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Bitops/extra-defs

Bitscan-rev

(bitscan-rev src) returns the bit position of the most significant bit in src that is set, or 0 when src is zero (and hence has no such bit).

Signature
(bitscan-rev src) → position
Arguments: src — Guard (natp src).
Returns: position — Type (natp position).

Examples:

(bitscan-rev #b0001) = 0
(bitscan-rev #b0011) = 1
(bitscan-rev #b0101) = 2
(bitscan-rev #b1001) = 3

Definitions and Theorems

Function: bitscan-rev

(defun bitscan-rev (src)
  (declare (xargs :guard (natp src)))
  (let ((__function__ 'bitscan-rev))
    (declare (ignorable __function__))
    (if (zp src)
        0
      (let ((next (ash src -1)))
        (if (= next 0)
            0
          (+ 1 (bitscan-rev next)))))))

Theorem: natp-of-bitscan-rev

(defthm acl2::natp-of-bitscan-rev
  (b* ((position (bitscan-rev src)))
    (natp position))
  :rule-classes :type-prescription)

Theorem: nat-equiv-implies-equal-bitscan-rev-1

(defthm nat-equiv-implies-equal-bitscan-rev-1
  (implies (nat-equiv src src-equiv)
           (equal (bitscan-rev src)
                  (bitscan-rev src-equiv)))
  :rule-classes (:congruence))