		Search-engine friendly clone of the ACL2 documentation.

!sib->scale

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

Signature
(!sib->scale scale x) → new-x
Arguments: scale — Guard (2bits-p scale).; x — Guard (sib-p x).
Returns: new-x — Type (sib-p new-x).

Definitions and Theorems

Function: !sib->scale$inline

(defun !sib->scale$inline (scale x)
  (declare (xargs :guard (and (2bits-p scale) (sib-p x))))
  (mbe :logic
       (b* ((scale (mbe :logic (2bits-fix scale)
                        :exec scale))
            (x (sib-fix x)))
         (part-install scale x :width 2 :low 6))
       :exec (the (unsigned-byte 8)
                  (logior (the (unsigned-byte 8)
                               (logand (the (unsigned-byte 8) x)
                                       (the (signed-byte 9) -193)))
                          (the (unsigned-byte 8)
                               (ash (the (unsigned-byte 2) scale)
                                    6))))))

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

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

Theorem: !sib->scale$inline-of-2bits-fix-scale

(defthm !sib->scale$inline-of-2bits-fix-scale
  (equal (!sib->scale$inline (2bits-fix scale) x)
         (!sib->scale$inline scale x)))

Theorem: !sib->scale$inline-2bits-equiv-congruence-on-scale

(defthm !sib->scale$inline-2bits-equiv-congruence-on-scale
  (implies (2bits-equiv scale scale-equiv)
           (equal (!sib->scale$inline scale x)
                  (!sib->scale$inline scale-equiv x)))
  :rule-classes :congruence)

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

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

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

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

Theorem: !sib->scale-is-sib

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

Theorem: sib->scale-of-!sib->scale

(defthm sib->scale-of-!sib->scale
  (b* ((?new-x (!sib->scale$inline scale x)))
    (equal (sib->scale new-x)
           (2bits-fix scale))))

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

(defthm !sib->scale-equiv-under-mask
  (b* ((?new-x (!sib->scale$inline scale x)))
    (sib-equiv-under-mask new-x x 63)))