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Parse-hex-from-charlist

Parse a hexadecimal number from the beginning of a character list.

Signature
(parse-hex-from-charlist x val len) → (mv val len rest)
Arguments: x — Characters to read from.
Guard (character-listp x).; val — Accumulator for the value of the hex digits we have read so far; typically 0 to start with.
Guard (natp val).; len — Accumulator for the number of hex digits we have read; typically 0 to start with.
Guard (natp len).
Returns: val — Value of the initial hex digits as a natural number.; len — Number of initial hex digits we read.; rest — The rest of x, past the leading hex digits.

This is like (parse-nat-from-charlist x val len), but deals with hex digits and returns their hexadecimal value.

Definitions and Theorems

Function: parse-hex-from-charlist

(defun parse-hex-from-charlist (x val len)
  (declare (xargs :guard (and (character-listp x)
                              (natp val)
                              (natp len))))
  (declare (type unsigned-byte val len))
  (declare (xargs :split-types t))
  (let ((acl2::__function__ 'parse-hex-from-charlist))
    (declare (ignorable acl2::__function__))
    (cond ((atom x)
           (mv (lnfix val) (lnfix len) nil))
          ((hex-digit-char-p (car x))
           (parse-hex-from-charlist
                (cdr x)
                (the unsigned-byte
                     (+ (the unsigned-byte
                             (hex-digit-char-value (car x)))
                        (the unsigned-byte
                             (ash (the unsigned-byte (lnfix val))
                                  4))))
                (the unsigned-byte
                     (+ 1 (the unsigned-byte (lnfix len))))))
          (t (mv (lnfix val) (lnfix len) x)))))

Theorem: val-of-parse-hex-from-charlist

(defthm val-of-parse-hex-from-charlist
  (equal (mv-nth 0 (parse-hex-from-charlist x val len))
         (+ (hex-digit-chars-value (take-leading-hex-digit-chars x))
            (ash (nfix val)
                 (* 4
                    (len (take-leading-hex-digit-chars x)))))))

Theorem: len-of-parse-hex-from-charlist

(defthm len-of-parse-hex-from-charlist
  (equal (mv-nth 1 (parse-hex-from-charlist x val len))
         (+ (nfix len)
            (len (take-leading-hex-digit-chars x)))))

Theorem: rest-of-parse-hex-from-charlist

(defthm rest-of-parse-hex-from-charlist
  (equal (mv-nth 2 (parse-hex-from-charlist x val len))
         (skip-leading-hex-digits x)))