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!sib->base

Update the |X86ISA|::|BASE| field of a sib bit structure.

Signature
(!sib->base base x) → new-x
Arguments: base — Guard (3bits-p base).; x — Guard (sib-p x).
Returns: new-x — Type (sib-p new-x).

Definitions and Theorems

Function: !sib->base$inline

(defun !sib->base$inline (base x)
  (declare (xargs :guard (and (3bits-p base) (sib-p x))))
  (mbe :logic
       (b* ((base (mbe :logic (3bits-fix base)
                       :exec base))
            (x (sib-fix x)))
         (part-install base x :width 3 :low 0))
       :exec (the (unsigned-byte 8)
                  (logior (the (unsigned-byte 8)
                               (logand (the (unsigned-byte 8) x)
                                       (the (signed-byte 4) -8)))
                          (the (unsigned-byte 3) base)))))

Theorem: sib-p-of-!sib->base

(defthm sib-p-of-!sib->base
  (b* ((new-x (!sib->base$inline base x)))
    (sib-p new-x))
  :rule-classes :rewrite)

Theorem: !sib->base$inline-of-3bits-fix-base

(defthm !sib->base$inline-of-3bits-fix-base
  (equal (!sib->base$inline (3bits-fix base) x)
         (!sib->base$inline base x)))

Theorem: !sib->base$inline-3bits-equiv-congruence-on-base

(defthm !sib->base$inline-3bits-equiv-congruence-on-base
  (implies (3bits-equiv base base-equiv)
           (equal (!sib->base$inline base x)
                  (!sib->base$inline base-equiv x)))
  :rule-classes :congruence)

Theorem: !sib->base$inline-of-sib-fix-x

(defthm !sib->base$inline-of-sib-fix-x
  (equal (!sib->base$inline base (sib-fix x))
         (!sib->base$inline base x)))

Theorem: !sib->base$inline-sib-equiv-congruence-on-x

(defthm !sib->base$inline-sib-equiv-congruence-on-x
  (implies (sib-equiv x x-equiv)
           (equal (!sib->base$inline base x)
                  (!sib->base$inline base x-equiv)))
  :rule-classes :congruence)

Theorem: !sib->base-is-sib

(defthm !sib->base-is-sib
  (equal (!sib->base base x)
         (change-sib x :base base)))

Theorem: sib->base-of-!sib->base

(defthm sib->base-of-!sib->base
  (b* ((?new-x (!sib->base$inline base x)))
    (equal (sib->base new-x)
           (3bits-fix base))))

Theorem: !sib->base-equiv-under-mask

(defthm !sib->base-equiv-under-mask
  (b* ((?new-x (!sib->base$inline base x)))
    (sib-equiv-under-mask new-x x -8)))