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Mxcsrbits

!mxcsrbits->oe

Update the |X86ISA|::|OE| field of a mxcsrbits bit structure.

Signature
(!mxcsrbits->oe oe x) → new-x
Arguments: oe — Guard (bitp oe).; x — Guard (mxcsrbits-p x).
Returns: new-x — Type (mxcsrbits-p new-x).

Definitions and Theorems

Function: !mxcsrbits->oe$inline

(defun !mxcsrbits->oe$inline (oe x)
 (declare (xargs :guard (and (bitp oe) (mxcsrbits-p x))))
 (mbe
     :logic
     (b* ((oe (mbe :logic (bfix oe) :exec oe))
          (x (mxcsrbits-fix x)))
       (part-install oe x :width 1 :low 3))
     :exec (the (unsigned-byte 32)
                (logior (the (unsigned-byte 32)
                             (logand (the (unsigned-byte 32) x)
                                     (the (signed-byte 5) -9)))
                        (the (unsigned-byte 4)
                             (ash (the (unsigned-byte 1) oe) 3))))))

Theorem: mxcsrbits-p-of-!mxcsrbits->oe

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

Theorem: !mxcsrbits->oe$inline-of-bfix-oe

(defthm !mxcsrbits->oe$inline-of-bfix-oe
  (equal (!mxcsrbits->oe$inline (bfix oe) x)
         (!mxcsrbits->oe$inline oe x)))

Theorem: !mxcsrbits->oe$inline-bit-equiv-congruence-on-oe

(defthm !mxcsrbits->oe$inline-bit-equiv-congruence-on-oe
  (implies (bit-equiv oe oe-equiv)
           (equal (!mxcsrbits->oe$inline oe x)
                  (!mxcsrbits->oe$inline oe-equiv x)))
  :rule-classes :congruence)

Theorem: !mxcsrbits->oe$inline-of-mxcsrbits-fix-x

(defthm !mxcsrbits->oe$inline-of-mxcsrbits-fix-x
  (equal (!mxcsrbits->oe$inline oe (mxcsrbits-fix x))
         (!mxcsrbits->oe$inline oe x)))

Theorem: !mxcsrbits->oe$inline-mxcsrbits-equiv-congruence-on-x

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

Theorem: !mxcsrbits->oe-is-mxcsrbits

(defthm !mxcsrbits->oe-is-mxcsrbits
  (equal (!mxcsrbits->oe oe x)
         (change-mxcsrbits x :oe oe)))

Theorem: mxcsrbits->oe-of-!mxcsrbits->oe

(defthm mxcsrbits->oe-of-!mxcsrbits->oe
  (b* ((?new-x (!mxcsrbits->oe$inline oe x)))
    (equal (mxcsrbits->oe new-x)
           (bfix oe))))

Theorem: !mxcsrbits->oe-equiv-under-mask

(defthm !mxcsrbits->oe-equiv-under-mask
  (b* ((?new-x (!mxcsrbits->oe$inline oe x)))
    (mxcsrbits-equiv-under-mask new-x x -9)))