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S4vecs

S4vec-shift-core

Signature
(s4vec-shift-core shift x) → res
Arguments: shift — Guard (integerp shift).; x — Guard (s4vec-p x).
Returns: res — Type (s4vec-p res).

Definitions and Theorems

Function: s4vec-shift-core

(defun s4vec-shift-core (shift x)
  (declare (xargs :guard (and (integerp shift) (s4vec-p x))))
  (let ((__function__ 's4vec-shift-core))
    (declare (ignorable __function__))
    (if-s2vec-p (x)
                (s2vec (sparseint-ash (s2vec->val x) shift))
                (b* (((s4vec x)))
                  (s4vec (sparseint-ash x.upper shift)
                         (sparseint-ash x.lower shift))))))

Theorem: s4vec-p-of-s4vec-shift-core

(defthm s4vec-p-of-s4vec-shift-core
  (b* ((res (s4vec-shift-core shift x)))
    (s4vec-p res))
  :rule-classes :rewrite)

Theorem: s4vec-shift-core-correct

(defthm s4vec-shift-core-correct
  (b* ((?res (s4vec-shift-core shift x)))
    (equal (s4vec->4vec res)
           (4vec-shift-core shift (s4vec->4vec x)))))

Theorem: s4vec-shift-core-of-ifix-shift

(defthm s4vec-shift-core-of-ifix-shift
  (equal (s4vec-shift-core (ifix shift) x)
         (s4vec-shift-core shift x)))

Theorem: s4vec-shift-core-int-equiv-congruence-on-shift

(defthm s4vec-shift-core-int-equiv-congruence-on-shift
  (implies (int-equiv shift shift-equiv)
           (equal (s4vec-shift-core shift x)
                  (s4vec-shift-core shift-equiv x)))
  :rule-classes :congruence)

Theorem: s4vec-shift-core-of-s4vec-fix-x

(defthm s4vec-shift-core-of-s4vec-fix-x
  (equal (s4vec-shift-core shift (s4vec-fix x))
         (s4vec-shift-core shift x)))

Theorem: s4vec-shift-core-s4vec-equiv-congruence-on-x

(defthm s4vec-shift-core-s4vec-equiv-congruence-on-x
  (implies (s4vec-equiv x x-equiv)
           (equal (s4vec-shift-core shift x)
                  (s4vec-shift-core shift x-equiv)))
  :rule-classes :congruence)