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• Vl-print-nat

Vl-print-natchars-aux

Optimized base-10 natural number printing into ps.

Signature

(vl-print-natchars-aux n acc col) → (mv acc new-col)

Arguments

n — Guard (natp n).

col — Guard (natp col).

Returns

new-col — Type (natp new-col).

Definitions and Theorems

Function: vl-print-natchars-aux

(defun
 vl-print-natchars-aux (n acc col)
 (declare (xargs :guard (and (natp n) (natp col))))
 (declare (type unsigned-byte n col))
 (declare (xargs :split-types t))
 (let
  ((__function__ 'vl-print-natchars-aux))
  (declare (ignorable __function__))
  (if
   (mbe :logic (zp n)
        :exec (eql (the integer n) 0))
   (mv acc (lnfix col))
   (mv-let
    (acc col)
    (vl-print-natchars-aux
         (the integer (truncate (the integer n) 10))
         acc col)
    (mv
     (cons
          (the character
               (code-char (the (unsigned-byte 8)
                               (+ (the (unsigned-byte 8) 48)
                                  (the (unsigned-byte 8)
                                       (rem (the integer n) 10))))))
          acc)
     (the (integer 0 *) (+ 1 col)))))))

Theorem: natp-of-vl-print-natchars-aux.new-col

(defthm natp-of-vl-print-natchars-aux.new-col
        (b* (((mv ?acc ?new-col)
              (vl-print-natchars-aux n acc col)))
            (natp new-col))
        :rule-classes :type-prescription)

Theorem: acc-of-vl-print-natchars-aux

(defthm acc-of-vl-print-natchars-aux
        (equal (mv-nth 0 (vl-print-natchars-aux n acc col))
               (str::revappend-nat-to-dec-chars-aux n acc)))

Theorem: vl-print-natchars-aux-of-nfix-n

(defthm vl-print-natchars-aux-of-nfix-n
        (equal (vl-print-natchars-aux (nfix n) acc col)
               (vl-print-natchars-aux n acc col)))

Theorem: vl-print-natchars-aux-nat-equiv-congruence-on-n

(defthm vl-print-natchars-aux-nat-equiv-congruence-on-n
        (implies (acl2::nat-equiv n n-equiv)
                 (equal (vl-print-natchars-aux n acc col)
                        (vl-print-natchars-aux n-equiv acc col)))
        :rule-classes :congruence)

Theorem: vl-print-natchars-aux-of-nfix-col

(defthm vl-print-natchars-aux-of-nfix-col
        (equal (vl-print-natchars-aux n acc (nfix col))
               (vl-print-natchars-aux n acc col)))

Theorem: vl-print-natchars-aux-nat-equiv-congruence-on-col

(defthm vl-print-natchars-aux-nat-equiv-congruence-on-col
        (implies (acl2::nat-equiv col col-equiv)
                 (equal (vl-print-natchars-aux n acc col)
                        (vl-print-natchars-aux n acc col-equiv)))
        :rule-classes :congruence)