		Search-engine friendly clone of the ACL2 documentation.

Mxcsrbits

!mxcsrbits->ue

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

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

Definitions and Theorems

Function: !mxcsrbits->ue$inline

(defun !mxcsrbits->ue$inline (ue x)
 (declare (xargs :guard (and (bitp ue) (mxcsrbits-p x))))
 (mbe
     :logic
     (b* ((ue (mbe :logic (bfix ue) :exec ue))
          (x (mxcsrbits-fix x)))
       (part-install ue x :width 1 :low 4))
     :exec (the (unsigned-byte 32)
                (logior (the (unsigned-byte 32)
                             (logand (the (unsigned-byte 32) x)
                                     (the (signed-byte 6) -17)))
                        (the (unsigned-byte 5)
                             (ash (the (unsigned-byte 1) ue) 4))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !mxcsrbits->ue-is-mxcsrbits

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

Theorem: mxcsrbits->ue-of-!mxcsrbits->ue

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

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

(defthm !mxcsrbits->ue-equiv-under-mask
  (b* ((?new-x (!mxcsrbits->ue$inline ue x)))
    (mxcsrbits-equiv-under-mask new-x x -17)))