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Svex-argmasks

Svmask-for-lsh

Implements svex-argmasks for LSH.

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

See svmask-for-rsh. This is entirely similar, just for left shifts instead of right shifts.

Definitions and Theorems

Function: svmask-for-lsh

(defun svmask-for-lsh (mask args)
 (declare (xargs :guard (and (4vmask-p mask)
                             (svexlist-p args))))
 (let ((__function__ 'svmask-for-lsh))
  (declare (ignorable __function__))
  (b* (((svex-nths n x) args)
       (mask (4vmask-fix mask)))
   (b*
    (((when (4vmask-empty mask)) (list 0 0))
     (nval (svex-s4xeval n))
     ((when (s4vec-2vec-p nval))
      (list
          -1
          (sparseint-ash
               mask
               (sparseint-val
                    (sparseint-unary-minus (s4vec->upper nval)))))))
    (list -1 -1)))))

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

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

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

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

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

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

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

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

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

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

Theorem: svmask-for-lsh-correct

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