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!sib->index

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

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

Definitions and Theorems

Function: !sib->index$inline

(defun !sib->index$inline (index x)
  (declare (xargs :guard (and (3bits-p index) (sib-p x))))
  (mbe :logic
       (b* ((index (mbe :logic (3bits-fix index)
                        :exec index))
            (x (sib-fix x)))
         (part-install index x :width 3 :low 3))
       :exec (the (unsigned-byte 8)
                  (logior (the (unsigned-byte 8)
                               (logand (the (unsigned-byte 8) x)
                                       (the (signed-byte 7) -57)))
                          (the (unsigned-byte 6)
                               (ash (the (unsigned-byte 3) index)
                                    3))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !sib->index-is-sib

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

Theorem: sib->index-of-!sib->index

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

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

(defthm !sib->index-equiv-under-mask
  (b* ((?new-x (!sib->index$inline index x)))
    (sib-equiv-under-mask new-x x -57)))