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Svex-argmasks

Svmask-for-partsel

Implements svex-argmasks for PARTSEL.

Signature
(svmask-for-partsel mask args) → argmasks
Arguments: mask — Care mask for the full expression.
Guard (4vmask-p mask).; args — Arguments to this PARTSEL operator.
Guard (svexlist-p args).
Returns: argmasks — The new care masks inferred for the args.
Type (4vmasklist-p argmasks).

Definitions and Theorems

Function: svmask-for-partsel

(defun svmask-for-partsel (mask args)
 (declare (xargs :guard (and (4vmask-p mask)
                             (svexlist-p args))))
 (let ((__function__ 'svmask-for-partsel))
  (declare (ignorable __function__))
  (b* (((svex-nths lsb width in) args)
       (mask (4vmask-fix mask)))
    (b*
     (((when (4vmask-empty mask))
       (list 0 0 0))
      (widthval (svex-s4xeval width))
      (lsbval (svex-s4xeval lsb))
      ((unless (s4vec-2vec-p widthval))
       (if
        (s4vec-2vec-p lsbval)
        (list -1 -1
              (sparseint-ash mask
                             (sparseint-val (s4vec->upper lsbval))))
        (list -1 -1 -1)))
      (widthval (s4vec->upper widthval))
      ((when (sparseint-< widthval 0))
       (list 0 -1 0))
      (widthval (sparseint-val widthval))
      ((unless (s4vec-2vec-p lsbval))
       (if (sparseint-equal 0
                            (sparseint-concatenate widthval mask 0))
           (list -1 -1 0)
         (list -1 -1 -1)))
      (lsbval (s4vec->upper lsbval)))
     (list -1 -1
           (sparseint-ash (sparseint-concatenate widthval mask 0)
                          (sparseint-val lsbval)))))))

Theorem: 4vmasklist-p-of-svmask-for-partsel

(defthm 4vmasklist-p-of-svmask-for-partsel
  (b* ((argmasks (svmask-for-partsel mask args)))
    (4vmasklist-p argmasks))
  :rule-classes :rewrite)

Theorem: svmask-for-partsel-of-4vmask-fix-mask

(defthm svmask-for-partsel-of-4vmask-fix-mask
  (equal (svmask-for-partsel (4vmask-fix mask)
                             args)
         (svmask-for-partsel mask args)))

Theorem: svmask-for-partsel-4vmask-equiv-congruence-on-mask

(defthm svmask-for-partsel-4vmask-equiv-congruence-on-mask
  (implies (4vmask-equiv mask mask-equiv)
           (equal (svmask-for-partsel mask args)
                  (svmask-for-partsel mask-equiv args)))
  :rule-classes :congruence)

Theorem: svmask-for-partsel-of-svexlist-fix-args

(defthm svmask-for-partsel-of-svexlist-fix-args
  (equal (svmask-for-partsel mask (svexlist-fix args))
         (svmask-for-partsel mask args)))

Theorem: svmask-for-partsel-svexlist-equiv-congruence-on-args

(defthm svmask-for-partsel-svexlist-equiv-congruence-on-args
  (implies (svexlist-equiv args args-equiv)
           (equal (svmask-for-partsel mask args)
                  (svmask-for-partsel mask args-equiv)))
  :rule-classes :congruence)

Theorem: svmask-for-partsel-correct

(defthm svmask-for-partsel-correct
 (implies
    (and (equal (4veclist-mask (svmask-for-partsel mask args)
                               (svexlist-eval args env))
                (4veclist-mask (svmask-for-partsel mask args)
                               args1))
         (syntaxp (not (equal args1
                              (cons 'svexlist-eval
                                    (cons args (cons env 'nil)))))))
    (equal (4vec-mask mask (svex-apply 'partsel args1))
           (4vec-mask mask
                      (svex-apply 'partsel
                                  (svexlist-eval args env))))))