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Mxcsrbits

!mxcsrbits->om

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

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

Definitions and Theorems

Function: !mxcsrbits->om$inline

(defun !mxcsrbits->om$inline (om x)
 (declare (xargs :guard (and (bitp om) (mxcsrbits-p x))))
 (mbe
    :logic
    (b* ((om (mbe :logic (bfix om) :exec om))
         (x (mxcsrbits-fix x)))
      (part-install om x :width 1 :low 10))
    :exec (the (unsigned-byte 32)
               (logior (the (unsigned-byte 32)
                            (logand (the (unsigned-byte 32) x)
                                    (the (signed-byte 12) -1025)))
                       (the (unsigned-byte 11)
                            (ash (the (unsigned-byte 1) om) 10))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !mxcsrbits->om-is-mxcsrbits

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

Theorem: mxcsrbits->om-of-!mxcsrbits->om

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

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

(defthm !mxcsrbits->om-equiv-under-mask
  (b* ((?new-x (!mxcsrbits->om$inline om x)))
    (mxcsrbits-equiv-under-mask new-x x -1025)))