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• Decimal

Nat-to-dec-string-size

Number of characters in the decimal representation of a natural.

Signature

(nat-to-dec-string-size x) → size

Arguments

x — Guard (natp x).

Returns

size — Type (posp size).

Definitions and Theorems

Function: nat-to-dec-string-size$inline

(defun nat-to-dec-string-size$inline (x)
  (declare (xargs :guard (natp x)))
  (let ((acl2::__function__ 'nat-to-dec-string-size))
    (declare (ignorable acl2::__function__))
    (mbe :logic
         (if (< (lnfix x) 10)
             1
           (+ 1
              (nat-to-dec-string-size (truncate x 10))))
         :exec
         (if (<= (mbe :logic (nfix x) :exec x)
                 536870911)
             (nat-to-dec-string-size-fast x)
           (nat-to-dec-string-size-slow x)))))

Theorem: posp-of-nat-to-dec-string-size

(defthm posp-of-nat-to-dec-string-size
  (b* ((size (nat-to-dec-string-size$inline x)))
    (posp size))
  :rule-classes :type-prescription)

Theorem: nat-to-dec-string-size-slow-removal

(defthm nat-to-dec-string-size-slow-removal
  (equal (nat-to-dec-string-size-slow x)
         (nat-to-dec-string-size x)))

Theorem: nat-to-dec-string-size-fast-removal

(defthm nat-to-dec-string-size-fast-removal
  (equal (nat-to-dec-string-size-fast x)
         (nat-to-dec-string-size x)))

Subtopics

Nat-to-dec-string-size-slow

Nat-to-dec-string-size-fast