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Vl-make-partselect

Safely creates expr[msb:lsb].

Signature

(vl-make-partselect expr msb lsb) → |expr[msb:lsb]|

Arguments

expr — Guard (vl-expr-p expr).

msb — Guard (natp msb).

lsb — Guard (natp lsb).

Returns

|expr[msb:lsb]| — Type (vl-expr-p |expr[msb:lsb]|).

We ensure that expr is an identifier and that msb >= lsb. Moreover, if msb = lsb, we create the bitselect expr[msb] instead.

Historic note. This used to have the same problem as vl-make-bitselect, and checked whether the msb was less than the final-width of expression. See the discussion there.

We no longer try to prevent you from creating part-selects with invalid ranges, since it's just not possible to do that correctly here. Garbage in, garbage out.

Definitions and Theorems

Function: vl-make-partselect

(defun vl-make-partselect (expr msb lsb)
  (declare (xargs :guard (and (vl-expr-p expr)
                              (natp msb)
                              (natp lsb))))
  (let ((__function__ 'vl-make-partselect))
    (declare (ignorable __function__))
    (b* ((msb (lnfix msb))
         (lsb (lnfix lsb))
         ((when (> lsb msb))
          (raise "LSB, ~x0, is larger than MSB, ~x1."
                 lsb msb)
          (vl-default-n-bit-expr 1))
         (width (+ 1 (- msb lsb)))
         (msb-index (vl-make-index msb))
         (lsb-index (vl-make-index lsb))
         ((unless (and (vl-fast-atom-p expr)
                       (vl-fast-id-p (vl-atom->guts expr))))
          (raise "Trying to select from a non-identifier: ~x0"
                 expr)
          (vl-default-n-bit-expr width))
         ((when (= lsb msb))
          (make-vl-nonatom :op :vl-bitselect
                           :args (list expr msb-index)
                           :finalwidth 1
                           :finaltype :vl-unsigned)))
      (make-vl-nonatom :op :vl-partselect-colon
                       :args (list expr msb-index lsb-index)
                       :finalwidth width
                       :finaltype :vl-unsigned))))

Theorem: vl-expr-p-of-vl-make-partselect

(defthm vl-expr-p-of-vl-make-partselect
  (b* ((|expr[msb:lsb]| (vl-make-partselect expr msb lsb)))
    (vl-expr-p |expr[msb:lsb]|))
  :rule-classes :rewrite)

Theorem: vl-expr->finalwidth-of-vl-make-partselect

(defthm vl-expr->finalwidth-of-vl-make-partselect
  (equal (vl-expr->finalwidth (vl-make-partselect expr msb lsb))
         (+ 1 (nfix (- (nfix msb) (nfix lsb))))))

Theorem: vl-expr-widthsfixed-p-of-vl-make-partselect

(defthm vl-expr-widthsfixed-p-of-vl-make-partselect
  (implies
       (force (vl-expr-widthsfixed-p expr))
       (vl-expr-widthsfixed-p (vl-make-partselect expr msb lsb))))

Theorem: vl-make-partselect-of-vl-expr-fix-expr

(defthm vl-make-partselect-of-vl-expr-fix-expr
  (equal (vl-make-partselect (vl-expr-fix expr)
                             msb lsb)
         (vl-make-partselect expr msb lsb)))

Theorem: vl-make-partselect-vl-expr-equiv-congruence-on-expr

(defthm vl-make-partselect-vl-expr-equiv-congruence-on-expr
  (implies (vl-expr-equiv expr expr-equiv)
           (equal (vl-make-partselect expr msb lsb)
                  (vl-make-partselect expr-equiv msb lsb)))
  :rule-classes :congruence)

Theorem: vl-make-partselect-of-nfix-msb

(defthm vl-make-partselect-of-nfix-msb
  (equal (vl-make-partselect expr (nfix msb) lsb)
         (vl-make-partselect expr msb lsb)))

Theorem: vl-make-partselect-nat-equiv-congruence-on-msb

(defthm vl-make-partselect-nat-equiv-congruence-on-msb
  (implies (acl2::nat-equiv msb msb-equiv)
           (equal (vl-make-partselect expr msb lsb)
                  (vl-make-partselect expr msb-equiv lsb)))
  :rule-classes :congruence)

Theorem: vl-make-partselect-of-nfix-lsb

(defthm vl-make-partselect-of-nfix-lsb
  (equal (vl-make-partselect expr msb (nfix lsb))
         (vl-make-partselect expr msb lsb)))

Theorem: vl-make-partselect-nat-equiv-congruence-on-lsb

(defthm vl-make-partselect-nat-equiv-congruence-on-lsb
  (implies (acl2::nat-equiv lsb lsb-equiv)
           (equal (vl-make-partselect expr msb lsb)
                  (vl-make-partselect expr msb lsb-equiv)))
  :rule-classes :congruence)