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;;;; "logical.scm", bit access and operations for integers for Scheme
;;; Copyright (C) 1991, 1993, 2001, 2003 Aubrey Jaffer
;
;Permission to copy this software, to modify it, to redistribute it,
;to distribute modified versions, and to use it for any purpose is
;granted, subject to the following restrictions and understandings.
;
;1. Any copy made of this software must include this copyright notice
;in full.
;
;2. I have made no warranty or representation that the operation of
;this software will be error-free, and I am under no obligation to
;provide any services, by way of maintenance, update, or otherwise.
;
;3. In conjunction with products arising from the use of this
;material, there shall be no use of my name in any advertising,
;promotional, or sales literature without prior written consent in
;each case.
;@
(define integer-expt
(if (provided? 'inexact)
expt
(lambda (n k)
(do ((x n (* x x))
(j k (quotient j 2))
(acc 1 (if (even? j) acc (* x acc))))
((<= j 1)
(case j
((0) acc)
((1) (* x acc))
(else (slib:error 'integer-expt n k))))))))
(define logical:boole-xor
'#(#(0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15)
#(1 0 3 2 5 4 7 6 9 8 11 10 13 12 15 14)
#(2 3 0 1 6 7 4 5 10 11 8 9 14 15 12 13)
#(3 2 1 0 7 6 5 4 11 10 9 8 15 14 13 12)
#(4 5 6 7 0 1 2 3 12 13 14 15 8 9 10 11)
#(5 4 7 6 1 0 3 2 13 12 15 14 9 8 11 10)
#(6 7 4 5 2 3 0 1 14 15 12 13 10 11 8 9)
#(7 6 5 4 3 2 1 0 15 14 13 12 11 10 9 8)
#(8 9 10 11 12 13 14 15 0 1 2 3 4 5 6 7)
#(9 8 11 10 13 12 15 14 1 0 3 2 5 4 7 6)
#(10 11 8 9 14 15 12 13 2 3 0 1 6 7 4 5)
#(11 10 9 8 15 14 13 12 3 2 1 0 7 6 5 4)
#(12 13 14 15 8 9 10 11 4 5 6 7 0 1 2 3)
#(13 12 15 14 9 8 11 10 5 4 7 6 1 0 3 2)
#(14 15 12 13 10 11 8 9 6 7 4 5 2 3 0 1)
#(15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0)))
(define logical:boole-and
'#(#(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0)
#(0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1)
#(0 0 2 2 0 0 2 2 0 0 2 2 0 0 2 2)
#(0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3)
#(0 0 0 0 4 4 4 4 0 0 0 0 4 4 4 4)
#(0 1 0 1 4 5 4 5 0 1 0 1 4 5 4 5)
#(0 0 2 2 4 4 6 6 0 0 2 2 4 4 6 6)
#(0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7)
#(0 0 0 0 0 0 0 0 8 8 8 8 8 8 8 8)
#(0 1 0 1 0 1 0 1 8 9 8 9 8 9 8 9)
#(0 0 2 2 0 0 2 2 8 8 10 10 8 8 10 10)
#(0 1 2 3 0 1 2 3 8 9 10 11 8 9 10 11)
#(0 0 0 0 4 4 4 4 8 8 8 8 12 12 12 12)
#(0 1 0 1 4 5 4 5 8 9 8 9 12 13 12 13)
#(0 0 2 2 4 4 6 6 8 8 10 10 12 12 14 14)
#(0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15)))
(define (logical:ash-4 x)
(if (negative? x)
(+ -1 (quotient (+ 1 x) 16))
(quotient x 16)))
;@
(define logand
(letrec
((lgand
(lambda (n2 n1 scl acc)
(cond ((= n1 n2) (+ acc (* scl n1)))
((zero? n2) acc)
((zero? n1) acc)
(else (lgand (logical:ash-4 n2)
(logical:ash-4 n1)
(* 16 scl)
(+ (* (vector-ref (vector-ref logical:boole-and
(modulo n1 16))
(modulo n2 16))
scl)
acc)))))))
(lambda (n1 n2) (lgand n2 n1 1 0))))
;@
(define logior
(letrec
((lgior
(lambda (n2 n1 scl acc)
(cond ((= n1 n2) (+ acc (* scl n1)))
((zero? n2) (+ acc (* scl n1)))
((zero? n1) (+ acc (* scl n2)))
(else (lgior (logical:ash-4 n2)
(logical:ash-4 n1)
(* 16 scl)
(+ (* (- 15 (vector-ref
(vector-ref logical:boole-and
(- 15 (modulo n1 16)))
(- 15 (modulo n2 16))))
scl)
acc)))))))
(lambda (n1 n2) (lgior n2 n1 1 0))))
;@
(define logxor
(letrec
((lgxor
(lambda (n2 n1 scl acc)
(cond ((= n1 n2) acc)
((zero? n2) (+ acc (* scl n1)))
((zero? n1) (+ acc (* scl n2)))
(else (lgxor (logical:ash-4 n2)
(logical:ash-4 n1)
(* 16 scl)
(+ (* (vector-ref (vector-ref logical:boole-xor
(modulo n1 16))
(modulo n2 16))
scl)
acc)))))))
(lambda (n1 n2) (lgxor n2 n1 1 0))))
;@
(define (lognot n) (- -1 n))
;@
(define (logtest n1 n2)
(not (zero? (logical:logand n1 n2))))
;@
(define (logbit? index n)
(logical:logtest (logical:integer-expt 2 index) n))
;@
(define (copy-bit index to bool)
(if bool
(logical:logior to (logical:ash 1 index))
(logical:logand to (logical:lognot (logical:ash 1 index)))))
;;@ This procedure is careful not to use more than DEG bits in
;; computing (- (expt 2 DEG) 1)
(define (logical:ones deg)
(if (zero? deg) 0 (+ (* 2 (+ -1 (logical:integer-expt 2 (- deg 1)))) 1)))
;@
(define (bit-field n start end)
(logical:logand (logical:ones (- end start))
(logical:ash n (- start))))
;@
(define (bitwise-if mask n0 n1)
(logical:logior (logical:logand mask n0)
(logical:logand (logical:lognot mask) n1)))
;@
(define (copy-bit-field to start end from)
(logical:bitwise-if (logical:ash (logical:ones (- end start)) start)
(logical:ash from start)
to))
;@
(define (ash n count)
(if (negative? count)
(let ((k (logical:integer-expt 2 (- count))))
(if (negative? n)
(+ -1 (quotient (+ 1 n) k))
(quotient n k)))
(* (logical:integer-expt 2 count) n)))
;@
(define integer-length
(letrec ((intlen (lambda (n tot)
(case n
((0 -1) (+ 0 tot))
((1 -2) (+ 1 tot))
((2 3 -3 -4) (+ 2 tot))
((4 5 6 7 -5 -6 -7 -8) (+ 3 tot))
(else (intlen (logical:ash-4 n) (+ 4 tot)))))))
(lambda (n) (intlen n 0))))
;@
(define logcount
(letrec ((logcnt (lambda (n tot)
(if (zero? n)
tot
(logcnt (quotient n 16)
(+ (vector-ref
'#(0 1 1 2 1 2 2 3 1 2 2 3 2 3 3 4)
(modulo n 16))
tot))))))
(lambda (n)
(cond ((negative? n) (logcnt (logical:lognot n) 0))
((positive? n) (logcnt n 0))
(else 0)))))
;;;; Bit order and lamination
;@
(define (logical:rotate k count len)
(set! count (modulo count len))
(logical:logior (logical:logand (ash k count) (logical:ones len))
(logical:ash k (- count len))))
;@
(define (bit-reverse k n)
(do ((m (if (negative? n) (lognot n) n) (ash m -1))
(k (+ -1 k) (+ -1 k))
(rvs 0 (logior (ash rvs 1) (logand 1 m))))
((negative? k) (if (negative? n) (lognot rvs) rvs))))
;@
(define (integer->list k . len)
(if (null? len)
(do ((k k (ash k -1))
(lst '() (cons (odd? k) lst)))
((<= k 0) lst))
(do ((idx (+ -1 (car len)) (+ -1 idx))
(k k (ash k -1))
(lst '() (cons (odd? k) lst)))
((negative? idx) lst))))
;@
(define (list->integer bools)
(do ((bs bools (cdr bs))
(acc 0 (+ acc acc (if (car bs) 1 0))))
((null? bs) acc)))
(define (booleans->integer . bools)
(list->integer bools))
;@
(define (bitwise:laminate . ks)
(define nks (length ks))
(define nbs (apply max (map integer-length ks)))
(do ((kdx (+ -1 nbs) (+ -1 kdx))
(ibs 0 (+ (list->integer (map (lambda (k) (logbit? kdx k)) ks))
(ash ibs nks))))
((negative? kdx) ibs)))
;@
(define (bitwise:delaminate count k)
(define nbs (* count (+ 1 (quotient (integer-length k) count))))
(do ((kdx (- nbs count) (- kdx count))
(lst (vector->list (make-vector count 0))
(map (lambda (k bool) (+ (if bool 1 0) (ash k 1)))
lst
(integer->list (ash k (- kdx)) count))))
((negative? kdx) lst)))
;;;; Gray-code
;@
(define (integer->gray-code k)
(logxor k (ash k -1)))
;@
(define (gray-code->integer k)
(if (negative? k)
(slib:error 'gray-code->integer 'negative? k)
(let ((kln (integer-length k)))
(do ((d 1 (* d 2))
(ans (logxor k (ash k -1)) ; == (integer->gray-code k)
(logxor ans (ash ans (* d -2)))))
((>= (* 2 d) kln) ans)))))
(define (grayter k1 k2)
(define kl1 (integer-length k1))
(define kl2 (integer-length k2))
(if (eqv? kl1 kl2)
(> (gray-code->integer k1) (gray-code->integer k2))
(> kl1 kl2)))
;@
(define (gray-code<? k1 k2)
(not (or (eqv? k1 k2) (grayter k1 k2))))
(define (gray-code<=? k1 k2)
(or (eqv? k1 k2) (not (grayter k1 k2))))
(define (gray-code>? k1 k2)
(and (not (eqv? k1 k2)) (grayter k1 k2)))
(define (gray-code>=? k1 k2)
(or (eqv? k1 k2) (grayter k1 k2)))
(define logical:logand logand)
(define logical:logior logior)
;;(define logical:logxor logxor)
(define logical:lognot lognot)
(define logical:logtest logtest)
;;(define logical:logbit? logbit?)
;;(define logical:copy-bit copy-bit)
(define logical:ash ash)
;;(define logical:logcount logcount)
;;(define logical:integer-length integer-length)
;;(define logical:bit-field bit-field)
;;(define bit-extract bit-field)
(define logical:bitwise-if bitwise-if)
;;(define logical:copy-bit-field copy-bit-field)
(define logical:integer-expt integer-expt)
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