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;;;; "logical.scm", bit access and operations for integers for Scheme
;;; Copyright (C) 1991, 1993, 2001, 2003, 2005 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 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 (logical:reduce op4 ident)
(lambda args
(do ((res ident (op4 res (car rgs) 1 0))
(rgs args (cdr rgs)))
((null? rgs) res))))
;@
(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)))))))
(logical:reduce lgand -1)))
;@
(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)))))))
(logical:reduce lgior 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)))))))
(logical:reduce lgxor 0)))
;@
(define (lognot n) (- -1 n))
;@
(define (logtest n1 n2)
(not (zero? (logand n1 n2))))
;@
(define (logbit? index n)
(logtest (expt 2 index) n))
;@
(define (copy-bit index to bool)
(if bool
(logior to (arithmetic-shift 1 index))
(logand to (lognot (arithmetic-shift 1 index)))))
;@
(define (bitwise-if mask n0 n1)
(logior (logand mask n0)
(logand (lognot mask) n1)))
;@
(define (bit-field n start end)
(logand (lognot (ash -1 (- end start)))
(arithmetic-shift n (- start))))
;@
(define (copy-bit-field to from start end)
(bitwise-if (arithmetic-shift (lognot (ash -1 (- end start))) start)
(arithmetic-shift from start)
to))
;@
(define (rotate-bit-field n count start end)
(define width (- end start))
(set! count (modulo count width))
(let ((mask (lognot (ash -1 width))))
(define zn (logand mask (arithmetic-shift n (- start))))
(logior (arithmetic-shift
(logior (logand mask (arithmetic-shift zn count))
(arithmetic-shift zn (- count width)))
start)
(logand (lognot (ash mask start)) n))))
;@
(define (arithmetic-shift n count)
(if (negative? count)
(let ((k (expt 2 (- count))))
(if (negative? n)
(+ -1 (quotient (+ 1 n) k))
(quotient n k)))
(* (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 bitwise-bit-count
(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) (lognot (logcnt (lognot n) 0)))
((positive? n) (logcnt n 0))
(else 0)))))
;@
(define (logcount n)
(cond ((negative? n) (bitwise-bit-count (lognot n)))
(else (bitwise-bit-count n))))
;@
(define (log2-binary-factors n)
(+ -1 (integer-length (logand n (- n)))))
(define (bit-reverse k n)
(do ((m (if (negative? n) (lognot n) n) (arithmetic-shift m -1))
(k (+ -1 k) (+ -1 k))
(rvs 0 (logior (arithmetic-shift rvs 1) (logand 1 m))))
((negative? k) (if (negative? n) (lognot rvs) rvs))))
;@
(define (reverse-bit-field n start end)
(define width (- end start))
(let ((mask (lognot (ash -1 width))))
(define zn (logand mask (arithmetic-shift n (- start))))
(logior (arithmetic-shift (bit-reverse width zn) start)
(logand (lognot (ash mask start)) n))))
;@
(define (integer->list k . len)
(if (null? len)
(do ((k k (arithmetic-shift k -1))
(lst '() (cons (odd? k) lst)))
((<= k 0) lst))
(do ((idx (+ -1 (car len)) (+ -1 idx))
(k k (arithmetic-shift 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))
;;;;@ SRFI-60 aliases
(define ash arithmetic-shift)
(define bitwise-ior logior)
(define bitwise-xor logxor)
(define bitwise-and logand)
(define bitwise-not lognot)
(define bit-count logcount)
(define bit-set? logbit?)
(define any-bits-set? logtest)
(define first-set-bit log2-binary-factors)
(define bitwise-merge bitwise-if)
(provide 'srfi-60)
;;; Legacy
;;(define (logical:rotate k count len) (rotate-bit-field k count 0 len))
;;(define (logical:ones deg) (lognot (ash -1 deg)))
;;(define integer-expt expt) ; legacy name
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