		Search-engine friendly clone of the ACL2 documentation.

Mxcsrbits

!mxcsrbits->dm

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

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

Definitions and Theorems

Function: !mxcsrbits->dm$inline

(defun !mxcsrbits->dm$inline (dm x)
 (declare (xargs :guard (and (bitp dm) (mxcsrbits-p x))))
 (mbe
     :logic
     (b* ((dm (mbe :logic (bfix dm) :exec dm))
          (x (mxcsrbits-fix x)))
       (part-install dm x :width 1 :low 8))
     :exec (the (unsigned-byte 32)
                (logior (the (unsigned-byte 32)
                             (logand (the (unsigned-byte 32) x)
                                     (the (signed-byte 10) -257)))
                        (the (unsigned-byte 9)
                             (ash (the (unsigned-byte 1) dm) 8))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !mxcsrbits->dm-is-mxcsrbits

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

Theorem: mxcsrbits->dm-of-!mxcsrbits->dm

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

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

(defthm !mxcsrbits->dm-equiv-under-mask
  (b* ((?new-x (!mxcsrbits->dm$inline dm x)))
    (mxcsrbits-equiv-under-mask new-x x -257)))