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;;; 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? $flround)
(except (ikarus) inexact->exact exact flpositive? flabs fixnum->flonum
flsin flcos fltan flasin flacos flatan fleven? flodd?
flfloor flceiling flnumerator fldenominator flexp fllog
flexpt flinteger? flonum-parts flonum-bytes flnan? flfinite?
flinfinite? flround))
(define (flonum-bytes f)
(unless (flonum? f)
(die 'flonum-bytes "not a flonum" f))
(values
($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)
($flonum-u8-ref f 7)))
(define (flonum-parts x)
(unless (flonum? x)
(die 'flonum-parts "not a flonum" x))
(let-values ([(b0 b1 b2 b3 b4 b5 b6 b7) (flonum-bytes x)])
(values
(zero? (fxlogand b0 128))
(+ (fxsll (fxlogand b0 127) 4)
(fxsra b1 4))
(+ (+ b7 (fxsll b6 8) (fxsll b5 16))
(* (+ b4
(fxsll b3 8)
(fxsll b2 16)
(fxsll (fxlogand b1 #b1111) 24))
(expt 2 24))))))
(define ($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)
(die '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
($flonum-signed-mantissa x)
(- be 1075))]
[else
;;; this really needs to get optimized.
(let-values ([(pos? be m) (flonum-parts x)])
(cond
[(= be 0) ;;; denormalized
(if (= m 0)
0
(* (if pos? 1 -1)
(/ m (ctexpt 2 1074))))]
[else ; normalized flonum
(/ (+ m (ctexpt 2 52))
(bitwise-arithmetic-shift-left
(if pos? 1 -1)
(- 1075 be)))]))])))))
(define (flnumerator x)
(unless (flonum? x)
(die 'flnumerator "not a flonum" x))
(cond
[($flonum-integer? x) x]
[($flonum-rational? x)
(exact->inexact (numerator ($flonum->exact x)))]
[else x]))
(define (fldenominator x)
(unless (flonum? x)
(die 'fldenominator "not a flonum" x))
(cond
[($flonum-integer? x) 1.0]
[($flonum-rational? x)
(exact->inexact (denominator ($flonum->exact x)))]
[(flnan? x) x]
[else 1.0]))
(define (fleven? x)
;;; FIXME: optimize
(unless (flonum? x)
(die 'fleven? "not a flonum" x))
(let ([v ($flonum->exact x)])
(cond
[(fixnum? v) ($fx= ($fxlogand v 1) 0)]
[(bignum? v)
(foreign-call "ikrt_even_bn" v)]
[else (die 'fleven? "not an integer flonum" x)])))
(define (flodd? x)
(unless (flonum? x)
(die 'flodd? "not a flonum" x))
;;; FIXME: optimize
(let ([v ($flonum->exact x)])
(cond
[(fixnum? v) ($fx= ($fxlogand v 1) 1)]
[(bignum? v)
(not (foreign-call "ikrt_even_bn" v))]
[else (die 'flodd? "not an integer flonum" x)])))
(define (flinteger? x)
(if (flonum? x)
($flonum-integer? x)
(die '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)))
(die '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))))
(die 'flnan? "not a flonum" x)))
(define (flfinite? x)
(if (flonum? x)
(let ([be (fxlogand ($flonum-sbe x) (sub1 (fxsll 1 11)))])
(not (fx= be 2047)))
(die 'flfinite? "not a flonum" x)))
(define ($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 ($flonum->exact x)
(die 'inexact->exact "no real value" x))]
[(or (fixnum? x) (ratnum? x) (bignum? x)) x]
[else
(die 'inexact->exact "not an inexact number" x)]))
(define (exact x)
(cond
[(flonum? x)
(or ($flonum->exact x)
(die 'exact "no real value" x))]
[(or (fixnum? x) (ratnum? x) (bignum? x)) x]
[else
(die 'exact "not an inexact number" x)]))
(define (flpositive? x)
(if (flonum? x)
($fl> x 0.0)
(die 'flpositive? "not a flonum" x)))
(define (flabs x)
(if (flonum? x)
(if ($fx> ($flonum-u8-ref x 0) 127)
($fl* x -1.0)
x)
(die 'flabs "not a flonum" x)))
(define (fixnum->flonum x)
(if (fixnum? x)
($fixnum->flonum x)
(die 'fixnum->flonum "not a fixnum")))
(define (flsin x)
(if (flonum? x)
(foreign-call "ikrt_fl_sin" x)
(die 'flsin "not a flonum" x)))
(define (flcos x)
(if (flonum? x)
(foreign-call "ikrt_fl_cos" x)
(die 'flcos "not a flonum" x)))
(define (fltan x)
(if (flonum? x)
(foreign-call "ikrt_fl_tan" x)
(die 'fltan "not a flonum" x)))
(define (flasin x)
(if (flonum? x)
(foreign-call "ikrt_fl_asin" x)
(die 'flasin "not a flonum" x)))
(define (flacos x)
(if (flonum? x)
(foreign-call "ikrt_fl_acos" x)
(die 'flacos "not a flonum" x)))
(define (flatan x)
(if (flonum? x)
(foreign-call "ikrt_fl_atan" x)
(die 'flatan "not a flonum" x)))
(define (flfloor x)
(define (ratnum-floor x)
(let ([n (numerator x)] [d (denominator x)])
(let ([q (quotient n d)])
(if (>= n 0) q (- q 1)))))
(cond
[(flonum? x)
;;; optimize for integer flonums case
(let ([e ($flonum->exact x)])
(cond
[(ratnum? e)
(exact->inexact (ratnum-floor e))]
[else x]))]
[else (die 'flfloor "not a flonum" x)]))
(define (flceiling x)
(cond
[(flonum? x)
;;; optimize for integer flonums case
(let ([e ($flonum->exact x)])
(cond
[(ratnum? e)
(exact->inexact (ceiling e))]
[else x]))]
[else (die 'flceiling "not a flonum" x)]))
(define (flexp x)
(if (flonum? x)
(foreign-call "ikrt_fl_exp" x ($make-flonum))
(die 'flexp "not a flonum" x)))
(define (fllog x)
(if (flonum? x)
(if ($fl>= x 0.0)
(foreign-call "ikrt_fl_log" x)
(die 'fllog "argument should not be negative" x))
(die 'fllog "not a flonum" x)))
(define (flexpt x y)
(if (flonum? x)
(if (flonum? y)
(let ([y^ ($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))]))
(die 'flexpt "not a flonum" y))
(die '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
bitwise-length
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 $flround)
(except (ikarus) + - * / zero? = < <= > >= add1 sub1 quotient
remainder modulo even? odd? quotient+remainder number->string
bitwise-arithmetic-shift-right bitwise-arithmetic-shift-left
bitwise-arithmetic-shift
bitwise-length
positive? negative? bitwise-and bitwise-not
string->number expt gcd lcm numerator denominator
exact->inexact inexact floor ceiling round log
exact-integer-sqrt min max abs real->flonum
fl=? fl<? fl<=? fl>? fl>=? fl+ fl- fl* fl/ flsqrt flmin
flzero? flnegative? sra sll exp
sin cos tan asin acos atan sqrt truncate fltruncate
flmax random))
(module (bignum->flonum)
; sbe f6 f5 f4 f3 f2 f1 f0
;SEEEEEEE|EEEEmmmm|mmmmmmmm|mmmmmmmm|mmmmmmmm|mmmmmmmm|mmmmmmmm|mmmmmmmm
; | | | | | | |
; v0 v1 v2 v3 v4 v5 v6 v7
(define ($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 (die '$float/aux "BUG: invalid b7" b7)]))
(define (bignum->flonum x)
(define (bignum/4->flonum x)
($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)
(die '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 ($bignum-byte-ref x bytes)])
(if (fx= bn 0)
(die 'bignum/n->flonum "malformed bignum")
(aux x bn bytes)))
(aux x bn bytes)))
(aux x bn bytes)))
(aux x bn bytes))))
(unless (bignum? x)
(die 'bignum->flonum "not a bignum" x))
(let ([bytes ($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
(die '+ "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))
($ratnum-d y))]
[else
(die '+ "not a number" y)])]
[(flonum? x)
(cond
[(fixnum? y)
($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
(die '+ "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 ($ratnum-d y)])
;;; FIXME: inefficient
(/ (+ (* n0 d1) (* n1 d0)) (* d0 d1)))]
[else
(die '+ "not a number" y)])]
[else (die '+ "not a number" x)])))
(define binary-bitwise-and
(lambda (x y)
(cond
[(fixnum? x)
(cond
[(fixnum? y) ($fxlogand x y)]
[(bignum? y)
(foreign-call "ikrt_fxbnlogand" x y)]
[else
(die '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
(die 'bitwise-and "not an exact integer" y)])]
[else (die '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
(die '- "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 ($ratnum-d y)])
(binary/ (binary- (binary* d x) n) d))]
[else
(die '- "not a number" y)])]
[(flonum? x)
(cond
[(fixnum? y)
($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 ($ratnum-d y)])
(binary/ (binary- (binary* d x) n) d))]
[else
(die '- "not a number" y)])]
[(ratnum? x)
(let ([nx ($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 ($ratnum-d y)])
(binary/ (binary- (binary* nx dy) (binary* ny dx))
(binary* dx dy)))]
[else
(die '- "not a number" y)]))]
[else (die '- "not a number" x)])))
(define binary*
(lambda (x y)
(cond
[(fixnum? x)
(cond
[(fixnum? y)
(foreign-call "ikrt_fxfxmult" x y)]
[(bignum? y)
(foreign-call "ikrt_fxbnmult" x y)]
[(flonum? y)
($fl* ($fixnum->flonum x) y)]
[(ratnum? y)
(binary/ (binary* x ($ratnum-n y)) ($ratnum-d y))]
[else
(die '* "not a number" y)])]
[(bignum? x)
(cond
[(fixnum? y)
(foreign-call "ikrt_fxbnmult" y x)]
[(bignum? y)
(foreign-call "ikrt_bnbnmult" x y)]
[(flonum? y)
($fl* (bignum->flonum x) y)]
[(ratnum? y)
(binary/ (binary* x ($ratnum-n y)) ($ratnum-d y))]
[else
(die '* "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
(die '* "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 (die '* "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 (die '+ "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 (die '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) ($fxlognot x)]
[(bignum? x) (foreign-call "ikrt_bnlognot" x)]
[else (die 'bitwise-not "invalid argument" x)]))
(define -
(case-lambda
[(x y) (binary- x y)]
[(x y z) (binary- (binary- x y) z)]
[(a) (binary- 0 a)]
[(a b c d . e*)
(let f ([ac (binary- (binary- (binary- a b) c) d)]
[e* e*])
(cond
[(null? e*) ac]
[else (f (binary- ac (car e*)) (cdr e*))]))]))
(define *
(case-lambda
[(x y) (binary* x y)]
[(x y z) (binary* (binary* x y) z)]
[(a)
(cond
[(fixnum? a) a]
[(bignum? a) a]
[else (die '* "not a number" a)])]
[() 1]
[(a b c d . e*)
(let f ([ac (binary* (binary* (binary* a b) c) d)]
[e* e*])
(cond
[(null? e*) ac]
[else (f (binary* ac (car e*)) (cdr e*))]))]))
(define (binary-gcd x y)
(define (gcd x y)
(cond
[($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)
(die 'gcd "not an exact integer" y)]
[else
(die 'gcd "not a number" y)])]
[(number? x)
(die 'gcd "not an exact integer" x)]
[else
(die 'gcd "not a number" x)])]
[(x)
(cond
[(or (fixnum? x) (bignum? x)) x]
[(number? x)
(die 'gcd "not an exact integer" x)]
[else
(die '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)
(die 'lcm "not an exact integer" y)]
[else
(die 'lcm "not a number" y)])]
[(number? x)
(die 'lcm "not an exact integer" x)]
[else
(die 'lcm "not a number" x)])]
[(x)
(cond
[(or (fixnum? x) (bignum? x)) x]
[(number? x)
(die 'lcm "not an exact integer" x)]
[else
(die '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) ($fl/ x (ratnum->flonum y))]
[else (die '/ "not a number" y)])]
[(fixnum? x)
(cond
[(flonum? y) ($fl/ ($fixnum->flonum x) y)]
[(fixnum? y)
(cond
[($fx= y 0) (die '/ "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)) ($ratnum-n y))]
[else (die '/ "not a number" y)])]
[(bignum? x)
(cond
[(fixnum? y)
(cond
[($fx= y 0) (die '/ "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 (die '/ "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 (die '/ "not a number" x)])))
(define /
(case-lambda
[(x y) (binary/ x y)]
[(x)
(cond
[(fixnum? x)
(cond
[($fxzero? x) (die '/ "division by 0")]
[($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 (die '/ "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 ($fl< x y)
y
x)
(die 'flmax "not a flonum" y))
(die 'flmax "not a flonum" x))]
[(x y z . rest)
(let f ([a (flmax x y)] [b z] [ls rest])
(cond
[(null? ls) (flmax a b)]
[else
(f (flmax a b) (car ls) (cdr ls))]))]
[(x)
(if (flonum? x)
x
(die 'flmax "not a number" x))]))
(define max
(case-lambda
[(x y)
(cond
[(fixnum? x)
(cond
[(fixnum? y)
(if ($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 (die '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 ($fl>= y x) y x))]
[(ratnum? y) ;;; FIXME: optimize
(if (>= x y) x y)]
[else (die 'max "not a number" y)])]
[(flonum? x)
(cond
[(flonum? y)
(if ($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 (die '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 ($fl>= x y) x y))]
[else (die 'max "not a number" y)])]
[else (die 'max "not a number" x)])]
[(x y z . rest)
(let f ([a (max x y)] [b z] [ls rest])
(cond
[(null? ls) (max a b)]
[else
(f (max a b) (car ls) (cdr ls))]))]
[(x)
(if (number? x)
x
(die 'max "not a number" x))]))
(define min
(case-lambda
[(x y)
(cond
[(fixnum? x)
(cond
[(fixnum? y)
(if ($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 (die '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 ($fl>= y x) x y))]
[(ratnum? y) ;;; FIXME: optimize
(if (>= x y) y x)]
[else (die 'min "not a number" y)])]
[(flonum? x)
(cond
[(flonum? y)
(if ($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 (die '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 ($fl>= x y) y x))]
[else (die 'min "not a number" y)])]
[else (die 'min "not a number" x)])]
[(x y z . rest)
(let f ([a (min x y)] [b z] [ls rest])
(cond
[(null? ls) (min a b)]
[else
(f (min a b) (car ls) (cdr ls))]))]
[(x)
(if (number? x)
x
(die 'min "not a number" x))]))
(define (abs x)
(cond
[(fixnum? x)
(if ($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) ($ratnum-d x))
x))]
[else (die 'abs "not a number" x)]))
(define flmin
(case-lambda
[(x y)
(if (flonum? x)
(if (flonum? y)
(if ($fl< x y) x y)
(die 'flmin "not a flonum" y))
(die '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
(die 'flmin "not a flonum" x))]))
(define exact->inexact
(lambda (x)
(cond
[(fixnum? x) ($fixnum->flonum x)]
[(bignum? x) (bignum->flonum x)]
[(ratnum? x) (ratnum->flonum x)]
[else
(die 'exact->inexact
"not an exact number" x)])))
(define inexact
(lambda (x)
(cond
[(fixnum? x) ($fixnum->flonum x)]
[(bignum? x) (bignum->flonum x)]
[(ratnum? x) (ratnum->flonum x)]
[(flonum? x) x]
[else
(die 'inexact "not a number" x)])))
(define real->flonum
(lambda (x)
(cond
[(fixnum? x) ($fixnum->flonum x)]
[(bignum? x) (bignum->flonum x)]
[(ratnum? x) (ratnum->flonum x)]
[(flonum? x) x]
[else
(die 'real->flonum "not a real number" x)])))
(define positive-bignum?
(lambda (x)
(foreign-call "ikrt_positive_bn" x)))
(define even-bignum?
(lambda (x)
(foreign-call "ikrt_even_bn" x)))
(define ($fxeven? x)
($fxzero? ($fxlogand x 1)))
(define (even? x)
(cond
[(fixnum? x) ($fxeven? x)]
[(bignum? x) (even-bignum? x)]
[(flonum? x) (die 'even? "BUG" x)]
[else (die 'even? "not an integer" x)]))
(define (odd? x)
(not
(cond
[(fixnum? x) ($fxeven? x)]
[(bignum? x) (even-bignum? x)]
[(flonum? x) (die 'odd? "BUG" x)]
[else (die '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 (die 'number->string "BUG")])))
(define ratnum->string
(lambda (x r)
(string-append
($number->string ($ratnum-n x) r)
"/"
($number->string ($ratnum-d x) r))))
(define $number->string
(lambda (x r)
(cond
[(fixnum? x) (fixnum->string x r)]
[(bignum? x) (bignum->string x r)]
[(flonum? x)
(unless (eqv? r 10)
(die 'number->string
"invalid radix for inexact number"
r x))
(flonum->string x)]
[(ratnum? x) (ratnum->string x r)]
[else (die 'number->string "not a number" x)])))
(define number->string
(case-lambda
[(x) ($number->string x 10)]
[(x r)
(unless (memv r '(2 8 10 16))
(die 'number->string "invalid radix" r))
($number->string x r)]
[(x r precision)
(die 'number->string
"BUG: precision is not supported yet")])))
(define modulo
(lambda (n m)
(cond
[(fixnum? n)
(cond
[(fixnum? m) ($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
(die 'modulo "not an integer" m)]))]
[(ratnum? m) (die 'modulo "not an integer" m)]
[else (die '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
(die 'modulo "not an integer" m)]))]
[(ratnum? m) (die 'modulo "not an integer" m)]
[else (die 'modulo "not a number" m)])]
[(flonum? n)
(let ([v ($flonum->integer n)])
(cond
[v (inexact (modulo v m))]
[else
(die 'modulo "not an integer" n)]))]
[(ratnum? n) (die 'modulo "not an integer" n)]
[else (die '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) (die '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)
(die 'fl<? "not a flonum" y))
(die 'fl<? "not a flonum" x))]
[(x y z)
(if (flonum? x)
(if (flonum? y)
(if (flonum? z)
(and ($fl< x y) ($fl< y z))
(die 'fl<? "not a flonum" z))
(die 'fl<? "not a flonum" y))
(die 'fl<? "not a flonum" x))]
[(x)
(or (flonum? x)
(die 'fl<? "not a flonum" x))]
[(x y . rest)
(let ()
(define (loopf a ls)
(unless (flonum? a)
(die '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))))
(die 'fl<? "not a flonum" y)))
(loopf (car rest) (cdr rest)))
(die 'fl<? "not a flonum" y))
(die '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)
(die 'fl+ "not a flonum" y))
(die '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
(die 'fl+ "not a flonum" x))]
[() (exact->inexact 0)]))
(define fl-
(case-lambda
[(x y)
(if (flonum? x)
(if (flonum? y)
($fl- x y)
(die 'fl- "not a flonum" y))
(die 'fl- "not a flonum" x))]
[(x y z)
(fl- (fl- x y) z)]
[(x y z q . rest)
(let f ([ac (fl- (fl- (fl- x y) z) q)] [rest rest])
(if (null? rest)
ac
(f (fl- ac (car rest)) (cdr rest))))]
[(x)
(if (flonum? x)
($fl* -1.0 x)
(die 'fl+ "not a flonum" x))]))
(define fl*
(case-lambda
[(x y)
(if (flonum? x)
(if (flonum? y)
($fl* x y)
(die 'fl* "not a flonum" y))
(die 'fl* "not a flonum" x))]
[(x y z)
(fl* (fl* x y) z)]
[(x y z q . rest)
(let f ([ac (fl* (fl* (fl* x y) z) q)] [rest rest])
(if (null? rest)
ac
(f (fl* ac (car rest)) (cdr rest))))]
[(x)
(if (flonum? x)
x
(die 'fl* "not a flonum" x))]
[() 1.0]))
(define fl/
(case-lambda
[(x y)
(if (flonum? x)
(if (flonum? y)
($fl/ x y)
(die 'fl/ "not a flonum" y))
(die '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)
(die '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< >= $fx>= fxbn> bnfx> bnbn>= fxfl>= flfx>= bnfl>= flbn>= flfl>=
exrt> rtex> exrt> rtex> flrt>= rtfl>= rtrt>=))
(define add1
(lambda (x)
(cond
[(fixnum? x)
(foreign-call "ikrt_fxfxplus" x 1)]
[(bignum? x)
(foreign-call "ikrt_fxbnplus" 1 x)]
[else (die 'add1 "not a number" x)])))
(define sub1
(lambda (x)
(cond
[(fixnum? x)
(foreign-call "ikrt_fxfxplus" x -1)]
[(bignum? x)
(foreign-call "ikrt_fxbnplus" -1 x)]
[else (die 'sub1 "not a number" x)])))
(define zero?
(lambda (x)
(cond
[(fixnum? x) (eq? x 0)]
[(bignum? x) #f]
[(flonum? x)
(or ($fl= x 0.0) ($fl= x -0.0))]
[else
(die 'zero? "not a number" x)])))
(define expt
(lambda (n m)
(define fxexpt
(lambda (n m)
(cond
[($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)
(die 'expt "not a numebr" n))
(cond
[(fixnum? m)
(if ($fx>= m 0)
(fxexpt n m)
(/ 1 (expt n (- m))))]
[(bignum? m)
(cond
[(eq? n 0) 0]
[(eq? n 1) 1]
[(eq? n -1)
(if (positive-bignum? m)
(if (even-bignum? m)
1
-1)
(/ 1 (expt n (- m))))]
[else
(die 'expt "result is too big to compute" n m)])]
[(flonum? m) (flexpt (inexact n) m)]
[(ratnum? m) (flexpt (inexact n) (inexact m))]
[else (die 'expt "not a number" m)])))
(define quotient
(lambda (x y)
(let-values ([(q r) (quotient+remainder x y)])
q)))
(define remainder
(lambda (x y)
(let-values ([(q r) (quotient+remainder x y)])
r)))
(define quotient+remainder
(lambda (x y)
(cond
[(eq? y 0)
(die 'quotient+remainder
"second argument must be non-zero")]
[(fixnum? x)
(cond
[(fixnum? y)
(values (fxquotient x y)
(fxremainder x y))]
[(bignum? y) (values 0 x)]
[(flonum? y)
(let ([v ($flonum->integer y)])
(cond
[v
(let-values ([(q r) (quotient+remainder x v)])
(values (inexact q) (inexact r)))]
[else
(die 'quotient+remainder "not an integer" y)]))]
[else (die '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 ($flonum->integer y)])
(cond
[v
(let-values ([(q r) (quotient+remainder x v)])
(values (inexact q) (inexact r)))]
[else
(die 'quotient+remainder "not an integer" y)]))]
[else (die 'quotient+remainder "not a number" y)])]
[(flonum? x)
(let ([v ($flonum->integer x)])
(cond
[v
(let-values ([(q r) (quotient+remainder v y)])
(values (inexact q) (inexact r)))]
[else (die 'quotient+remainder "not an integer" x)]))]
[else (die '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? ($ratnum-n x))]
[else (die 'positive? "not a number" x)])))
(define negative?
(lambda (x)
(cond
[(fixnum? x) ($fx< x 0)]
[(flonum? x) ($fl< x 0.0)]
[(bignum? x) (not (positive-bignum? x))]
[(ratnum? x) (negative? ($ratnum-n x))]
[else (die '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 (die '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 (die '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 (die '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 (die '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 (die '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 (die '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) (die 'sqrt "BUG: bignum sqrt not implemented")]
[(ratnum? x) (/ (sqrt ($ratnum-n x)) (sqrt ($ratnum-d x)))]
[else (die 'sqrt "BUG: unsupported" x)])))
(define flsqrt
(lambda (x)
(if (flonum? x)
(foreign-call "ikrt_fl_sqrt" x)
(die 'flsqrt "not a flonum" x))))
(define flzero?
(lambda (x)
(if (flonum? x)
($flzero? x)
(die 'flzero? "not a flonum" x))))
(define flnegative?
(lambda (x)
(if (flonum? x)
($fl< x 0.0)
(die '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
[($fx< x 0) (die who "invalid argument" x)]
[($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
[($bignum-positive? x)
(bnsqrt x 23170 (quotient x 23170))]
[else (die who "invalid argument" x)])]
[else (die who "invalid argument" x)])))
(define numerator
(lambda (x)
(cond
[(ratnum? x) ($ratnum-n x)]
[(or (fixnum? x) (bignum? x)) x]
[(flonum? x) (flnumerator x)]
[else (die 'numerator "not an exact integer" x)])))
(define denominator
(lambda (x)
(cond
[(ratnum? x) ($ratnum-d x)]
[(or (fixnum? x) (bignum? x)) 1]
[(flonum? x) (fldenominator x)]
[else (die 'denominator "not an exact integer" x)])))
(define (floor x)
(define (ratnum-floor x)
(let ([n (numerator x)] [d (denominator x)])
(let ([q (quotient n d)])
(if (>= n 0) q (- q 1)))))
(cond
[(flonum? x)
;;; optimize for integer flonums
(let ([e (or ($flonum->exact x)
(die '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 (die '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 ($flonum->exact x)
(die 'ceiling "number has no real value" x))])
(cond
[(ratnum? e) (exact->inexact (ratnum-ceiling e))]
[else x]))]
[(ratnum? x) (ratnum-ceiling x)]
[(or (fixnum? x) (bignum? x)) x]
[else (die 'ceiling "not a number" x)]))
(define ($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) ($ratnum-round x)]
[(or (fixnum? x) (bignum? x)) x]
[else (die 'round "not a number" x)]))
(define (truncate x)
;;; FIXME: fltruncate should preserve the sign of -0.0.
;;;
(cond
[(flonum? x)
(let ([e (or ($flonum->exact x)
(die '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 (die 'truncate "not a number" x)]))
(define (fltruncate x)
;;; FIXME: fltruncate should preserve the sign of -0.0.
(unless (flonum? x)
(die '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) (die 'log "undefined around 0")]
[($fx> x 0) (foreign-call "ikrt_fx_log" x)]
[else (die 'log "negative argument" x)])]
[(flonum? x)
(cond
[(>= x 0) (foreign-call "ikrt_fl_log" x)]
[else (die 'log "negative argument" x)])]
[(bignum? x) (log (exact->inexact x))]
[(ratnum? x) (- (log (numerator x)) (log (denominator x)))]
[else (die 'log "not a number" x)])))
(define string->number
(case-lambda
[(x) (string->number-radix-10 x)]
[(x r)
(unless (eqv? r 10)
(die '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 (die '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)
(die '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
(die 'random "incorrect argument" n)))
(die 'random "not a fixnum" n)))
(define (shift-right-arithmetic n m who)
(cond
[(fixnum? m)
(cond
[(fixnum? n)
(cond
[($fx>= m 0) ($fxsra n m)]
[else (die who "offset must be non-negative" m)])]
[(bignum? n)
(cond
[($fx> m 0)
(foreign-call "ikrt_bignum_shift_right" n m)]
[($fx= m 0) n]
[else (die who "offset must be non-negative" m)])]
[else (die who "not an exact integer" n)])]
[(bignum? m)
(cond
[(fixnum? n) (if ($fx>= n 0) 0 -1)]
[(bignum? n) (if ($bignum-positive? n) 0 -1)]
[else (die who "not an exact integer" n)])]
[else (die who "not an exact integer offset" m)]))
(define (sra n m)
(shift-right-arithmetic n m 'sra))
(define (shift-left-logical n m who)
(unless (fixnum? m)
(die who "shift amount is not a fixnum"))
(cond
[(fixnum? n)
(cond
[($fx> m 0)
(foreign-call "ikrt_fixnum_shift_left" n m)]
[($fx= m 0) n]
[else (die who "offset must be non-negative" m)])]
[(bignum? n)
(cond
[($fx> m 0)
(foreign-call "ikrt_bignum_shift_left" n m)]
[($fx= m 0) n]
[else (die who "offset must be non-negative" m)])]
[else (die who "not an exact integer" n)]))
(define (sll n m)
(shift-left-logical n m 'sll))
(define (bitwise-arithmetic-shift-right n m)
(shift-right-arithmetic n m 'bitwise-arithmetic-shift-right))
(define (bitwise-arithmetic-shift-left n m)
(shift-left-logical n m 'bitwise-arithmetic-shift-left))
(define (bitwise-arithmetic-shift n m)
(define who 'bitwise-arithmetic-shift)
(unless (fixnum? m)
(die who "shift amount is not a fixnum"))
(cond
[(fixnum? n)
(cond
[($fx> m 0)
(foreign-call "ikrt_fixnum_shift_left" n m)]
[($fx= m 0) n]
[else
(let ([m^ (- m)])
(unless (fixnum? m^)
(die who "shift amount is too big" m))
($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^)
(die who "shift amount is too big" m))
(foreign-call "ikrt_bignum_shift_right" n m^))])]
[else (die 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 (die 'exp "not a number" x)]))
(define (bitwise-length n)
(cond
[(fixnum? n) (fxlength n)]
[(bignum? n) (foreign-call "ikrt_bignum_length" n)]
[else (error 'bitwise-length "not an exact integer" n)]))
)
(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
(die '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
(die '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 (die 'flonum->string "cannot happen")]))))
;;;
(define (string->flonum x)
(cond
[(string? x)
(foreign-call "ikrt_bytevector_to_flonum"
(string->utf8 x))]
[else
(die '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 (die who "not a number" eps)])
(cond
[(flonum? eps)
(if (flfinite? eps) x +nan.0)]
[(or (fixnum? eps) (bignum? eps) (ratnum? eps))
x]
[else (die 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 (die who "not a number" eps)])]
[else (die 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 who)
(import (ikarus system $fx)
(only (ikarus system $flonums) $fl=)
(ikarus flonums))
(define (int-div-and-mod n m)
(let ([d0 (quotient n m)])
(let ([m0 (- n (* d0 m))])
(if (>= m0 0)
(values d0 m0)
(if (>= m 0)
(values (- d0 1) (+ m0 m))
(values (+ d0 1) (- m0 m)))))))
(define (rat-div-and-mod n m)
(let ([x (/ n m)])
(cond
[(or (fixnum? x) (bignum? x))
(values x 0)]
[else
(let-values ([(a b)
(int-div-and-mod (numerator x) (denominator x))])
(values a (/ b m)))])))
(cond
[(fixnum? m)
(cond
[($fx= m 0)
(die who "division by 0")]
[(or (fixnum? n) (bignum? n))
(int-div-and-mod n m)]
[(flonum? n)
(fldiv-and-mod n (fixnum->flonum m))]
[(ratnum? n)
(rat-div-and-mod n m)]
[else (die who "not a number" n)])]
[(bignum? m)
(cond
[(or (fixnum? n) (bignum? n))
(int-div-and-mod n m)]
[(flonum? n)
(let ([v ($flonum->exact n)])
(unless v
(die who "invalid argument" n))
(let-values ([(a b) (div-and-mod* v m who)])
(values (inexact a) (inexact b))))]
[(ratnum? n)
(rat-div-and-mod n m)]
[else (die who "not a number" n)])]
[(ratnum? m)
(cond
[(or (fixnum? n) (bignum? n) (ratnum? n))
(rat-div-and-mod n m)]
[(flonum? n)
(let ([v ($flonum->exact n)])
(unless v
(die who "invalid argument" n))
(let-values ([(a b) (div-and-mod* v m who)])
(values (inexact a) (inexact b))))]
[else (die who "not a number" n)])]
[(flonum? m)
(cond
[($fl= m 0.0)
(die who "division by 0.0")]
[(flonum? n) (fldiv-and-mod n m)]
[(fixnum? n)
(fldiv-and-mod (fixnum->flonum n) m)]
[(or (bignum? n) (ratnum? n))
(let ([v ($flonum->exact m)])
(unless v
(die who "invalid argument" m))
(let-values ([(a b) (div-and-mod* n v who)])
(values (inexact a) (inexact b))))]
[else (die who "not a number" n)])]
[else (die who "not a number" m)]))
(define (div-and-mod n m)
(div-and-mod* n m 'div-and-mod))
(define (div n m)
(let-values ([(a b) (div-and-mod* n m 'div)])
a))
(define (mod n m)
(let-values ([(a b) (div-and-mod* n m 'mod)])
b))
(define (div0-and-mod0 x y)
(define who 'div0-and-mod0)
(unless (integer? x)
(die who "not an integer" x))
(unless (and (integer? y) (not (= y 0)))
(die 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)
($fldiv n m)
(die 'fldiv "not a flonum" m))
(die 'fldiv "not a flonum" n)))
(define (flmod n m)
(if (flonum? n)
(if (flonum? m)
($flmod n m)
(die 'flmod "not a flonum" m))
(die 'flmod "not a flonum" n)))
(define (fldiv-and-mod n m)
(if (flonum? n)
(if (flonum? m)
($fldiv-and-mod n m)
(die 'fldiv-and-mod "not a flonum" m))
(die 'fldiv-and-mod "not a flonum" n)))
(define ($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)
($fldiv0 n m)
(die 'fldiv0 "not a flonum" m))
(die 'fldiv0 "not a flonum" n)))
(define (flmod0 n m)
(if (flonum? n)
(if (flonum? m)
($flmod0 n m)
(die 'flmod0 "not a flonum" m))
(die 'flmod0 "not a flonum" n)))
(define (fldiv0-and-mod0 n m)
(if (flonum? n)
(if (flonum? m)
($fldiv0-and-mod0 n m)
(die 'fldiv0-and-mod0 "not a flonum" m))
(die '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 (die '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 (die '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) ($fxbitcount n)]
[else (die 'fxbit-count "not a fixnum" n)]))
(define (bitwise-bit-count n)
(cond
[(fixnum? n) ($fxbitcount n)]
[(bignum? n) (bnbitcount n)]
[else (die '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)])))
(die '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 ($fxsra x i) 1)))
(die who "index out of range" i))
(die who "index is not a fixnum" i))
(die who "not a fixnum" x)))
(define (bitwise-bit-set? x i)
(define who 'bitwise-bit-set?)
(cond
[(fixnum? i)
(when ($fx< i 0)
(die 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 (die who "not an exact integer" x)])]
[(bignum? i)
(unless ($bignum-positive? i)
(die who "index must be non-negative"))
(cond
[(fixnum? x) ($fx< x 0)]
[(bignum? x)
(= 1 (bitwise-and (bitwise-arithmetic-shift-right x i) 1))]
[else (die who "not an exact integer" x)])]
[else
(die 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 ($fxsll 1 i))]
[else (die who "invalid bit value" b)])
(die who "index out of range" i))
(die who "index is not a fixnum" i))
(die who "not a fixnum" x)))
(define (fxcopy-bit-field x i j b)
(define who 'fxcopy-bit-field)
(if (fixnum? x)
(if (fixnum? i)
(if ($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 ($fxlognot m) x)))
(die who "not a fixnum" b))
(if ($fx<= 0 j)
(die who "index out of range" j)
(die who "indices not in order" i j)))
(die who "index out of range" j))
(die who "not a fixnum" j))
(die who "index out of range" i))
(die who "not a fixnum" i))
(die 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)
(die who "index out of range" j)
(die who "indices not in order" i j)))
(die who "index out of range" j))
(die who "not a fixnum" j))
(die who "index out of range" i))
(die who "not a fixnum" i))
(die who "not a fixnum" x)))
)
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