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Mxcsrbits

!mxcsrbits->ze

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

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

Definitions and Theorems

Function: !mxcsrbits->ze$inline

(defun !mxcsrbits->ze$inline (ze x)
 (declare (xargs :guard (and (bitp ze) (mxcsrbits-p x))))
 (mbe
     :logic
     (b* ((ze (mbe :logic (bfix ze) :exec ze))
          (x (mxcsrbits-fix x)))
       (part-install ze x :width 1 :low 2))
     :exec (the (unsigned-byte 32)
                (logior (the (unsigned-byte 32)
                             (logand (the (unsigned-byte 32) x)
                                     (the (signed-byte 4) -5)))
                        (the (unsigned-byte 3)
                             (ash (the (unsigned-byte 1) ze) 2))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !mxcsrbits->ze-is-mxcsrbits

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

Theorem: mxcsrbits->ze-of-!mxcsrbits->ze

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

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

(defthm !mxcsrbits->ze-equiv-under-mask
  (b* ((?new-x (!mxcsrbits->ze$inline ze x)))
    (mxcsrbits-equiv-under-mask new-x x -5)))