or (fixnum? y) (bignum? y) (flonum? y))
|
|
(binary/ (binary- nx (binary* dx y)) dx)]
|
|
[(ratnum? y)
|
|
(let ([ny ($ratnum-n y)] [dy ($ratnum-d y)])
|
|
(binary/ (binary- (binary* nx dy) (binary* ny dx))
|
|
(binary* dx dy)))]
|
|
[else
|
|
(error '- "not a number" y)]))]
|
|
[else (error '- "not a number" x)])))
|
|
|
|
(define binary*
|
|
(lambda (x y)
|
|
(cond
|
|
[(fixnum? x)
|
|
(cond
|
|
[(fixnum? y)
|
|
(foreign-call "ikrt_fxfxmult" x y)]
|
|
[(bignum? y)
|
|
(foreign-call "ikrt_fxbnmult" x y)]
|
|
[(flonum? y)
|
|
($fl* ($fixnum->flonum x) y)]
|
|
[(ratnum? y)
|
|
(binary/ (binary* x ($ratnum-n y)) ($ratnum-d y))]
|
|
[else
|
|
(error '* "not a number" y)])]
|
|
[(bignum? x)
|
|
(cond
|
|
[(fixnum? y)
|
|
(foreign-call "ikrt_fxbnmult" y x)]
|
|
[(bignum? y)
|
|
(foreign-call "ikrt_bnbnmult" x y)]
|
|
[(flonum? y)
|
|
($fl* (bignum->flonum x) y)]
|
|
[(ratnum? y)
|
|
(binary/ (binary* x ($ratnum-n y)) ($ratnum-d y))]
|
|
[else
|
|
(error '* "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)]
|
|
[(ratnum? y)
|
|
(binary/ (binary* x ($ratnum-n y)) ($ratnum-d y))]
|
|
[else
|
|
(error '* "not a number" y)])]
|
|
[(ratnum? x)
|
|
(if (ratnum? y)
|
|
(binary/ (binary* ($ratnum-n x) ($ratnum-n y))
|
|
(binary* ($ratnum-d x) ($ratnum-d y)))
|
|
(binary* y x))]
|
|
[else (error '* "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 '+ "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 bitwise-and
|
|
(case-lambda
|
|
[(x y) (binary-bitwise-and x y)]
|
|
[(x y z) (binary-bitwise-and (binary-bitwise-and x y) z)]
|
|
[(a)
|
|
(cond
|
|
[(fixnum? a) a]
|
|
[(bignum? a) a]
|
|
[else (error 'bitwise-and "not a number" a)])]
|
|
[() -1]
|
|
[(a b c d . e*)
|
|
(let f ([ac (binary-bitwise-and a
|
|
(binary-bitwise-and b
|
|
(binary-bitwise-and c d)))]
|
|
[e* e*])
|
|
(cond
|
|
[(null? e*) ac]
|
|
[else (f (binary-bitwise-and ac (car e*)) (cdr e*))]))]))
|
|
|
|
(define (bitwise-not x)
|
|
(cond
|
|
[(fixnum? x) ($fxlognot x)]
|
|
[(bignum? x) (foreign-call "ikrt_bnlognot" x)]
|
|
[else (error 'bitwise-not "invalid argument" x)]))
|
|
|
|
(define -
|
|
(case-lambda
|
|
[(x y) (binary- x y)]
|
|
[(x y z) (binary- (binary- x y) z)]
|
|
[(a) (binary- 0 a)]
|
|
[(a b c d . e*)
|
|
(let f ([ac (binary- (binary- (binary- a b) c) d)]
|
|
[e* e*])
|
|
(cond
|
|
[(null? e*) ac]
|
|
[else (f (binary- ac (car e*)) (cdr e*))]))]))
|
|
|
|
(define *
|
|
(case-lambda
|
|
[(x y) (binary* x y)]
|
|
[(x y z) (binary* (binary* x y) z)]
|
|
[(a)
|
|
(cond
|
|
[(fixnum? a) a]
|
|
[(bignum? a) a]
|
|
[else (error '* "not a number" a)])]
|
|
[() 1]
|
|
[(a b c d . e*)
|
|
(let f ([ac (binary* (binary* (binary* a b) c) d)]
|
|
[e* e*])
|
|
(cond
|
|
[(null? e*) ac]
|
|
[else (f (binary* ac (car e*)) (cdr e*))]))]))
|
|
|
|
(define (binary-gcd x y)
|
|
(define (gcd x y)
|
|
(cond
|
|
[($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 "not an exact integer" y)]
|
|
[else
|
|
(error 'gcd "not a number" y)])]
|
|
[(number? x)
|
|
(error 'gcd "not an exact integer" x)]
|
|
[else
|
|
(error 'gcd "not a number" x)])]
|
|
[(x)
|
|
(cond
|
|
[(or (fixnum? x) (bignum? x)) x]
|
|
[(number? x)
|
|
(error 'gcd "not an exact integer" x)]
|
|
[else
|
|
(error 'gcd "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 lcm
|
|
(case-lambda
|
|
[(x y)
|
|
(cond
|
|
[(or (fixnum? x) (bignum? x))
|
|
(cond
|
|
[(or (fixnum? y) (bignum? y))
|
|
(let ([x (if (< x 0) (- x) x)]
|
|
[y (if (< y 0) (- y) y)])
|
|
(let ([g (binary-gcd x y)])
|
|
(binary* y (quotient x g))))]
|
|
[(number? y)
|
|
(error 'lcm "not an exact integer" y)]
|
|
[else
|
|
(error 'lcm "not a number" y)])]
|
|
[(number? x)
|
|
(error 'lcm "not an exact integer" x)]
|
|
[else
|
|
(error 'lcm "not a number" x)])]
|
|
[(x)
|
|
(cond
|
|
[(or (fixnum? x) (bignum? x)) x]
|
|
[(number? x)
|
|
(error 'lcm "not an exact integer" x)]
|
|
[else
|
|
(error 'lcm "not a number" x)])]
|
|
[() 1]
|
|
[(x y z . ls)
|
|
(let f ([g (lcm (lcm x y) z)] [ls ls])
|
|
(cond
|
|
[(null? ls) g]
|
|
[else (f (lcm g (car ls)) (cdr ls))]))]))
|
|
|
|
|
|
|
|
|
|
(define binary/ ;;; implements ratnums
|
|
(lambda (x y)
|
|
(cond
|
|
[(flonum? x)
|
|
(cond
|
|
[(flonum? y) ($fl/ x y)]
|
|
[(fixnum? y) ($fl/ x ($fixnum->flonum y))]
|
|
[(bignum? y) ($fl/ x (bignum->flonum y))]
|
|
[(ratnum? y) ($fl/ x (ratnum->flonum y))]
|
|
[else (error '/ "not a number" y)])]
|
|
[(fixnum? x)
|
|
(cond
|
|
[(flonum? y) ($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)) ($ratnum-n y))]
|
|
[else (error '/ "not a number" y)])]
|
|
[(bignum? x)
|
|
(cond
|
|
[(fixnum? y)
|
|
(cond
|
|
[($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 '/ "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 '/ "not a number" x)])))
|
|
|
|
(define /
|
|
(case-lambda
|
|
[(x y) (binary/ x y)]
|
|
[(x)
|
|
(cond
|
|
[(fixnum? x)
|
|
(cond
|
|
[($fxzero? x) (error '/ "division by 0")]
|
|
[($fx> x 0)
|
|
(if ($fx= x 1)
|
|
1
|
|
($make-ratnum 1 x))]
|
|
[else
|
|
(if ($fx= x -1)
|
|
-1
|
|
($make-ratnum -1 (- x)))])]
|
|
[(bignum? x)
|
|
(if ($bignum-positive? x)
|
|
($make-ratnum 1 x)
|
|
($make-ratnum -1 (- x)))]
|
|
[(flonum? x) (foreign-call "ikrt_fl_invert" x)]
|
|
[(ratnum? x)
|
|
(let ([n ($ratnum-n x)] [d ($ratnum-d x)])
|
|
(cond
|
|
[($fx= n 1) d]
|
|
[($fx= n -1) (- d)]
|
|
[else ($make-ratnum d n)]))]
|
|
[else (error '/ "not a number" 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 flmax
|
|
(case-lambda
|
|
[(x y)
|
|
(if (flonum? x)
|
|
(if (flonum? y)
|
|
(if ($fl< x y)
|
|
y
|
|
x)
|
|
(error 'flmax "not a flonum" y))
|
|
(error 'flmax "not a flonum" x))]
|
|
[(x y z . rest)
|
|
(let f ([a (flmax x y)] [b z] [ls rest])
|
|
(cond
|
|
[(null? ls) (flmax a b)]
|
|
[else
|
|
(f (flmax a b) (car ls) (cdr ls))]))]
|
|
[(x)
|
|
(if (flonum? x)
|
|
x
|
|
(error 'flmax "not a number" x))]))
|
|
|
|
(define max
|
|
(case-lambda
|
|
[(x y)
|
|
(cond
|
|
[(fixnum? x)
|
|
(cond
|
|
[(fixnum? y)
|
|
(if ($fx> x y) x y)]
|
|
[(bignum? y)
|
|
(if (positive-bignum? y) y x)]
|
|
[(flonum? y)
|
|
(let ([x ($fixnum->flonum x)])
|
|
(if ($fl>= y x) y x))]
|
|
[(ratnum? y) ;;; FIXME: optimize
|
|
(if (>= x y) x y)]
|
|
[else (error 'max "not a number" y)])]
|
|
[(bignum? x)
|
|
(cond
|
|
[(fixnum? y)
|
|
(if (positive-bignum? x) x y)]
|
|
[(bignum? y)
|
|
(if (bnbn> x y) x y)]
|
|
[(flonum? y)
|
|
(let ([x (bignum->flonum x)])
|
|
(if ($fl>= y x) y x))]
|
|
[(ratnum? y) ;;; FIXME: optimize
|
|
(if (>= x y) x y)]
|
|
[else (error 'max "not a number" y)])]
|
|
[(flonum? x)
|
|
(cond
|
|
[(flonum? y)
|
|
(if ($fl>= x y) x y)]
|
|
[(fixnum? y)
|
|
(let ([y ($fixnum->flonum y)])
|
|
(if ($fl>= y x) y x))]
|
|
[(bignum? y)
|
|
(let ([y (bignum->flonum y)])
|
|
(if ($fl>= y x) y x))]
|
|
[(ratnum? y)
|
|
;;; FIXME: may be incorrect
|
|
(let ([y (ratnum->flonum y)])
|
|
(if ($fl>= y x) y x))]
|
|
[else (error 'max "not a number" y)])]
|
|
[(ratnum? x)
|
|
(cond
|
|
[(or (fixnum? y) (bignum? y) (ratnum? y))
|
|
(if (>= x y) x y)]
|
|
[(flonum? y)
|
|
(let ([x (ratnum->flonum x)])
|
|
(if ($fl>= x y) x y))]
|
|
[else (error 'max "not a number" y)])]
|
|
[else (error 'max "not a number" x)])]
|
|
[(x y z . rest)
|
|
(let f ([a (max x y)] [b z] [ls rest])
|
|
(cond
|
|
[(null? ls) (max a b)]
|
|
[else
|
|
(f (max a b) (car ls) (cdr ls))]))]
|
|
[(x)
|
|
(if (number? x)
|
|
x
|
|
(error 'max "not a number" x))]))
|
|
|
|
(define min
|
|
(case-lambda
|
|
[(x y)
|
|
(cond
|
|
[(fixnum? x)
|
|
(cond
|
|
[(fixnum? y)
|
|
(if ($fx> x y) y x)]
|
|
[(bignum? y)
|
|
(if (positive-bignum? y) x y)]
|
|
[(flonum? y)
|
|
(let ([x ($fixnum->flonum x)])
|
|
(if ($fl>= y x) x y))]
|
|
[(ratnum? y) ;;; FIXME: optimize
|
|
(if (>= x y) y x)]
|
|
[else (error 'min "not a number" y)])]
|
|
[(bignum? x)
|
|
(cond
|
|
[(fixnum? y)
|
|
(if (positive-bignum? x) y x)]
|
|
[(bignum? y)
|
|
(if (bnbn> x y) y x)]
|
|
[(flonum? y)
|
|
(let ([x (bignum->flonum x)])
|
|
(if ($fl>= y x) x y))]
|
|
[(ratnum? y) ;;; FIXME: optimize
|
|
(if (>= x y) y x)]
|
|
[else (error 'min "not a number" y)])]
|
|
[(flonum? x)
|
|
(cond
|
|
[(flonum? y)
|
|
(if ($fl>= x y) y x)]
|
|
[(fixnum? y)
|
|
(let ([y ($fixnum->flonum y)])
|
|
(if ($fl>= y x) x y))]
|
|
[(bignum? y)
|
|
(let ([y (bignum->flonum y)])
|
|
(if ($fl>= y x) x y))]
|
|
[(ratnum? y)
|
|
;;; FIXME: may be incorrect
|
|
(let ([y (ratnum->flonum y)])
|
|
(if ($fl>= y x) x y))]
|
|
[else (error 'min "not a number" y)])]
|
|
[(ratnum? x)
|
|
(cond
|
|
[(or (fixnum? y) (bignum? y) (ratnum? y))
|
|
(if (>= x y) y x)]
|
|
[(flonum? y)
|
|
(let ([x (ratnum->flonum x)])
|
|
(if ($fl>= x y) y x))]
|
|
[else (error 'min "not a number" y)])]
|
|
[else (error 'min "not a number" x)])]
|
|
[(x y z . rest)
|
|
(let f ([a (min x y)] [b z] [ls rest])
|
|
(cond
|
|
[(null? ls) (min a b)]
|
|
[else
|
|
(f (min a b) (car ls) (cdr ls))]))]
|
|
[(x)
|
|
(if (number? x)
|
|
x
|
|
(error 'min "not a number" x))]))
|
|
|
|
(define (abs x)
|
|
(cond
|
|
[(fixnum? x)
|
|
(if ($fx< x 0) (- x) x)]
|
|
[(bignum? x)
|
|
(if ($bignum-positive? x) x (- x))]
|
|
[(flonum? x)
|
|
(if ($fx> ($flonum-u8-ref x 0) 127)
|
|
($fl* x -1.0)
|
|
x)]
|
|
[(ratnum? x)
|
|
(let ([n ($ratnum-n x)])
|
|
(if (< n 0)
|
|
($make-ratnum (- n) ($ratnum-d x))
|
|
x))]
|
|
[else (error 'abs "not a number" x)]))
|
|
|
|
(define flmin
|
|
(case-lambda
|
|
[(x y)
|
|
(if (flonum? x)
|
|
(if (flonum? y)
|
|
(if ($fl< x y) x y)
|
|
(error 'flmin "not a flonum" y))
|
|
(error 'flmin "not a flonum" x))]
|
|
[(x y z . rest)
|
|
(let f ([a (flmin x y)] [b z] [ls rest])
|
|
(cond
|
|
[(null? ls) (flmin a b)]
|
|
[else
|
|
(f (flmin a b) (car ls) (cdr ls))]))]
|
|
[(x)
|
|
(if (flonum? x)
|
|
x
|
|
(error 'flmin "not a flonum" x))]))
|
|
|
|
(define exact->inexact
|
|
(lambda (x)
|
|
(cond
|
|
[(fixnum? x) ($fixnum->flonum x)]
|
|
[(bignum? x) (bignum->flonum x)]
|
|
[(ratnum? x) (ratnum->flonum x)]
|
|
[else
|
|
(error 'exact->inexact
|
|
"not an exact number" x)])))
|
|
|
|
(define inexact
|
|
(lambda (x)
|
|
(cond
|
|
[(fixnum? x) ($fixnum->flonum x)]
|
|
[(bignum? x) (bignum->flonum x)]
|
|
[(ratnum? x) (ratnum->flonum x)]
|
|
[(flonum? x) x]
|
|
[else
|
|
(error 'inexact "not a number" x)])))
|
|
|
|
(define real->flonum
|
|
(lambda (x)
|
|
(cond
|
|
[(fixnum? x) ($fixnum->flonum x)]
|
|
[(bignum? x) (bignum->flonum x)]
|
|
[(ratnum? x) (ratnum->flonum x)]
|
|
[(flonum? x) x]
|
|
[else
|
|
(error 'real->flonum "not a real number" x)])))
|
|
|
|
(define positive-bignum?
|
|
(lambda (x)
|
|
(foreign-call "ikrt_positive_bn" x)))
|
|
|
|
(define even-bignum?
|
|
(lambda (x)
|
|
(foreign-call "ikrt_even_bn" x)))
|
|
|
|
(define ($fxeven? x)
|
|
($fxzero? ($fxlogand x 1)))
|
|
|
|
(define (even? x)
|
|
(cond
|
|
[(fixnum? x) ($fxeven? x)]
|
|
[(bignum? x) (even-bignum? x)]
|
|
[(flonum? x) (error 'even? "BUG" x)]
|
|
[else (error 'even? "not an integer" x)]))
|
|
|
|
(define (odd? x)
|
|
(not
|
|
(cond
|
|
[(fixnum? x) ($fxeven? x)]
|
|
[(bignum? x) (even-bignum? x)]
|
|
[(flonum? x) (error 'odd? "BUG" x)]
|
|
[else (error 'odd? "not an integer" x)])))
|
|
|
|
(module (number->string)
|
|
(module (bignum->string)
|
|
(define (bignum->decimal-string x)
|
|
(utf8->string (foreign-call "ikrt_bignum_to_bytevector" x)))
|
|
(module (bignum->power-string)
|
|
(define string-map "0123456789ABCDEF")
|
|
(define (init-string x chars)
|
|
(if ($bignum-positive? x)
|
|
(make-string chars)
|
|
(let ([s (make-string ($fxadd1 chars))])
|
|
(string-set! s 0 #\-)
|
|
s)))
|
|
(define (bignum-bits x)
|
|
(define (add-bits b n)
|
|
(cond
|
|
[($fxzero? b) n]
|
|
[else (add-bits ($fxsra b 1) ($fx+ n 1))]))
|
|
(let f ([i ($fxsub1 ($bignum-size x))])
|
|
(let ([b ($bignum-byte-ref x i)])
|
|
(cond
|
|
[($fxzero? b) (f ($fxsub1 i))]
|
|
[else (add-bits b ($fxsll i 3))]))))
|
|
(define (bignum->power-string x mask shift)
|
|
(let ([bits (bignum-bits x)])
|
|
(let ([chars (fxquotient (fx+ bits (fx- shift 1)) shift)])
|
|
(let* ([s (init-string x chars)]
|
|
[n ($fx- (string-length s) 1)])
|
|
(let f ([i 0] [j 0] [k 0] [b 0])
|
|
(cond
|
|
[($fx= i chars) s]
|
|
[($fx< k 8)
|
|
(f i ($fxadd1 j) ($fx+ k 8)
|
|
($fxlogor b
|
|
($fxsll ($bignum-byte-ref x j) k)))]
|
|
[else
|
|
(string-set! s ($fx- n i)
|
|
(string-ref string-map
|
|
($fxlogand mask b)))
|
|
(f ($fxadd1 i) j ($fx- k shift) ($fxsra b shift))])))))))
|
|
(define (bignum->string x r)
|
|
(case r
|
|
[(10) (bignum->decimal-string x)]
|
|
[(2) (bignum->power-string x 1 1)]
|
|
[(8) (bignum->power-string x 7 3)]
|
|
[(16) (bignum->power-string x 15 4)]
|
|
[else (error 'number->string "BUG")])))
|
|
(define ratnum->string
|
|
(lambda (x r)
|
|
(string-append
|
|
($number->string ($ratnum-n x) r)
|
|
"/"
|
|
($number->string ($ratnum-d x) r))))
|
|
(define $number->string
|
|
(lambda (x r)
|
|
(cond
|
|
[(fixnum? x) (fixnum->string x r)]
|
|
[(bignum? x) (bignum->string x r)]
|
|
[(flonum? x)
|
|
(unless (eqv? r 10)
|
|
(error 'number->string
|
|
"invalid radix for inexact number"
|
|
r x))
|
|
(flonum->string x)]
|
|
[(ratnum? x) (ratnum->string x r)]
|
|
[else (error 'number->string "not a number" x)])))
|
|
(define number->string
|
|
(case-lambda
|
|
[(x) ($number->string x 10)]
|
|
[(x r)
|
|
(unless (memv r '(2 8 10 16))
|
|
(error 'number->string "invalid radix" r))
|
|
($number->string x r)]
|
|
[(x r precision)
|
|
(error 'number->string
|
|
"BUG: precision is not supported yet")])))
|
|
|
|
(define modulo
|
|
(lambda (n m)
|
|
(cond
|
|
[(fixnum? n)
|
|
(cond
|
|
[(fixnum? m) ($fxmodulo n m)]
|
|
[(bignum? m)
|
|
(if ($fx< n 0)
|
|
(if ($bignum-positive? m)
|
|
(foreign-call "ikrt_fxbnplus" n m)
|
|
n)
|
|
(if ($bignum-positive? m)
|
|
n
|
|
(foreign-call "ikrt_fxbnplus" n m)))]
|
|
[(flonum? m)
|
|
(let ([v ($flonum->integer m)])
|
|
(cond
|
|
[v (inexact (modulo n v))]
|
|
[else
|
|
(error 'modulo "not an integer" m)]))]
|
|
[(ratnum? m) (error 'modulo "not an integer" m)]
|
|
[else (error 'modulo "not a number" m)])]
|
|
[(bignum? n)
|
|
(cond
|
|
[(fixnum? m)
|
|
(foreign-call "ikrt_bnfx_modulo" n m)]
|
|
[(bignum? m)
|
|
(if ($bignum-positive? n)
|
|
(if ($bignum-positive? m)
|
|
(remainder n m)
|
|
(+ m (remainder n m)))
|
|
(if ($bignum-positive? m)
|
|
(+ m (remainder n m))
|
|
(remainder n m)))]
|
|
[(flonum? m)
|
|
(let ([v ($flonum->integer m)])
|
|
(cond
|
|
[v (inexact (modulo n v))]
|
|
[else
|
|
(error 'modulo "not an integer" m)]))]
|
|
[(ratnum? m) (error 'modulo "not an integer" m)]
|
|
[else (error 'modulo "not a number" m)])]
|
|
[(flonum? n)
|
|
(let ([v ($flonum->integer n)])
|
|
(cond
|
|
[v (inexact (modulo v m))]
|
|
[else
|
|
(error 'modulo "not an integer" n)]))]
|
|
[(ratnum? n) (error 'modulo "not an integer" n)]
|
|
[else (error 'modulo "not a number" n)])))
|
|
|
|
(define-syntax mk<
|
|
(syntax-rules ()
|
|
[(_ name fxfx< fxbn< bnfx< bnbn<
|
|
fxfl< flfx< bnfl< flbn< flfl<
|
|
fxrt< rtfx< bnrt< rtbn< flrt< rtfl< rtrt<)
|
|
(let ()
|
|
(define err
|
|
(lambda (x) (error 'name "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))))]
|
|
[(ratnum? y)
|
|
(if (null? ls)
|
|
(fxrt< x y)
|
|
(if (fxrt< x y)
|
|
(rtloopt 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))))]
|
|
[(ratnum? y)
|
|
(if (null? ls)
|
|
(bnrt< x y)
|
|
(if (bnrt< x y)
|
|
(rtloopt 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))))]
|
|
[(ratnum? y)
|
|
(if (null? ls)
|
|
(flrt< x y)
|
|
(if (flrt< x y)
|
|
(rtloopt y (car ls) (cdr ls))
|
|
(loopf (car ls) (cdr ls))))]
|
|
[else (err y)])))
|
|
(define rtloopt
|
|
(lambda (x y ls)
|
|
(cond
|
|
[(fixnum? y)
|
|
(if (null? ls)
|
|
(rtfx< x y)
|
|
(if (rtfx< x y)
|
|
(fxloopt y (car ls) (cdr ls))
|
|
(loopf (car ls) (cdr ls))))]
|
|
[(bignum? y)
|
|
(if (null? ls)
|
|
(rtbn< x y)
|
|
(if (rtbn< x y)
|
|
(bnloopt y (car ls) (cdr ls))
|
|
(loopf (car ls) (cdr ls))))]
|
|
[(flonum? y)
|
|
(if (null? ls)
|
|
(rtfl< x y)
|
|
(if (rtfl< x y)
|
|
(flloopt y (car ls) (cdr ls))
|
|
(loopf (car ls) (cdr ls))))]
|
|
[(ratnum? y)
|
|
(if (null? ls)
|
|
(rtrt< x y)
|
|
(if (rtrt< x y)
|
|
(rtloopt y (car ls) (cdr ls))
|
|
(loopf (car ls) (cdr ls))))]
|
|
[else (err y)])))
|
|
(define loopf
|
|
(lambda (x ls)
|
|
(cond
|
|
[(number? x)
|
|
(if (null? ls)
|
|
#f
|
|
(loopf (car ls) (cdr ls)))]
|
|
[else (err x)])))
|
|
(define f
|
|
(case-lambda
|
|
[(x y)
|
|
(cond
|
|
[(fixnum? x)
|
|
(cond
|
|
[(fixnum? y) (fxfx< x y)]
|
|
[(bignum? y) (fxbn< x y)]
|
|
[(flonum? y) (fxfl< x y)]
|
|
[(ratnum? y) (fxrt< x y)]
|
|
[else (err y)])]
|
|
[(bignum? x)
|
|
(cond
|
|
[(fixnum? y) (bnfx< x y)]
|
|
[(bignum? y) (bnbn< x y)]
|
|
[(flonum? y) (bnfl< x y)]
|
|
[(ratnum? y) (bnrt< x y)]
|
|
[else (err y)])]
|
|
[(flonum? x)
|
|
(cond
|
|
[(fixnum? y) (flfx< x y)]
|
|
[(bignum? y) (flbn< x y)]
|
|
[(flonum? y) (flfl< x y)]
|
|
[(ratnum? y) (flrt< x y)]
|
|
[else (err y)])]
|
|
[(ratnum? x)
|
|
(cond
|
|
[(fixnum? y) (rtfx< x y)]
|
|
[(bignum? y) (rtbn< x y)]
|
|
[(flonum? y) (rtfl< x y)]
|
|
[(ratnum? y) (rtrt< x y)]
|
|
[else (err y)])]
|
|
[else (err x)])]
|
|
[(x y z) (and (f x y) (f y z))]
|
|
[(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)]
|
|
[(ratnum? x) (rtloopt x y ls)]
|
|
[else (err x)])]))
|
|
f)]))
|
|
|
|
(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)])))]))
|
|
|
|
;;; #;
|
|
;;; (begin
|
|
;;; (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)])))
|
|
|
|
(define-syntax define-flcmp
|
|
(syntax-rules ()
|
|
[(_ fl<? $fl<)
|
|
(define fl<?
|
|
(case-lambda
|
|
[(x y)
|
|
(if (flonum? x)
|
|
(if (flonum? y)
|
|
($fl< x y)
|
|
(error 'fl<? "not a flonum" y))
|
|
(error 'fl<? "not a flonum" x))]
|
|
[(x y z)
|
|
(if (flonum? x)
|
|
(if (flonum? y)
|
|
(if (flonum? z)
|
|
(and ($fl< x y) ($fl< y z))
|
|
(error 'fl<? "not a flonum" z))
|
|
(error 'fl<? "not a flonum" y))
|
|
(error 'fl<? "not a flonum" x))]
|
|
[(x)
|
|
(or (flonum? x)
|
|
(error 'fl<? "not a flonum" x))]
|
|
[(x y . rest)
|
|
(let ()
|
|
(define (loopf a ls)
|
|
(unless (flonum? a)
|
|
(error 'fl<? "not a flonum" a))
|
|
(if (null? ls)
|
|
#f
|
|
(loopf (car ls) (cdr ls))))
|
|
(if (flonum? x)
|
|
(if (flonum? y)
|
|
(if ($fl< x y)
|
|
(let f ([x y] [y (car rest)] [ls (cdr rest)])
|
|
(if (flonum? y)
|
|
(if (null? ls)
|
|
($fl< x y)
|
|
(if ($fl< x y)
|
|
(f y (car ls) (cdr ls))
|
|
(loopf (car ls) (cdr ls))))
|
|
(error 'fl<? "not a flonum" y)))
|
|
(loopf (car rest) (cdr rest)))
|
|
(error 'fl<? "not a flonum" y))
|
|
(error 'fl<? "not a flonum" x)))]))]))
|
|
(define-flcmp fl=? $fl=)
|
|
(define-flcmp fl<? $fl<)
|
|
(define-flcmp fl<=? $fl<=)
|
|
(define-flcmp fl>? $fl>)
|
|
(define-flcmp fl>=? $fl>=)
|
|
|
|
(define fl+
|
|
(case-lambda
|
|
[(x y)
|
|
(if (flonum? x)
|
|
(if (flonum? y)
|
|
($fl+ x y)
|
|
(error 'fl+ "not a flonum" y))
|
|
(error 'fl+ "not a flonum" x))]
|
|
[(x y z)
|
|
(fl+ (fl+ x y) z)]
|
|
[(x y z q . rest)
|
|
(let f ([ac (fl+ (fl+ (fl+ x y) z) q)] [rest rest])
|
|
(if (null? rest)
|
|
ac
|
|
(f (fl+ ac (car rest)) (cdr rest))))]
|
|
[(x)
|
|
(if (flonum? x)
|
|
x
|
|
(error 'fl+ "not a flonum" x))]
|
|
[() (exact->inexact 0)]))
|
|
|
|
|
|
(define fl-
|
|
(case-lambda
|
|
[(x y)
|
|
(if (flonum? x)
|
|
(if (flonum? y)
|
|
($fl- x y)
|
|
(error 'fl- "not a flonum" y))
|
|
(error 'fl- "not a flonum" x))]
|
|
[(x y z)
|
|
(fl- (fl- x y) z)]
|
|
[(x y z q . rest)
|
|
(let f ([ac (fl- (fl- (fl- x y) z) q)] [rest rest])
|
|
(if (null? rest)
|
|
ac
|
|
(f (fl- ac (car rest)) (cdr rest))))]
|
|
[(x)
|
|
(if (flonum? x)
|
|
($fl* -1.0 x)
|
|
(error 'fl+ "not a flonum" x))]))
|
|
|
|
(define fl*
|
|
(case-lambda
|
|
[(x y)
|
|
(if (flonum? x)
|
|
(if (flonum? y)
|
|
($fl* x y)
|
|
(error 'fl* "not a flonum" y))
|
|
(error 'fl* "not a flonum" x))]
|
|
[(x y z)
|
|
(fl* (fl* x y) z)]
|
|
[(x y z q . rest)
|
|
(let f ([ac (fl* (fl* (fl* x y) z) q)] [rest rest])
|
|
(if (null? rest)
|
|
ac
|
|
(f (fl* ac (car rest)) (cdr rest))))]
|
|
[(x)
|
|
(if (flonum? x)
|
|
x
|
|
(error 'fl* "not a flonum" x))]
|
|
[() 1.0]))
|
|
|
|
(define fl/
|
|
(case-lambda
|
|
[(x y)
|
|
(if (flonum? x)
|
|
(if (flonum? y)
|
|
($fl/ x y)
|
|
(error 'fl/ "not a flonum" y))
|
|
(error 'fl/ "not a flonum" x))]
|
|
[(x y z)
|
|
(fl/ (fl/ x y) z)]
|
|
[(x y z q . rest)
|
|
(let f ([ac (fl/ (fl/ (fl/ x y) z) q)] [rest rest])
|
|
(if (null? rest)
|
|
ac
|
|
(f (fl/ ac (car rest)) (cdr rest))))]
|
|
[(x)
|
|
(if (flonum? x)
|
|
($fl/ 1.0 x)
|
|
(error 'fl/ "not a flonum" 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>= $fl>=)
|
|
|
|
(define-syntax flrt= (syntax-rules () [(_ x y) (= (inexact->exact x) y)]))
|
|
(define-syntax rtfl= (syntax-rules () [(_ x y) (= x (inexact->exact y))]))
|
|
(define-syntax flrt< (syntax-rules () [(_ x y) (< (inexact->exact x) y)]))
|
|
(define-syntax rtfl< (syntax-rules () [(_ x y) (< x (inexact->exact y))]))
|
|
(define-syntax flrt<= (syntax-rules () [(_ x y) (<= (inexact->exact x) y)]))
|
|
(define-syntax rtfl<= (syntax-rules () [(_ x y) (<= x (inexact->exact y))]))
|
|
(define-syntax flrt> (syntax-rules () [(_ x y) (> (inexact->exact x) y)]))
|
|
(define-syntax rtfl> (syntax-rules () [(_ x y) (> x (inexact->exact y))]))
|
|
(define-syntax flrt>= (syntax-rules () [(_ x y) (>= (inexact->exact x) y)]))
|
|
(define-syntax rtfl>= (syntax-rules () [(_ x y) (>= x (inexact->exact y))]))
|
|
(define (exrt< x y) (< (* x ($ratnum-d y)) ($ratnum-n y)))
|
|
(define (rtex< x y) (< ($ratnum-n x) (* y ($ratnum-d x))))
|
|
(define (rtrt< x y) (< (* ($ratnum-n x) ($ratnum-d y)) (* ($ratnum-n y) ($ratnum-d x))))
|
|
(define (rtrt<= x y) (<= (* ($ratnum-n x) ($ratnum-d y)) (* ($ratnum-n y) ($ratnum-d x))))
|
|
(define (exrt> x y) (> (* x ($ratnum-d y)) ($ratnum-n y)))
|
|
(define (rtex> x y) (> ($ratnum-n x) (* y ($ratnum-d x))))
|
|
(define (rtrt> x y) (> (* ($ratnum-n x) ($ratnum-d y)) (* ($ratnum-n y) ($ratnum-d x))))
|
|
(define (rtrt>= x y) (>= (* ($ratnum-n x) ($ratnum-d y)) (* ($ratnum-n y) ($ratnum-d x))))
|
|
(define (rtrt= x y)
|
|
(and (= ($ratnum-n x) ($ratnum-n y)) (= ($ratnum-d x) ($ratnum-d y))))
|
|
|
|
(define =
|
|
(mk< = $fx= false false bnbn= fxfl= flfx= bnfl= flbn= flfl=
|
|
false false false false flrt= rtfl= rtrt=))
|
|
(define <
|
|
(mk< < $fx< fxbn< bnfx< bnbn< fxfl< flfx< bnfl< flbn< flfl<
|
|
exrt< rtex< exrt< rtex< flrt< rtfl< rtrt<))
|
|
(define >
|
|
(mk< > $fx> fxbn> bnfx> bnbn> fxfl> flfx> bnfl> flbn> flfl>
|
|
exrt> rtex> exrt> rtex> flrt> rtfl> rtrt>))
|
|
(define <=
|
|
(mk< <= $fx<= fxbn< bnfx< bnbn<= fxfl<= flfx<= bnfl<= flbn<= flfl<=
|
|
exrt< rtex< exrt< rtex< flrt<= rtfl<= rtrt<=))
|
|
(define >=
|
|
(mk< >= $fx>= fxbn> bnfx> bnbn>= fxfl>= flfx>= bnfl>= flbn>= flfl>=
|
|
exrt> rtex> exrt> rtex> flrt>= rtfl>= rtrt>=))
|
|
|
|
(define add1
|
|
(lambda (x)
|
|
(cond
|
|
[(fixnum? x)
|
|
(foreign-call "ikrt_fxfxplus" x 1)]
|
|
[(bignum? x)
|
|
(foreign-call "ikrt_fxbnplus" 1 x)]
|
|
[else (error 'add1 "not a number" x)])))
|
|
|
|
(define sub1
|
|
(lambda (x)
|
|
(cond
|
|
[(fixnum? x)
|
|
(foreign-call "ikrt_fxfxplus" x -1)]
|
|
[(bignum? x)
|
|
(foreign-call "ikrt_fxbnplus" -1 x)]
|
|
[else (error 'sub1 "not a number" x)])))
|
|
|
|
(define zero?
|
|
(lambda (x)
|
|
(cond
|
|
[(fixnum? x) (eq? x 0)]
|
|
[(bignum? x) #f]
|
|
[(flonum? x)
|
|
(or ($fl= x 0.0) ($fl= x -0.0))]
|
|
[else
|
|
(error 'zero? "not a number" x)])))
|
|
|
|
(define expt
|
|
(lambda (n m)
|
|
(define fxexpt
|
|
(lambda (n m)
|
|
(cond
|
|
[($fxzero? m) 1]
|
|
[($fxzero? ($fxlogand m 1))
|
|
(fxexpt (binary* n n) ($fxsra m 1))]
|
|
[else
|
|
(binary* n (fxexpt (binary* n n) ($fxsra m 1)))])))
|
|
(unless (number? n)
|
|
(error 'expt "not a numebr" n))
|
|
(cond
|
|
[(fixnum? m)
|
|
(if ($fx>= m 0)
|
|
(fxexpt n m)
|
|
(/ 1 (expt n (- m))))]
|
|
[(bignum? m)
|
|
(cond
|
|
[(eq? n 0) 0]
|
|
[(eq? n 1) 1]
|
|
[(eq? n -1)
|
|
(if (positive-bignum? m)
|
|
(if (even-bignum? m)
|
|
1
|
|
-1)
|
|
(/ 1 (expt n (- m))))]
|
|
[else
|
|
(error 'expt "result is too big to compute" n m)])]
|
|
[(flonum? m) (flexpt (inexact n) m)]
|
|
[(ratnum? m) (flexpt (inexact n) (inexact m))]
|
|
[else (error 'expt "not a number" m)])))
|
|
|
|
(define quotient
|
|
(lambda (x y)
|
|
(let-values ([(q r) (quotient+remainder x y)])
|
|
q)))
|
|
|
|
(define remainder
|
|
(lambda (x y)
|
|
(let-values ([(q r) (quotient+remainder x y)])
|
|
r)))
|
|
|
|
(define quotient+remainder
|
|
(lambda (x y)
|
|
(cond
|
|
[(eq? y 0)
|
|
(error 'quotient+remainder
|
|
"second argument must be non-zero")]
|
|
[(fixnum? x)
|
|
(cond
|
|
[(fixnum? y)
|
|
(values (fxquotient x y)
|
|
(fxremainder x y))]
|
|
[(bignum? y) (values 0 x)]
|
|
[(flonum? y)
|
|
(let ([v ($flonum->integer y)])
|
|
(cond
|
|
[v
|
|
(let-values ([(q r) (quotient+remainder x v)])
|
|
(values (inexact q) (inexact r)))]
|
|
[else
|
|
(error 'quotient+remainder "not an integer" y)]))]
|
|
[else (error 'quotient+remainder "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)))]
|
|
[(flonum? y)
|
|
(let ([v ($flonum->integer y)])
|
|
(cond
|
|
[v
|
|
(let-values ([(q r) (quotient+remainder x v)])
|
|
(values (inexact q) (inexact r)))]
|
|
[else
|
|
(error 'quotient+remainder "not an integer" y)]))]
|
|
[else (error 'quotient+remainder "not a number" y)])]
|
|
[(flonum? x)
|
|
(let ([v ($flonum->integer x)])
|
|
(cond
|
|
[v
|
|
(let-values ([(q r) (quotient+remainder v y)])
|
|
(values (inexact q) (inexact r)))]
|
|
[else (error 'quotient+remainder "not an integer" x)]))]
|
|
[else (error 'quotient+remainder "not a number" x)])))
|
|
|
|
(define positive?
|
|
(lambda (x)
|
|
(cond
|
|
[(fixnum? x) ($fx> x 0)]
|
|
[(flonum? x) ($fl> x 0.0)]
|
|
[(bignum? x) (positive-bignum? x)]
|
|
[(ratnum? x) (positive? ($ratnum-n x))]
|
|
[else (error 'positive? "not a number" x)])))
|
|
|
|
(define negative?
|
|
(lambda (x)
|
|
(cond
|
|
[(fixnum? x) ($fx< x 0)]
|
|
[(flonum? x) ($fl< x 0.0)]
|
|
[(bignum? x) (not (positive-bignum? x))]
|
|
[(ratnum? x) (negative? ($ratnum-n x))]
|
|
[else (error 'negative? "not a number" x)])))
|
|
|
|
(define sin
|
|
(lambda (x)
|
|
(cond
|
|
[(flonum? x) (foreign-call "ikrt_fl_sin" x)]
|
|
[(fixnum? x) (foreign-call "ikrt_fx_sin" x)]
|
|
[else (error 'sin "BUG: unsupported" 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 "BUG: unsupported" x)])))
|
|
|
|
(define tan
|
|
(lambda (x)
|
|
(cond
|
|
[(flonum? x) (foreign-call "ikrt_fl_tan" x)]
|
|
[(fixnum? x) (foreign-call "ikrt_fx_tan" x)]
|
|
[else (error 'tan "BUG: unsupported" x)])))
|
|
|
|
(define asin
|
|
(lambda (x)
|
|
(cond
|
|
[(flonum? x) (foreign-call "ikrt_fl_asin" x)]
|
|
[(fixnum? x) (foreign-call "ikrt_fx_asin" x)]
|
|
[else (error 'asin "BUG: unsupported" x)])))
|
|
|
|
(define acos
|
|
(lambda (x)
|
|
(cond
|
|
[(flonum? x) (foreign-call "ikrt_fl_acos" x)]
|
|
[(fixnum? x) (foreign-call "ikrt_fx_acos" x)]
|
|
[else (error 'acos "BUG: unsupported" 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 "BUG: unsupported" x)])))
|
|
|
|
(define sqrt
|
|
(lambda (x)
|
|
(cond
|
|
[(flonum? x) (foreign-call "ikrt_fl_sqrt" x)]
|
|
[(fixnum? x) (foreign-call "ikrt_fx_sqrt" x)]
|
|
[(bignum? x) (error 'sqrt "BUG: bignum sqrt not implemented")]
|
|
[(ratnum? x) (/ (sqrt ($ratnum-n x)) (sqrt ($ratnum-d x)))]
|
|
[else (error 'sqrt "BUG: unsupported" x)])))
|
|
|
|
(define flsqrt
|
|
(lambda (x)
|
|
(if (flonum? x)
|
|
(foreign-call "ikrt_fl_sqrt" x)
|
|
(error 'flsqrt "not a flonum" x))))
|
|
|
|
(define flzero?
|
|
(lambda (x)
|
|
(if (flonum? x)
|
|
($flzero? x)
|
|
(error 'flzero? "not a flonum" x))))
|
|
|
|
(define flnegative?
|
|
(lambda (x)
|
|
(if (flonum? x)
|
|
($fl< x 0.0)
|
|
(error 'flnegative? "not a flonum" x))))
|
|
|
|
(define exact-integer-sqrt
|
|
(lambda (x)
|
|
(define who 'exact-integer-sqrt)
|
|
(define (fxsqrt x i k)
|
|
(let ([j ($fxsra ($fx+ i k) 1)])
|
|
(let ([j^2 ($fx* j j)])
|
|
(if ($fx> j^2 x)
|
|
(fxsqrt x i j)
|
|
(if ($fx= i j)
|
|
(values j ($fx- x j^2))
|
|
(fxsqrt x j k))))))
|
|
(define (bnsqrt x i k)
|
|
(let ([j (quotient (+ i k) 2)])
|
|
(let ([j^2 (* j j)])
|
|
(if (> j^2 x)
|
|
(bnsqrt x i j)
|
|
(if (= i j)
|
|
(values j (- x j^2))
|
|
(bnsqrt x j k))))))
|
|
(cond
|
|
[(fixnum? x)
|
|
(cond
|
|
[($fx< x 0) (error who "invalid argument" x)]
|
|
[($fx= x 0) (values 0 0)]
|
|
[($fx< x 4) (values 1 ($fx- x 1))]
|
|
[($fx< x 9) (values 2 ($fx- x 4))]
|
|
[($fx< x 46340) (fxsqrt x 3 ($fxsra x 1))]
|
|
[else (fxsqrt x 215 23171)])]
|
|
[(bignum? x)
|
|
(cond
|
|
[($bignum-positive? x)
|
|
(bnsqrt x 23170 (quotient x 23170))]
|
|
[else (error who "invalid argument" x)])]
|
|
[else (error who "invalid argument" x)])))
|
|
|
|
|
|
(define numerator
|
|
(lambda (x)
|
|
(cond
|
|
[(ratnum? x) ($ratnum-n x)]
|
|
[(or (fixnum? x) (bignum? x)) x]
|
|
[(flonum? x) (flnumerator x)]
|
|
[else (error 'numerator "not an exact integer" x)])))
|
|
|
|
(define denominator
|
|
(lambda (x)
|
|
(cond
|
|
[(ratnum? x) ($ratnum-d x)]
|
|
[(or (fixnum? x) (bignum? x)) 1]
|
|
[(flonum? x) (fldenominator x)]
|
|
[else (error 'denominator "not an exact integer" x)])))
|
|
|
|
|
|
(define (floor x)
|
|
(define (ratnum-floor x)
|
|
(let ([n (numerator x)] [d (denominator x)])
|
|
(let ([q (quotient n d)])
|
|
(if (>= n 0) q (- q 1)))))
|
|
(cond
|
|
[(flonum? x)
|
|
;;; optimize for integer flonums
|
|
(let ([e (or ($flonum->exact x)
|
|
(error 'floor "number has no real value" x))])
|
|
(cond
|
|
[(ratnum? e)
|
|
(exact->inexact (ratnum-floor e))]
|
|
[else x]))]
|
|
[(ratnum? x) (ratnum-floor x)]
|
|
[(or (fixnum? x) (bignum? x)) x]
|
|
[else (error 'floor "not a number" x)]))
|
|
|
|
(define (ceiling x)
|
|
(define (ratnum-ceiling x)
|
|
(let ([n (numerator x)] [d (denominator x)])
|
|
(let ([q (quotient n d)])
|
|
(if (< n 0) q (+ q 1)))))
|
|
(cond
|
|
[(flonum? x)
|
|
;;; optimize for integer flonums
|
|
(let ([e (or ($flonum->exact x)
|
|
(error 'ceiling "number has no real value" x))])
|
|
(cond
|
|
[(ratnum? e) (exact->inexact (ratnum-ceiling e))]
|
|
[else x]))]
|
|
[(ratnum? x) (ratnum-ceiling x)]
|
|
[(or (fixnum? x) (bignum? x)) x]
|
|
[else (error 'ceiling "not a number" x)]))
|
|
|
|
|
|
(define ($ratnum-round x)
|
|
(let ([n ($ratnum-n x)] [d ($ratnum-d x)])
|
|
(let-values ([(q r) (quotient+remainder n d)])
|
|
(let ([r2 (+ r r)])
|
|
(if (> n 0)
|
|
(cond
|
|
[(< r2 d) q]
|
|
[(> r2 d) (+ q 1)]
|
|
[else
|
|
(if (even? q) q (+ q 1))])
|
|
(let ([r2 (- r2)])
|
|
(cond
|
|
[(< r2 d) q]
|
|
[(< r2 d) (- q 1)]
|
|
[else
|
|
(if (even? q) q (- q 1))])))))))
|
|
|
|
(define ($ratnum-truncate x)
|
|
(let ([n ($ratnum-n x)] [d ($ratnum-d x)])
|
|
(quotient n d)))
|
|
|
|
|
|
(define (round x)
|
|
(cond
|
|
[(flonum? x) ($flround x)]
|
|
[(ratnum? x) ($ratnum-round x)]
|
|
[(or (fixnum? x) (bignum? x)) x]
|
|
[else (error 'round "not a number" x)]))
|
|
|
|
(define (truncate x)
|
|
;;; FIXME: fltruncate should preserve the sign of -0.0.
|
|
;;;
|
|
(cond
|
|
[(flonum? x)
|
|
(let ([e (or ($flonum->exact x)
|
|
(error 'truncate "number has no real value" x))])
|
|
(cond
|
|
[(ratnum? e) (exact->inexact ($ratnum-truncate e))]
|
|
[else x]))]
|
|
[(ratnum? x) ($ratnum-truncate x)]
|
|
[(or (fixnum? x) (bignum? x)) x]
|
|
[else (error 'truncate "not a number" x)]))
|
|
|
|
|
|
(define (fltruncate x)
|
|
;;; FIXME: fltruncate should preserve the sign of -0.0.
|
|
(unless (flonum? x)
|
|
(error 'fltruncate "not a flonum" x))
|
|
(let ([v ($flonum->exact x)])
|
|
(cond
|
|
[(ratnum? v) (exact->inexact ($ratnum-truncate v))]
|
|
[else x])))
|
|
|
|
(define log
|
|
(lambda (x)
|
|
(cond
|
|
[(fixnum? x)
|
|
(cond
|
|
[($fx= x 1) 0]
|
|
[($fx= x 0) (error 'log "undefined around 0")]
|
|
[($fx> x 0) (foreign-call "ikrt_fx_log" x)]
|
|
[else (error 'log "negative argument" x)])]
|
|
[(flonum? x)
|
|
(cond
|
|
[(>= x 0) (foreign-call "ikrt_fl_log" x)]
|
|
[else (error 'log "negative argument" x)])]
|
|
[(bignum? x) (log (exact->inexact x))]
|
|
[(ratnum? x) (- (log (numerator x)) (log (denominator x)))]
|
|
[else (error 'log "not a number" x)])))
|
|
|
|
(define string->number
|
|
(case-lambda
|
|
[(x) (string->number-radix-10 x)]
|
|
[(x r)
|
|
(unless (eqv? r 10)
|
|
(error 'string->number
|
|
"BUG: only radix 10 is supported"
|
|
x r))
|
|
(string->number-radix-10 x)]))
|
|
|
|
(define string->number-radix-10
|
|
(lambda (x)
|
|
(define (convert-char c radix)
|
|
(case radix
|
|
[(10)
|
|
(cond
|
|
[(char<=? #\0 c #\9)
|
|
(fx- (char->integer c) (char->integer #\0))]
|
|
[else #f])]
|
|
[(16)
|
|
(cond
|
|
[(char<=? #\0 c #\9)
|
|
(fx- (char->integer c) (char->integer #\0))]
|
|
[(char<=? #\a c #\f)
|
|
(fx- (char->integer c) (fx- (char->integer #\a) 10))]
|
|
[(char<=? #\A c #\F)
|
|
(fx- (char->integer c) (fx- (char->integer #\A) 10))]
|
|
[else #f])]
|
|
[(8)
|
|
(cond
|
|
[(char<=? #\0 c #\7)
|
|
(fx- (char->integer c) (char->integer #\0))]
|
|
[else #f])]
|
|
[(2)
|
|
(case c
|
|
[(#\0) 0]
|
|
[(#\1) 1]
|
|
[else #f])]
|
|
[else (error 'convert-char "invalid radix" radix)]))
|
|
(define (parse-exponent-start x n i radix)
|
|
(define (parse-exponent x n i radix ac)
|
|
(cond
|
|
[(fx= i n) ac]
|
|
[else
|
|
(let ([c (string-ref x i)])
|
|
(cond
|
|
[(convert-char c radix) =>
|
|
(lambda (d)
|
|
(parse-exponent x n (fxadd1 i) radix
|
|
(+ d (* ac radix))))]
|
|
[else #f]))]))
|
|
(define (parse-exponent-sign x n i radix)
|
|
(cond
|
|
[(fx= i n) #f]
|
|
[else
|
|
(let ([c (string-ref x i)])
|
|
(cond
|
|
[(convert-char c radix) =>
|
|
(lambda (d) (parse-exponent x n (fxadd1 i) radix d))]
|
|
[else #f]))]))
|
|
(cond
|
|
[(fx= i n) #f]
|
|
[else
|
|
(let ([c (string-ref x i)])
|
|
(cond
|
|
[(convert-char c radix) =>
|
|
(lambda (d)
|
|
(parse-exponent x n (fxadd1 i) radix d))]
|
|
[(char=? c #\+)
|
|
(parse-exponent-sign x n (fxadd1 i) radix)]
|
|
[(char=? c #\-)
|
|
(let ([v (parse-exponent-sign x n (fxadd1 i) radix)])
|
|
(and v (- v)))]
|
|
[else #f]))]))
|
|
(define (parse-decimal x n i pos? radix exact? ac exp)
|
|
(cond
|
|
[(fx= i n)
|
|
(let ([ac (* (if pos? ac (- ac)) (expt radix exp))])
|
|
(exact-conv (or exact? 'i) ac))]
|
|
[else
|
|
(let ([c (string-ref x i)])
|
|
(cond
|
|
[(convert-char c radix) =>
|
|
(lambda (d)
|
|
(parse-decimal x n (fxadd1 i) pos? radix exact?
|
|
(+ (* ac radix) d) (fxsub1 exp)))]
|
|
[(memv c '(#\e #\E))
|
|
(let ([ex (parse-exponent-start x n (fxadd1 i) radix)])
|
|
(and ex
|
|
(exact-conv (or exact? 'i)
|
|
(* (if pos? ac (- ac)) (expt radix (+ exp ex))))))]
|
|
[else #f]))]))
|
|
(define (parse-decimal-no-digits x n i pos? radix exact?)
|
|
(cond
|
|
[(fx= i n) #f]
|
|
[else
|
|
(let ([c (string-ref x i)])
|
|
(cond
|
|
[(convert-char c radix) =>
|
|
(lambda (d)
|
|
(parse-decimal x n (fxadd1 i) pos? radix exact? d -1))]
|
|
[else #f]))]))
|
|
(define (parse-integer x n i pos? radix exact? ac)
|
|
(define (parse-denom-start x n i radix)
|
|
(define (parse-denom x n i radix ac)
|
|
(cond
|
|
[(fx= n i) ac]
|
|
[else
|
|
(let ([c (string-ref x i)])
|
|
(cond
|
|
[(convert-char c radix) =>
|
|
(lambda (d)
|
|
(parse-denom x n (fxadd1 i) radix
|
|
(+ (* radix ac) d)))]
|
|
[else #f]))]))
|
|
(cond
|
|
[(fx= n i) #f]
|
|
[else
|
|
(let ([c (string-ref x i)])
|
|
(cond
|
|
[(convert-char c radix) =>
|
|
(lambda (d)
|
|
(parse-denom x n (fxadd1 i) radix d))]
|
|
[else #f]))]))
|
|
(cond
|
|
[(fx= i n)
|
|
(let ([ac (exact-conv exact? ac)])
|
|
(if pos? ac (- ac)))]
|
|
[else
|
|
(let ([c (string-ref x i)])
|
|
(cond
|
|
[(convert-char c radix) =>
|
|
(lambda (d)
|
|
(parse-integer x n (fxadd1 i) pos? radix exact? (+ (* ac radix) d)))]
|
|
[(char=? c #\.)
|
|
(parse-decimal x n (fxadd1 i) pos? radix exact? ac 0)]
|
|
[(char=? c #\/)
|
|
(let ([denom (parse-denom-start x n (fxadd1 i) radix)])
|
|
(and denom
|
|
(not (= denom 0))
|
|
(let ([ac (exact-conv exact? ac)])
|
|
(/ (if pos? ac (- ac)) denom))))]
|
|
[(memv c '(#\e #\E))
|
|
(let ([ex (parse-exponent-start x n (fxadd1 i) radix)])
|
|
(and ex
|
|
(let ([ac (* (if pos? ac (- ac)) (expt radix ex))])
|
|
(exact-conv (or exact? 'i) ac))))]
|
|
[else #f]))]))
|
|
(define (parse-integer-no-digits x n i pos? radix exact?)
|
|
(cond
|
|
[(fx= i n) #f]
|
|
[else
|
|
(let ([c (string-ref x i)])
|
|
(cond
|
|
[(convert-char c radix) =>
|
|
(lambda (d)
|
|
(parse-integer x n (fxadd1 i) pos? radix exact? d))]
|
|
[(char=? c #\.)
|
|
(parse-decimal-no-digits x n (fxadd1 i) pos? radix exact?)]
|
|
[else #f]))]))
|
|
(define (exact-conv exact? x)
|
|
(and x (if (eq? exact? 'i) (exact->inexact x) x)))
|
|
(define (start x n i exact? radix?)
|
|
(cond
|
|
[(fx= i n) #f]
|
|
[else
|
|
(let ([c (string-ref x i)])
|
|
(cond
|
|
[(char=? c #\-)
|
|
(parse-integer-no-digits x n (fxadd1 i) #f (or radix? 10) exact?)]
|
|
[(char=? c #\+)
|
|
(parse-integer-no-digits x n (fxadd1 i) #t (or radix? 10) exact?)]
|
|
[(char=? c #\#)
|
|
(let ([i (fxadd1 i)])
|
|
(cond
|
|
[(fx= i n) #f]
|
|
[else
|
|
(let ([c (string-ref x i)])
|
|
(case c
|
|
[(#\x #\X)
|
|
(and (not radix?) (start x n (fxadd1 i) exact? 16))]
|
|
[(#\b #\B)
|
|
(and (not radix?) (start x n (fxadd1 i) exact? 2))]
|
|
[(#\o #\O)
|
|
(and (not radix?) (start x n (fxadd1 i) exact? 8))]
|
|
[(#\d #\D)
|
|
(and (not radix?) (start x n (fxadd1 i) exact? 10))]
|
|
[(#\e #\E)
|
|
(and (not exact?) (start x n (fxadd1 i) 'e radix?))]
|
|
[(#\i #\I)
|
|
(and (not exact?) (start x n (fxadd1 i) 'i radix?))]
|
|
[else #f]))]))]
|
|
[(char=? c #\.)
|
|
(parse-decimal-no-digits x n (fxadd1 i) #t (or radix? 10) exact?)]
|
|
[(convert-char c (or radix? 10)) =>
|
|
(lambda (d)
|
|
(parse-integer x n (fxadd1 i) #t (or radix? 10) exact? d))]
|
|
[else #f]))]))
|
|
;;;
|
|
(unless (string? x)
|
|
(error 'string->number "not a string" x))
|
|
(let ([n (string-length x)])
|
|
(cond
|
|
[(fx= n (string-length "+xxx.0"))
|
|
(cond
|
|
[(string-ci=? x "+inf.0") +inf.0]
|
|
[(string-ci=? x "-inf.0") -inf.0]
|
|
[(string-ci=? x "+nan.0") +nan.0]
|
|
[(string-ci=? x "-nan.0") -nan.0]
|
|
[else (start x n 0 #f #f)])]
|
|
[(fx> n 0) (start x n 0 #f #f)]
|
|
[else #f]))))
|
|
|
|
|
|
(define (random n)
|
|
(if (fixnum? n)
|
|
(if (fx> n 1)
|
|
(foreign-call "ikrt_fxrandom" n)
|
|
(if (fx= n 1)
|
|
0
|
|
(error 'random "incorrect argument" n)))
|
|
(error 'random "not a fixnum" n)))
|
|
|
|
|
|
(define (shift-right-arithmetic n m who)
|
|
(cond
|
|
[(fixnum? m)
|
|
(cond
|
|
[(fixnum? n)
|
|
(cond
|
|
[($fx>= m 0) ($fxsra n m)]
|
|
[else (error who "offset must be non-negative" m)])]
|
|
[(bignum? n)
|
|
(cond
|
|
[($fx> m 0)
|
|
(foreign-call "ikrt_bignum_shift_right" n m)]
|
|
[($fx= m 0) n]
|
|
[else (error who "offset must be non-negative" m)])]
|
|
[else (error who "not an exact integer" n)])]
|
|
[(bignum? m)
|
|
(cond
|
|
[(fixnum? n) (if ($fx>= n 0) 0 -1)]
|
|
[(bignum? n) (if ($bignum-positive? n) 0 -1)]
|
|
[else (error who "not an exact integer" n)])]
|
|
[else (error who "not an exact integer offset" m)]))
|
|
|
|
(define (sra n m)
|
|
(shift-right-arithmetic n m 'sra))
|
|
|
|
(define (shift-left-logical n m who)
|
|
(unless (fixnum? m)
|
|
(error who "shift amount is not a fixnum"))
|
|
(cond
|
|
[(fixnum? n)
|
|
(cond
|
|
[($fx> m 0)
|
|
(foreign-call "ikrt_fixnum_shift_left" n m)]
|
|
[($fx= m 0) n]
|
|
[else (error who "offset must be non-negative" m)])]
|
|
[(bignum? n)
|
|
(cond
|
|
[($fx> m 0)
|
|
(foreign-call "ikrt_bignum_shift_left" n m)]
|
|
[($fx= m 0) n]
|
|
[else (error who "offset must be non-negative" m)])]
|
|
[else (error who "not an exact integer" n)]))
|
|
|
|
(define (sll n m)
|
|
(shift-left-logical n m 'sll))
|
|
|
|
(define (bitwise-arithmetic-shift-right n m)
|
|
(shift-right-arithmetic n m 'bitwise-arithmetic-shift-right))
|
|
(define (bitwise-arithmetic-shift-left n m)
|
|
(shift-left-logical n m 'bitwise-arithmetic-shift-left))
|
|
(define (bitwise-arithmetic-shift n m)
|
|
(define who 'bitwise-arithmetic-shift)
|
|
(unless (fixnum? m)
|
|
(error who "shift amount is not a fixnum"))
|
|
(cond
|
|
[(fixnum? n)
|
|
(cond
|
|
[($fx> m 0)
|
|
(foreign-call "ikrt_fixnum_shift_left" n m)]
|
|
[($fx= m 0) n]
|
|
[else
|
|
(let ([m^ (- m)])
|
|
(unless (fixnum? m^)
|
|
(error who "shift amount is too big" m))
|
|
($fxsra n m^))])]
|
|
[(bignum? n)
|
|
(cond
|
|
[($fx> m 0)
|
|
(foreign-call "ikrt_bignum_shift_left" n m)]
|
|
[($fx= m 0) n]
|
|
[else
|
|
(let ([m^ (- m)])
|
|
(unless (fixnum? m^)
|
|
(error who "shift amount is too big" m))
|
|
(foreign-call "ikrt_bignum_shift_right" n m^))])]
|
|
[else (error who "not an exact integer" n)]))
|
|
|
|
(define (exp x)
|
|
(cond
|
|
[(flonum? x) (flexp x)]
|
|
[(fixnum? x)
|
|
(if ($fx= x 0) 1 (flexp (fixnum->flonum x)))]
|
|
[(bignum? x) (flexp (bignum->flonum x))]
|
|
[(ratnum? x) (flexp (ratnum->flonum x))]
|
|
[else (error 'exp "not a number" x)]))
|
|
|
|
|
|
)
|
|
|
|
(library (ikarus complexnums)
|
|
(export real-part imag-part)
|
|
(import (except (ikarus) real-part imag-part))
|
|
;;; stub implementation since we don't have a way of
|
|
;;; constructing complex numbers yet.
|
|
|
|
(define real-part
|
|
(lambda (x)
|
|
(if (number? x)
|
|
x
|
|
(error 'real-part "not a number" x))))
|
|
|
|
(define imag-part
|
|
(lambda (x)
|
|
(cond
|
|
[(fixnum? x) 0]
|
|
[(bignum? x) 0]
|
|
[(ratnum? x) 0]
|
|
[(flonum? x) 0.0]
|
|
[else
|
|
(error 'imag-part "not a number" x)]))))
|
|
|
|
|
|
|
|
(library (ikarus flonum-conversion)
|
|
(export string->flonum flonum->string)
|
|
(import
|
|
(rnrs bytevectors)
|
|
(ikarus system $bytevectors)
|
|
(ikarus system $flonums)
|
|
(except (ikarus) flonum->string string->flonum ))
|
|
|
|
(module (flonum->string)
|
|
(module (flonum->digits)
|
|
(define flonum->digits
|
|
(lambda (f e min-e p b B)
|
|
;;; flonum v = f * b^e
|
|
;;; p = precision (p >= 1)
|
|
(let ([round? (even? f)])
|
|
(if (>= e 0)
|
|
(if (not (= f (expt b (- p 1))))
|
|
(let ([be (expt b e)])
|
|
(scale (* f be 2) 2 be be 0 B round? f e))
|
|
(let* ([be (expt b e)] [be1 (* be b)])
|
|
(scale (* f be1 2) (* b 2) be1 be 0 B round? f e)))
|
|
(if (or (= e min-e) (not (= f (expt b (- p 1)))))
|
|
(scale (* f 2) (* (expt b (- e)) 2) 1 1 0 B round? f e)
|
|
(scale (* f b 2) (* (expt b (- 1 e)) 2) b 1 0 B round? f e))))))
|
|
(define (len n)
|
|
(let f ([n n] [i 0])
|
|
(cond
|
|
[(zero? n) i]
|
|
[else (f (quotient n 2) (+ i 1))])))
|
|
(define scale
|
|
(lambda (r s m+ m- k B round? f e)
|
|
(let ([est (inexact->exact
|
|
(ceiling
|
|
(- (* (+ e (len f) -1) (invlog2of B))
|
|
1e-10)))])
|
|
(if (>= est 0)
|
|
(fixup r (* s (exptt B est)) m+ m- est B round?)
|
|
(let ([scale (exptt B (- est))])
|
|
(fixup (* r scale) s (* m+ scale) (* m- scale) est B round?))))))
|
|
(define fixup
|
|
(lambda (r s m+ m- k B round?)
|
|
(if ((if round? >= >) (+ r m+) s) ; too low?
|
|
(values (+ k 1) (generate r s m+ m- B round?))
|
|
(values k (generate (* r B) s (* m+ B) (* m- B) B round?)))))
|
|
(define (chr x)
|
|
(vector-ref '#(#\0 #\1 #\2 #\3 #\4 #\5 #\6 #\7 #\8 #\9) x))
|
|
(define generate
|
|
(lambda (r s m+ m- B round?)
|
|
(let-values ([(q r) (quotient+remainder r s)])
|
|
(let ([tc1 ((if round? <= <) r m-)]
|
|
[tc2 ((if round? >= >) (+ r m+) s)])
|
|
(if (not tc1)
|
|
(if (not tc2)
|
|
(cons (chr q) (generate (* r B) s (* m+ B) (* m- B) B round?))
|
|
(list (chr (+ q 1))))
|
|
(if (not tc2)
|
|
(list (chr q))
|
|
(if (< (* r 2) s)
|
|
(list (chr q))
|
|
(list (chr (+ q 1))))))))))
|
|
(define invlog2of
|
|
(let ([table (make-vector 37)]
|
|
[log2 (log 2)])
|
|
(do ([B 2 (+ B 1)])
|
|
((= B 37))
|
|
(vector-set! table B (/ log2 (log B))))
|
|
(lambda (B)
|
|
(if (<= 2 B 36)
|
|
(vector-ref table B)
|
|
(/ log2 (log B))))))
|
|
(define exptt
|
|
(let ([table (make-vector 326)])
|
|
(do ([k 0 (+ k 1)] [v 1 (* v 10)])
|
|
((= k 326))
|
|
(vector-set! table k v))
|
|
(lambda (B k)
|
|
(if (and (= B 10) (<= 0 k 325))
|
|
(vector-ref table k)
|
|
(expt B k))))))
|
|
(define (format-flonum pos? expt digits)
|
|
(define (next x)
|
|
(if (null? x)
|
|
(values #\0 '())
|
|
(values (car x) (cdr x))))
|
|
(define (format-flonum-no-expt expt d0 d*)
|
|
(cond
|
|
[(= expt 1)
|
|
(cons d0 (if (null? d*) '(#\. #\0) (cons #\. d*)))]
|
|
[else
|
|
(cons d0
|
|
(let-values ([(d0 d*) (next d*)])
|
|
(format-flonum-no-expt (- expt 1) d0 d*)))]))
|
|
(define (format-flonum-no-expt/neg expt d*)
|
|
(cond
|
|
[(= expt 0) d*]
|
|
[else (cons #\0 (format-flonum-no-expt/neg (+ expt 1) d*))]))
|
|
(define (sign pos? ls)
|
|
(if pos?
|
|
(list->string ls)
|
|
(list->string (cons #\- ls))))
|
|
(let ([d0 (car digits)] [d* (cdr digits)])
|
|
(cond
|
|
[(null? d*)
|
|
(if (char=? d0 #\0)
|
|
(if pos? "0.0" "-0.0")
|
|
(if (= expt 1)
|
|
(if pos?
|
|
(string d0 #\. #\0)
|
|
(string #\- d0 #\. #\0))
|
|
(if (= expt 0)
|
|
(if pos?
|
|
(string #\0 #\. d0)
|
|
(string #\- #\0 #\. d0))
|
|
(string-append
|
|
(if pos? "" "-")
|
|
(string d0) "e" (fixnum->string (- expt 1))))))]
|
|
[(and (null? d*) (char=? d0 #\0)) (if pos? "0.0" "-0.0")]
|
|
[(<= 1 expt 9)
|
|
(sign pos? (format-flonum-no-expt expt d0 d*))]
|
|
[(<= -3 expt 0)
|
|
(sign pos? (cons* #\0 #\. (format-flonum-no-expt/neg expt digits)))]
|
|
[else
|
|
(string-append
|
|
(if pos? "" "-")
|
|
(string d0) "." (list->string d*)
|
|
"e" (fixnum->string (- expt 1)))])))
|
|
(define (flo->string pos? m e p)
|
|
(let-values ([(expt digits) (flonum->digits m e 10 p 2 10)])
|
|
(format-flonum pos? expt digits)))
|
|
(define (flonum->string x)
|
|
(let-values ([(pos? be m) (flonum-parts x)])
|
|
(cond
|
|
[(<= 1 be 2046) ; normalized flonum
|
|
(flo->string pos? (+ m (expt 2 52)) (- be 1075) 53)]
|
|
[(= be 0)
|
|
(flo->string pos? m -1074 52)]
|
|
[(= be 2047)
|
|
(if (= m 0)
|
|
(if pos? "+inf.0" "-inf.0")
|
|
;;; Gee! nans have no sign!
|
|
"+nan.0")]
|
|
[else (error 'flonum->string "cannot happen")]))))
|
|
;;;
|
|
(define (string->flonum x)
|
|
(cond
|
|
[(string? x)
|
|
(foreign-call "ikrt_bytevector_to_flonum"
|
|
(string->utf8 x))]
|
|
[else
|
|
(error 'string->flonum "not a string" x)])) )
|
|
|
|
(library (ikarus rationalize)
|
|
(export rationalize)
|
|
(import
|
|
(except (ikarus) rationalize))
|
|
|
|
(define (rationalize x eps)
|
|
(define who 'rationalize)
|
|
(define (simplest x y)
|
|
(cond
|
|
[(< y x) (simplest y x)]
|
|
[(= x y) x]
|
|
[(> x 0)
|
|
(let ([n (numerator x)] [d (denominator x)]
|
|
[n^ (numerator y)] [d^ (denominator y)])
|
|
(simplest^ n d n^ d^))]
|
|
[(< y 0)
|
|
(let ([n (numerator x)] [d (denominator x)]
|
|
[n^ (numerator y)] [d^ (denominator y)])
|
|
(- (simplest^ (- n^) d^ (- n) d)))]
|
|
[else 1]))
|
|
(define (simplest^ n d n^ d^)
|
|
(let-values ([(q r) (quotient+remainder n d)])
|
|
(if (= r 0)
|
|
q
|
|
(let-values ([(q^ r^) (quotient+remainder n^ d^)])
|
|
(if (= q q^)
|
|
(let ([v (simplest^ d^ r^ d r)])
|
|
(let ([n^^ (numerator v)] [d^^ (denominator v)])
|
|
(/ (+ (* q n^^) d^^) n^^)))
|
|
(+ q 1))))))
|
|
(define (go x eps)
|
|
(simplest (- x eps) (+ x eps)))
|
|
(cond
|
|
[(flonum? x)
|
|
(if (flfinite? x)
|
|
(cond
|
|
[(flonum? eps)
|
|
(if (flfinite? eps) (go x eps) +nan.0)]
|
|
[(or (fixnum? eps) (bignum? eps) (ratnum? eps))
|
|
(go x eps)]
|
|
[else (error who "not a number" eps)])
|
|
(cond
|
|
[(flonum? eps)
|
|
(if (flfinite? eps) x +nan.0)]
|
|
[(or (fixnum? eps) (bignum? eps) (ratnum? eps))
|
|
x]
|
|
[else (error who "not a number" eps)]))]
|
|
[(or (fixnum? x) (bignum? x) (ratnum? x))
|
|
(cond
|
|
[(flonum? eps)
|
|
(if (flfinite? eps) (go x eps) +nan.0)]
|
|
[(or (fixnum? eps) (bignum? eps) (ratnum? eps))
|
|
(go x eps)]
|
|
[else (error who "not a number" eps)])]
|
|
[else (error who "not a number" x)])))
|
|
|
|
|
|
(library (ikarus r6rs-fu div/mod)
|
|
(export div mod div-and-mod div0 mod0 div0-and-mod0)
|
|
(import
|
|
(except (ikarus)
|
|
div mod div-and-mod div0 mod0 div0-and-mod0))
|
|
|
|
(define (div-and-mod n m)
|
|
(define who 'div-and-mod)
|
|
(unless (integer? n)
|
|
(error who "not an integer" n))
|
|
(unless (and (integer? m) (not (= m 0)))
|
|
(error who "not an integer" m))
|
|
(let ([d0 (quotient n m)])
|
|
(let ([m0 (- n (* d0 m))])
|
|
(if (>= m0 0)
|
|
(values d0 m0)
|
|
(if (>= m 0)
|
|
(values (- d0 1) (+ m0 m))
|
|
(values (+ d0 1) (- m0 m)))))))
|
|
|
|
(define (div n m)
|
|
(define who 'div)
|
|
(unless (integer? n)
|
|
(error who "not an integer" n))
|
|
(unless (and (integer? m) (not (= m 0)))
|
|
(error who "not an integer" m))
|
|
(let ([d0 (quotient n m)])
|
|
(let ([m0 (- n (* d0 m))])
|
|
(if (>= m0 0)
|
|
d0
|
|
(if (>= m 0)
|
|
(- d0 1)
|
|
(+ d0 1))))))
|
|
|
|
(define (mod n m)
|
|
(define who 'mod)
|
|
(unless (integer? n)
|
|
(error who "not an integer" n))
|
|
(unless (and (integer? m) (not (= m 0)))
|
|
(error who "not an integer" m))
|
|
(let ([d0 (quotient n m)])
|
|
(let ([m0 (- n (* d0 m))])
|
|
(if (>= m0 0)
|
|
m0
|
|
(if (>= m 0)
|
|
(+ m0 m)
|
|
(- m0 m))))))
|
|
|
|
|
|
(define (div0-and-mod0 x y)
|
|
(define who 'div0-and-mod0)
|
|
(unless (integer? x)
|
|
(error who "not an integer" x))
|
|
(unless (and (integer? y) (not (= y 0)))
|
|
(error who "not an integer" y))
|
|
(let-values ([(d m) (div-and-mod x y)])
|
|
(if (> y 0)
|
|
(if (< m (/ y 2))
|
|
(values d m)
|
|
(values (+ d 1) (- m y)))
|
|
(if (> m (/ y -2))
|
|
(values (- d 1) (+ m y))
|
|
(values d m)))))
|
|
|
|
(define (div0 x y)
|
|
(let-values ([(n m) (div0-and-mod0 x y)])
|
|
n))
|
|
|
|
(define (mod0 x y)
|
|
(let-values ([(n m) (div0-and-mod0 x y)])
|
|
m)))
|
|
|
|
|
|
(library (ikarus flonums div-and-mod)
|
|
(export fldiv flmod fldiv-and-mod fldiv0 flmod0 fldiv0-and-mod0)
|
|
(import
|
|
(ikarus system $flonums)
|
|
(ikarus system $fx)
|
|
(except (ikarus)
|
|
fldiv flmod fldiv-and-mod fldiv0 flmod0 fldiv0-and-mod0))
|
|
|
|
(define ($flmod n m)
|
|
(let ([d0 (fltruncate ($fl/ n m))])
|
|
(let ([m0 ($fl- n ($fl* d0 m))])
|
|
(if ($fl>= m0 0.0)
|
|
m0
|
|
(if ($fl>= m 0.0)
|
|
($fl+ m0 m)
|
|
($fl- m0 m))))))
|
|
|
|
(define ($fldiv n m)
|
|
(let ([d0 (fltruncate ($fl/ n m))])
|
|
(if ($fl>= n ($fl* d0 m))
|
|
d0
|
|
(if ($fl>= m 0.0)
|
|
($fl- d0 1.0)
|
|
($fl+ d0 1.0)))))
|
|
|
|
(define ($fldiv-and-mod n m)
|
|
(let ([d0 (fltruncate ($fl/ n m))])
|
|
(let ([m0 ($fl- n ($fl* d0 m))])
|
|
(if ($fl>= m0 0.0)
|
|
(values d0 m0)
|
|
(if ($fl>= m 0.0)
|
|
(values ($fl- d0 1.0) ($fl+ m0 m))
|
|
(values ($fl+ d0 1.0) ($fl- m0 m)))))))
|
|
|
|
(define (fldiv n m)
|
|
(if (flonum? n)
|
|
(if (flonum? m)
|
|
($fldiv n m)
|
|
(error 'fldiv "not a flonum" m))
|
|
(error 'fldiv "not a flonum" n)))
|
|
|
|
(define (flmod n m)
|
|
(if (flonum? n)
|
|
(if (flonum? m)
|
|
($flmod n m)
|
|
(error 'flmod "not a flonum" m))
|
|
(error 'flmod "not a flonum" n)))
|
|
|
|
(define (fldiv-and-mod n m)
|
|
(if (flonum? n)
|
|
(if (flonum? m)
|
|
($fldiv-and-mod n m)
|
|
(error 'fldiv-and-mod "not a flonum" m))
|
|
(error 'fldiv-and-mod "not a flonum" n)))
|
|
|
|
(define ($fldiv0-and-mod0 n m)
|
|
(let ([d0 (fltruncate ($fl/ n m))])
|
|
(let ([m0 ($fl- n ($fl* d0 m))])
|
|
(if ($fl>= m 0.0)
|
|
(if ($fl< m0 ($fl/ m 2.0))
|
|
(if ($fl>= m0 ($fl/ m -2.0))
|
|
(values d0 m0)
|
|
(values ($fl- d0 1.0) ($fl+ m0 m)))
|
|
(values ($fl+ d0 1.0) ($fl- m0 m)))
|
|
(if ($fl< m0 ($fl/ m -2.0))
|
|
(if ($fl>= m0 ($fl/ m 2.0))
|
|
(values d0 m0)
|
|
(values ($fl+ d0 1.0) ($fl- m0 m)))
|
|
(values ($fl- d0 1.0) ($fl+ m0 m)))))))
|
|
|
|
(define ($fldiv0 n m)
|
|
(let ([d0 (fltruncate ($fl/ n m))])
|
|
(let ([m0 ($fl- n ($fl* d0 m))])
|
|
(if ($fl>= m 0.0)
|
|
(if ($fl< m0 ($fl/ m 2.0))
|
|
(if ($fl>= m0 ($fl/ m -2.0))
|
|
d0
|
|
($fl- d0 1.0))
|
|
($fl+ d0 1.0))
|
|
(if ($fl< m0 ($fl/ m -2.0))
|
|
(if ($fl>= m0 ($fl/ m 2.0))
|
|
d0
|
|
($fl+ d0 1.0))
|
|
($fl- d0 1.0))))))
|
|
|
|
(define ($flmod0 n m)
|
|
(let ([d0 (fltruncate ($fl/ n m))])
|
|
(let ([m0 ($fl- n ($fl* d0 m))])
|
|
(if ($fl>= m 0.0)
|
|
(if ($fl< m0 ($fl/ m 2.0))
|
|
(if ($fl>= m0 ($fl/ m -2.0))
|
|
m0
|
|
($fl+ m0 m))
|
|
($fl- m0 m))
|
|
(if ($fl< m0 ($fl/ m -2.0))
|
|
(if ($fl>= m0 ($fl/ m 2.0))
|
|
m0
|
|
($fl- m0 m))
|
|
($fl+ m0 m))))))
|
|
|
|
(define (fldiv0 n m)
|
|
(if (flonum? n)
|
|
(if (flonum? m)
|
|
($fldiv0 n m)
|
|
(error 'fldiv0 "not a flonum" m))
|
|
(error 'fldiv0 "not a flonum" n)))
|
|
|
|
(define (flmod0 n m)
|
|
(if (flonum? n)
|
|
(if (flonum? m)
|
|
($flmod0 n m)
|
|
(error 'flmod0 "not a flonum" m))
|
|
(error 'flmod0 "not a flonum" n)))
|
|
|
|
(define (fldiv0-and-mod0 n m)
|
|
(if (flonum? n)
|
|
(if (flonum? m)
|
|
($fldiv0-and-mod0 n m)
|
|
(error 'fldiv0-and-mod0 "not a flonum" m))
|
|
(error 'fldiv0-and-mod0 "not a flonum" n))))
|
|
|
|
(library (ikarus bitwise misc)
|
|
(export fxfirst-bit-set bitwise-bit-set? bitwise-first-bit-set
|
|
fxbit-count bitwise-bit-count
|
|
fxlength
|
|
fxbit-set?
|
|
fxcopy-bit
|
|
fxcopy-bit-field
|
|
fxbit-field)
|
|
(import
|
|
(ikarus system $fx)
|
|
(ikarus system $bignums)
|
|
(ikarus system $flonums)
|
|
(except (ikarus)
|
|
fxfirst-bit-set bitwise-bit-set? bitwise-first-bit-set
|
|
fxbit-count bitwise-bit-count
|
|
fxlength
|
|
fxbit-set?
|
|
fxcopy-bit
|
|
fxcopy-bit-field
|
|
fxbit-field))
|
|
|
|
(module (bitwise-first-bit-set fxfirst-bit-set)
|
|
(define (byte-first-bit-set x i)
|
|
(import (ikarus system $bytevectors))
|
|
(define-syntax make-first-bit-set-bytevector
|
|
(lambda (x)
|
|
(define (fst n)
|
|
(cond
|
|
[(zero? n) 0]
|
|
[(even? n) (fst (bitwise-arithmetic-shift-right n 1))]
|
|
[else (+ 1 (fst (bitwise-arithmetic-shift-right n 1)))]))
|
|
(u8-list->bytevector
|
|
(let f ([i 0])
|
|
(cond
|
|
[(= i 256) '()]
|
|
[else (cons (fst i) (f (+ i 1)))])))))
|
|
(define bv (make-first-bit-set-bytevector))
|
|
($fx+ i ($bytevector-u8-ref bv i)))
|
|
(define ($fxloop x i)
|
|
(let ([y ($fxlogand x 255)])
|
|
(if ($fx= y 0)
|
|
($fxloop ($fxsra x 8) ($fx+ i 8))
|
|
(byte-first-bit-set y i))))
|
|
(define ($bnloop x i idx)
|
|
(let ([b ($bignum-byte-ref x idx)])
|
|
(if ($fxzero? b)
|
|
($bnloop x ($fx+ i 8) ($fx+ idx 1))
|
|
(byte-first-bit-set b i))))
|
|
(define ($fxfirst-bit-set x)
|
|
(if ($fx> x 0)
|
|
($fxloop x 0)
|
|
(if ($fx= x 0)
|
|
-1
|
|
(if ($fx> x (least-fixnum))
|
|
($fxloop ($fx- 0 x) 0)
|
|
($bnloop (- x) 0 0)))))
|
|
(define (fxfirst-bit-set x)
|
|
(cond
|
|
[(fixnum? x)
|
|
($fxfirst-bit-set x)]
|
|
[else (error 'fxfirst-bit-set "not a fixnum" x)]))
|
|
(define (bitwise-first-bit-set x)
|
|
(cond
|
|
[(fixnum? x)
|
|
($fxfirst-bit-set x)]
|
|
[(bignum? x) ($bnloop x 0 0)]
|
|
[else (error 'bitwise-first-bit-set "not an exact integer" x)])))
|
|
|
|
(module (fxbit-count bitwise-bit-count)
|
|
(define (pos-fxbitcount n)
|
|
;;; nifty parrallel count from:
|
|
;;; http://infolab.stanford.edu/~manku/bitcount/bitcount.html
|
|
(let ([m0 #x15555555]
|
|
[m1 #x13333333]
|
|
[m2 #x0f0f0f0f])
|
|
(let* ([n ($fx+ ($fxlogand n m0) ($fxlogand ($fxsra n 1) m0))]
|
|
[n ($fx+ ($fxlogand n m1) ($fxlogand ($fxsra n 2) m1))]
|
|
[n ($fx+ ($fxlogand n m2) ($fxlogand ($fxsra n 4) m2))])
|
|
($fxmodulo n 255))))
|
|
(define ($fxbitcount n)
|
|
(if ($fx< n 0)
|
|
(fxlognot (pos-fxbitcount (fxlognot n)))
|
|
(pos-fxbitcount n)))
|
|
(define (bnbitcount n)
|
|
(define (poscount x idx c)
|
|
(let ([c (+ c
|
|
($fx+ (pos-fxbitcount
|
|
($fxlogor
|
|
($fxsll ($bignum-byte-ref x ($fx+ idx 3)) 8)
|
|
($bignum-byte-ref x ($fx+ idx 2))))
|
|
(pos-fxbitcount
|
|
($fxlogor
|
|
($fxsll ($bignum-byte-ref x ($fxadd1 idx)) 8)
|
|
($bignum-byte-ref x idx)))))])
|
|
(if ($fx= idx 0)
|
|
c
|
|
(poscount x ($fx- idx 4) c))))
|
|
(if ($bignum-positive? n)
|
|
(poscount n ($fx- ($bignum-size n) 4) 0)
|
|
(let ([n (bitwise-not n)])
|
|
(bitwise-not (poscount n ($fx- ($bignum-size n) 4) 0)))))
|
|
(define (fxbit-count n)
|
|
(cond
|
|
[(fixnum? n) ($fxbitcount n)]
|
|
[else (error 'fxbit-count "not a fixnum" n)]))
|
|
(define (bitwise-bit-count n)
|
|
(cond
|
|
[(fixnum? n) ($fxbitcount n)]
|
|
[(bignum? n) (bnbitcount n)]
|
|
[else (error 'bitwise-bit-count "not an exact integer" n)])))
|
|
|
|
(define (fxlength x)
|
|
(if (fixnum? x)
|
|
(let ([fl ($fixnum->flonum
|
|
(if ($fx< x 0) ($fxlognot x) x))])
|
|
(let ([sbe ($fxlogor
|
|
($fxsll ($flonum-u8-ref fl 0) 4)
|
|
($fxsra ($flonum-u8-ref fl 1) 4))])
|
|
(cond
|
|
[($fx= sbe 0) 0]
|
|
[else ($fx- sbe 1022)])))
|
|
(error 'fxlength "not a fixnum" x)))
|
|
|
|
(define (fxbit-set? x i)
|
|
(define who 'fxbit-set?)
|
|
(if (fixnum? x)
|
|
(if (fixnum? i)
|
|
(if (and ($fx<= 0 i) ($fx< i (fixnum-width)))
|
|
(not ($fxzero? ($fxlogand ($fxsra x i) 1)))
|
|
(error who "index out of range" i))
|
|
(error who "index is not a fixnum" i))
|
|
(error who "not a fixnum" x)))
|
|
|
|
(define (bitwise-bit-set? x i)
|
|
(define who 'bitwise-bit-set?)
|
|
(cond
|
|
[(fixnum? i)
|
|
(when ($fx< i 0)
|
|
(error who "index must be non-negative" i))
|
|
(cond
|
|
[(fixnum? x)
|
|
(if ($fx< i (fixnum-width))
|
|
($fx= ($fxlogand ($fxsra x i) 1) 1)
|
|
($fx< x 0))]
|
|
[(bignum? x)
|
|
(let ([n ($bignum-size x)])
|
|
(let ([m ($fx* n 8)])
|
|
(if ($fx< m i)
|
|
(not ($bignum-positive? x))
|
|
(if ($bignum-positive? x)
|
|
(let ([b ($bignum-byte-ref x ($fxsra i 3))])
|
|
($fx= ($fxlogand ($fxsra b ($fxlogand i 7)) 1) 1))
|
|
(= 1 (bitwise-and
|
|
(bitwise-arithmetic-shift-right x i)
|
|
1))))))]
|
|
[else (error who "not an exact integer" x)])]
|
|
[(bignum? i)
|
|
(unless ($bignum-positive? i)
|
|
(error who "index must be non-negative"))
|
|
(cond
|
|
[(fixnum? x) ($fx< x 0)]
|
|
[(bignum? x)
|
|
(= 1 (bitwise-and (bitwise-arithmetic-shift-right x i) 1))]
|
|
[else (error who "not an exact integer" x)])]
|
|
[else
|
|
(error who "index is not an exact integer" i)]))
|
|
|
|
|
|
(define (fxcopy-bit x i b)
|
|
(define who 'fxcopy-bit)
|
|
(if (fixnum? x)
|
|
(if (fixnum? i)
|
|
(if (and ($fx<= 0 i) ($fx< i (fixnum-width)))
|
|
(case b
|
|
[(0) ($fxlogand x ($fxlognot ($fxsll 1 i)))]
|
|
[(1) ($fxlogor x ($fxsll 1 i))]
|
|
[else (error who "invalid bit value" b)])
|
|
(error who "index out of range" i))
|
|
(error who "index is not a fixnum" i))
|
|
(error who "not a fixnum" x)))
|
|
|
|
(define (fxcopy-bit-field x i j b)
|
|
(define who 'fxcopy-bit-field)
|
|
(if (fixnum? x)
|
|
(if (fixnum? i)
|
|
(if ($fx<= 0 i)
|
|
(if (fixnum? j)
|
|
(if ($fx< j (fixnum-width))
|
|
(if ($fx<= i j)
|
|
(if (fixnum? b)
|
|
(let ([m
|
|
($fxlogxor
|
|
($fxsub1 ($fxsll 1 i))
|
|
($fxsub1 ($fxsll 1 j)))])
|
|
($fxlogor
|
|
($fxlogand m b)
|
|
($fxlogand ($fxlognot m) x)))
|
|
(error who "not a fixnum" b))
|
|
(if ($fx<= 0 j)
|
|
(error who "index out of range" j)
|
|
(error who "indices not in order" i j)))
|
|
(error who "index out of range" j))
|
|
(error who "not a fixnum" j))
|
|
(error who "index out of range" i))
|
|
(error who "not a fixnum" i))
|
|
(error who "not a fixnum" x)))
|
|
|
|
(define (fxbit-field x i j)
|
|
(define who 'fxbit-field)
|
|
(if (fixnum? x)
|
|
(if (fixnum? i)
|
|
(if ($fx<= 0 i)
|
|
(if (fixnum? j)
|
|
(if ($fx< j (fixnum-width))
|
|
(if ($fx<= i j)
|
|
($fxsra
|
|
($fxlogand x ($fxsub1 ($fxsll 1 j)))
|
|
i)
|
|
(if ($fx<= 0 j)
|
|
(error who "index out of range" j)
|
|
(error who "indices not in order" i j)))
|
|
(error who "index out of range" j))
|
|
(error who "not a fixnum" j))
|
|
(error who "index out of range" i))
|
|
(error who "not a fixnum" i))
|
|
(error who "not a fixnum" x)))
|
|
|
|
)
|
|
|
|
|