4000 lines
131 KiB
Scheme
4000 lines
131 KiB
Scheme
;;; Ikarus Scheme -- A compiler for R6RS Scheme.
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;;; Copyright (C) 2006,2007,2008 Abdulaziz Ghuloum
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;;;
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;;; This program is free software: you can redistribute it and/or modify
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;;; it under the terms of the GNU General Public License version 3 as
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;;; published by the Free Software Foundation.
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;;;
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;;; This program is distributed in the hope that it will be useful, but
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;;; WITHOUT ANY WARRANTY; without even the implied warranty of
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;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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;;; General Public License for more details.
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;;;
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;;; You should have received a copy of the GNU General Public License
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;;; along with this program. If not, see <http://www.gnu.org/licenses/>.
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(library (ikarus flonums)
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(export $flonum->exact flonum-parts
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inexact->exact exact $flonum-rational? $flonum-integer? $flzero?
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$flnegative? flpositive? flabs fixnum->flonum
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flsin flcos fltan flasin flacos flatan fleven? flodd?
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flfloor flceiling flnumerator fldenominator flexp fllog
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flinteger? flonum-bytes flnan? flfinite? flinfinite?
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flexpt $flround flround)
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(import
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(ikarus system $bytevectors)
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(ikarus system $fx)
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(only (ikarus system $flonums) $fl>= $flonum-sbe)
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(ikarus system $bignums)
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(except (ikarus system $flonums) $flonum-rational?
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$flonum-integer? $flround)
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(except (ikarus) inexact->exact exact flpositive? flabs fixnum->flonum
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flsin flcos fltan flasin flacos flatan fleven? flodd?
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flfloor flceiling flnumerator fldenominator flexp fllog
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flexpt flinteger? flonum-parts flonum-bytes flnan? flfinite?
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flinfinite? flround))
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(define (flonum-bytes f)
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(unless (flonum? f)
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(die 'flonum-bytes "not a flonum" f))
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(values
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($flonum-u8-ref f 0)
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($flonum-u8-ref f 1)
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($flonum-u8-ref f 2)
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($flonum-u8-ref f 3)
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($flonum-u8-ref f 4)
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($flonum-u8-ref f 5)
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($flonum-u8-ref f 6)
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($flonum-u8-ref f 7)))
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(define (flonum-parts x)
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(unless (flonum? x)
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(die 'flonum-parts "not a flonum" x))
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(let-values ([(b0 b1 b2 b3 b4 b5 b6 b7) (flonum-bytes x)])
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(values
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(zero? (fxlogand b0 128))
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(+ (fxsll (fxlogand b0 127) 4)
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(fxsra b1 4))
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(+ (+ b7 (fxsll b6 8) (fxsll b5 16))
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(* (+ b4
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(fxsll b3 8)
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(fxsll b2 16)
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(fxsll (fxlogand b1 #b1111) 24))
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(expt 2 24))))))
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(define ($zero-m? f)
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(and ($fxzero? ($flonum-u8-ref f 7))
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($fxzero? ($flonum-u8-ref f 6))
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($fxzero? ($flonum-u8-ref f 5))
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($fxzero? ($flonum-u8-ref f 4))
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($fxzero? ($flonum-u8-ref f 3))
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($fxzero? ($flonum-u8-ref f 2))
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($fxzero? ($fxlogand ($flonum-u8-ref f 1) #b1111))))
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(define ($flonum-rational? x)
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(let ([be ($fxlogand ($flonum-sbe x)
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($fxsub1 ($fxsll 1 11)))])
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($fx< be 2047)))
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(define ($flonum-integer? x)
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(let ([be ($fxlogand ($flonum-sbe x)
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($fxsub1 ($fxsll 1 11)))])
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(cond
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[($fx= be 2047) ;;; nans and infs
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#f]
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[($fx>= be 1075) ;;; magnitue large enough
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#t]
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[($fx= be 0) ;;; denormalized double, only +/-0.0 is integer
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(and ($fx= ($flonum-u8-ref x 7) 0)
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($fx= ($flonum-u8-ref x 6) 0)
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($fx= ($flonum-u8-ref x 5) 0)
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($fx= ($flonum-u8-ref x 4) 0)
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($fx= ($flonum-u8-ref x 3) 0)
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($fx= ($flonum-u8-ref x 2) 0)
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($fx= ($flonum-u8-ref x 1) 0))]
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[($fx< be ($fx+ 1075 -52)) ;;; too small to be an integer
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#f]
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[else ($fl= x ($$flround x))])))
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(define ($$flround x)
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(foreign-call "ikrt_fl_round" x ($make-flonum)))
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(define ($flround x)
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;;; optimize for integer flonums case
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(define (ratnum-round n nbe)
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(let ([d (sll 1 nbe)])
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(let ([q (sra n nbe)]
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[r (bitwise-and n (sub1 d))])
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(let ([r2 (+ r r)])
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(cond
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[(< r2 d) q]
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[(> r2 d) (+ q 1)]
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[else (if (even? q) q (+ q 1))])))))
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(let ([sbe ($flonum-sbe x)])
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(let ([be ($fxlogand sbe #x7FF)])
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(cond
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;;; nans/infs/magnitude large enough to be an integer
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[($fx>= be 1075) x]
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[else
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;;; this really needs to get optimized.
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(let-values ([(pos? be m) (flonum-parts x)])
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(cond
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[(= be 0) ;;; denormalized
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(if pos? +0.0 -0.0)]
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[else ; normalized flonum
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(let ([r
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(inexact
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(ratnum-round (+ m (expt 2 52)) (- 1075 be)))])
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(if pos? r ($fl* r -1.0)))]))]))))
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(define (flround x)
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(if (flonum? x)
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($flround x)
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(die 'flround "not a flonum" x)))
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(module ($flonum->exact)
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(define ($flonum-signed-mantissa x)
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(let ([b0 ($flonum-u8-ref x 0)])
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(let ([m0 ($fx+ ($flonum-u8-ref x 7)
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($fx+ ($fxsll ($flonum-u8-ref x 6) 8)
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($fxsll ($flonum-u8-ref x 5) 16)))]
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[m1 ($fx+ ($flonum-u8-ref x 4)
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($fx+ ($fxsll ($flonum-u8-ref x 3) 8)
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($fxsll ($flonum-u8-ref x 2) 16)))]
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[m2 (let ([b1 ($flonum-u8-ref x 1)])
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(if (and ($fx= ($fxlogand b0 #x7F) 0)
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($fx= ($fxsra b1 4) 0))
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($fxlogand b1 #xF)
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($fxlogor ($fxlogand b1 #xF) #x10)))])
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(if ($fx= 0 ($fxlogand #x80 b0))
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(+ (bitwise-arithmetic-shift-left ($fxlogor m1 ($fxsll m2 24)) 24) m0)
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(+ (bitwise-arithmetic-shift-left
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($fx- 0 ($fxlogor m1 ($fxsll m2 24))) 24)
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($fx- 0 m0))))))
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(define ($flonum->exact x)
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(import (ikarus))
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(let ([sbe ($flonum-sbe x)])
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(let ([be ($fxlogand sbe #x7FF)])
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(cond
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[($fx= be 2047) #f] ;;; nans/infs
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[($fx>= be 1075) ;;; magnitude large enough to be an integer
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(bitwise-arithmetic-shift-left
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($flonum-signed-mantissa x)
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(- be 1075))]
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[else
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;;; this really needs to get optimized.
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(let-values ([(pos? be m) (flonum-parts x)])
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(cond
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[(= be 0) ;;; denormalized
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(if (= m 0)
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0
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(* (if pos? 1 -1)
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(/ m (expt 2 1074))))]
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[else ; normalized flonum
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(/ (+ m (expt 2 52))
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(bitwise-arithmetic-shift-left
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(if pos? 1 -1)
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(- 1075 be)))]))])))))
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(define (flnumerator x)
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(unless (flonum? x)
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(die 'flnumerator "not a flonum" x))
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(cond
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[($flonum-integer? x) x]
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[($flonum-rational? x)
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(exact->inexact (numerator ($flonum->exact x)))]
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[else x]))
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(define (fldenominator x)
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(unless (flonum? x)
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(die 'fldenominator "not a flonum" x))
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(cond
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[($flonum-integer? x) 1.0]
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[($flonum-rational? x)
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(exact->inexact (denominator ($flonum->exact x)))]
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[(flnan? x) x]
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[else 1.0]))
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(define (fleven? x)
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;;; FIXME: optimize
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(unless (flonum? x)
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(die 'fleven? "not a flonum" x))
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(let ([v ($flonum->exact x)])
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(cond
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[(fixnum? v) ($fx= ($fxlogand v 1) 0)]
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[(bignum? v)
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(foreign-call "ikrt_even_bn" v)]
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[else (die 'fleven? "not an integer flonum" x)])))
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(define (flodd? x)
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(unless (flonum? x)
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(die 'flodd? "not a flonum" x))
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;;; FIXME: optimize
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(let ([v ($flonum->exact x)])
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(cond
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[(fixnum? v) ($fx= ($fxlogand v 1) 1)]
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[(bignum? v)
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(not (foreign-call "ikrt_even_bn" v))]
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[else (die 'flodd? "not an integer flonum" x)])))
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(define (flinteger? x)
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(if (flonum? x)
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($flonum-integer? x)
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(die 'flinteger? "not a flonum" x)))
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(define (flinfinite? x)
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(if (flonum? x)
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(let ([be (fxlogand ($flonum-sbe x) (sub1 (fxsll 1 11)))])
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(and (fx= be 2047) ;;; nans and infs
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($zero-m? x)))
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(die 'flinfinite? "not a flonum" x)))
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(define (flnan? x)
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(if (flonum? x)
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(let ([be (fxlogand ($flonum-sbe x) (sub1 (fxsll 1 11)))])
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(and (fx= be 2047) ;;; nans and infs
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(not ($zero-m? x))))
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(die 'flnan? "not a flonum" x)))
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(define (flfinite? x)
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(if (flonum? x)
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(let ([be (fxlogand ($flonum-sbe x) (sub1 (fxsll 1 11)))])
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(not (fx= be 2047)))
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(die 'flfinite? "not a flonum" x)))
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(define ($flzero? x)
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(let ([be (fxlogand ($flonum-sbe x) (sub1 (fxsll 1 11)))])
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(and
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(fx= be 0) ;;; denormalized double, only +/-0.0 is integer
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(and (fx= ($flonum-u8-ref x 7) 0)
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(fx= ($flonum-u8-ref x 6) 0)
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(fx= ($flonum-u8-ref x 5) 0)
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(fx= ($flonum-u8-ref x 4) 0)
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(fx= ($flonum-u8-ref x 3) 0)
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(fx= ($flonum-u8-ref x 2) 0)
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(fx= ($flonum-u8-ref x 1) 0)))))
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(define ($flnegative? x)
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(let ([b0 ($flonum-u8-ref x 0)])
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(fx> b0 127)))
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(define ($exact x who)
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(import (ikarus system $compnums))
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(cond
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[(flonum? x)
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(or ($flonum->exact x)
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(die who "number has no real value" x))]
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[(cflonum? x)
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(make-rectangular
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(or ($flonum->exact ($cflonum-real x))
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(die who "number has no real value" x))
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(or ($flonum->exact ($cflonum-imag x))
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(die who "number has no real value" x)))]
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[(or (fixnum? x) (ratnum? x) (bignum? x) (compnum? x)) x]
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[else (die who "not a number" x)]))
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(define (inexact->exact x) ($exact x 'inexact->exact))
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(define (exact x) ($exact x 'exact))
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(define (flpositive? x)
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(if (flonum? x)
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($fl> x 0.0)
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(die 'flpositive? "not a flonum" x)))
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(define (flabs x)
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(if (flonum? x)
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(if ($fx> ($flonum-u8-ref x 0) 127)
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($fl* x -1.0)
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x)
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(die 'flabs "not a flonum" x)))
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(define (fixnum->flonum x)
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(if (fixnum? x)
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($fixnum->flonum x)
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(die 'fixnum->flonum "not a fixnum")))
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(define (flsin x)
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(if (flonum? x)
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(foreign-call "ikrt_fl_sin" x)
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(die 'flsin "not a flonum" x)))
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(define (flcos x)
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(if (flonum? x)
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(foreign-call "ikrt_fl_cos" x)
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(die 'flcos "not a flonum" x)))
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(define (fltan x)
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(if (flonum? x)
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(foreign-call "ikrt_fl_tan" x)
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(die 'fltan "not a flonum" x)))
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(define (flasin x)
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(if (flonum? x)
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(foreign-call "ikrt_fl_asin" x)
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(die 'flasin "not a flonum" x)))
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(define (flacos x)
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(if (flonum? x)
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(foreign-call "ikrt_fl_acos" x)
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(die 'flacos "not a flonum" x)))
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(define flatan
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(case-lambda
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[(x)
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(if (flonum? x)
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(foreign-call "ikrt_fl_atan" x)
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(die 'flatan "not a flonum" x))]
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[(x y)
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(if (flonum? x)
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(if (flonum? y)
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(foreign-call "ikrt_atan2" x y)
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(die 'flatan "not a flonum" y))
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(die 'flatan "not a flonum" x))]))
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(define (flfloor x)
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(define (ratnum-floor x)
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(let ([n (numerator x)] [d (denominator x)])
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(let ([q (quotient n d)])
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(if (>= n 0) q (- q 1)))))
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(cond
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[(flonum? x)
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;;; optimize for integer flonums case
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(let ([e ($flonum->exact x)])
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(cond
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[(ratnum? e)
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(exact->inexact (ratnum-floor e))]
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[else x]))]
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[else (die 'flfloor "not a flonum" x)]))
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(define (flceiling x)
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(cond
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[(flonum? x)
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;;; optimize for integer flonums case
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(let ([e ($flonum->exact x)])
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(cond
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[(ratnum? e)
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(exact->inexact (ceiling e))]
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[else x]))]
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[else (die 'flceiling "not a flonum" x)]))
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(define (flexp x)
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(if (flonum? x)
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(foreign-call "ikrt_fl_exp" x ($make-flonum))
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(die 'flexp "not a flonum" x)))
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(define fllog
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(case-lambda
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[(x)
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(if (flonum? x)
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(foreign-call "ikrt_fl_log" x)
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(die 'fllog "not a flonum" x))]
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[(x y)
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(if (flonum? x)
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(if (flonum? y)
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(fl/ (foreign-call "ikrt_fl_log" x)
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(foreign-call "ikrt_fl_log" y))
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(die 'fllog "not a flonum" y))
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(die 'fllog "not a flonum" x))]))
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(define (flexpt x y)
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(if (flonum? x)
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(if (flonum? y)
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(let ([y^ ($flonum->exact y)])
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;;; FIXME: performance bottleneck?
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(cond
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[(fixnum? y^) (inexact (expt x y^))]
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[(bignum? y^) (inexact (expt x y^))]
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[else
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(foreign-call "ikrt_flfl_expt" x y ($make-flonum))]))
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(die 'flexpt "not a flonum" y))
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(die 'fllog "not a flonum" x)))
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)
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(library (ikarus generic-arithmetic)
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(export + - * / zero? = < <= > >= add1 sub1 quotient remainder
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modulo even? odd? bitwise-and bitwise-not bitwise-ior
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bitwise-xor bitwise-if
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bitwise-arithmetic-shift-right bitwise-arithmetic-shift-left
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bitwise-arithmetic-shift
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bitwise-length bitwise-copy-bit-field
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bitwise-copy-bit bitwise-bit-field
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positive? negative? expt gcd lcm numerator denominator
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exact-integer-sqrt
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quotient+remainder number->string min max
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abs truncate fltruncate sra sll real->flonum
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exact->inexact inexact floor ceiling round log fl=? fl<? fl<=? fl>?
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fl>=? fl+ fl- fl* fl/ flsqrt flmin flzero? flnegative?
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sin cos tan asin acos atan sqrt exp
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sinh cosh tanh asinh acosh atanh
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flmax random
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error@add1 error@sub1)
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(import
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(ikarus system $fx)
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(ikarus system $flonums)
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(ikarus system $ratnums)
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(ikarus system $bignums)
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(ikarus system $compnums)
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(ikarus system $chars)
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(ikarus system $strings)
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(only (ikarus flonums) $flonum->exact $flzero? $flnegative?
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$flround)
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(except (ikarus) + - * / zero? = < <= > >= add1 sub1 quotient
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remainder modulo even? odd? quotient+remainder number->string
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bitwise-arithmetic-shift-right bitwise-arithmetic-shift-left
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bitwise-arithmetic-shift
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bitwise-length bitwise-copy-bit-field
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bitwise-copy-bit bitwise-bit-field
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positive? negative? bitwise-and bitwise-not bitwise-ior
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bitwise-xor bitwise-if
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expt gcd lcm numerator denominator
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exact->inexact inexact floor ceiling round log
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exact-integer-sqrt min max abs real->flonum
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fl=? fl<? fl<=? fl>? fl>=? fl+ fl- fl* fl/ flsqrt flmin
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flzero? flnegative? sra sll exp
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sin cos tan asin acos atan sqrt truncate fltruncate
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sinh cosh tanh asinh acosh atanh
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flmax random))
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(define (bignum->flonum x)
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|
(foreign-call "ikrt_bignum_to_flonum" x 0 ($make-flonum)))
|
|
|
|
|
|
;;; (define (ratnum->flonum x)
|
|
;;; (define (->flonum n d)
|
|
;;; (let-values ([(q r) (quotient+remainder n d)])
|
|
;;; (if (= r 0)
|
|
;;; (inexact q)
|
|
;;; (if (= q 0)
|
|
;;; (/ (->flonum d n))
|
|
;;; (+ q (->flonum r d))))))
|
|
;;; (let ([n (numerator x)] [d (denominator x)])
|
|
;;; (let ([b (bitwise-first-bit-set n)])
|
|
;;; (if (eqv? b 0)
|
|
;;; (let ([b (bitwise-first-bit-set d)])
|
|
;;; (if (eqv? b 0)
|
|
;;; (->flonum n d)
|
|
;;; (/ (->flonum n (bitwise-arithmetic-shift-right d b))
|
|
;;; (expt 2.0 b))))
|
|
;;; (* (->flonum (bitwise-arithmetic-shift-right n b) d)
|
|
;;; (expt 2.0 b))))))
|
|
|
|
;;; (define (ratnum->flonum x)
|
|
;;; (let f ([n ($ratnum-n x)] [d ($ratnum-d x)])
|
|
;;; (let-values ([(q r) (quotient+remainder n d)])
|
|
;;; (if (= q 0)
|
|
;;; (/ 1.0 (f d n))
|
|
;;; (if (= r 0)
|
|
;;; (inexact q)
|
|
;;; (+ q (f r d)))))))
|
|
|
|
;;; (define (ratnum->flonum num)
|
|
;;; (define (rat n m)
|
|
;;; (let-values ([(q r) (quotient+remainder n m)])
|
|
;;; (if (= r 0)
|
|
;;; (inexact q)
|
|
;;; (fl+ (inexact q) (fl/ 1.0 (rat m r))))))
|
|
;;; (define (pos n d)
|
|
;;; (cond
|
|
;;; [(even? n)
|
|
;;; (* (pos (sra n 1) d) 2.0)]
|
|
;;; [(even? d)
|
|
;;; (/ (pos n (sra d 1)) 2.0)]
|
|
;;; [(> n d) (rat n d)]
|
|
;;; [else
|
|
;;; (/ (rat d n))]))
|
|
;;; (let ([n ($ratnum-n num)] [d ($ratnum-d num)])
|
|
;;; (if (> n 0)
|
|
;;; (pos n d)
|
|
;;; (- (pos (- n) d)))))
|
|
|
|
(define (ratnum->flonum num)
|
|
(define *precision* 53)
|
|
(define (long-div1 n d)
|
|
(let-values ([(q r) (quotient+remainder n d)])
|
|
(cond
|
|
[(< (* r 2) d) (inexact q)]
|
|
[else (inexact (+ q 1))]
|
|
;[else (error #f "invalid" n d q r)]
|
|
)))
|
|
(define (long-div2 n d bits)
|
|
(let f ([bits bits] [ac (long-div1 n d)])
|
|
(cond
|
|
[(= bits 0) ac]
|
|
[else (f (- bits 1) (/ ac 2.0))])))
|
|
(define (pos n d)
|
|
(let ([nbits (bitwise-length n)]
|
|
[dbits (bitwise-length d)])
|
|
(let ([diff-bits (- nbits dbits)])
|
|
(if (>= diff-bits *precision*)
|
|
(long-div1 n d)
|
|
(let ([extra-bits (- *precision* diff-bits)])
|
|
(long-div2 (sll n extra-bits) d extra-bits))))))
|
|
(let ([n ($ratnum-n num)] [d ($ratnum-d num)])
|
|
(if (> n 0)
|
|
(pos n d)
|
|
(- (pos (- n) d)))))
|
|
|
|
(define (err who x)
|
|
(die who (if (number? x) "invalid argument" "not a number") x))
|
|
|
|
|
|
(define binary+
|
|
(lambda (x y)
|
|
(cond
|
|
[(fixnum? x)
|
|
(cond
|
|
[(fixnum? y)
|
|
(foreign-call "ikrt_fxfxplus" x y)]
|
|
[(bignum? y)
|
|
(foreign-call "ikrt_fxbnplus" x y)]
|
|
[(flonum? y)
|
|
($fl+ ($fixnum->flonum x) y)]
|
|
[(ratnum? y)
|
|
($make-ratnum
|
|
(+ (* x ($ratnum-d y)) ($ratnum-n y))
|
|
($ratnum-d y))]
|
|
[(compnum? y)
|
|
($make-compnum
|
|
(binary+ x ($compnum-real y))
|
|
($compnum-imag y))]
|
|
[(cflonum? y)
|
|
($make-cflonum
|
|
(binary+ x ($cflonum-real y))
|
|
($cflonum-imag y))]
|
|
[else (err '+ y)])]
|
|
[(bignum? x)
|
|
(cond
|
|
[(fixnum? y)
|
|
(foreign-call "ikrt_fxbnplus" y x)]
|
|
[(bignum? y)
|
|
(foreign-call "ikrt_bnbnplus" x y)]
|
|
[(flonum? y)
|
|
($fl+ (bignum->flonum x) y)]
|
|
[(ratnum? y)
|
|
($make-ratnum
|
|
(+ (* x ($ratnum-d y)) ($ratnum-n y))
|
|
($ratnum-d y))]
|
|
[(compnum? y)
|
|
($make-compnum
|
|
(binary+ x ($compnum-real y))
|
|
($compnum-imag y))]
|
|
[(cflonum? y)
|
|
($make-cflonum
|
|
(binary+ x ($cflonum-real y))
|
|
($cflonum-imag y))]
|
|
[else (err '+ 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)
|
|
($fl+ x (ratnum->flonum y))]
|
|
[(cflonum? y)
|
|
($make-cflonum
|
|
($fl+ x ($cflonum-real y))
|
|
($cflonum-imag y))]
|
|
[(compnum? y)
|
|
($make-cflonum
|
|
(binary+ x ($compnum-real y))
|
|
(inexact ($compnum-imag y)))]
|
|
[else (err '+ 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 ($ratnum-d y)])
|
|
;;; FIXME: inefficient
|
|
(/ (+ (* n0 d1) (* n1 d0)) (* d0 d1)))]
|
|
[(compnum? y)
|
|
($make-compnum
|
|
(binary+ x ($compnum-real y))
|
|
($compnum-imag y))]
|
|
[(cflonum? y)
|
|
($make-cflonum
|
|
(binary+ x ($cflonum-real y))
|
|
($cflonum-imag y))]
|
|
[else (err '+ y)])]
|
|
[(compnum? x)
|
|
(cond
|
|
[(or (fixnum? y) (bignum? y) (ratnum? y))
|
|
($make-compnum
|
|
(binary+ ($compnum-real x) y)
|
|
($compnum-imag x))]
|
|
[(compnum? y)
|
|
($make-rectangular
|
|
(binary+ ($compnum-real x) ($compnum-real y))
|
|
(binary+ ($compnum-imag x) ($compnum-imag y)))]
|
|
[(flonum? y)
|
|
($make-cflonum
|
|
(binary+ y ($compnum-real x))
|
|
(inexact ($compnum-imag x)))]
|
|
[(cflonum? y)
|
|
($make-cflonum
|
|
(binary+ ($compnum-real x) ($cflonum-real y))
|
|
(binary+ ($compnum-imag x) ($cflonum-imag y)))]
|
|
[else (err '+ y)])]
|
|
[(cflonum? x)
|
|
(cond
|
|
[(cflonum? y)
|
|
($make-cflonum
|
|
(binary+ ($cflonum-real x) ($cflonum-real y))
|
|
(binary+ ($cflonum-imag x) ($cflonum-imag y)))]
|
|
[(flonum? y)
|
|
($make-cflonum
|
|
($fl+ ($cflonum-real x) y)
|
|
($cflonum-imag x))]
|
|
[(or (fixnum? y) (bignum? y) (ratnum? y))
|
|
($make-compnum
|
|
(binary+ ($compnum-real x) y)
|
|
($compnum-imag x))]
|
|
[(compnum? y)
|
|
($make-cflonum
|
|
(binary+ ($cflonum-real x) ($compnum-real y))
|
|
(binary+ ($cflonum-imag x) ($compnum-imag y)))]
|
|
[else (err '+ y)])]
|
|
[else (err '+ x)])))
|
|
|
|
(define binary-bitwise-and
|
|
(lambda (x y)
|
|
(cond
|
|
[(fixnum? x)
|
|
(cond
|
|
[(fixnum? y) ($fxlogand x y)]
|
|
[(bignum? y)
|
|
(foreign-call "ikrt_fxbnlogand" x y)]
|
|
[else
|
|
(die 'bitwise-and "not an exact integer" y)])]
|
|
[(bignum? x)
|
|
(cond
|
|
[(fixnum? y)
|
|
(foreign-call "ikrt_fxbnlogand" y x)]
|
|
[(bignum? y)
|
|
(foreign-call "ikrt_bnbnlogand" x y)]
|
|
[else
|
|
(die 'bitwise-and "not an exact integer" y)])]
|
|
[else (die 'bitwise-and "not an exact integer" x)])))
|
|
|
|
(define binary-bitwise-ior
|
|
(lambda (x y)
|
|
(cond
|
|
[(fixnum? x)
|
|
(cond
|
|
[(fixnum? y) ($fxlogor x y)]
|
|
[(bignum? y)
|
|
(foreign-call "ikrt_fxbnlogor" x y)]
|
|
[else
|
|
(die 'bitwise-ior "not an exact integer" y)])]
|
|
[(bignum? x)
|
|
(cond
|
|
[(fixnum? y)
|
|
(foreign-call "ikrt_fxbnlogor" y x)]
|
|
[(bignum? y)
|
|
(foreign-call "ikrt_bnbnlogor" x y)]
|
|
[else
|
|
(die 'bitwise-ior "not an exact integer" y)])]
|
|
[else (die 'bitwise-ior "not an exact integer" x)])))
|
|
|
|
|
|
(define binary-bitwise-xor
|
|
(lambda (x y)
|
|
(define (fxbn x y)
|
|
(let ([y0 (bitwise-and y (greatest-fixnum))]
|
|
[y1 (bitwise-arithmetic-shift-right y (- (fixnum-width) 1))])
|
|
(bitwise-ior
|
|
($fxlogand ($fxlogxor x y0) (greatest-fixnum))
|
|
(bitwise-arithmetic-shift-left
|
|
(bitwise-arithmetic-shift-right
|
|
(if ($fx>= x 0) y (bitwise-not y))
|
|
(- (fixnum-width) 1))
|
|
(- (fixnum-width) 1)))))
|
|
(define (bnbn x y)
|
|
(let ([x0 (bitwise-and x (greatest-fixnum))]
|
|
[x1 (bitwise-arithmetic-shift-right x (- (fixnum-width) 1))]
|
|
[y0 (bitwise-and y (greatest-fixnum))]
|
|
[y1 (bitwise-arithmetic-shift-right y (- (fixnum-width) 1))])
|
|
(bitwise-ior
|
|
($fxlogand ($fxlogxor x0 y0) (greatest-fixnum))
|
|
(bitwise-arithmetic-shift-left
|
|
(binary-bitwise-xor x1 y1)
|
|
(- (fixnum-width) 1)))))
|
|
(cond
|
|
[(fixnum? x)
|
|
(cond
|
|
[(fixnum? y) ($fxlogxor x y)]
|
|
[(bignum? y) (fxbn x y)]
|
|
[else
|
|
(die 'bitwise-xor "not an exact integer" y)])]
|
|
[(bignum? x)
|
|
(cond
|
|
[(fixnum? y) (fxbn y x)]
|
|
[(bignum? y) (bnbn x y)]
|
|
[else
|
|
(die 'bitwise-xor "not an exact integer" y)])]
|
|
[else (die 'bitwise-xor "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))]
|
|
[(compnum? y)
|
|
($make-compnum
|
|
(binary- x ($compnum-real y))
|
|
(binary- 0 ($compnum-imag y)))]
|
|
[(cflonum? y)
|
|
($make-cflonum
|
|
(binary- x ($cflonum-real y))
|
|
($fl- 0.0 ($cflonum-imag y)))]
|
|
[else (err '- y)])]
|
|
[(bignum? x)
|
|
(cond
|
|
[(fixnum? y)
|
|
(foreign-call "ikrt_bnfxminus" x y)]
|
|
[(bignum? y)
|
|
(foreign-call "ikrt_bnbnminus" x y)]
|
|
[(flonum? y)
|
|
($fl- (bignum->flonum x) y)]
|
|
[(ratnum? y)
|
|
(let ([n ($ratnum-n y)] [d ($ratnum-d y)])
|
|
(binary/ (binary- (binary* d x) n) d))]
|
|
[(compnum? y)
|
|
($make-compnum
|
|
(binary- x ($compnum-real y))
|
|
(binary- 0 ($compnum-imag y)))]
|
|
[(cflonum? y)
|
|
($make-cflonum
|
|
(binary- x ($cflonum-real y))
|
|
($fl- 0.0 ($cflonum-imag y)))]
|
|
[else (err '- y)])]
|
|
[(flonum? x)
|
|
(cond
|
|
[(flonum? y)
|
|
($fl- x y)]
|
|
[(cflonum? y)
|
|
($make-cflonum
|
|
($fl- x ($cflonum-real y))
|
|
($fl- 0.0 ($cflonum-imag y)))]
|
|
[(fixnum? y)
|
|
($fl- x ($fixnum->flonum y))]
|
|
[(bignum? y)
|
|
($fl- x (bignum->flonum y))]
|
|
[(ratnum? y)
|
|
(let ([n ($ratnum-n y)] [d ($ratnum-d y)])
|
|
(binary/ (binary- (binary* d x) n) d))]
|
|
[(compnum? y)
|
|
($make-cflonum
|
|
(binary- x ($compnum-real y))
|
|
(binary- 0.0 ($compnum-imag y)))]
|
|
[else (err '- y)])]
|
|
[(ratnum? x)
|
|
(let ([nx ($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 ($ratnum-d y)])
|
|
(binary/ (binary- (binary* nx dy) (binary* ny dx))
|
|
(binary* dx dy)))]
|
|
[(compnum? y)
|
|
($make-compnum
|
|
(binary- x ($compnum-real y))
|
|
(binary- 0 ($compnum-imag y)))]
|
|
[(cflonum? y)
|
|
($make-cflonum
|
|
(binary- x ($cflonum-real y))
|
|
($fl- 0.0 ($cflonum-imag y)))]
|
|
[else (err '- y)]))]
|
|
[(compnum? x)
|
|
(cond
|
|
[(or (fixnum? y) (bignum? y) (ratnum? y))
|
|
($make-compnum
|
|
(binary- ($compnum-real x) y)
|
|
($compnum-imag x))]
|
|
[(compnum? y)
|
|
($make-rectangular
|
|
(binary- ($compnum-real x) ($compnum-real y))
|
|
(binary- ($compnum-imag x) ($compnum-imag y)))]
|
|
[(flonum? y)
|
|
($make-cflonum
|
|
(binary- ($compnum-real x) y)
|
|
(binary- ($compnum-imag x) 0.0))]
|
|
[(cflonum? y)
|
|
($make-cflonum
|
|
(binary- ($compnum-real x) ($cflonum-real y))
|
|
(binary- ($compnum-imag x) ($cflonum-imag y)))]
|
|
[else
|
|
(err '- y)])]
|
|
[(cflonum? x)
|
|
(cond
|
|
[(flonum? y)
|
|
($make-cflonum
|
|
($fl- ($cflonum-real x) y)
|
|
($cflonum-imag x))]
|
|
[(cflonum? y)
|
|
($make-cflonum
|
|
(binary- ($cflonum-real x) ($cflonum-real y))
|
|
(binary- ($cflonum-imag x) ($cflonum-imag y)))]
|
|
[(or (fixnum? y) (bignum? y) (ratnum? y))
|
|
($make-cflonum
|
|
(binary- ($cflonum-real x) y)
|
|
($cflonum-imag x))]
|
|
[(compnum? y)
|
|
($make-cflonum
|
|
(binary- ($cflonum-real x) ($compnum-real y))
|
|
(binary- ($cflonum-imag x) ($compnum-imag y)))]
|
|
[else
|
|
(err '- y)])]
|
|
[else (err '- x)])))
|
|
|
|
(define binary*
|
|
(lambda (x y)
|
|
(cond
|
|
[(fixnum? x)
|
|
(cond
|
|
[(fixnum? y)
|
|
(foreign-call "ikrt_fxfxmult" x y)]
|
|
[(bignum? y)
|
|
(foreign-call "ikrt_fxbnmult" x y)]
|
|
[(flonum? y)
|
|
($fl* ($fixnum->flonum x) y)]
|
|
[(ratnum? y)
|
|
(binary/ (binary* x ($ratnum-n y)) ($ratnum-d y))]
|
|
[(compnum? y)
|
|
($make-rectangular
|
|
(binary* x ($compnum-real y))
|
|
(binary* x ($compnum-imag y)))]
|
|
[(cflonum? y)
|
|
($make-cflonum
|
|
(binary* x ($cflonum-real y))
|
|
(binary* x ($cflonum-imag y)))]
|
|
[else (err '* y)])]
|
|
[(bignum? x)
|
|
(cond
|
|
[(fixnum? y)
|
|
(foreign-call "ikrt_fxbnmult" y x)]
|
|
[(bignum? y)
|
|
(foreign-call "ikrt_bnbnmult" x y)]
|
|
[(flonum? y)
|
|
($fl* (bignum->flonum x) y)]
|
|
[(ratnum? y)
|
|
(binary/ (binary* x ($ratnum-n y)) ($ratnum-d y))]
|
|
[(compnum? y)
|
|
($make-rectangular
|
|
(binary* x ($compnum-real y))
|
|
(binary* x ($compnum-imag y)))]
|
|
[(cflonum? y)
|
|
($make-cflonum
|
|
(binary* x ($cflonum-real y))
|
|
(binary* x ($cflonum-imag y)))]
|
|
[else (err '* y)])]
|
|
[(flonum? x)
|
|
(cond
|
|
[(flonum? y)
|
|
($fl* x y)]
|
|
[(cflonum? y)
|
|
($make-cflonum
|
|
($fl* x ($cflonum-real y))
|
|
($fl* x ($cflonum-imag y)))]
|
|
[(fixnum? y)
|
|
($fl* x ($fixnum->flonum y))]
|
|
[(bignum? y)
|
|
($fl* x (bignum->flonum y))]
|
|
[(ratnum? y)
|
|
(binary/ (binary* x ($ratnum-n y)) ($ratnum-d y))]
|
|
[(compnum? y)
|
|
($make-cflonum
|
|
(binary* x ($compnum-real y))
|
|
(binary* x ($compnum-imag y)))]
|
|
[else (err '* y)])]
|
|
[(ratnum? x)
|
|
(cond
|
|
[(ratnum? y)
|
|
(binary/ (binary* ($ratnum-n x) ($ratnum-n y))
|
|
(binary* ($ratnum-d x) ($ratnum-d y)))]
|
|
[(compnum? y)
|
|
($make-rectangular
|
|
(binary* x ($compnum-real y))
|
|
(binary* x ($compnum-imag y)))]
|
|
[(cflonum? y)
|
|
($make-cflonum
|
|
(binary* x ($cflonum-real y))
|
|
(binary* x ($cflonum-imag y)))]
|
|
[else (binary* y x)])]
|
|
[(compnum? x)
|
|
(cond
|
|
[(or (fixnum? y) (bignum? y) (ratnum? y))
|
|
($make-rectangular
|
|
(binary* ($compnum-real x) y)
|
|
(binary* ($compnum-imag x) y))]
|
|
[(flonum? y)
|
|
($make-cflonum
|
|
(binary* ($compnum-real x) y)
|
|
(binary* ($compnum-imag x) y))]
|
|
[(compnum? y)
|
|
(let ([r0 ($compnum-real x)]
|
|
[r1 ($compnum-real y)]
|
|
[i0 ($compnum-imag x)]
|
|
[i1 ($compnum-imag y)])
|
|
(make-rectangular
|
|
(- (* r0 r1) (* i0 i1))
|
|
(+ (* r0 i1) (* i0 r1))))]
|
|
[(cflonum? y)
|
|
(let ([r0 ($compnum-real x)]
|
|
[r1 ($cflonum-real y)]
|
|
[i0 ($compnum-imag x)]
|
|
[i1 ($cflonum-imag y)])
|
|
(make-rectangular
|
|
(- (* r0 r1) (* i0 i1))
|
|
(+ (* r0 i1) (* i0 r1))))]
|
|
[else (err '* y)])]
|
|
[(cflonum? x)
|
|
(cond
|
|
[(flonum? y)
|
|
($make-cflonum
|
|
($fl* ($cflonum-real x) y)
|
|
($fl* ($cflonum-imag x) y))]
|
|
[(cflonum? y)
|
|
(let ([r0 ($cflonum-real x)]
|
|
[r1 ($cflonum-real y)]
|
|
[i0 ($cflonum-imag x)]
|
|
[i1 ($cflonum-imag y)])
|
|
($make-cflonum
|
|
($fl- ($fl* r0 r1) ($fl* i0 i1))
|
|
($fl+ ($fl* r0 i1) ($fl* i0 r1))))]
|
|
[(or (fixnum? y) (bignum? y) (ratnum? y))
|
|
($make-cflonum
|
|
(binary* ($compnum-real x) y)
|
|
(binary* ($compnum-imag x) y))]
|
|
[(compnum? y)
|
|
(let ([r0 ($compnum-real x)]
|
|
[r1 ($compnum-real y)]
|
|
[i0 ($compnum-imag x)]
|
|
[i1 ($compnum-imag y)])
|
|
(make-rectangular
|
|
(- (* r0 r1) (* i0 i1))
|
|
(+ (* r0 i1) (* i0 r1))))]
|
|
[else (err '* y)])]
|
|
[else (err '* x)])))
|
|
|
|
(define +
|
|
(case-lambda
|
|
[(x y) (binary+ x y)]
|
|
[(x y z) (binary+ (binary+ x y) z)]
|
|
[(a)
|
|
(cond
|
|
[(fixnum? a) a]
|
|
[(number? 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-ior
|
|
(case-lambda
|
|
[(x y) (binary-bitwise-ior x y)]
|
|
[(x y z) (binary-bitwise-ior (binary-bitwise-ior x y) z)]
|
|
[(a)
|
|
(cond
|
|
[(fixnum? a) a]
|
|
[(bignum? a) a]
|
|
[else (die 'bitwise-ior "not a number" a)])]
|
|
[() 0]
|
|
[(a b c d . e*)
|
|
(let f ([ac (binary-bitwise-ior a
|
|
(binary-bitwise-ior b
|
|
(binary-bitwise-ior c d)))]
|
|
[e* e*])
|
|
(cond
|
|
[(null? e*) ac]
|
|
[else (f (binary-bitwise-ior ac (car e*)) (cdr e*))]))]))
|
|
|
|
(define bitwise-xor
|
|
(case-lambda
|
|
[(x y) (binary-bitwise-xor x y)]
|
|
[(x y z) (binary-bitwise-xor (binary-bitwise-xor x y) z)]
|
|
[(a)
|
|
(cond
|
|
[(fixnum? a) a]
|
|
[(bignum? a) a]
|
|
[else (die 'bitwise-xor "not a number" a)])]
|
|
[() 0]
|
|
[(a b c d . e*)
|
|
(let f ([ac (binary-bitwise-xor a
|
|
(binary-bitwise-xor b
|
|
(binary-bitwise-xor c d)))]
|
|
[e* e*])
|
|
(cond
|
|
[(null? e*) ac]
|
|
[else (f (binary-bitwise-xor 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 (bitwise-if x y z)
|
|
(define who 'bitwise-if)
|
|
(define (err x) (die who "not an exact integer" x))
|
|
(unless (or (fixnum? x) (bignum? x)) (err x))
|
|
(unless (or (fixnum? y) (bignum? y)) (err y))
|
|
(unless (or (fixnum? z) (bignum? z)) (err z))
|
|
(bitwise-ior
|
|
(bitwise-and x y)
|
|
(bitwise-and (bitwise-not x) z)))
|
|
|
|
(define (bitwise-copy-bit-field x i j n)
|
|
(define who 'bitwise-copy-bit-field)
|
|
(define (err x) (die who "not an exact integer" x))
|
|
(define (err2 x) (die who "index must be nonnegative" x))
|
|
(define (err3 x y) (die who "indices must be in nondescending order" x y))
|
|
(unless (or (fixnum? x) (bignum? x)) (err x))
|
|
(unless (or (fixnum? i) (bignum? i)) (err i))
|
|
(unless (or (fixnum? j) (bignum? j)) (err j))
|
|
(unless (or (fixnum? n) (bignum? n)) (err n))
|
|
(when (< i 0) (err2 i))
|
|
(when (< j i) (err3 i j))
|
|
(bitwise-if (sll (sub1 (sll 1 (- j i))) i) (sll n i) 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]
|
|
[(number? 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
|
|
[($fx= y 0) x]
|
|
[else (gcd y (remainder x y))]))
|
|
(let ([x (if (< x 0) (- x) x)]
|
|
[y (if (< y 0) (- y) y)])
|
|
(cond
|
|
[(> x y) (gcd x y)]
|
|
[(< x y) (gcd y x)]
|
|
[else x])))
|
|
|
|
(define gcd
|
|
(case-lambda
|
|
[(x y)
|
|
(cond
|
|
[(or (fixnum? x) (bignum? x))
|
|
(cond
|
|
[(or (fixnum? y) (bignum? y))
|
|
(binary-gcd x y)]
|
|
[(number? y)
|
|
(die 'gcd "not an exact integer" y)]
|
|
[else
|
|
(die 'gcd "not a number" y)])]
|
|
[(number? x)
|
|
(die 'gcd "not an exact integer" x)]
|
|
[else
|
|
(die 'gcd "not a number" x)])]
|
|
[(x)
|
|
(cond
|
|
[(or (fixnum? x) (bignum? x)) x]
|
|
[(number? x)
|
|
(die 'gcd "not an exact integer" x)]
|
|
[else
|
|
(die 'gcd "not a number" x)])]
|
|
[() 0]
|
|
[(x y z . ls)
|
|
(let f ([g (gcd (gcd x y) z)] [ls ls])
|
|
(cond
|
|
[(null? ls) g]
|
|
[else (f (gcd g (car ls)) (cdr ls))]))]))
|
|
|
|
|
|
(define lcm
|
|
(case-lambda
|
|
[(x y)
|
|
(cond
|
|
[(or (fixnum? x) (bignum? x))
|
|
(cond
|
|
[(or (fixnum? y) (bignum? y))
|
|
(let ([x (if (< x 0) (- x) x)]
|
|
[y (if (< y 0) (- y) y)])
|
|
(let ([g (binary-gcd x y)])
|
|
(binary* y (quotient x g))))]
|
|
[(flonum? y)
|
|
(let ([v ($flonum->exact y)])
|
|
(cond
|
|
[(or (fixnum? v) (bignum? v))
|
|
(inexact (lcm x v))]
|
|
[else (die 'lcm "not an integer" y)]))]
|
|
[else
|
|
(die 'lcm "not an integer" y)])]
|
|
[(flonum? x)
|
|
(let ([v ($flonum->exact x)])
|
|
(cond
|
|
[(or (fixnum? v) (bignum? v))
|
|
(inexact (lcm v y))]
|
|
[else (die 'lcm "not an integer" x)]))]
|
|
[else
|
|
(die 'lcm "not an integer" x)])]
|
|
[(x)
|
|
(cond
|
|
[(or (fixnum? x) (bignum? x)) x]
|
|
[(flonum? x)
|
|
(let ([v ($flonum->exact x)])
|
|
(cond
|
|
[(or (fixnum? v) (bignum? v)) x]
|
|
[else (die 'lcm "not an integer" x)]))]
|
|
[else
|
|
(die 'lcm "not an integer" x)])]
|
|
[() 1]
|
|
[(x y z . ls)
|
|
;;; FIXME: incorrect for multiple roundings
|
|
(let f ([g (lcm (lcm x y) z)] [ls ls])
|
|
(cond
|
|
[(null? ls) g]
|
|
[else (f (lcm g (car ls)) (cdr ls))]))]))
|
|
|
|
|
|
(define binary/
|
|
(lambda (x y)
|
|
(define (x/compy x y)
|
|
(let ([yr (real-part y)]
|
|
[yi (imag-part y)])
|
|
(let ([denom (+ (* yr yr) (* yi yi))])
|
|
(make-rectangular
|
|
(binary/ (* x yr) denom)
|
|
(binary/ (* (- x) yi) denom)))))
|
|
(define (compx/y x y)
|
|
(let ([xr (real-part x)]
|
|
[xi (imag-part x)])
|
|
(make-rectangular
|
|
(binary/ xr y)
|
|
(binary/ xi y))))
|
|
(define (compx/compy x y)
|
|
(let ([xr (real-part x)]
|
|
[xi (imag-part x)]
|
|
[yr (real-part y)]
|
|
[yi (imag-part y)])
|
|
(let ([denom (+ (* yr yr) (* yi yi))])
|
|
(make-rectangular
|
|
(binary/ (+ (* xr yr) (* xi yi)) denom)
|
|
(binary/ (- (* xi yr) (* xr yi)) denom)))))
|
|
(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) ($fl/ x (ratnum->flonum y))]
|
|
[(or (cflonum? y) (compnum? y)) (x/compy x y)]
|
|
[else (err '/ y)])]
|
|
[(fixnum? x)
|
|
(cond
|
|
[(flonum? y) ($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)
|
|
(if ($fx= x 0)
|
|
0
|
|
(let ([g (binary-gcd x y)])
|
|
(cond
|
|
[(= g y) (quotient x g)]
|
|
[($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))]
|
|
[(or (compnum? y) (cflonum? y)) (x/compy x y)]
|
|
[else (err '/ 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)
|
|
(if ($bignum-positive? y)
|
|
($make-ratnum x y)
|
|
($make-ratnum
|
|
(binary- 0 x)
|
|
(binary- 0 y)))]
|
|
[($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-d y)) ($ratnum-n y))]
|
|
[(or (compnum? y) (cflonum? y)) (x/compy x y)]
|
|
[else (err '/ y)])]
|
|
[(ratnum? x)
|
|
(cond
|
|
[(ratnum? y)
|
|
(binary/
|
|
(binary* ($ratnum-n x) ($ratnum-d y))
|
|
(binary* ($ratnum-n y) ($ratnum-d x)))]
|
|
[(or (compnum? y) (cflonum? y)) (x/compy x y)]
|
|
[else (binary/ 1 (binary/ y x))])]
|
|
[(or (compnum? x) (cflonum? x))
|
|
(cond
|
|
[(or (compnum? y) (cflonum? y)) (compx/compy x y)]
|
|
[(or (fixnum? y) (bignum? y) (ratnum? y) (flonum? y)) (compx/y x y)]
|
|
[else (err '/ y)])]
|
|
[else (err '/ x)])))
|
|
|
|
|
|
(define /
|
|
(case-lambda
|
|
[(x y) (binary/ x y)]
|
|
[(x)
|
|
(cond
|
|
[(fixnum? x)
|
|
(cond
|
|
[($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 ($make-ratnum d n)]))]
|
|
[(compnum? x) (binary/ 1 x)]
|
|
[else (die '/ "not a number" x)])]
|
|
[(x y z . ls)
|
|
(let f ([a (binary/ x y)] [b z] [ls ls])
|
|
(cond
|
|
[(null? ls) (binary/ a b)]
|
|
[else (f (binary/ a b) (car ls) (cdr ls))]))]))
|
|
|
|
|
|
(define flmax
|
|
(case-lambda
|
|
[(x y)
|
|
(if (flonum? x)
|
|
(if (flonum? y)
|
|
(if ($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)
|
|
(cond
|
|
[(or (fixnum? x) (bignum? x) (ratnum? x) (flonum? x)) x]
|
|
[else (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)
|
|
(cond
|
|
[(or (fixnum? x) (bignum? x) (ratnum? x) (flonum? x)) x]
|
|
[else (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 real number" x)]))
|
|
|
|
(define flmin
|
|
(case-lambda
|
|
[(x y)
|
|
(if (flonum? x)
|
|
(if (flonum? y)
|
|
(if ($fl< x y) x y)
|
|
(die 'flmin "not a flonum" y))
|
|
(die 'flmin "not a flonum" x))]
|
|
[(x y z . rest)
|
|
(let f ([a (flmin x y)] [b z] [ls rest])
|
|
(cond
|
|
[(null? ls) (flmin a b)]
|
|
[else
|
|
(f (flmin a b) (car ls) (cdr ls))]))]
|
|
[(x)
|
|
(if (flonum? x)
|
|
x
|
|
(die 'flmin "not a flonum" x))]))
|
|
|
|
(define (->inexact x who)
|
|
(cond
|
|
[(fixnum? x) ($fixnum->flonum x)]
|
|
[(bignum? x) (bignum->flonum x)]
|
|
[(ratnum? x) (ratnum->flonum x)]
|
|
[(flonum? x) x]
|
|
[(compnum? x)
|
|
(make-rectangular
|
|
(->inexact (real-part x) who)
|
|
(->inexact (imag-part x) who))]
|
|
[(cflonum? x) x]
|
|
[else
|
|
(die who "not a number" x)]))
|
|
|
|
(define (exact->inexact x)
|
|
(->inexact x 'exact->inexact))
|
|
|
|
(define (inexact x)
|
|
(->inexact x 'inexact))
|
|
|
|
(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) ($fxeven? x)]
|
|
[(bignum? x) (even-bignum? x)]
|
|
[(flonum? x)
|
|
(let ([v ($flonum->exact x)])
|
|
(cond
|
|
[(fixnum? v) ($fxeven? v)]
|
|
[(bignum? v) (even-bignum? v)]
|
|
[else (die 'even? "not an integer" x)]))]
|
|
[else (die 'even? "not an integer" x)]))
|
|
|
|
(define (odd? x)
|
|
(cond
|
|
[(fixnum? x) (not ($fxeven? x))]
|
|
[(bignum? x) (not (even-bignum? x))]
|
|
[(flonum? x)
|
|
(let ([v ($flonum->exact x)])
|
|
(cond
|
|
[(fixnum? v) (not ($fxeven? v))]
|
|
[(bignum? v) (not (even-bignum? v))]
|
|
[else (die 'odd? "not an integer" 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 (imag x r)
|
|
(cond
|
|
[(eqv? x 1) "+"]
|
|
[(eqv? x -1) "-"]
|
|
[(or (< x 0) (eqv? x -0.0))
|
|
($number->string x r)]
|
|
[else (string-append "+" ($number->string x r))]))
|
|
(define $number->string
|
|
(lambda (x r)
|
|
(import (ikarus system $compnums))
|
|
(cond
|
|
[(fixnum? x) (fixnum->string x r)]
|
|
[(bignum? x) (bignum->string x r)]
|
|
[(flonum? x)
|
|
(unless (eqv? r 10)
|
|
(die 'number->string
|
|
"invalid radix for inexact number"
|
|
r x))
|
|
(flonum->string x)]
|
|
[(ratnum? x) (ratnum->string x r)]
|
|
[(compnum? x)
|
|
(let ([xr ($compnum-real x)]
|
|
[xi ($compnum-imag x)])
|
|
(if (eqv? xr 0)
|
|
(string-append (imag xi r) "i")
|
|
(string-append
|
|
($number->string xr r)
|
|
(imag xi r)
|
|
"i")))]
|
|
[(cflonum? x)
|
|
(let ([xr ($cflonum-real x)]
|
|
[xi ($cflonum-imag x)])
|
|
(cond
|
|
[(flnan? xi)
|
|
(string-append ($number->string xr r) "+nan.0i")]
|
|
[(flinfinite? xi)
|
|
(string-append ($number->string xr r)
|
|
(if ($fl> xi 0.0) "+inf.0i" "-inf.0i"))]
|
|
[else
|
|
(string-append
|
|
($number->string xr r) (imag xi r) "i")]))]
|
|
[else (die 'number->string "not a number" x)])))
|
|
(define do-warn
|
|
(lambda ()
|
|
(set! do-warn values)
|
|
(raise-continuable
|
|
(condition
|
|
(make-warning)
|
|
(make-who-condition 'number->string)
|
|
(make-message-condition
|
|
"precision argument is not supported")))))
|
|
(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)
|
|
;(do-warn)
|
|
(number->string x r)])))
|
|
|
|
(define modulo
|
|
(lambda (n m)
|
|
(cond
|
|
[(fixnum? n)
|
|
(cond
|
|
[(fixnum? m)
|
|
(if (eqv? m 0)
|
|
(die 'modulo "division by zero" n 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 ($flonum->exact m)])
|
|
(cond
|
|
[(or (fixnum? v) (bignum? v))
|
|
(inexact (modulo n v))]
|
|
[else
|
|
(die 'modulo "not an integer" m)]))]
|
|
[(ratnum? m) (die 'modulo "not an integer" m)]
|
|
[else (die 'modulo "not a number" m)])]
|
|
[(bignum? n)
|
|
(cond
|
|
[(fixnum? m)
|
|
(if (eqv? m 0)
|
|
(die 'modulo "division by zero" n m)
|
|
(foreign-call "ikrt_bnfx_modulo" n m))]
|
|
[(bignum? m)
|
|
(if ($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 ($flonum->exact m)])
|
|
(cond
|
|
[(or (fixnum? v) (bignum? v))
|
|
(inexact (modulo n v))]
|
|
[else
|
|
(die 'modulo "not an integer" m)]))]
|
|
[(ratnum? m) (die 'modulo "not an integer" m)]
|
|
[else (die 'modulo "not a number" m)])]
|
|
[(flonum? n)
|
|
(let ([v ($flonum->exact n)])
|
|
(cond
|
|
[(or (fixnum? v) (bignum? 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 real 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 name
|
|
(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 (name x y) (name 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)])]))
|
|
name)]))
|
|
|
|
|
|
(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>= $fl>=)
|
|
|
|
(define-syntax cmp-ex/in
|
|
(syntax-rules ()
|
|
[(_ pred)
|
|
(syntax-rules ()
|
|
[(_ ex in)
|
|
(let ([x ex] [y in])
|
|
(if ($flonum-rational? y)
|
|
(pred x (exact y))
|
|
(pred (inexact x) y)))])]))
|
|
(define-syntax cmp-in/ex
|
|
(syntax-rules ()
|
|
[(_ pred)
|
|
(syntax-rules ()
|
|
[(_ in ex)
|
|
(let ([x in] [y ex])
|
|
(if ($flonum-rational? x)
|
|
(pred (exact x) y)
|
|
(pred x (inexact y))))])]))
|
|
|
|
(define-syntax flrt= (cmp-in/ex =))
|
|
(define-syntax rtfl= (cmp-ex/in =))
|
|
(define-syntax flrt< (cmp-in/ex <))
|
|
(define-syntax rtfl< (cmp-ex/in <))
|
|
(define-syntax flrt<= (cmp-in/ex <=))
|
|
(define-syntax rtfl<= (cmp-ex/in <=))
|
|
(define-syntax flrt> (cmp-in/ex >))
|
|
(define-syntax rtfl> (cmp-ex/in >))
|
|
(define-syntax flrt>= (cmp-in/ex >=))
|
|
(define-syntax rtfl>= (cmp-ex/in >=))
|
|
|
|
(define (exrt< x y) (< (* x ($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) ($ratnum-d y))))
|
|
|
|
|
|
|
|
(define =
|
|
(let ()
|
|
(define err
|
|
(lambda (x) (die '= "not a number" x)))
|
|
(define (fx? x y)
|
|
(cond
|
|
[(fixnum? y) ($fx= x y)]
|
|
[(flonum? y) (fxfl= x y)]
|
|
[(or (bignum? y) (ratnum? y) (compnum? y)) #f]
|
|
[(cflonum? y)
|
|
(and (flfl= 0.0 ($cflonum-imag y)) (fxfl= x ($cflonum-real y)))]
|
|
[else (err y)]))
|
|
(define (bn? x y)
|
|
(cond
|
|
[(bignum? y) (bnbn= x y)]
|
|
[(flonum? y) (bnfl= x y)]
|
|
[(or (fixnum? y) (ratnum? y) (compnum? y)) #f]
|
|
[(cflonum? y)
|
|
(and (flfl= 0.0 ($cflonum-imag y)) (bnfl= x ($cflonum-real y)))]
|
|
[else (err y)]))
|
|
(define (fl? x y)
|
|
(cond
|
|
[(flonum? y) (flfl= x y)]
|
|
[(fixnum? y) (flfx= x y)]
|
|
[(bignum? y) (flbn= x y)]
|
|
[(ratnum? y) (flrt= x y)]
|
|
[(compnum? y) #f]
|
|
[(cflonum? y)
|
|
(and (flfl= 0.0 ($cflonum-imag y)) (flfl= x ($cflonum-real y)))]
|
|
[else (err y)]))
|
|
(define (rn? x y)
|
|
(cond
|
|
[(flonum? y) (rtfl= x y)]
|
|
[(ratnum? y) (rtrt= x y)]
|
|
[(or (fixnum? y) (bignum? y) (compnum? y)) #f]
|
|
[(cflonum? y)
|
|
(and (flfl= 0.0 ($cflonum-imag y)) (rtfl= x ($cflonum-real y)))]
|
|
[else (err y)]))
|
|
(define (cn? x y)
|
|
(cond
|
|
[(compnum? y) (cncn= x y)]
|
|
[(cflonum? y) (cncf= x y)]
|
|
[(or (fixnum? y) (bignum? y) (flonum? y) (ratnum? y)) #f]
|
|
[else (err y)]))
|
|
(define (cf? x y)
|
|
(cond
|
|
[(cflonum? y) (cfcf= x y)]
|
|
[(compnum? y) (cncf= y x)]
|
|
[(or (fixnum? y) (bignum? y) (flonum? y) (ratnum? y))
|
|
(and (flfl= 0.0 ($cflonum-imag x)) (= ($cflonum-real x) y))]
|
|
[else (err y)]))
|
|
(define-syntax doloop
|
|
(syntax-rules ()
|
|
[(_ cmp x0 y0 ls0)
|
|
(let loop ([x x0] [y y0] [ls ls0])
|
|
(if (cmp x y)
|
|
(if (null? ls) #t (loop x (car ls) (cdr ls)))
|
|
(if (null? ls) #f (loopf (car ls) (cdr ls)))))]))
|
|
(define loopf
|
|
(lambda (x ls)
|
|
(if (number? x)
|
|
(if (null? ls)
|
|
#f
|
|
(loopf (car ls) (cdr ls)))
|
|
(err x))))
|
|
(define (cncn= x y)
|
|
(and
|
|
(= ($compnum-real x) ($compnum-real y))
|
|
(= ($compnum-imag x) ($compnum-imag y))))
|
|
(define (cncf= x y)
|
|
(and
|
|
(= ($compnum-real x) ($cflonum-real y))
|
|
(= ($compnum-imag x) ($cflonum-imag y))))
|
|
(define (cfcf= x y)
|
|
(and
|
|
(= ($cflonum-real x) ($cflonum-real y))
|
|
(= ($cflonum-imag x) ($cflonum-imag y))))
|
|
(define =
|
|
(case-lambda
|
|
[(x y)
|
|
(cond
|
|
[(fixnum? x) (fx? x y)]
|
|
[(bignum? x) (bn? x y)]
|
|
[(flonum? x) (fl? x y)]
|
|
[(ratnum? x) (rn? x y)]
|
|
[(compnum? x) (cn? x y)]
|
|
[(cflonum? x) (cf? x y)]
|
|
[else (err x)])]
|
|
[(x y z) (if (= x y) (= y z) (if (number? z) #f (err z)))]
|
|
[(x) (if (number? x) #t (err x))]
|
|
[(x y . ls)
|
|
(cond
|
|
[(fixnum? x) (doloop fx? x y ls)]
|
|
[(bignum? x) (doloop bn? x y ls)]
|
|
[(flonum? x) (doloop fl? x y ls)]
|
|
[(ratnum? x) (doloop rn? x y ls)]
|
|
[(compnum? x) (doloop cn? x y ls)]
|
|
[(cflonum? x) (doloop cf? x y ls)]
|
|
[else (err x)])]))
|
|
=))
|
|
|
|
;(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< >= $fx>= fxbn> bnfx> bnbn>= fxfl>= flfx>= bnfl>= flbn>= flfl>=
|
|
exrt> rtex> exrt> rtex> flrt>= rtfl>= rtrt>=))
|
|
|
|
(define error@add1
|
|
(lambda (x)
|
|
(import (ikarus))
|
|
(cond
|
|
[(fixnum? x) (+ (greatest-fixnum) 1)]
|
|
[(number? x) (+ x 1)]
|
|
[else (die 'add1 "not a number" x)])))
|
|
|
|
(define add1
|
|
(lambda (x)
|
|
(import (ikarus))
|
|
(add1 x)))
|
|
|
|
(define error@sub1
|
|
(lambda (x)
|
|
(import (ikarus))
|
|
(cond
|
|
[(fixnum? x) (- (least-fixnum) 1)]
|
|
[(number? x) (- x 1)]
|
|
[else (die 'sub1 "not a number" x)])))
|
|
|
|
(define sub1
|
|
(lambda (x)
|
|
(import (ikarus))
|
|
(sub1 x)))
|
|
|
|
(define zero?
|
|
(lambda (x)
|
|
(cond
|
|
[(fixnum? x) (eq? x 0)]
|
|
[(bignum? x) #f]
|
|
[(ratnum? x) #f]
|
|
[(flonum? x)
|
|
(or ($fl= x 0.0) ($fl= x -0.0))]
|
|
[(cflonum? x)
|
|
(and ($fl= ($cflonum-real x) 0.0) ($fl= ($cflonum-imag x) 0.0))]
|
|
[(compnum? x) #f]
|
|
[else
|
|
(die 'zero? "not a number" x)])))
|
|
|
|
(define expt
|
|
(lambda (n m)
|
|
(define fxexpt
|
|
(lambda (n m)
|
|
(cond
|
|
[($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 ($fx>= m 0)
|
|
(cond
|
|
[(ratnum? n)
|
|
($make-ratnum (expt ($ratnum-n n) m) (expt ($ratnum-d n) m))]
|
|
[else (fxexpt n m)])
|
|
(let ([v (expt n (- m))])
|
|
(if (eq? v 0)
|
|
0
|
|
(/ 1 v))))]
|
|
[(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))]
|
|
[(or (compnum? m) (cflonum? m))
|
|
(if (eq? n 0)
|
|
0
|
|
(let ([e 2.718281828459045])
|
|
(define (ln x) (/ (log x) (log e)))
|
|
(exp (* m (ln n)))))]
|
|
[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)
|
|
(if (eq? y -1)
|
|
(values (- x) 0)
|
|
(values (fxquotient x y) (fxremainder x y)))]
|
|
[(bignum? y) (values 0 x)]
|
|
[(flonum? y)
|
|
(let ([v ($flonum->exact y)])
|
|
(cond
|
|
[(or (fixnum? v) (bignum? v))
|
|
(let-values ([(q r) (quotient+remainder x v)])
|
|
(values (inexact q) (inexact r)))]
|
|
[else
|
|
(die 'quotient+remainder "not an integer" y)]))]
|
|
[else (die 'quotient+remainder "not an integer" y)])]
|
|
[(bignum? x)
|
|
(cond
|
|
[(fixnum? y)
|
|
(let ([p (foreign-call "ikrt_bnfxdivrem" x y)])
|
|
(values (car p) (cdr p)))]
|
|
[(bignum? y)
|
|
(let ([p (foreign-call "ikrt_bnbndivrem" x y)])
|
|
(values (car p) (cdr p)))]
|
|
[(flonum? y)
|
|
(let ([v ($flonum->exact y)])
|
|
(cond
|
|
[(or (fixnum? v) (bignum? 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 an integer" y)])]
|
|
[(flonum? x)
|
|
(let ([v ($flonum->exact x)])
|
|
(cond
|
|
[(or (fixnum? v) (bignum? v))
|
|
(let-values ([(q r) (quotient+remainder v y)])
|
|
(values (inexact q) (inexact r)))]
|
|
[else (die 'quotient+remainder "not an integer" x)]))]
|
|
[else (die 'quotient+remainder "not an integer" x)])))
|
|
|
|
(define positive?
|
|
(lambda (x)
|
|
(cond
|
|
[(fixnum? x) ($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 real 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 real number" x)])))
|
|
|
|
(define sinh
|
|
(lambda (x)
|
|
(define who 'sinh)
|
|
(cond
|
|
[(flonum? x) (foreign-call "ikrt_fl_sinh" x)]
|
|
[(or (fixnum? x) (bignum? x) (ratnum? x))
|
|
(sinh (inexact x))]
|
|
[(or (compnum? x) (cflonum? x))
|
|
(let ([r (real-part x)] [i (imag-part x)])
|
|
(make-rectangular
|
|
(* (sinh r) (cos i))
|
|
(* (cosh r) (sin i))))]
|
|
[else (die who "not a number" x)])))
|
|
|
|
(define cosh
|
|
(lambda (x)
|
|
(define who 'cosh)
|
|
(cond
|
|
[(flonum? x) (foreign-call "ikrt_fl_cosh" x)]
|
|
[(or (fixnum? x) (bignum? x) (ratnum? x))
|
|
(cosh (inexact x))]
|
|
[(or (compnum? x) (cflonum? x))
|
|
(let ([r (real-part x)] [i (imag-part x)])
|
|
(make-rectangular
|
|
(* (cosh r) (cos i))
|
|
(* (sinh r) (sin i))))]
|
|
[else (die who "not a number" x)])))
|
|
|
|
(define tanh
|
|
(lambda (x)
|
|
(define who 'tanh)
|
|
(cond
|
|
[(flonum? x) (foreign-call "ikrt_fl_tanh" x)]
|
|
[(or (fixnum? x) (bignum? x) (ratnum? x))
|
|
(tanh (inexact x))]
|
|
[(or (compnum? x) (cflonum? x))
|
|
(let ([r (real-part x)] [i (imag-part x)])
|
|
(let ([rr (* 2 r)] [ii (* 2 i)])
|
|
(let ([cos2i (cos ii)] [cosh2r (cosh rr)])
|
|
(make-rectangular
|
|
(/ (tanh rr) (+ 1 (/ cos2i cosh2r)))
|
|
(/ (sin ii) (+ cosh2r cos2i))))))]
|
|
[else (die who "not a number" x)])))
|
|
|
|
(define asinh
|
|
(lambda (x)
|
|
(define who 'asinh)
|
|
(cond
|
|
[(flonum? x) (foreign-call "ikrt_fl_asinh" x)]
|
|
[(or (fixnum? x) (bignum? x) (ratnum? x))
|
|
(asinh (inexact x))]
|
|
[(or (cflonum? x) (compnum? x))
|
|
(let ([x (real-part x)] [y (imag-part x)])
|
|
(cond
|
|
[(= x 0)
|
|
(let ([v (asin y)])
|
|
(make-rectangular (imag-part v) (real-part v)))]
|
|
[else
|
|
(let* ([z^2 (+ (* x x) (* y y))]
|
|
[z^2-1 (- z^2 1)]
|
|
[z^2-1^2 (* z^2-1 z^2-1)]
|
|
[y^2 (* y y)]
|
|
[q (sqrt (+ z^2-1^2 (* 4 y^2)))])
|
|
(define (sgn x) (if (< x 0) -1 1))
|
|
(make-rectangular
|
|
(* 0.5 (sgn x) (acosh (+ q z^2)))
|
|
(* 0.5 (sgn y) (acos (- q z^2)))))]))]
|
|
[else (die who "not a number" x)])))
|
|
|
|
(define acosh
|
|
(lambda (x)
|
|
(define who 'acosh)
|
|
(cond
|
|
[(flonum? x)
|
|
(cond
|
|
[($fl>= x 1.0) (foreign-call "ikrt_fl_acosh" x)]
|
|
[($fl>= x -1.0)
|
|
(make-rectangular 0 (atan (sqrt (- 1 (* x x))) x))]
|
|
[($fl< x -1.0)
|
|
(make-rectangular (acosh (- x)) PI)]
|
|
[else +nan.0])]
|
|
[(or (fixnum? x) (bignum? x) (ratnum? x))
|
|
(acosh (inexact x))]
|
|
[(or (cflonum? x) (compnum? x))
|
|
(let ([x (real-part x)] [y (imag-part x)])
|
|
(cond
|
|
[(= x 0) (+ (asinh y) (make-rectangular 0 PI/2))]
|
|
[else
|
|
(let* ([z^2 (+ (* x x) (* y y))]
|
|
[z^2-1 (- z^2 1)]
|
|
[z^2-1^2 (* z^2-1 z^2-1)]
|
|
[y^2 (* y y)]
|
|
[q (sqrt (+ z^2-1^2 (* 4 y^2)))])
|
|
(define (sgn x) (if (< x 0) -1 1))
|
|
(+ (* 0.5 (sgn x) (acosh (+ q z^2)))
|
|
(* 0.5i (sgn y)
|
|
(- PI (* (sgn x) (acos (- q z^2)))))))]))]
|
|
[else (die who "not a number" x)])))
|
|
|
|
(define atanh
|
|
(lambda (x)
|
|
(define who 'atanh)
|
|
(cond
|
|
[(flonum? x)
|
|
(cond
|
|
[(and (fl<=? x 1.0) (fl>=? x -1.0))
|
|
(foreign-call "ikrt_fl_atanh" x)]
|
|
[else
|
|
(- (atanh (fl/ 1.0 x))
|
|
(if (fl<? x 0.0) (* -i PI/2) (* +i PI/2)))])]
|
|
[(or (fixnum? x) (bignum? x) (ratnum? x))
|
|
(atanh (inexact x))]
|
|
[(number? x) (error who "not implemented" x)]
|
|
[else (die who "not a number" x)])))
|
|
|
|
(define sin
|
|
(lambda (x)
|
|
(cond
|
|
[(flonum? x) (foreign-call "ikrt_fl_sin" x)]
|
|
[(fixnum? x)
|
|
(if (fx=? x 0)
|
|
0
|
|
(foreign-call "ikrt_fx_sin" x))]
|
|
[(or (cflonum? x) (compnum? x))
|
|
(let ([r (real-part x)] [i (imag-part x)])
|
|
(make-rectangular
|
|
(* (sin r) (cosh i))
|
|
(* (cos r) (sinh i))))]
|
|
[(number? x) (sin (inexact x))]
|
|
[else (die 'sin "not a number" x)])))
|
|
|
|
(define cos
|
|
(lambda (x)
|
|
(cond
|
|
[(flonum? x) (foreign-call "ikrt_fl_cos" x)]
|
|
[(fixnum? x)
|
|
(if (fx=? x 0)
|
|
1
|
|
(foreign-call "ikrt_fx_cos" x))]
|
|
[(or (cflonum? x) (compnum? x))
|
|
(let ([r (real-part x)] [i (imag-part x)])
|
|
(make-rectangular
|
|
(* (cos r) (cosh i))
|
|
(* (sin r) (sinh i))))]
|
|
[(number? x) (cos (inexact x))]
|
|
[else (die 'cos "not a number" x)])))
|
|
|
|
(define tan
|
|
(lambda (x)
|
|
(cond
|
|
[(flonum? x) (foreign-call "ikrt_fl_tan" x)]
|
|
[(fixnum? x)
|
|
(if (fx=? x 0)
|
|
0
|
|
(foreign-call "ikrt_fx_tan" x))]
|
|
[(or (cflonum? x) (compnum? x))
|
|
(let ([r (real-part x)] [i (imag-part x)])
|
|
(make-rectangular
|
|
(/ (sin (* 2 r))
|
|
(+ (cos (* 2 r)) (cosh (* 2 i))))
|
|
(/ (tanh (* 2 i))
|
|
(+ 1 (/ (cos (* 2 r)) (cosh (* 2 i)))))))]
|
|
[(number? x) (tan (inexact x))]
|
|
[else (die 'tan "not a number" x)])))
|
|
|
|
(module (PI PI/2)
|
|
(import (ikarus))
|
|
(define PI (acos -1))
|
|
(define PI/2 (/ PI 2)))
|
|
|
|
(define asin
|
|
(lambda (x)
|
|
(cond
|
|
[(flonum? x)
|
|
(cond
|
|
[($fl> x 1.0)
|
|
(make-rectangular PI/2 (acosh x))]
|
|
[($fl< x -1.0)
|
|
(make-rectangular (- PI/2) (- (acosh (- x))))]
|
|
[else
|
|
(foreign-call "ikrt_fl_asin" x)])]
|
|
[(or (cflonum? x) (compnum? x))
|
|
(let ([x (real-part x)] [y (imag-part x)])
|
|
(cond
|
|
[(= x 0) (make-rectangular 0 (asinh y))]
|
|
[else
|
|
(let* ([z^2 (+ (* x x) (* y y))]
|
|
[z^2-1 (- z^2 1.0)]
|
|
[z^2-1^2 (* z^2-1 z^2-1)]
|
|
[y^2 (* y y)]
|
|
[q (sqrt (+ z^2-1^2 (* 4.0 y^2)))])
|
|
(define (sgn x) (if (< x 0) -1.0 1.0))
|
|
(make-rectangular
|
|
(* 0.5 (sgn x) (acos (- q z^2)))
|
|
(* 0.5 (sgn y) (acosh (+ q z^2)))))]))]
|
|
[(number? x) (asin (inexact x))]
|
|
[else (die 'asin "not a number" x)])))
|
|
|
|
(define acos
|
|
(lambda (x)
|
|
(cond
|
|
[(flonum? x)
|
|
(cond
|
|
[($fl> x 1.0)
|
|
(make-rectangular 0 (acosh x))]
|
|
[($fl< x -1.0)
|
|
(make-rectangular PI (- (acosh (- x))))]
|
|
[else
|
|
(foreign-call "ikrt_fl_acos" x)])]
|
|
[(or (cflonum? x) (compnum? x))
|
|
(- PI/2 (asin x))]
|
|
[(number? x) (acos (inexact x))]
|
|
[else (die 'acos "not a number" x)])))
|
|
|
|
(define atan
|
|
(case-lambda
|
|
[(x)
|
|
(cond
|
|
[(flonum? x) (foreign-call "ikrt_fl_atan" x)]
|
|
[(fixnum? x) (foreign-call "ikrt_fx_atan" x)]
|
|
[(or (ratnum? x) (bignum? x)) (atan (inexact x))]
|
|
[else (die 'atan "not a number" x)])]
|
|
[(y x)
|
|
(unless (real? x) (die 'atan "not a real number" x))
|
|
(unless (real? y) (die 'atan "not a real number" y))
|
|
(foreign-call "ikrt_atan2" (inexact y) (inexact x))]))
|
|
|
|
(define sqrt
|
|
(lambda (x)
|
|
(cond
|
|
[(flonum? x)
|
|
(if ($fl< x 0.0)
|
|
(make-rectangular 0.0
|
|
(foreign-call "ikrt_fl_sqrt" ($fl- 0.0 x)))
|
|
(foreign-call "ikrt_fl_sqrt" x))]
|
|
[(fixnum? x)
|
|
(cond
|
|
[($fx< x 0)
|
|
(make-rectangular 0 (sqrt (- x)))]
|
|
[else
|
|
(let-values ([(s r) (exact-integer-sqrt x)])
|
|
(cond
|
|
[(eq? r 0) s]
|
|
[else (foreign-call "ikrt_fx_sqrt" x)]))])]
|
|
[(bignum? x)
|
|
(cond
|
|
[($bignum-positive? x)
|
|
(let-values ([(s r) (exact-integer-sqrt x)])
|
|
(cond
|
|
[(eq? r 0) s]
|
|
[else
|
|
(let ([v (sqrt (inexact x))])
|
|
;;; could the [dropped] residual ever affect the answer?
|
|
(cond
|
|
[(infinite? v)
|
|
(if (bignum? s)
|
|
(foreign-call "ikrt_bignum_to_flonum"
|
|
s
|
|
1 ;;; round up in case of a tie
|
|
($make-flonum))
|
|
(inexact s))]
|
|
[else v]))]))]
|
|
[else
|
|
(make-rectangular 0 (sqrt (- x)))])]
|
|
[(ratnum? x)
|
|
;;; FIXME: incorrect as per bug 180170
|
|
(/ (sqrt ($ratnum-n x)) (sqrt ($ratnum-d x)))]
|
|
[(or (compnum? x) (cflonum? x))
|
|
(let ([xr (real-part x)] [xi (imag-part x)])
|
|
(let ([m (sqrt (+ (* xr xr) (* xi xi)))]
|
|
[s (if (> xi 0) 1 -1)])
|
|
(make-rectangular
|
|
(sqrt (/ (+ m xr) 2))
|
|
(* s (sqrt (/ (- m xr) 2))))))]
|
|
[else (die 'sqrt "not a number" x)])))
|
|
|
|
(define flsqrt
|
|
(lambda (x)
|
|
(if (flonum? x)
|
|
(foreign-call "ikrt_fl_sqrt" x)
|
|
(die 'flsqrt "not a flonum" x))))
|
|
|
|
(define flzero?
|
|
(lambda (x)
|
|
(if (flonum? x)
|
|
($flzero? x)
|
|
(die 'flzero? "not a flonum" x))))
|
|
|
|
(define flnegative?
|
|
(lambda (x)
|
|
(if (flonum? x)
|
|
($fl< x 0.0)
|
|
(die 'flnegative? "not a flonum" x))))
|
|
|
|
(define exact-integer-sqrt
|
|
(lambda (x)
|
|
(define who 'exact-integer-sqrt)
|
|
(cond
|
|
[(fixnum? x)
|
|
(cond
|
|
[($fx= x 0) (values 0 0)]
|
|
[($fx< x 0) (die who "invalid argument" x)]
|
|
[else
|
|
(let ([s (foreign-call "ikrt_exact_fixnum_sqrt" x)])
|
|
(values s ($fx- x ($fx* s s))))])]
|
|
[(bignum? x)
|
|
(cond
|
|
[($bignum-positive? x)
|
|
(let ([r (foreign-call "ikrt_exact_bignum_sqrt" x)])
|
|
(values (car r) (cdr r)))]
|
|
[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 ($flonum->exact x)])
|
|
(cond
|
|
[(ratnum? e)
|
|
(exact->inexact (ratnum-floor e))]
|
|
[else x]))]
|
|
[(ratnum? x) (ratnum-floor x)]
|
|
[(or (fixnum? x) (bignum? x)) x]
|
|
[else (die 'floor "not a number" x)]))
|
|
|
|
(define (ceiling x)
|
|
(define (ratnum-ceiling x)
|
|
(let ([n (numerator x)] [d (denominator x)])
|
|
(let ([q (quotient n d)])
|
|
(if (< n 0) q (+ q 1)))))
|
|
(cond
|
|
[(flonum? x)
|
|
;;; optimize for integer flonums
|
|
(let ([e ($flonum->exact 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 ($ratnum-d x)])
|
|
(let-values ([(q r) (div-and-mod n d)])
|
|
(let ([r2 (+ r r)])
|
|
(cond
|
|
[(< r2 d) q]
|
|
[(> r2 d) (+ q 1)]
|
|
[else (if (even? q) q (+ q 1))])))))
|
|
|
|
(define ($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 ($flonum->exact x)])
|
|
(cond
|
|
[(ratnum? e) (exact->inexact ($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 ($ratnum-truncate v))]
|
|
[else x])))
|
|
|
|
(define log
|
|
(case-lambda
|
|
[(x)
|
|
(cond
|
|
[(fixnum? x)
|
|
(cond
|
|
[($fx= x 1) 0]
|
|
[($fx= x 0) (die 'log "undefined around 0")]
|
|
[($fx> x 0) (foreign-call "ikrt_fx_log" x)]
|
|
[else (make-rectangular (log (- x)) (acos -1))])]
|
|
[(flonum? x)
|
|
(cond
|
|
[(fl>=? x 0.0) (foreign-call "ikrt_fl_log" x)]
|
|
[else
|
|
(make-rectangular
|
|
(log (fl- 0.0 x))
|
|
(acos -1))])]
|
|
[(bignum? x)
|
|
(if ($bignum-positive? x)
|
|
(let ([v (log (inexact x))])
|
|
(cond
|
|
[(infinite? v)
|
|
(let-values ([(s r) (exact-integer-sqrt x)])
|
|
;;; could the [dropped] residual ever affect the answer?
|
|
(fl* 2.0 (log s)))]
|
|
[else v]))
|
|
(make-rectangular (log (- x)) (acos -1)))]
|
|
[(ratnum? x)
|
|
;;; FIXME: incorrect as per bug 180170
|
|
(- (log (numerator x)) (log (denominator x)))]
|
|
[(or (compnum? x) (cflonum? x))
|
|
(let ([e 2.718281828459045])
|
|
(define (ln x) (/ (log x) (log e)))
|
|
(let ([xr (real-part x)] [xi (imag-part x)])
|
|
(make-rectangular
|
|
(/ (ln (+ (* xr xr) (* xi xi))) 2)
|
|
(atan xi xr))))]
|
|
[else (die 'log "not a number" x)])]
|
|
[(x y)
|
|
(let ([ly (log y)])
|
|
(if (eqv? ly 0)
|
|
(die 'log "invalid arguments" x y)
|
|
(/ (log x) ly)))]))
|
|
|
|
(define (random n)
|
|
(if (fixnum? n)
|
|
(if (fx> n 1)
|
|
(foreign-call "ikrt_fxrandom" n)
|
|
(if (fx= n 1)
|
|
0
|
|
(die 'random "incorrect argument" n)))
|
|
(die 'random "not a fixnum" n)))
|
|
|
|
|
|
(define (shift-right-arithmetic n m who)
|
|
(cond
|
|
[(fixnum? m)
|
|
(cond
|
|
[(fixnum? n)
|
|
(cond
|
|
[($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 ($fx= x 0) 1 (flexp (fixnum->flonum x)))]
|
|
[(bignum? x) (flexp (bignum->flonum x))]
|
|
[(ratnum? x) (flexp (ratnum->flonum x))]
|
|
[(or (compnum? x) (cflonum? x))
|
|
;; e^x = e^(xr + xi i)
|
|
;; = e^xr cos(xi) + e^xr sin(xi) i
|
|
(let ([xr (real-part x)] [xi (imag-part x)])
|
|
(let ([e^xr (exp xr)])
|
|
(make-rectangular
|
|
(* e^xr (cos xi))
|
|
(* e^xr (sin xi)))))]
|
|
[else (die 'exp "not a number" x)]))
|
|
|
|
(define (bitwise-length n)
|
|
(cond
|
|
[(fixnum? n) (fxlength n)]
|
|
[(bignum? n) (foreign-call "ikrt_bignum_length" n)]
|
|
[else (die 'bitwise-length "not an exact integer" n)]))
|
|
|
|
(define (bitwise-copy-bit n idx bit)
|
|
(define who 'bitwise-copy-bit)
|
|
(define (do-copy-bit n idx bit)
|
|
(case bit
|
|
[(0)
|
|
(cond
|
|
[(bitwise-bit-set? n idx)
|
|
(bitwise-and n (bitwise-not (sll 1 idx)))]
|
|
[else n])]
|
|
[(1)
|
|
(cond
|
|
[(bitwise-bit-set? n idx) n]
|
|
[(>= n 0) (+ n (sll 1 idx))]
|
|
[else
|
|
(bitwise-not
|
|
(bitwise-and
|
|
(bitwise-not n)
|
|
(bitwise-not (sll 1 idx))))])]
|
|
[else (die who "bit must be either 0 or 1" bit)]))
|
|
(cond
|
|
[(fixnum? idx)
|
|
(cond
|
|
[(fx< idx 0)
|
|
(die who "negative bit index" idx)]
|
|
[(or (fixnum? n) (bignum? n))
|
|
(do-copy-bit n idx bit)]
|
|
[else (die who "not an exact integer" n)])]
|
|
[(bignum? idx)
|
|
(unless (or (fixnum? n) (bignum? n))
|
|
(die who "not an exact integer" n))
|
|
(if ($bignum-positive? idx)
|
|
(case bit
|
|
[(0)
|
|
(if (>= n 0)
|
|
n
|
|
(die who "unrepresentable result"))]
|
|
[(1)
|
|
(if (< n 0)
|
|
n
|
|
(die who "unrepresentable result"))]
|
|
[else (die who "bit must be either 0 or 1" bit)])
|
|
(die who "negative bit index" idx))]
|
|
[else (die who "index is not an exact integer" idx)]))
|
|
|
|
(define (bitwise-bit-field n idx1 idx2)
|
|
(define who 'bitwise-bit-field)
|
|
(cond
|
|
[(and (fixnum? idx1) (fx>= idx1 0))
|
|
(cond
|
|
[(and (fixnum? idx2) (fx>= idx2 0))
|
|
(cond
|
|
[(fx<= idx1 idx2)
|
|
(cond
|
|
[(or (fixnum? n) (bignum? n))
|
|
(bitwise-and
|
|
(sra n idx1)
|
|
(- (sll 1 (- idx2 idx1)) 1))]
|
|
[else (die who "not an exact integer" n)])]
|
|
[else (die who "invalid order for indices" idx1 idx2)])]
|
|
[else
|
|
(if (not (fixnum? idx2))
|
|
(die who "invalid index" idx2)
|
|
(die who "negative index" idx2))])]
|
|
[else
|
|
(if (not (fixnum? idx1))
|
|
(die who "invalid index" idx1)
|
|
(die who "negative index" idx1))]))
|
|
|
|
)
|
|
|
|
|
|
|
|
|
|
(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 0]))
|
|
(define (simplest^ n d n^ d^)
|
|
(let-values ([(q r) (div-and-mod n d)])
|
|
(if (= r 0)
|
|
q
|
|
(let-values ([(q^ r^) (div-and-mod 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) +0.0)]
|
|
[(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) +0.0)]
|
|
[(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) $fl=)
|
|
(ikarus flonums))
|
|
(define (int-div-and-mod n m)
|
|
(let ([d0 (quotient n m)])
|
|
(let ([m0 (- n (* d0 m))])
|
|
(if (>= m0 0)
|
|
(values d0 m0)
|
|
(if (>= m 0)
|
|
(values (- d0 1) (+ m0 m))
|
|
(values (+ d0 1) (- m0 m)))))))
|
|
(define (rat-div-and-mod n m)
|
|
(let ([x (/ n m)])
|
|
(cond
|
|
[(or (fixnum? x) (bignum? x))
|
|
(values x 0)]
|
|
[else
|
|
(let ([n0 (numerator x)] [d0 (denominator x)])
|
|
(let ([q (quotient n0 d0)])
|
|
(let ([r (- n (* q m))])
|
|
(if (>= r 0)
|
|
(values q r)
|
|
(if (> m 0)
|
|
(values (- q 1) (+ r m))
|
|
(values (+ q 1) (- r m)))))))])))
|
|
(cond
|
|
[(fixnum? m)
|
|
(cond
|
|
[($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)
|
|
(import (ikarus system $fx))
|
|
(cond
|
|
[(and (fixnum? n) (fixnum? m))
|
|
(cond
|
|
[(eq? m 0) (die 'div "division by 0")]
|
|
[(eq? m -1) (- n)]
|
|
[else
|
|
(let ([d0 ($fxquotient n m)])
|
|
(if ($fx>= n ($fx* d0 m))
|
|
d0
|
|
(if ($fx>= m 0)
|
|
($fx- d0 1)
|
|
($fx+ d0 1))))])]
|
|
[else
|
|
(let-values ([(a b) (div-and-mod* n m 'div)])
|
|
a)]))
|
|
|
|
(define (mod n m)
|
|
(import (ikarus system $fx))
|
|
(cond
|
|
[(and (fixnum? n) (fixnum? m))
|
|
(cond
|
|
[(eq? m 0) (die 'mod "division by 0")]
|
|
[else
|
|
(let ([d0 ($fxquotient n m)])
|
|
(let ([m0 ($fx- n ($fx* d0 m))])
|
|
(if ($fx>= m0 0)
|
|
m0
|
|
(if ($fx>= m 0)
|
|
($fx+ m0 m)
|
|
($fx- m0 m)))))])]
|
|
[else
|
|
(let-values ([(a b) (div-and-mod* n m 'mod)])
|
|
b)]))
|
|
|
|
(define (div0-and-mod0 x y)
|
|
(let-values ([(d m) (div-and-mod* x y 'div0-and-mod0)])
|
|
(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 ([(d m) (div-and-mod* x y 'div0)])
|
|
(if (> y 0)
|
|
(if (< m (/ y 2))
|
|
d
|
|
(+ d 1))
|
|
(if (>= m (/ y -2))
|
|
(- d 1)
|
|
d))))
|
|
|
|
(define (mod0 x y)
|
|
(let-values ([(d m) (div-and-mod* x y 'mod0)])
|
|
(if (> y 0)
|
|
(if (< m (/ y 2))
|
|
m
|
|
(- m y))
|
|
(if (>= m (/ y -2))
|
|
(+ m 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 fxrotate-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 fxrotate-bit-field
|
|
fxbit-field))
|
|
|
|
(module (bitwise-first-bit-set fxfirst-bit-set)
|
|
(define (byte-first-bit-set x i)
|
|
(import (ikarus system $bytevectors))
|
|
(define-syntax make-first-bit-set-bytevector
|
|
(lambda (x)
|
|
(define (fst n)
|
|
(cond
|
|
[(odd? n) 0]
|
|
[else (+ 1 (fst (bitwise-arithmetic-shift-right n 1)))]))
|
|
(u8-list->bytevector
|
|
(cons 0 #| not used |#
|
|
(let f ([i 1])
|
|
(cond
|
|
[(= i 256) '()]
|
|
[else (cons (fst i) (f (+ i 1)))]))))))
|
|
(define bv (make-first-bit-set-bytevector))
|
|
($fx+ i ($bytevector-u8-ref bv x)))
|
|
(define ($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
|
|
(case (fixnum-width)
|
|
[(30)
|
|
(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))])
|
|
($fxmodulo n 255)))]
|
|
[else
|
|
(let ([m0 #x0555555555555555]
|
|
[m1 #x0333333333333333]
|
|
[m2 #x0f0f0f0f0f0f0f0f]
|
|
[m3 #x00ff00ff00ff00ff])
|
|
(let* ([n ($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 ($fxsra n 4) m2))]
|
|
[n ($fx+ ($fxlogand n m3) ($fxlogand ($fxsra n 8) m3))])
|
|
($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) ($fxbitcount n)]
|
|
[(bignum? n) (bnbitcount n)]
|
|
[else (die 'bitwise-bit-count "not an exact integer" n)])))
|
|
|
|
(define (fxlength x)
|
|
(define (fxlength32 x)
|
|
(let ([fl ($fixnum->flonum x)])
|
|
(let ([sbe ($fxlogor
|
|
($fxsll ($flonum-u8-ref fl 0) 4)
|
|
($fxsra ($flonum-u8-ref fl 1) 4))])
|
|
(cond
|
|
[($fx= sbe 0) 0]
|
|
[else ($fx- sbe 1022)]))))
|
|
(define (fxlength64 x)
|
|
(if ($fx> x #x7FFFFFFF)
|
|
($fx+ 31 (fxlength32 ($fxsra x 31)))
|
|
(fxlength32 x)))
|
|
(if (fixnum? x)
|
|
(case (fixnum-width)
|
|
[(30)
|
|
(fxlength32 (if ($fx< x 0) ($fxlognot x) x))]
|
|
[else
|
|
(fxlength64 (if ($fx< x 0) ($fxlognot x) x))])
|
|
(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
|
|
($fxlogand m ($fxsll b i))
|
|
($fxlogand ($fxlognot m) x)))
|
|
(die who "not a fixnum" b))
|
|
(if ($fx<= 0 j)
|
|
(die who "index out of range" j)
|
|
(die who "indices not in order" i j)))
|
|
(die who "index out of range" j))
|
|
(die who "not a fixnum" j))
|
|
(die who "index out of range" i))
|
|
(die who "not a fixnum" i))
|
|
(die who "not a fixnum" x)))
|
|
|
|
(define ($fxrotate-bit-field x i j c w)
|
|
(let ([m ($fxsll ($fxsub1 ($fxsll 1 w)) i)])
|
|
(let ([x0 ($fxlogand x m)])
|
|
(let ([lt ($fxsll x0 c)] [rt ($fxsra x0 ($fx- w c))])
|
|
(let ([x0 ($fxlogand ($fxlogor lt rt) m)])
|
|
($fxlogor x0 ($fxlogand x ($fxlognot m))))))))
|
|
|
|
(define (fxrotate-bit-field x i j c)
|
|
(define who 'fxrotate-bit-field)
|
|
(if (fixnum? x)
|
|
(if (fixnum? i)
|
|
(if ($fx>= i 0)
|
|
(if (fixnum? j)
|
|
(if ($fx< j (fixnum-width))
|
|
(let ([w ($fx- j i)])
|
|
(if ($fx>= w 0)
|
|
(if (fixnum? c)
|
|
(if (and ($fx>= c 0) ($fx< c w))
|
|
($fxrotate-bit-field x i j c w)
|
|
(die who "count is invalid" c))
|
|
(die who "count is not a fixnum" c))
|
|
(die who "field width is negative" i j)))
|
|
(die who "end index is out of range" j))
|
|
(die who "end index is not a fixnum" j))
|
|
(die who "start index is out of range" i))
|
|
(die who "start index is not a fixnum" i))
|
|
(die who "not a fixnum" x)))
|
|
|
|
|
|
|
|
(define (fxbit-field x i j)
|
|
(define who 'fxbit-field)
|
|
(if (fixnum? x)
|
|
(if (fixnum? i)
|
|
(if ($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)))
|
|
|
|
)
|
|
|
|
|
|
(library (ikarus complex-numbers)
|
|
(export make-rectangular $make-rectangular make-polar
|
|
real-part imag-part angle magnitude)
|
|
(import
|
|
(except (ikarus) make-rectangular make-polar
|
|
real-part imag-part angle magnitude)
|
|
(except (ikarus system $compnums) $make-rectangular))
|
|
|
|
(define ($make-rectangular r i)
|
|
;;; should be called with 2 exacts
|
|
(if (eqv? i 0)
|
|
r
|
|
($make-compnum r i)))
|
|
|
|
(define (make-rectangular r i)
|
|
(define who 'make-rectangular)
|
|
(define (err x)
|
|
(die who "invalid argument" x))
|
|
(cond
|
|
[(flonum? i)
|
|
(cond
|
|
[(flonum? r) ($make-cflonum r i)]
|
|
[(or (fixnum? r) (bignum? r) (ratnum? r))
|
|
($make-cflonum (inexact r) i)]
|
|
[else (err r)])]
|
|
[(eqv? i 0) (if (number? r) r (err r))]
|
|
[(or (fixnum? i) (bignum? i) (ratnum? i))
|
|
(cond
|
|
[(or (fixnum? r) (bignum? r) (ratnum? r))
|
|
($make-rectangular r i)]
|
|
[(flonum? r)
|
|
($make-cflonum r (inexact i))]
|
|
[else (err r)])]
|
|
[else (err i)]))
|
|
|
|
(define (make-polar mag angle)
|
|
(define who 'make-polar)
|
|
(unless (real? mag)
|
|
(die who "not a real number" mag))
|
|
(unless (real? angle)
|
|
(die who "not a real number" angle))
|
|
(make-rectangular
|
|
(* mag (cos angle))
|
|
(* mag (sin angle))))
|
|
|
|
(define magnitude
|
|
(lambda (x)
|
|
(cond
|
|
[(or (fixnum? x) (bignum? x) (ratnum? x) (flonum? x))
|
|
(abs x)]
|
|
[(compnum? x)
|
|
(let ([r ($compnum-real x)]
|
|
[i ($compnum-imag x)])
|
|
(sqrt (+ (* r r) (* i i))))]
|
|
[(cflonum? x)
|
|
(let ([r ($cflonum-real x)]
|
|
[i ($cflonum-imag x)])
|
|
(sqrt (+ (* r r) (* i i))))]
|
|
[else
|
|
(die 'magnitude "not a number" x)])))
|
|
|
|
(define angle
|
|
(lambda (x)
|
|
(import (ikarus system $bignums) (ikarus system $ratnums))
|
|
(define PI (acos -1))
|
|
(cond
|
|
[(fixnum? x)
|
|
(if (fx>? x 0)
|
|
0
|
|
(if (fx<? x 0)
|
|
PI
|
|
(die 'angle "undefined for 0")))]
|
|
[(bignum? x)
|
|
(if ($bignum-positive? x) 0 PI)]
|
|
[(ratnum? x)
|
|
(let ([n ($ratnum-n x)])
|
|
(if (> n 0) 0 PI))]
|
|
[(flonum? x)
|
|
(atan 0.0 x)]
|
|
[(compnum? x)
|
|
(let ([r ($compnum-real x)]
|
|
[i ($compnum-imag x)])
|
|
(atan i r))]
|
|
[(cflonum? x)
|
|
(let ([r ($cflonum-real x)]
|
|
[i ($cflonum-imag x)])
|
|
(atan i r))]
|
|
[else
|
|
(die 'angle "not a number" x)])))
|
|
|
|
(define real-part
|
|
(lambda (x)
|
|
(cond
|
|
[(fixnum? x) x]
|
|
[(bignum? x) x]
|
|
[(ratnum? x) x]
|
|
[(flonum? x) x]
|
|
[(compnum? x) ($compnum-real x)]
|
|
[(cflonum? x) ($cflonum-real x)]
|
|
[else
|
|
(die 'real-part "not a number" x)])))
|
|
|
|
(define imag-part
|
|
(lambda (x)
|
|
(cond
|
|
[(fixnum? x) 0]
|
|
[(bignum? x) 0]
|
|
[(ratnum? x) 0]
|
|
[(flonum? x) 0]
|
|
[(compnum? x) ($compnum-imag x)]
|
|
[(cflonum? x) ($cflonum-imag x)]
|
|
[else
|
|
(die 'imag-part "not a number" x)])))
|
|
)
|
|
|
|
(library (ikarus system flonums)
|
|
(export $fixnum->flonum)
|
|
(import (ikarus))
|
|
(define $fixnum->flonum fixnum->flonum))
|