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;;;; "logical.scm", bit access and operations for integers for Scheme
;;; Copyright (C) 1991, 1993 Aubrey Jaffer.
;
;Permission to copy this software, to redistribute it, 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 warrantee 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 logical:integer-expt
(if (provided? 'inexact)
expt
(lambda (n k)
(logical:ipow-by-squaring n k 1 *))))
(define (logical:ipow-by-squaring x k acc proc)
(cond ((zero? k) acc)
((= 1 k) (proc acc x))
(else (logical:ipow-by-squaring (proc x x)
(quotient k 2)
(if (even? k) acc (proc acc x))
proc))))
(define (logical:logand n1 n2)
(cond ((= n1 n2) n1)
((zero? n1) 0)
((zero? n2) 0)
(else
(+ (* (logical:logand (logical:ash-4 n1) (logical:ash-4 n2)) 16)
(vector-ref (vector-ref logical:boole-and (modulo n1 16))
(modulo n2 16))))))
(define (logical:logior n1 n2)
(cond ((= n1 n2) n1)
((zero? n1) n2)
((zero? n2) n1)
(else
(+ (* (logical:logior (logical:ash-4 n1) (logical:ash-4 n2)) 16)
(- 15 (vector-ref (vector-ref logical:boole-and
(- 15 (modulo n1 16)))
(- 15 (modulo n2 16))))))))
(define (logical:logxor n1 n2)
(cond ((= n1 n2) 0)
((zero? n1) n2)
((zero? n2) n1)
(else
(+ (* (logical:logxor (logical:ash-4 n1) (logical:ash-4 n2)) 16)
(vector-ref (vector-ref logical:boole-xor (modulo n1 16))
(modulo n2 16))))))
(define (logical:lognot n) (- -1 n))
(define (logical:logtest int1 int2)
(not (zero? (logical:logand int1 int2))))
(define (logical:logbit? index int)
(logical:logtest (logical:integer-expt 2 index) int))
(define (logical:bit-extract n start end)
(logical:logand (- (logical:integer-expt 2 (- end start)) 1)
(logical:ash n (- start))))
(define (logical:ash int cnt)
(if (negative? cnt)
(let ((n (logical:integer-expt 2 (- cnt))))
(if (negative? int)
(+ -1 (quotient (+ 1 int) n))
(quotient int n)))
(* (logical:integer-expt 2 cnt) int)))
(define (logical:ash-4 x)
(if (negative? x)
(+ -1 (quotient (+ 1 x) 16))
(quotient x 16)))
(define (logical:logcount n)
(cond ((zero? n) 0)
((negative? n) (logical:logcount (logical:lognot n)))
(else
(+ (logical:logcount (logical:ash-4 n))
(vector-ref '#(0 1 1 2 1 2 2 3 1 2 2 3 2 3 3 4)
(modulo n 16))))))
(define (logical:integer-length n)
(case n
((0 -1) 0)
((1 -2) 1)
((2 3 -3 -4) 2)
((4 5 6 7 -5 -6 -7 -8) 3)
(else (+ 4 (logical:integer-length (logical:ash-4 n))))))
(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 logand logical:logand)
(define logior logical:logior)
(define logxor logical:logxor)
(define lognot logical:lognot)
(define logtest logical:logtest)
(define logbit? logical:logbit?)
(define ash logical:ash)
(define logcount logical:logcount)
(define integer-length logical:integer-length)
(define bit-extract logical:bit-extract)
(define ipow-by-squaring logical:ipow-by-squaring)
(define integer-expt logical:integer-expt)
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