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• Trunc

Vl-truncate-constint

Special routine for truncating ordinary, unsigned constant integers, without introducing temporary wires.

Signature

(vl-truncate-constint n x) → chopped-expr

Arguments

n — width to truncate down to.
    Guard (posp n).

x — resolved, unsigned, constant integer expression to truncate.
    Guard (vl-expr-p x).

Returns

chopped-expr — Type (vl-expr-p chopped-expr).

We can truncate resolved constants by just creating a new constant that has its width and value chopped down to size.

Definitions and Theorems

Function: vl-truncate-constint

(defun vl-truncate-constint (n x)
  (declare (xargs :guard (and (posp n) (vl-expr-p x))))
  (declare (xargs :guard (and (vl-atom-p x)
                              (vl-expr-welltyped-p x)
                              (vl-constint-p (vl-atom->guts x))
                              (equal (vl-expr->finaltype x)
                                     :vl-unsigned)
                              (< n (vl-expr->finalwidth x)))))
  (let ((__function__ 'vl-truncate-constint))
    (declare (ignorable __function__))
    (b* ((n (lposfix n))
         (guts (vl-atom->guts x))
         (value (vl-constint->value guts))
         (val-chop (mod value (expt 2 n)))
         (new-guts (make-vl-constint :value val-chop
                                     :origwidth n
                                     :origtype :vl-unsigned))
         (new-atom (make-vl-atom :guts new-guts
                                 :finalwidth n
                                 :finaltype :vl-unsigned)))
      new-atom)))

Theorem: vl-expr-p-of-vl-truncate-constint

(defthm vl-expr-p-of-vl-truncate-constint
  (b* ((chopped-expr (vl-truncate-constint n x)))
    (vl-expr-p chopped-expr))
  :rule-classes :rewrite)

Theorem: vl-truncate-constint-basics

(defthm vl-truncate-constint-basics
  (implies
       (and (force (posp n))
            (force (vl-atom-p x))
            (force (vl-expr-welltyped-p x))
            (force (vl-constint-p (vl-atom->guts x)))
            (force (< n (vl-expr->finalwidth x)))
            (force (equal (vl-expr->finaltype x)
                          :vl-unsigned)))
       (and (equal (vl-expr->finalwidth (vl-truncate-constint n x))
                   n)
            (equal (vl-expr->finaltype (vl-truncate-constint n x))
                   :vl-unsigned)
            (vl-expr-welltyped-p (vl-truncate-constint n x)))))

Theorem: vl-truncate-constint-of-pos-fix-n

(defthm vl-truncate-constint-of-pos-fix-n
  (equal (vl-truncate-constint (pos-fix n) x)
         (vl-truncate-constint n x)))

Theorem: vl-truncate-constint-pos-equiv-congruence-on-n

(defthm vl-truncate-constint-pos-equiv-congruence-on-n
  (implies (acl2::pos-equiv n n-equiv)
           (equal (vl-truncate-constint n x)
                  (vl-truncate-constint n-equiv x)))
  :rule-classes :congruence)

Theorem: vl-truncate-constint-of-vl-expr-fix-x

(defthm vl-truncate-constint-of-vl-expr-fix-x
  (equal (vl-truncate-constint n (vl-expr-fix x))
         (vl-truncate-constint n x)))

Theorem: vl-truncate-constint-vl-expr-equiv-congruence-on-x

(defthm vl-truncate-constint-vl-expr-equiv-congruence-on-x
  (implies (vl-expr-equiv x x-equiv)
           (equal (vl-truncate-constint n x)
                  (vl-truncate-constint n x-equiv)))
  :rule-classes :congruence)