		Search-engine friendly clone of the ACL2 documentation.

Binary

Nat-to-bin-chars

Convert a natural number into a list of bits.

Signature
(nat-to-bin-chars n) → chars
Arguments: n — Guard (natp n).
Returns: chars — Type (bin-digit-char-list*p chars).

For instance, (nat-to-dec-chars 8) is (#\1 #\0 #\0 #\0).

This is like ACL2's built-in function explode-nonnegative-integer, except that it doesn't deal with accumulators and is limited to base 2 numbers. These simplifications lead to particularly nice rules, e.g., about bin-digit-chars-value, and somewhat better performance:

;; Times reported by an AMD FX-8350, Linux, 64-bit CCL:

;; .204 seconds, 303 MB allocated
(progn (gc$)
       (time (loop for i fixnum from 1 to 1000000 do
                   (str::nat-to-bin-chars i))))

;; 1.04 seconds, 303 MB allocated
(progn (gc$)
       (time (loop for i fixnum from 1 to 1000000 do
          (explode-nonnegative-integer i 2 nil))))

Definitions and Theorems

Function: nat-to-bin-chars$inline

(defun nat-to-bin-chars$inline (n)
  (declare (xargs :guard (natp n)))
  (let ((acl2::__function__ 'nat-to-bin-chars))
    (declare (ignorable acl2::__function__))
    (or (nat-to-bin-chars-aux n nil)
        '(#\0))))

Theorem: bin-digit-char-list*p-of-nat-to-bin-chars

(defthm bin-digit-char-list*p-of-nat-to-bin-chars
  (b* ((chars (nat-to-bin-chars$inline n)))
    (bin-digit-char-list*p chars))
  :rule-classes :rewrite)

Theorem: true-listp-of-nat-to-bin-chars

(defthm true-listp-of-nat-to-bin-chars
  (and (true-listp (nat-to-bin-chars n))
       (consp (nat-to-bin-chars n)))
  :rule-classes :type-prescription)

Theorem: character-listp-of-nat-to-bin-chars

(defthm character-listp-of-nat-to-bin-chars
  (character-listp (nat-to-bin-chars n)))

Theorem: nat-to-bin-chars-one-to-one

(defthm nat-to-bin-chars-one-to-one
  (equal (equal (nat-to-bin-chars n)
                (nat-to-bin-chars m))
         (equal (nfix n) (nfix m))))

Theorem: bin-digit-chars-value-of-nat-to-bin-chars

(defthm bin-digit-chars-value-of-nat-to-bin-chars
  (equal (bin-digit-chars-value (nat-to-bin-chars n))
         (nfix n)))

Subtopics

Basic-nat-to-bin-chars: Logically simple definition that is similar to nat-to-bin-chars.
Nat-to-bin-chars-aux