#| -*-Scheme-*-

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    2017, 2018, 2019, 2020 Massachusetts Institute of Technology

This file is part of MIT/GNU Scheme.

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it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or (at
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WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
General Public License for more details.

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|#

;;;; Tests of integer bit operations

(declare (usual-integrations))

(define (random-integer-of-weight w n)
  (let ((bit-string (make-bit-string n #f)))
    (do ((i 0 (+ i 1))) ((>= i w)) (bit-string-set! bit-string i))
    (do ((i 1 (+ i 1))) ((>= i n))
      (let ((j (random-integer (+ i 1))))
        (let ((t (bit-string-ref bit-string i)))
          ((if (bit-string-ref bit-string j) bit-string-set! bit-string-clear!)
           bit-string i)
          ((if t bit-string-set! bit-string-clear!) bit-string j))))
    (let ((integer (bit-string->unsigned-integer bit-string)))
      (if (zero? (random-integer 2))
          (- -1 integer)
          integer))))

(define (random-fixnum)
  (+ (smallest-fixnum)
     (random-integer (- (+ 1 (largest-fixnum)) (smallest-fixnum)))))

(define (random-large-integer)
  (let ((n (random-integer #x100)))
    (random-integer-of-weight (random-integer (+ n 1)) n)))

(define (randomly-generate-integers procedure)
  (do ((i 0 (+ i 1))) ((= i (if keep-it-fast!? 8 #x100)))
    (procedure (random-large-integer))))

(define (randomly-generate-fixnums procedure)
  (do ((i 0 (+ i 1))) ((= i (if keep-it-fast!? #x10 #x1000)))
    (procedure (random-fixnum))))

(define (randomly-generate-integer-pairs procedure)
  (do ((i 0 (+ i 1))) ((= i (if keep-it-fast!? 8 #x100)))
    (procedure (random-large-integer) (random-large-integer))))

(define (randomly-generate-fixnum-pairs procedure)
  (do ((i 0 (+ i 1))) ((= i (if keep-it-fast!? #x10 #x1000)))
    (procedure (random-fixnum) (random-fixnum))))

(define (define-random-unary-fixnum-test name procedure)
  (define-test name
    (lambda ()
      (randomly-generate-fixnums procedure))))

(define (define-random-unary-integer-test name procedure)
  (define-test name
    (lambda ()
      (randomly-generate-integers procedure))))

(define (define-random-binary-fixnum-test name procedure)
  (define-test name
    (lambda ()
      (randomly-generate-fixnum-pairs procedure))))

(define (define-random-binary-integer-test name procedure)
  (define-test name
    (lambda ()
      (randomly-generate-integer-pairs procedure))))

;;;; Shift

(define-test 'SHIFT-LEFT/0
  (lambda ()
    (do ((i 0 (+ i 1))) ((>= i #x1000))
      (assert-eqv (shift-left 0 i) 0))))

(define-test 'SHIFT-LEFT/+1
  (lambda ()
    (do ((i 0 (+ i 1))) ((>= i #x1000))
      (assert-eqv (shift-left 1 i) (expt 2 i)))))

(define-test 'SHIFT-LEFT/-1
  (lambda ()
    (do ((i 0 (+ i 1))) ((>= i #x1000))
      (assert-eqv (shift-left -1 i) (* -1 (expt 2 i))))))

(define-test 'SHIFT-LEFT/POSITIVE
  (lambda ()
    (do ((i 0 (+ i 1))) ((>= i #x10))
      (let ((n (random-integer #x1000)))
        (do ((i 0 (+ i 1))) ((>= i #x100))
          (assert-eqv (shift-left n i) (* n (expt 2 i))))))))

(define-test 'SHIFT-LEFT/NEGATIVE
  (lambda ()
    (do ((i 0 (+ i 1))) ((>= i #x10))
      (let ((n (- -1 (random-integer #x1000))))
        (do ((i 0 (+ i 1))) ((>= i #x100))
          (assert-eqv (shift-left n i) (* n (expt 2 i))))))))

(define-test 'SHIFT-RIGHT/0
  (lambda ()
    (do ((i 0 (+ i 1))) ((>= i #x1000))
      (assert-eqv (shift-right 0 i) 0))))

(define-test 'SHIFT-RIGHT/1
  (lambda ()
    (assert-eqv (shift-right 1 0) 1)
    (do ((i 1 (+ i 1))) ((>= i #x1000))
      (assert-eqv (shift-right 0 i) 0))))

(define-test 'SHIFT-RIGHT/-1
  (lambda ()
    (do ((i 0 (+ i 1))) ((>= i #x1000))
      (assert-eqv (shift-right -1 i) -1))))

(define-test 'SHIFT-LEFT-THEN-RIGHT/POSITIVE
  (lambda ()
    (do ((i 0 (+ i 1))) ((>= i #x10))
      (let ((n (random-integer #x1000)))
        (do ((i 0 (+ i 1))) ((>= i #x100))
          (assert-eqv (shift-right (shift-left n i) i) n))))))

(define-test 'SHIFT-LEFT-THEN-RIGHT/NEGATIVE
  (lambda ()
    (do ((i 0 (+ i 1))) ((>= i #x10))
      (let ((n (- -1 (random-integer #x1000))))
        (do ((i 0 (+ i 1))) ((>= i #x100))
          (assert-eqv (shift-right (shift-left n i) i) n))))))

;;;; Bitwise NOT

(define-test 'BITWISE-NOT/0
  (lambda ()
    (assert-eqv (bitwise-not 0) -1)
    (assert-eqv (bitwise-not -1) 0)))

(define-test 'BITWISE-NOT/1
  (lambda ()
    (assert-eqv (bitwise-not 1) -2)
    (assert-eqv (bitwise-not -2) 1)))

(define-test 'BITWISE-NOT/EXTREME-FIXNUM
  (lambda ()
    (assert-eqv (bitwise-not (largest-fixnum)) (smallest-fixnum))
    (assert-eqv (bitwise-not (smallest-fixnum)) (largest-fixnum))))

(define-random-unary-fixnum-test 'BITWISE-NOT/FIXNUM
  (lambda (n)
    (assert-eqv (bitwise-not n) (- -1 n))
    (assert-eqv (bitwise-not (bitwise-not n)) n)
    (assert-eqv (bitwise-not n) (fix:not n))
    (assert-eqv (bitwise-not (fix:not n)) n)))

(define-random-unary-integer-test 'BITWISE-NOT
  (lambda (n)
    (assert-eqv (bitwise-not n) (- -1 n))
    (assert-eqv (bitwise-not (bitwise-not n)) n)))

;;;; Binary Bitwise Operators

(define (define-bitwise/fixnum-test name general-operator fixnum-operator)
  (define-random-binary-fixnum-test (symbol name '/ 'FIXNUM)
    (lambda (a b)
      (assert-eqv (general-operator a b) (fixnum-operator a b)))))

(define-bitwise/fixnum-test 'BITWISE-AND bitwise-and fix:and)
(define-bitwise/fixnum-test 'BITWISE-ANDC2 bitwise-andc2 fix:andc)
(define-bitwise/fixnum-test 'BITWISE-IOR bitwise-ior fix:or)
(define-bitwise/fixnum-test 'BITWISE-XOR bitwise-xor fix:xor)

(define (euclidean-divide n d)
  (let ((q ((if (negative? d) ceiling floor) (/ n d))))
    (values q (- n (* d q)))))

(define (define-binary-bitwise-test name operator ff ft tf tt)
  (define (bit a b)
    (vector-ref (vector ff ft tf tt) (+ (* a 2) b)))
  (define (result? object)
    (or (= object -1) (= object 0)))
  (define (result-bit result)
    (case result ((-1) 1) ((0) 0) (else -1)))
  (define (check-integer a b)
    (let ((a*b (operator a b)))
      (define (check-bit a0 b0 a*b0)
        (if (not (eqv? a*b0 (bit a0 b0)))
            (error "Failed:" `(,name ,a ,b) '=> a*b)))
      (let loop ((a a) (b b) (a*b a*b))
        (if (and (result? a) (result? b))
            (check-bit (result-bit a) (result-bit b) (result-bit a*b))
            (receive (a a0) (euclidean-divide a 2)
              (receive (b b0) (euclidean-divide b 2)
                (receive (a*b a*b0) (euclidean-divide a*b 2)
                  (check-bit a0 b0 a*b0)
                  (loop a b a*b))))))))
  (define (define-trivial-test subname a b)
    (define (signum x) (cond ((< x 0) -1) ((< 0 x) +1) (else 0)))
    (define-test (symbol name '/ subname '/ (signum a) '/ (signum b))
      (lambda ()
        (check-integer a b))))
  (define-trivial-test 'TRIVIAL-FIXNUM 0 0)
  (define-trivial-test 'TRIVIAL-FIXNUM 0 1)
  (define-trivial-test 'TRIVIAL-FIXNUM 1 0)
  (define-trivial-test 'TRIVIAL-FIXNUM 1 1)
  (define-trivial-test 'TRIVIAL-FIXNUM 0 -1)
  (define-trivial-test 'TRIVIAL-FIXNUM -1 0)
  (define-trivial-test 'TRIVIAL-FIXNUM -1 -1)
  (let ((s (expt 2 100)))
    (define-trivial-test 'TRIVIAL-BIGNUM 0 s)
    (define-trivial-test 'TRIVIAL-BIGNUM s 0)
    (define-trivial-test 'TRIVIAL-BIGNUM s s))
  (define-random-binary-integer-test (symbol name '/ 'RANDOM) check-integer))

;; (define-binary-bitwise-test 'BITWISE-CLEAR bitwise-clear 0 0 0 0)
(define-binary-bitwise-test 'BITWISE-AND bitwise-and 0 0 0 1)
(define-binary-bitwise-test 'BITWISE-ANDC2 bitwise-andc2 0 0 1 0)
;; (define-binary-bitwise-test 'BITWISE-ARG1 bitwise-arg1 0 0 1 1)
(define-binary-bitwise-test 'BITWISE-ANDC1 bitwise-andc1 0 1 0 0)
;; (define-binary-bitwise-test 'BITWISE-ARG2 bitwise-arg2 0 1 0 1)
(define-binary-bitwise-test 'BITWISE-XOR bitwise-xor 0 1 1 0)
(define-binary-bitwise-test 'BITWISE-IOR bitwise-ior 0 1 1 1)
(define-binary-bitwise-test 'BITWISE-NOR bitwise-nor 1 0 0 0)
(define-binary-bitwise-test 'BITWISE-EQV bitwise-eqv 1 0 0 1)
;; (define-binary-bitwise-test 'BITWISE-NOT2 bitwise-not2 1 0 1 0)
(define-binary-bitwise-test 'BITWISE-ORC2 bitwise-orc2 1 0 1 1)
;; (define-binary-bitwise-test 'BITWISE-NOT1 bitwise-not2 1 1 0 0)
(define-binary-bitwise-test 'BITWISE-ORC1 bitwise-orc1 1 1 0 1)
(define-binary-bitwise-test 'BITWISE-NAND bitwise-nand 1 1 1 0)
;; (define-binary-bitwise-test 'BITWISE-SET bitwise-set 1 1 1 1)

;;;;; Binary Bitwise Identities

(define (define-bitwise-identity-test name operator identity)
  (define-random-unary-integer-test (symbol name '/ 'IDENTITY)
    (lambda (n)
      (assert-eqv (operator n identity) n)
      (assert-eqv (operator identity n) n))))

(define-bitwise-identity-test 'BITWISE-AND bitwise-and -1)
(define-bitwise-identity-test 'BITWISE-XOR bitwise-xor 0)
(define-bitwise-identity-test 'BITWISE-IOR bitwise-ior 0)
(define-bitwise-identity-test 'BITWISE-EQV bitwise-eqv -1)

(define (define-bitwise-commutativity-test name operator)
  (define-random-binary-integer-test (symbol name '/ 'COMMUTATIVITY)
    (lambda (a b)
      (assert-eqv (operator a b) (operator b a)))))

(define-bitwise-commutativity-test 'BITWISE-AND bitwise-and)
(define-bitwise-commutativity-test 'BITWISE-XOR bitwise-xor)
(define-bitwise-commutativity-test 'BITWISE-IOR bitwise-ior)
(define-bitwise-commutativity-test 'BITWISE-NOR bitwise-nor)
(define-bitwise-commutativity-test 'BITWISE-EQV bitwise-eqv)
(define-bitwise-commutativity-test 'BITWISE-NAND bitwise-nand)

(define-random-binary-integer-test 'BITWISE-AND/DEMORGAN
  (lambda (a b)
    (assert-eqv (bitwise-and a b)
                (bitwise-not (bitwise-ior (bitwise-not a) (bitwise-not b))))))

(define-random-binary-integer-test 'BITWISE-ANDC2/AND-NOT2
  (lambda (a b)
    (assert-eqv (bitwise-andc2 a b) (bitwise-and a (bitwise-not b)))))

(define-random-binary-integer-test 'BITWISE-ANDC1/AND-NOT1
  (lambda (a b)
    (assert-eqv (bitwise-andc1 a b) (bitwise-and (bitwise-not a) b))))

(define-random-binary-integer-test 'BITWISE-NOR/NOT-IOR
  (lambda (a b)
    (assert-eqv (bitwise-nor a b) (bitwise-not (bitwise-ior a b)))))

(define-random-binary-integer-test 'BITWISE-XOR/AND-NAND-IOR
  (lambda (a b)
    (assert-eqv (bitwise-xor a b)
                (bitwise-and (bitwise-nand a b) (bitwise-ior a b)))))

(define-random-binary-integer-test 'BITWISE-EQV/NOT-XOR
  (lambda (a b)
    (assert-eqv (bitwise-eqv a b) (bitwise-not (bitwise-xor a b)))))

(define-random-binary-integer-test 'BITWISE-ORC1/IOR-NOT1
  (lambda (a b)
    (assert-eqv (bitwise-orc1 a b) (bitwise-ior (bitwise-not a) b))))

(define-random-binary-integer-test 'BITWISE-ORC2/IOR-NOT2
  (lambda (a b)
    (assert-eqv (bitwise-orc2 a b) (bitwise-ior a (bitwise-not b)))))

(define-random-binary-integer-test 'BITWISE-NAND/NOT-AND
  (lambda (a b)
    (assert-eqv (bitwise-nand a b) (bitwise-not (bitwise-and a b)))))

(define-test 'BIT-COUNT
  (lambda ()
    (do ((i 0 (+ i 1))) ((= i #x100))
      (let* ((w (random-integer #x1000))
             (n (random-integer-of-weight w #x1000))
             (c (bit-count n)))
        (if (not (eqv? c w))
            (error "Failed:" `(BIT-COUNT ,n) '=> c 'EXPECTED w))))))

(define-test 'BIT-COUNT/COMPLEMENT
  (lambda ()
    (do ((i 0 (+ i 1))) ((= i #x100))
      (let* ((w (random-integer #x1000))
             (n (random-integer-of-weight w #x1000))
             (c (bit-count (bitwise-not n))))
        (if (not (eqv? c w))
            (error "Failed:" `(BIT-COUNT (BITWISE-NOT ,n))
                   '=> c
                   'EXPECTED w))))))

(define-random-unary-integer-test 'INTEGER-LENGTH
  (let ((integer-length-in-bits
         (make-primitive-procedure 'INTEGER-LENGTH-IN-BITS 1)))
    (lambda (n)
      (assert-eqv (integer-length n)
                  (integer-length-in-bits
                   (if (negative? n) (bitwise-not n) n))))))

(define-test 'FIRST-SET-BIT/0 (lambda () (assert-eqv (first-set-bit 0) -1)))
(define-test 'FIRST-SET-BIT/+1 (lambda () (assert-eqv (first-set-bit +1) 0)))
(define-test 'FIRST-SET-BIT/-1 (lambda () (assert-eqv (first-set-bit -1) 0)))

(define-random-unary-integer-test 'FIRST-SET-BIT/ODD
  (lambda (n)
    (if (not (zero? n))
        (let ((i (random-integer #x1000)))
          (assert-eqv (first-set-bit (shift-left (bitwise-ior n 1) i)) i)))))

(define-random-unary-integer-test 'FIRST-SET-BIT/RANDOM
  (lambda (n)
    (if (not (zero? n))
        (let ((i (random-integer #x1000)))
          (assert-eqv (first-set-bit (shift-left n i))
                      (+ i (first-set-bit n)))))))

((lambda (procedure)
   (for-each (lambda (entry) (procedure (car entry) (cadr entry) (cddr entry)))
             '((0 0 . 0)
               (0 -1 . -1)
               (-1 0 . -1)
               (-1 -1 . 0))))
 (lambda (a b a*b)
   (define-test (symbol 'HAMMING-DISTANCE '/ a '/ b)
     (lambda ()
       (assert-eqv (hamming-distance a b) a*b)))))

(define-random-binary-integer-test 'HAMMING-DISTANCE
  (lambda (a b)
    (if (not (eqv? (hamming-distance a b)
                   (if (eqv? (negative? a) (negative? b))
                       (bit-count (bitwise-xor a b))
                       -1)))
        (error "Failed:" `(HAMMING-DISTANCE ,a ,b)
               '=> (hamming-distance a b)))))

(define-test 'BIT-MASK
  (lambda ()
    (do ((i 0 (+ i 1))) ((>= i (if keep-it-fast!? #x10 #x1000)))
      (let ((size (random-integer #x1000))
            (position (random-integer #x1000)))
        (assert-eqv (bit-mask size position)
                    (shift-left
                     (bitwise-not (shift-left -1 size))
                     position))))))

(define-test 'BIT-ANTIMASK
  (lambda ()
    (do ((i 0 (+ i 1))) ((>= i (if keep-it-fast!? #x10 #x1000)))
      (let ((size (random-integer #x1000))
            (position (random-integer #x1000)))
        (assert-eqv (bit-antimask size position)
                    (bitwise-not
                     (shift-left (bitwise-not (shift-left -1 size))
                                 position)))))))

(define (define-per-bit-test name procedure)
  (define-test name
    (lambda ()
      (do ((i 0 (+ i 1))) ((>= i (if keep-it-fast!? 8 #x100)))
        (procedure (random-integer-of-weight (random-integer #x1000) #x1000)
                   (random-integer #x1000))))))

(define-per-bit-test 'SET-BIT
  (lambda (n i) (assert-true (bit-set? i (set-bit i n)))))

(define-per-bit-test 'CLEAR-BIT
  (lambda (n i) (assert-true (bit-clear? i (clear-bit i n)))))

(define-per-bit-test 'TOGGLE-BIT
  (lambda (n i) (assert-eqv (bit-clear? i (toggle-bit i n)) (bit-set? i n))))

(define-per-bit-test 'EXTRACT-BIT
  (lambda (n i) (assert-eqv (zero? (extract-bit i n)) (bit-clear? i n))))

(define-test 'FFS:0 (lambda () (assert-= 0 (ffs 0))))
(define-test 'FFS:1 (lambda () (assert-= 1 (ffs 1))))
(define-test 'FFS:2 (lambda () (assert-= 2 (ffs 2))))
(define-test 'FFS:3 (lambda () (assert-= 1 (ffs 3))))
(define-test 'FFS:-1 (lambda () (assert-= 1 (ffs -1))))
(define-test 'FFS:-2 (lambda () (assert-= 2 (ffs -2))))
(define-test 'FFS:-3 (lambda () (assert-= 1 (ffs -3))))

(define-per-bit-test 'FFS
  (lambda (n i)
    (assert-= (ffs n) (bit-count (bitwise-xor n (- n 1)))
              'EXPRESSION `(FFS ,n))
    (assert-= (ffs n) (+ 1 (first-set-bit n)) 'EXPRESSION `(FFS ,n))
    (assert-= (ffs n) (+ 1 (first-set-bit n)) 'EXPRESSION `(FFS ,n))
    (assert-= (ffs (- 0 n)) (ffs n) 'EXPRESSION `(FFS (- 0 ,n)))
    ;; Clear the low i bits of n.
    (let ((n (bitwise-andc2 n (bit-mask i 0))))
      (assert-= (ffs n) (bit-count (bitwise-xor n (- n 1)))
                'EXPRESSION `(FFS ,n))
      (assert-= (ffs n) (+ 1 (first-set-bit n)) 'EXPRESSION `(FFS ,n))
      (assert-= (ffs (- 0 n)) (ffs n) 'EXPRESSION `(FFS (- 0 ,n)))
      (if (not (zero? n))
          (assert->= (ffs n) (+ i 1) 'EXPRESSION `(FFS ,n)))
      ;; Set the ith bit of n and make equality hold exactly.
      (assert-= (ffs (bitwise-ior n (shift-left 1 i))) (+ i 1)
                'EXPRESSION `(FFS (BITWISE-IOR ,n (SHIFT-LEFT 1 ,i))))
      (assert-= (ffs (- 0 (bitwise-ior n (shift-left 1 i)))) (+ i 1)
                'EXPRESSION `(FFS (- 0 (BITWISE-IOR ,N (SHIFT-LEFT 1 ,i))))))))

(define-test 'CLZ:8:0 (lambda () (assert-= 8 ((clz 8) 0))))
(define-test 'CLZ:8:1 (lambda () (assert-= 7 ((clz 8) 1))))
(define-test 'CLZ:8:2 (lambda () (assert-= 6 ((clz 8) 2))))
(define-test 'CLZ:8:3 (lambda () (assert-= 6 ((clz 8) 3))))
(define-test 'CLZ:8:FF (lambda () (assert-= 0 ((clz 8) #xff))))

;;; Number of octets in a UTF-8 sequence given the initial octet.

(define (utf8-n o)
  (max 1 ((clz 8) (bitwise-andc1 o #xff))))

(define-test 'UTF8-N:1 (lambda () (assert-= 1 (utf8-n #b01101101))))
(define-test 'UTF8-N:2 (lambda () (assert-= 2 (utf8-n #b11001101))))
(define-test 'UTF8-N:3 (lambda () (assert-= 3 (utf8-n #b11101101))))
(define-test 'UTF8-N:4 (lambda () (assert-= 4 (utf8-n #b11110011))))

;;; Not real UTF-8, but the arithmetic works out the same!

(define-test 'UTF8-N:5 (lambda () (assert-= 5 (utf8-n #b11111001))))
(define-test 'UTF8-N:6 (lambda () (assert-= 6 (utf8-n #b11111101))))

(define-test 'SHIFT-RIGHT/TOO-MANY
  (lambda ()
    (assert-= (shift-right (identity-procedure 1234567) 100) 0)))